intro - formance Library functions and subroutines
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Oracle Solaris Studio Performance Library intro(3P) NAME intro: sunperf, libsunperf - Introduction to Oracle Solaris Studio Per- formance Library functions and subroutines DESCRIPTION Oracle Solaris Studio Performance Library (sunperf) is a set of opti- mized, high-speed mathematical subroutines for solving linear algebra and other numerically intensive problems. Oracle Solaris Studio Perfor- mance Library is based on a collection of public domain applications available from Netlib at http://www.netlib.org. Oracle Solaris Studio has enhanced these public domain applications and bundled them as the Oracle Solaris Studio Performance Library. More information about Oracle Solaris Studio Performance Library can be found in the Oracle Solaris Studio Performance Library User's Guide and Oracle Solaris Studio Performance Library Reference Manual. LIBRARIES Oracle Solaris Studio Performance Library contains enhanced versions of the following standard libraries: Library Version Description LAPACK 3.1.1 solving linear algebra problems BLAS1 - performing vector-vector operations BLAS2 - performing matrix-vector operations BLAS3 - performing matrix-matrix operations Netlib Sparse-BLAS - performing sparse vector operations NIST Sparse-BLAS 0.5 performing fundamental sparse matrix operations SuperLU 3.0 solving sparse linear systems of equations Sparse Solver - direct sparse solver routines FFTPACK - performing fast Fourier transform VFFTPACK - performing vectorized fast Fourier transform IBLAS - interval BLAS routines Other Routines - trabspose, Convolution, correlation and sort A list of the individual subroutines is included at the bottom of this page. FEATURES Oracle Solaris Studio Performance Library routines can increase appli- cation performance on both serial and multiprocessor (MP) platforms, because the serial speed of many Oracle Solaris Studio Performance Library routines has been increased, and many routines have been paral- lelized. Oracle Solaris Studio Performance Library routines also have SPARC, AMD and Intel specific optimizations that are not present in the base Netlib libraries. Oracle Solaris Studio Performance Library provides the following opti- mizations and extensions to the base Netlib libraries: Extensions that support Fortran 95 and C language inter- faces Fortran 95 language features, including type indepen- dence, compile time checking, and optional arguments. Consistent API across the different libraries in Oracle Solaris Studio Performance Library Compatibility with LAPACK 1, 2.0, 3.0, and 3.1.1 libraries Increased performance, and in some cases, greater accu- racy Optimizations for specific SPARC and x86/x64 instruction set architectures Support for 64-bit enabled Solaris and Linux operating environments Support for parallel processing compiler options for SPARC and x86/x64 platforms Support for multiple processor hardware options USAGE To use the Oracle Solaris Studio Performance Library, type one of the following commands. % f95 -dalign file.f -library=sunperf or % cc -dalign file.c -library=sunperf or % CC -dalign file.c -library=sunperf To link with the Oracle Solaris Studio Performance Library statically, add -staticlib=sunperf to the commandline. SUBROUTINES Copy_CompCol_Matrix - A utility C function in the serial SuperLU solver that copies one SuperMatrix into another. Create_CompCol_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse column format (also known as the Harwell-Boeing format). Create_CompRow_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse row format. Create_Dense_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in dense format. Create_SuperNode_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in supernodal format. Destroy_CompCol_Matrix - Precision-independent C function in the serial SuperLU solver that deallocates a supermatrix in compressed sparse column format (also known as the Harwell-Boeing for- mat). Destroy_CompCol_Permuted - Precision-independent C function in the serial SuperLU solver that deallocates a supermatrix in per- muted, compressed sparse column format. Destroy_CompRow_Matrix - Precision-independent C function in the serial SuperLU solver that deallocates a supermatrix in compressed sparse row format. Destroy_Dense_Matrix - Precision-independent C function in the serial SuperLU solver that deallocates a SuperMatrix in dense for- mat. Destroy_SuperMatrix_Store - Precision-independent C function in the serial SuperLU solver that deallocates the actual storage used to store the matrix in a SuperMatrix. Destroy_SuperNode_Matrix - Precision-independent C function in the serial SuperLU solver that deallocates a SuperMatrix in supernodal format. LUFactFlops - A query function that returns the floating point opera- tion count of the factorization step of the SuperLU solver. LUFactTime - A query function that returns the time spent in the fac- torization step by the SuperLU solver. LUSolveFlops - A query function that returns the floating point opera- tion count of the solve step of the SuperLU solver. LUSolveTime - A query function that returns the time spent in the solve stage by the SuperLU solver. PrintPerf - A utility function of the SuperLU solver that prints sta- tistics collected by the computational routines. QuerySpace - A inquiry function that provides information on the memory statistics of the SuperLU solver. StatFree - frees storage that was previously allocated to hold perfor- mance statistics of the SuperLU solver. StatInit - A utility C function that allocates and initializes vari- ables in structure that stores performance statistics col- lected during the computation of the SuperLU solver. SuperMatrix - C data structure in the SuperLU software that represents a sparse or dense general matrix. available_threads - returns information about current thread usage blas_dpermute - permutes a real (double precision) array in terms of the permutation vector P, output by dsortv blas_dsort - sorts a real (double precision) vector X in increasing or decreasing order using quick sort algorithm blas_dsortv - sorts a real (double precision) vector X in increasing or decreasing order using quick sort algorithm and overwrite P with the permutation vector blas_ipermute - permutes an integer array in terms of the permutation vector P, output by dsortv blas_isort - sorts an integer vector X in increasing or decreasing order using quick sort algorithm blas_isortv - sorts a real vector X in increasing or decreasing order using quick sort algorithm and overwrite P with the permuta- tion vector blas_spermute - permutes a real array in terms of the permutation vec- tor P, output by dsortv blas_ssort - sorts a real vector X in increasing or decreasing order using quick sort algorithm blas_ssortv - sorts a real vector X in increasing or decreasing order using quick sort algorithm and overwrite P with the permuta- tion vector cCopy_CompCol_Matrix - A utility C function in the serial SuperLU solver that copies one SuperMatrix into another. cCreate_CompCol_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse column format (also known as the Harwell-Boeing format). cCreate_CompRow_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse row format. cCreate_Dense_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in dense format. cCreate_SuperNode_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in supernodal format. cPrintPerf - A utility function of the SuperLU solver that prints sta- tistics collected by the computational routines. cQuerySpace - A inquiry function that provides information on the mem- ory statistics of the SuperLU solver. caxpy - compute y := alpha * x + y caxpyi - Compute y := alpha * x + y cbbcsd - compute the CS decomposition of a unitary matrix in bidiago- nal-block form cbcomm - block coordinate matrix-matrix multiply cbdimm - block diagonal format matrix-matrix multiply cbdism - block diagonal format triangular solve cbdsqr - compute the singular value decomposition (SVD) of a real N-by- N (upper or lower) bidiagonal matrix B cbelmm - block Ellpack format matrix-matrix multiply cbelsm - block Ellpack format triangular solve cblas - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_caxpy - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ccopy - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cdotc_sub - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cdotu_sub - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cgbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cgemm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cgemv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cgerc - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cgeru - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_chbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_chemm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_chemv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cher - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cher2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cher2k - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cherk - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_chpmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_chpr - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_chpr2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cscal - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_csscal - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_cswap - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_csymm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_csyr2k - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_csyrk - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ctbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ctbsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ctpmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ctpsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ctrmm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ctrmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ctrsm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ctrsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dasum - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_daxpy - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dcopy - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ddot - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dgbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dgemm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dgemv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dger - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dnrm2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_drot - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_drotg - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_drotm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_drotmg - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dsbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dscal - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dsdot - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dspmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dspr - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dspr2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dswap - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dsymm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dsymv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dsyr - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dsyr2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dsyr2k - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dsyrk - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dtbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dtbsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dtpmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dtpsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dtrmm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dtrmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dtrsm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dtrsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dzasum - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_dznrm2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_icamax - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_idamax - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_isamax - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_izamax - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_memerr - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sasum - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_saxpy - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_scasum - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_scnrm2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_scopy - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sdot - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sdsdot - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sgbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sgemm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sgemv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sger - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_snrm2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_srot - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_srotg - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_srotm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_srotmg - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ssbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sscal - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sspmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sspr - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sspr2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_sswap - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ssymm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ssymv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ssyr - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ssyr2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ssyr2k - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ssyrk - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_stbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_stbsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_stpmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_stpsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_strmm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_strmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_strsm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_strsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_xerbla - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zaxpy - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zcopy - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zdotc_sub - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zdotu_sub - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zdscal - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zgbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zgemm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zgemv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zgerc - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zgeru - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zhbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zhemm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zhemv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zher - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zher2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zher2k - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zherk - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zhpmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zhpr - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zhpr2 - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zscal - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zswap - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zsymm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zsyr2k - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_zsyrk - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ztbmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ztbsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ztpmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ztpsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ztrmm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ztrmv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ztrsm - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cblas_ztrsv - C interface to the original Level 1, 2 and 3 BLAS, or the Legacy BLAS cbscmm - block sparse column matrix-matrix multiply cbscsm - block sparse column format triangular solve cbsrmm - block sparse row format matrix-matrix multiply cbsrsm - block sparse row format triangular solve ccnvcor - compute the convolution or correlation of complex vectors ccnvcor2 - compute the convolution or correlation of complex matrices ccoomm - coordinate matrix-matrix multiply ccopy - copy x to y ccscmm - compressed sparse column format matrix-matrix multiply ccscsm - compressed sparse column format triangular solve ccsrmm - compressed sparse row format matrix-matrix multiply ccsrsm - compressed sparse row format triangular solve cdiamm - diagonal format matrix-matrix multiply cdiasm - diagonal format triangular solve cdotc - compute the dot product of two vectors conjg(x) and y. cdotci - Compute the complex conjugated indexed dot product. cdotu - compute the dot product of two vectors x and y. cdotui - Compute the complex unconjugated indexed dot product. cellmm - Ellpack format matrix-matrix multiply cellsm - Ellpack format triangular solve cfft2b - compute a periodic sequence from its Fourier coefficients. The xFFT operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply the input sequence by M*N. cfft2f - compute the Fourier coefficients of a periodic sequence. The xFFT operations are unnormalized, so a call of xFFT2F fol- lowed by a call of xFFT2B will multiply the input sequence by M*N. cfft2i - initialize the array WSAVE, which is used in both the forward and backward transforms. cfft3b - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of CFFT3F fol- lowed by a call of CFFT3B will multiply the input sequence by M*N*K. cfft3f - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of CFFT3F followed by a call of CFFT3B will multiply the input sequence by M*N*K. cfft3i - initialize the array WSAVE, which is used in both CFFT3F and CFFT3B. cfftb - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of CFFTF followed by a call of CFFTB will multiply the input sequence by N. cfftc - initialize the trigonometric weight and factor tables or com- pute the Fast Fourier transform (forward or inverse) of a complex sequence. cfftc2 - initialize the trigonometric weight and factor tables or com- pute the two-dimensional Fast Fourier Transform (forward or inverse) of a two-dimensional complex array. cfftc3 - initialize the trigonometric weight and factor tables or com- pute the three-dimensional Fast Fourier Transform (forward or inverse) of a three-dimensional complex array. cfftcm - initialize the trigonometric weight and factor tables or com- pute the one-dimensional Fast Fourier Transform (forward or inverse) of a set of data sequences stored in a two-dimen- sional complex array. cfftf - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of CFFTF followed by a call of CFFTB will multiply the input sequence by N. cffti - initialize the array WSAVE, which is used in both CFFTF and CFFTB. cfftopt - compute the length of the closest fast FFT cffts - initialize the trigonometric weight and factor tables or com- pute the inverse Fast Fourier Transform of a complex sequence as follows. cffts2 - initialize the trigonometric weight and factor tables or com- pute the two-dimensional inverse Fast Fourier Transform of a two-dimensional complex array. cffts3 - initialize the trigonometric weight and factor tables or com- pute the three-dimensional inverse Fast Fourier Transform of a three-dimensional complex array. cfftsm - initialize the trigonometric weight and factor tables or com- pute the one-dimensional inverse Fast Fourier Transform of a set of complex data sequences stored in a two-dimensional array. cgbbrd - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation cgbcon - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity- norm, using the LU factorization computed by CGBTRF cgbequ - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number cgbequb - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number cgbmv - perform one of the matrix-vector operations y:=alpha*A*x + beta*y, or y:=alpha*A'*x + beta*y, or y:=alpha*conjg(A')*x + beta*y cgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provide error bounds and backward error estimates for the solution cgbrfsx - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution cgbsv - compute the solution to a complex system of linear equations A*X=B, where A is a band matrix of order N with KL subdiago- nals and KU superdiagonals, and X and B are N-by-NRHS matri- ces cgbsvx - use the LU factorization to compute the solution to a complex system of linear equations A*X=B, A**T*X=B, or A**H*X=B, where A is a band matrix cgbsvxx - compute the solution to system of linear equations A * X = B for ganeral band matrices cgbtf2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges cgbtrf - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges cgbtrs - solve a system of linear equations A*X=B, A**T*X=B, or A**H*X=B with a general band matrix A using the LU factoriza- tion computed by CGBTRF cgebak - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvec- tors of the balanced matrix output by CGEBAL cgebal - balance a general complex matrix A cgebd2 - reduce a general matrix to bidiagonal form using an unblocked algorithm cgebrd - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation cgecon - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF cgeequ - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number cgeequb - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number cgees - compute for an N-by-N complex nonsymmetric matrix A, the eigen- values, the Schur form T, and, optionally, the matrix of Schur vectors Z cgeesx - compute for an N-by-N complex nonsymmetric matrix A, the ei- genvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z cgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigen- values and, optionally, the left and/or right eigenvectors cgeevx - compute for an N-by-N complex nonsymmetric matrix A, the ei- genvalues and, optionally, the left and/or right eigenvectors cgegs - routine is deprecated and has been replaced by routine CGGES cgegv - routine is deprecated and has been replaced by routine CGGEV cgehd2 - reduce a general square matrix to upper Hessenberg form using an unblocked algorithm cgehrd - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation cgelq2 - compute the LQ factorization of a general rectangular matrix using an unblocked algorithm cgelqf - compute an LQ factorization of a complex M-by-N matrix A cgels - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A cgelsd - compute the minimum-norm solution to a real linear least squares problem cgelss - compute the minimum norm solution to a complex linear least squares problem cgelsx - routine is deprecated and has been replaced by routine CGELSY cgelsy - compute the minimum-norm solution to a complex linear least squares problem cgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C cgemqrt - overwrite the general complex M-by-N matrix C with Q*C, C*Q, Q**H*C, or C*Q**H depending on values of SIDE and TRANS cgemv - perform one of the matrix-vector operationsy := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y cgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm cgeqlf - compute a QL factorization of a complex M-by-N matrix A cgeqp3 - compute a QR factorization with column pivoting of a matrix A cgeqpf - routine is deprecated and has been replaced by routine CGEQP3 cgeqr2 - computes the QR factorization of a general rectangular matrix using an unblocked algorithm. cgeqr2p - computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algo- rithm. cgeqrf - compute a QR factorization of a complex M-by-N matrix A cgeqrfp - compute a QR factorization of a complex M-by-N matrix A: A = Q * R cgeqrt - compute a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q cgeqrt2 - compute a QR factorization of a general complex matrix using the compact WY representation of Q cgeqrt3 - recursively compute a QR factorization of a general complex matrix using the compact WY representation of Q cgerc - perform the rank 1 operation A := alpha*x*conjg( y' ) + A cgerfs - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution cgerfsx - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution cgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm cgerqf - compute an RQ factorization of a complex M-by-N matrix A cgeru - perform the rank 1 operation A := alpha*x*y' + A cgesdd - compute the singular value decomposition (SVD) of a complex M- by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method cgesv - compute the solution to a complex system of linear equations A*X=B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices cgesvd - compute the singular value decomposition (SVD) of a complex M- by-N matrix A, optionally computing the left and/or right singular vectors cgesvx - use the LU factorization to compute the solution to a complex system of linear equations A*X=B, where is an N-by-N gen- eral matrix cgesvxx - compute the solution to system of linear equations A*X=B for general matrices cgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges cgetrf - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges cgetri - compute the inverse of a matrix using the LU factorization computed by CGETRF cgetrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF cggbak - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transforma- tion on the computed eigenvectors of the balanced pair of matrices output by CGGBAL cggbal - balance a pair of general complex matrices (A,B) cgges - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR) cggesx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T), and, optionally, the left and/or right matrices of Schur vectors cggev - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors cggevx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B) the generalized eigenvalues, and, optionally, the left and/or right generalized eigenvectors cggglm - solve a general Gauss-Markov linear model (GLM) problem cgghrd - reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular cgglse - solve the linear equality-constrained least squares (LSE) problem cggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B. cggrqf - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B cggsvd - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B cggsvp - compute unitary matrices cgscon - estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SuperLU routine sgstrf. cgsequ - computes row and column scalings intended to equilibrate an M- by-N sparse matrix A and reduce its condition number. cgsrfs - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. It is a SuperLU routine. cgssco - General sparse solver condition number estimate. cgssda - Deallocate working storage for the general sparse solver. cgssfa - General sparse solver numeric factorization. cgssfs - General sparse solver one call interface. cgssin - Initialize the general sparse solver. cgssor - General sparse solver ordering and symbolic factorization. cgssps - Print general sparse solver statics. cgssrp - Return permutation used by the general sparse solver. cgsssl - Solve routine for the general sparse solver. cgssuo - Provide general sparse solvers SPSOLVE and SuperLU a user- supplied permutation for ordering. cgssv - solves a system of linear equations A*X=B using the LU factor- ization from sgstrf. cgssvx - solves the system of linear equations A*X=B or A'*X=B, using the LU factorization from sgstrf(). Error bounds on the solu- tion and a condition estimate are also provided. cgstrf - computes an LU factorization of a general sparse m-by-n matrix A using partial pivoting with row interchanges. cgstrs - solves a system of linear equations A*X=B or A'*X=B with A sparse and B dense, using the LU factorization computed by sgstrf. cgtcon - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF cgthr - Gathers specified elements from y into x. cgthrz - Gather and zero. cgtrfs - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, provide error bounds and backward error estimates for the solution cgtsv - solve the equation A*X = B, where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting cgtsvx - use the LU factorization to compute the solution to a complex system of linear equations A*X=B, A**T*X=B, or A**H*X=B, where A is a tridiagonal matrix of order N and X and B are N- by-NRHS matrices cgttrf - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges cgttrs - solve one of the systems of equations A*X=B, A**T*X=B, or A**H*X=B, with a tridiagonal matrix A using the LU factoriza- tion computed by CGTTRF cgtts2 - solve a system of linear equations with a tridiagonal matrix using the LU factorization computed by cgttrf chbev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A chbevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A chbevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A chbgst - reduce a complex Hermitian-definite banded generalized eigen- problem A*x=lambda*B*x to standard form C*y=lambda*y, such that C has the same bandwidth as A chbgv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenprob- lem, of the form A*x=(lambda)*B*x chbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenprob- lem, of the form A*x=(lambda)*B*x chbgvx - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenprob- lem, of the form A*x=(lambda)*B*x chbmv - perform the matrix-vector operationy := alpha*A*x + beta*y chbtrd - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation checon - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF checon_rook - estimate the reciprocal of the condition number for Her- mitian matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) cheequb - compute row and column scalings intended to equilibrate a Hermitian matrix A and reduce its condition number (with respect to the two-norm) cheev - compute all eigenvalues and, optionally, eigenvectors of a com- plex Hermitian matrix A cheevd - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A cheevr - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian tridiagonal matrix T cheevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A chegs2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form chegst - reduce a complex Hermitian-definite generalized eigenproblem to standard form chegv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x chegvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x chegvx - compute selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x chemm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C chemv - perform the matrix-vector operationy := alpha*A*x + beta*y cher - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A cher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A cher2k - perform one of the Hermitian rank 2k operations C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C or C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C cherfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and pro- vide error bounds and backward error estimates for the solu- tion cherfsx - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and pro- vide error bounds and backward error estimates for the solu- tion cherk - perform one of the Hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C or C := alpha*conjg( A' )*A + beta*C chesv - compute the solution to a complex system of linear equations A*X=B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices chesv_rook - compute the solution to a system of linear equations A*X=B for Hermitian matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method chesvx - use the diagonal pivoting factorization to compute the solu- tion to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices chesvxx - compute the solution to system of linear equations A*X = B for Hermitian matrices chetd2 - reduce a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm) chetf2 - compute the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm calling Level 2 BLAS) chetf2_rook - compute the factorization of a complex Hermitian indefi- nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm) chetrd - reduce a complex Hermitian matrix A to real symmetric tridiag- onal form T by a unitary similarity transformation chetrf - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method chetrf_rook - compute the factorization of a complex Hermitian indefi- nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS) chetri - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF chetri2 - compute the inverse of a COMPLEX Hermitian indefinite matrix A using the factorization A=U*D*U**T or A=L*D*L**T computed by CHETRF chetri2x - computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF chetri_rook - compute the inverse of a Hermitian matrix using the fac- torization obtained with the bounded Bunch-Kaufman ("rook") diagonal pivoting method chetrs - solve a system of linear equations A*X = B with a complex Her- mitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF chetrs2 - solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF and converted by CSYCONV chetrs_rook - compute the solution to a system of linear equations A*X=B for Hermitian matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) chfrk - perform a Hermitian rank-k operation for matrix in RFP format chgeqz - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A-w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranforma- tion (usually called Q) on the left and another (usually called Z) on the right chla_transtype - translate from a BLAST-specified integer constant to the character string specifying a transposition operation chpcon - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF chpev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage chpevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage chpevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage chpgst - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage chpgv - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x chpgvd - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x chpgvx - compute selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x chpmv - perform the matrix-vector operationy := alpha*A*x + beta*y chpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A chpr2 - perform the Hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A chprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provide error bounds and backward error estimates for the solution chpsv - compute the solution to a complex system of linear equationsA*X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices chpsvx - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of lin- ear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices chptrd - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation chptrf - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method chptri - compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF chptrs - solve a system of linear equations A*X = B with a complex Her- mitian matrix A stored in packed format using the factoriza- tion A = U*D*U**H or A = L*D*L**H computed by CHPTRF chsein - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H chseqr - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors cinfinite_norm_error - A utility function of the SuperLU solver that computes the infinity-norm of an array of vectors that are approximations to the exact solution vector. cjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack) cjadrp - right permutation of a jagged diagonal matrix cjadsm - Jagged-diagonal format triangular solve cla_gbamv - perform a matrix-vector operation to calculate error bounds cla_gbrcond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices cla_gbrcond_x - compute the infinity norm condition number of op(A)*diag(x) for general banded matrices cla_gbrfsx_extended - improve the computed solution to a system of lin- ear equations for general banded matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution cla_gbrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix cla_geamv - compute a matrix-vector product using a general matrix to calculate error bounds cla_gercond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for general matrices cla_gercond_x - compute the infinity norm condition number of op(A)*diag(x) for general matrices cla_gerfsx_extended - improve the computed solution to a system of lin- ear equations by performing extra-precise iterative refine- ment and provide error bounds and backward error estimates for the solution cla_gerpvgrw - compute the reciprocal pivot growth factor using the "max absolute element" norm cla_heamv - compute a matrix-vector product using a Hermitian indefi- nite matrix to calculate error bounds cla_hercond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices cla_hercond_x - compute the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices cla_herfsx_extended - improve the computed solution to a system of lin- ear equations for Hermitian indefinite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution cla_herpvgrw - compute the reciprocal pivot growth factor using the "max absolute element" norm cla_lin_berr - compute a component-wise relative backward error cla_porcond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices cla_porcond_x - compute the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices cla_porfsx_extended - improve the computed solution to a system of lin- ear equations for symmetric or Hermitian positive-definite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution cla_porpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-defi- nite matrix cla_syamv - compute a matrix-vector product using a symmetric indefi- nite matrix to calculate error bounds cla_syrcond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices cla_syrcond_x - compute the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices cla_syrfsx_extended - improve the computed solution to a system of lin- ear equations for symmetric indefinite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution cla_syrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix cla_wwaddw - add a vector into a doubled-single vector claed0 - compute all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Used by cstedc claed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used by cstedc, when the original matrix is dense claed8 - merge eigenvalues and deflates secular equation. Used by cst- edc, when the original matrix is dense clahef - compute a partial factorization of a complex Hermitian indefi- nite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS) clahef_rook - compute a partial factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS) clals0 - apply back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by cgelsd clalsa - compute the SVD of the coefficient matrix in compact form. Used by cgelsd clalsd - use the singular value decomposition of A to solve the least squares problem clangs - returns the value of the one-norm, or the Frobenius-norm, or the infinity-norm, or the element with largest absolute value of a general real matrix A in sparse format. clanhf - return the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian matrix in RFP format claqgs - a SuperLU function that equilibrates a general sparse M by N matrix A. clarscl2 - perform reciprocal diagonal scaling on a vector clarz - apply a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right clarzb - apply a complex block reflector H or its transpose H**H to a complex distributed M-by-N C from the left or the right clarzt - form the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors clascl2 - perform diagonal scaling on a vector clasyf - compute a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method clasyf_rook - compute a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal piv- oting method clatrz - factor an upper trapezoidal matrix by means of unitary trans- formations clatzm - routine is deprecated and has been replaced by routine CUNMRZ cosqb - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The COSQ operations are unnormalized inverses of themselves, so a call to COSQF followed by a call to COSQB will multiply the input sequence by 4 * N. cosqf - compute the Fourier coefficients in a cosine series representa- tion with only odd wave numbers. The COSQ operations are unnormalized inverses of themselves, so a call to COSQF fol- lowed by a call to COSQB will multiply the input sequence by 4 * N. cosqi - initialize the array WSAVE, which is used in both COSQF and COSQB. cost - compute the discrete Fourier cosine transform of an even sequence. The COST transforms are unnormalized inverses of themselves, so a call of COST followed by another call of COST will multiply the input sequence by 2 * (N-1). costi - initialize the array WSAVE, which is used in COST. cpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF cpbequ - compute row and column scalings intended to equilibrate a Her- mitian positive definite band matrix A and reduce its condi- tion number (with respect to the two-norm) cpbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, provide error bounds and backward error estimates for the solution cpbstf - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A cpbsv - compute the solution to a complex system of linear equations A*X=B, where A is an N-by-N Hermitian positive definite band matrix and X and B are N-by-NRHS matrices cpbsvx - use the Cholesky factorization to compute the solution to a complex system of linear equations A*X=B, where A is an N-by- N Hermitian positive definite band matrix and X and B are N- by-NRHS matrices cpbtf2 - compute the Cholesky factorization of a complex Hermitian pos- itive definite band matrix A cpbtrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite band matrix A cpbtrs - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factoriza- tion A = U**H*U or A = L*L**H computed by CPBTRF cpftrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A, the block version of the algorithm cpftri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization computed by CPFTRF cpftrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization computed by CPFTRF cpocon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF cpoequ - compute row and column scalings intended to equilibrate a Her- mitian positive definite matrix A and reduce its condition number (with respect to the two-norm) cpoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm cporfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, provide error bounds and backward error estimates for the solution cporfsx - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, provide error bounds and backward error estimates for the solution cposv - compute the solution to a complex system of linear equationsA*X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices cposvx - use the Cholesky factorization to compute the solution to a complex system of linear equations A*X = B, where A is an N- by-N Hermitian positive definite matrix and X and B are N-by- NRHS matrices cposvxx - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices cpotf2 - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A cpotrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A cpotri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF cpotrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPOTRF cppcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF cppequ - compute row and column scalings intended to equilibrate a Her- mitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) cpprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, provide error bounds and backward error estimates for the solution cppsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite matrix stored in packed format and X and B are N-by-NRHS matrices cppsvx - use the Cholesky factorization to compute the solution to a complex system of linear equations A*X = B, where A is an N- by-N Hermitian positive definite matrix stored in packed for- mat and X and B are N-by-NRHS matrices cpptrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A stored in packed format cpptri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF cpptrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF cpstf2 - compute the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A cpstrf - compute the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A cptcon - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF cpteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first fac- toring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor cptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, provide error bounds and backward error estimates for the solution cptsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices cptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices cpttrf - compute the L*D*L' factorization of a complex Hermitian posi- tive definite tridiagonal matrix A cpttrs - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF cptts2 - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF crot - apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors X and Y are complex crotg - Construct a Given's plane rotation cscal - Compute y := alpha * y csctr - Scatters elements from x into y cskymm - Skyline format matrix-matrix multiply cskysm - Skyline format triangular solve cspcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the fac- torization A = U*D*U**T or A = L*D*L**T computed by CSPTRF csprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, provide error bounds and backward error estimates for the solution cspsv - compute the solution to a complex system of linear equationsA*X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices cspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of lin- ear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices csptrf - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal piv- oting method csptri - compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF csptrs - solve a system of linear equations A*X = B with a complex sym- metric matrix A stored in packed format using the factoriza- tion A = U*D*U**T or A = L*D*L**T computed by CSPTRF csrot - Apply a plane rotation csscal - Compute y := alpha * y cstedc - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method cstegr - Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation cstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration cstemr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T csteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method cstsv - compute the solution to a complex system of linear equations A * X = B where A is a symmetric tridiagonal matrix csttrf - compute the factorization of a complex symmetric tridiagonal matrix A using the Bunch-Kaufman diagonal pivoting method csttrs - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N symmetric tridiagonal matrix and X and B are N-by-NRHS matrices cswap - Exchange vectors x and y csycon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factoriza- tion A = U*D*U**T or A = L*D*L**T computed by CSYTRF csycon_rook - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factoriza- tion A = U*D*U**T or A = L*D*L**T computed by CSYTRF_ROOK csyconv - convert A given by TRF into L and D and vice-versa csyequb - compute row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number with respect to the two-norm csymm - perform one of the matrix-matrix operationsC := alpha*A*B + beta*C or C := alpha*B*A + beta*C csyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C csyrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provide error bounds and backward error estimates for the solution csyrfsx - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provide error bounds and backward error estimates for the solution csyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C csysv - compute the solution to a complex system of linear equationsA*X = B, where A is an N-by-N symmetric matrix and X and B are N- by-NRHS matrices csysv_rook - compute the solution to system of linear equations A*X = B for symmetric matrices. CSYTRF_ROOK is called to compute the factorization of A csysvx - use the diagonal pivoting factorization to compute the solu- tion to a complex system of linear equations A*X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices csysvxx - compute the solution to complex system of linear equations A*X = B for symmetric matrices csytf2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method csytf2_rook - compute the factorization of a complex symmetric indefi- nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm) csytrf - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method csytrf_rook - compute the factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm) csytri - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF csytri2 - compute the inverse of a COMPLEX symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T com- puted by CSYTRF csytri2x - compute the inverse of a real symmetric indefinite matrix A using the factorization computed by CSYTRF csytrii_rook - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF_ROOK csytrs - solve a system of linear equations A*X = B with a complex sym- metric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF csytrs2 - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization computed by CSYTRF and converted by CSYCONV csytrs_rook - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF_ROOK ctbcon - estimate the reciprocal of the condition number of a triangu- lar band matrix A, in either the 1-norm or the infinity-norm ctbmv - perform one of the matrix-vector operationsx := A*x, or x := A'*x, or x := conjg( A' )*x ctbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix ctbsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b ctbtrs - solve a triangular system of the form A*X = B, A**T*X = B, or A**H*X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix ctfsm - solve a matrix equation (one operand is a triangular matrix in RFP format) ctftri - compute the inverse of a triangular matrix A stored in RFP format ctfttp - copy a triangular matrix from the rectangular full packed for- mat (TF) to the standard packed format (TP) ctfttr - copy a triangular matrix from the rectangular full packed for- mat (TF) to the standard full format (TR) ctgevc - compute the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices with real diagonal elements (A,B) obtained from the generalized Schur factoriza- tion of an original pair of complex nonsymmetric matrices (AO,BO) ctgexc - reorder the generalized Schur decomposition of a complex matrix pair using an orthogonal or unitary equivalence trans- formation ctgsen - reorder the generalized Schur decomposition of a complex matrix pair (A, B), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the pair (A,B) ctgsja - compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B ctgsna - estimate reciprocal condition numbers for specified eigenval- ues and/or eigenvectors of a matrix pair (A, B) ctgsyl - solve the generalized Sylvester equation ctpcon - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity- norm ctpmqrt - apply a complex orthogonal matrix Q obtained from a "triangu- lar-pentagonal" complex block reflector H to a general com- plex matrix C, which consists of two blocks ctpmv - perform one of the matrix-vector operationsx := A*x, or x := A'*x, or x := conjg( A' )*x ctpqrt - compute a blocked QR factorization of a complex "triangular- pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q ctpqrt2 - compute a QR factorization of a real or complex "triangular- pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q ctprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix ctpsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b ctptri - compute the inverse of a complex upper or lower triangular matrix A stored in packed format ctptrs - solve a triangular system of the form A*X = B, A**T*X = B, or A**H*X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix ctpttf - copy a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF) ctpttr - copy a triangular matrix from the standard packed format (TP) to the standard full format (TR) ctrans - transpose and scale source matrix ctrcon - estimate the reciprocal of the condition number of a triangu- lar matrix A, in either the 1-norm or the infinity-norm ctrevc - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T ctrexc - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST ctrmm - perform one of the matrix-matrix operationsB := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ) ctrmv - perform one of the matrix-vector operationsx := A*x, or x := A'*x, or x := conjg( A' )*x ctrrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix ctrsen - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper trian- gular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant sub- space ctrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B ctrsna - estimate reciprocal condition numbers for specified eigenval- ues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary) ctrsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b ctrsyl - solve the complex Sylvester matrix equation ctrti2 - compute the inverse of a complex upper or lower triangular matrix ctrtri - compute the inverse of a complex upper or lower triangular matrix A ctrtrs - solve a triangular system of the form A*X = B, A**T*X = B, or A**H*X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix ctrttf - copy a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF) ctrttp - copy a triangular matrix from the standard full format (TR) to the standard packed format (TP) ctzrqf - routine is deprecated and has been replaced by routine CTZRZF ctzrzf - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations cunbdb - simultaneously bidiagonalizes the blocks of an M-by-M parti- tioned unitary matrix cunbdb1 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns cunbdb2 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns cunbdb3 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns cunbdb4 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns cunbdb5 - orthogonalize one column vector with respect to the orthonor- mal columns of another column vector cunbdb6 - orthogonalize one column vector with respect to the orthonor- mal columns of another column vector cuncsd - compute the CS decomposition of an M-by-M partitioned unitary matrix cuncsd2by1 - compute the CS decomposition of an M-by-Q matrix with orthonormal columns that has been partitioned into a 2-by-1 block structure cung2l - generate all or part of the unitary matrix Q from a QL factor- ization determined by cgeqlf (unblocked algorithm) cung2r - generate an M-by-N complex matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M cungbr - generate one of the complex unitary matrices Q or P**H deter- mined by CGEBRD when reducing a complex matrix A to bidiago- nal form cunghr - generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by CGEHRD cungl2 - generate all or part of the unitary matrix Q from an LQ fac- torization determined by cgelqf (unblocked algorithm) cunglq - generate an M-by-N complex matrix Q with orthonormal rows, which is defined as the first M rows of a product of K ele- mentary reflectors of order N cungql - generate an M-by-N complex matrix Q with orthonormal columns, which is defined as the last N columns of a product of K ele- mentary reflectors of order M cungqr - generate an M-by-N complex matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M cungr2 - generate all or part of the unitary matrix Q from an RQ fac- torization determined by cgerqf (unblocked algorithm) cungrq - generate an M-by-N complex matrix Q with orthonormal rows, which is defined as the last M rows of a product of K elemen- tary reflectors of order N cungtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD cunm2l - multiply a general matrix by the unitary matrix from a QL fac- torization determined by cgeqlf (unblocked algorithm) cunm2r - multiply a general matrix by the unitary matrix from a QR fac- torization determined by cgeqrf (unblocked algorithm) cunmbr - overwrite the general complex M-by-N matrix C with Q*C or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H cunmhr - overwrite the general complex M-by-N matrix C with Q*C or Q**H*C or C*Q**H or C*Q cunml2 - multiply a general matrix by the unitary matrix from a LQ fac- torization determined by cgelqf (unblocked algorithm) cunmlq - overwrite the general complex M-by-N matrix C with Q*C, or Q**H*C, or C*Q**H, or C*Q, where Q is a complex unitary matrix defined as the product of K elementary reflectors cunmql - overwrite the general complex M-by-N matrix C with Q*C, or Q**H*C, or C*Q**H, or C*Q, where Q is a complex unitary matrix defined as the product of K elementary reflectors cunmqr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' cunmr2 - multiply a general matrix by the unitary matrix from a RQ fac- torization determined by cgerqf (unblocked algorithm) cunmr3 - multiply a general matrix by the unitary matrix from a RZ fac- torization determined by ctzrzf (unblocked algorithm) cunmrq - overwrite the general complex M-by-N matrix C with Q*C, or Q**H*C, or C*Q**H, or C*Q, where Q is a complex unitary matrix defined as the product of K elementary reflectors cunmrz - overwrite the general complex M-by-N matrix C with Q*C or Q**H*C or C*Q**H or C*Q. cunmtr - overwrite the general complex M-by-N matrix C with Q*C, or Q**H*C, or C*Q**H, or C*Q, where Q is defined as the product of elementary reflectors, as returned by CHETRD cupgtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage cupmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' cvbrmm - variable block sparse row format matrix-matrix multiply cvbrsm - variable block sparse row format triangular solve cvmul - compute the scaled product of complex vectors dCopy_CompCol_Matrix - A utility C function in the serial SuperLU solver that copies one SuperMatrix into another. dCreate_CompCol_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse column format (also known as the Harwell-Boeing format). dCreate_CompRow_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse row format. dCreate_Dense_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in dense format. dCreate_SuperNode_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in supernodal format. dPrintPerf - A utility function of the SuperLU solver that prints sta- tistics collected by the computational routines. dQuerySpace - A inquiry function that provides information on the mem- ory statistics of the SuperLU solver. dasum - Return the sum of the absolute values of a vector x. daxpy - compute y := alpha * x + y daxpyi - Compute y := alpha * x + y dbbcsd - compute the CS decomposition of an orthogonal matrix in bidi- agonal-block form dbcomm - block coordinate matrix-matrix multiply dbdimm - block diagonal format matrix-matrix multiply dbdism - block diagonal format triangular solve dbdsdc - compute the singular value decomposition (SVD) of a real N-by- N (upper or lower) bidiagonal matrix B dbdsqr - compute the singular value decomposition (SVD) of a real N-by- N (upper or lower) bidiagonal matrix B dbelmm - block Ellpack format matrix-matrix multiply dbelsm - block Ellpack format triangular solve dbscmm - block sparse column matrix-matrix multiply dbscsm - block sparse column format triangular solve dbsrmm - block sparse row format matrix-matrix multiply dbsrsm - block sparse row format triangular solve dcnvcor - compute the convolution or correlation of real vectors dcnvcor2 - compute the convolution or correlation of real matrices dcoomm - coordinate matrix-matrix multiply dcopy - copy x to y dcosqb - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The COSQ operations are unnormalized inverses of themselves, so a call to COSQF followed by a call to COSQB will multiply the input sequence by 4 * N. dcosqf - compute the Fourier coefficients in a cosine series represen- tation with only odd wave numbers. The COSQ operations are unnormalized inverses of themselves, so a call to COSQF fol- lowed by a call to COSQB will multiply the input sequence by 4 * N. dcosqi - initialize the array WSAVE, which is used in both COSQF and COSQB. dcost - compute the discrete Fourier cosine transform of an even sequence. The COST transforms are unnormalized inverses of themselves, so a call of COST followed by another call of COST will multiply the input sequence by 2 * (N-1). dcosti - initialize the array WSAVE, which is used in COST. dcscmm - compressed sparse column format matrix-matrix multiply dcscsm - compressed sparse column format triangular solve dcsrmm - compressed sparse row format matrix-matrix multiply dcsrsm - compressed sparse row format triangular solve ddiamm - diagonal format matrix-matrix multiply ddiasm - diagonal format triangular solve ddisna - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix ddot - compute the dot product of two vectors x and y. ddoti - Compute the indexed dot product. dellmm - Ellpack format matrix-matrix multiply dellsm - Ellpack format triangular solve dezftb - computes a periodic sequence from its Fourier coefficients. DEZFTB is a simplified but slower version of DFFTB. dezftf - computes the Fourier coefficients of a periodic sequence. DEZFTF is a simplified but slower version of DFFTF. dezfti - initializes the array WSAVE, which is used in both DEZFTF and DEZFTB. dfft2b - compute a periodic sequence from its Fourier coefficients. The DFFT operations are unnormalized, so a call of DFFT2F followed by a call of DFFT2B will multiply the input sequence by M*N. dfft2f - compute the Fourier coefficients of a periodic sequence. The DFFT operations are unnormalized, so a call of DFFT2F fol- lowed by a call of DFFT2B will multiply the input sequence by M*N. dfft2i - initialize the array WSAVE, which is used in both the forward and backward transforms. dfft3b - compute a periodic sequence from its Fourier coefficients. The DFFT operations are unnormalized, so a call of DFFT3F fol- lowed by a call of DFFT3B will multiply the input sequence by M*N*K. dfft3f - compute the Fourier coefficients of a real periodic sequence. The DFFT operations are unnormalized, so a call of DFFT3F followed by a call of DFFT3B will multiply the input sequence by M*N*K. dfft3i - initialize the array WSAVE, which is used in both DFFT3F and DFFT3B. dfftb - compute a periodic sequence from its Fourier coefficients. The DFFT operations are unnormalized, so a call of DFFTF followed by a call of DFFTB will multiply the input sequence by N. dfftf - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of DFFTF followed by a call of DFFTB will multiply the input sequence by N. dffti - initialize the array WSAVE, which is used in both DFFTF and DFFTB. dfftopt - compute the length of the closest fast FFT dfftz - initialize the trigonometric weight and factor tables or com- pute the forward Fast Fourier Transform of a double precision sequence. dfftz2 - initialize the trigonometric weight and factor tables or com- pute the two-dimensional forward Fast Fourier Transform of a two-dimensional double precision array. dfftz3 - initialize the trigonometric weight and factor tables or com- pute the three-dimensional forward Fast Fourier Transform of a three-dimensional double complex array. dfftzm - initialize the trigonometric weight and factor tables or com- pute the one-dimensional forward Fast Fourier Transform of a set of double precision data sequences stored in a two-dimen- sional array. dgbbrd - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation dgbcon - estimate the reciprocal of the condition number of a real gen- eral band matrix A, in either the 1-norm or the infinity- norm, using the LU factorization computed by DGBTRF dgbequ - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number dgbequb - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number dgbmv - perform one of the matrix-vector operationsy := alpha*A*x + beta*y or y := alpha*A'*x + beta*y dgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provide error bounds and backward error estimates for the solution dgbrfsx - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution dgbsv - compute the solution to a real system of linear equations A*X=B, where A is a band matrix of order N with KL subdiago- nals and KU superdiagonals, and X and B are N-by-NRHS matri- ces dgbsvx - use the LU factorization to compute the solution to a real system of linear equations A*X=B, A**T*X=B, or A**H*X=B, where A is a band matrix dgbsvxx - compute the solution to system of linear equations A * X = B for general band matrices dgbtf2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges dgbtrf - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges dgbtrs - solve a system of linear equations A*X=B or A'*X=B with a gen- eral band matrix A using the LU factorization computed by DGBTRF dgebak - form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by DGEBAL dgebal - balance a general real matrix A dgebd2 - reduce a general matrix to bidiagonal form using an unblocked algorithm dgebrd - reduce a general real M-by-N matrix A to upper or lower bidi- agonal form B by an orthogonal transformation dgecon - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF dgeequ - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number dgeequb - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number dgees - compute for an N-by-N real nonsymmetric matrix A, the eigenval- ues, the real Schur form T, and, optionally, the matrix of Schur vectors Z dgeesx - compute for an N-by-N real nonsymmetric matrix A, the eigen- values, the real Schur form T, and, optionally, the matrix of Schur vectors Z dgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenval- ues and, optionally, the left and/or right eigenvectors dgeevx - compute for an N-by-N real nonsymmetric matrix A, the eigen- values and, optionally, the left and/or right eigenvectors dgegs - routine is deprecated and has been replaced by routine DGGES dgegv - routine is deprecated and has been replaced by routine DGGEV dgehd2 - reduce a general square matrix to upper Hessenberg form using an unblocked algorithm dgehrd - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation dgejsv - compute the singular value decomposition (SVD) of a real M-by- N matrix A, where M >= N dgelq2 - compute the LQ factorization of a general rectangular matrix using an unblocked algorithm dgelqf - compute an LQ factorization of a real M-by-N matrix A dgels - solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A dgelsd - compute the minimum-norm solution to a real linear least squares problem dgelss - compute the minimum norm solution to a real linear least squares problem dgelsx - routine is deprecated and has been replaced by routine DGELSY dgelsy - compute the minimum-norm solution to a real linear least squares problem dgemm - perform one of the matrix-matrix operationsC := alpha*op( A )*op( B ) + beta*C dgemqrt - overwrite the general real M-by-N matrix C with Q*C, C*Q, Q**T*C, or C*Q**T depending on values of SIDE and TRANS dgemv - perform one of the matrix-vector operationsy := alpha*A*x + beta*y or y := alpha*A'*x + beta*y dgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm dgeqlf - compute a QL factorization of a real M-by-N matrix A dgeqp3 - compute a QR factorization with column pivoting of a matrix A dgeqpf - routine is deprecated and has been replaced by routine DGEQP3 dgeqr2 - computes the QR factorization of a general rectangular matrix using an unblocked algorithm. dgeqr2p - computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algo- rithm. dgeqrf - compute a QR factorization of a real M-by-N matrix A dgeqrfp - compute a QR factorization of a real M-by-N matrix A: A = Q * R dgeqrt - compute a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q dgeqrt2 - compute a QR factorization of a general real matrix using the compact WY representation of Q dgeqrt3 - recursively compute a QR factorization of a general real matrix using the compact WY representation of Q dger - perform the rank 1 operation A := alpha*x*y' + A dgerfs - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution dgerfsx - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution dgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm dgerqf - compute an RQ factorization of a real M-by-N matrix A dgesdd - compute the singular value decomposition (SVD) of a real M-by- N matrix A, optionally computing the left and right singular vectors dgesv - compute the solution to a real system of linear equations A*X=B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices dgesvd - compute the singular value decomposition (SVD) of a real M-by- N matrix A, optionally computing the left and/or right singu- lar vectors dgesvj - compute the singular value decomposition (SVD) of a real M-by- N matrix A, where M >= N dgesvx - use the LU factorization to compute the solution to a real system of linear equations A*X=B, where A is an N-by-N gen- eral matrix dgesvxx - compute the solution to system of linear equations A*X=B for geberal matrices dgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges dgetrf - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges dgetri - compute the inverse of a matrix using the LU factorization computed by DGETRF dgetrs - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by DGETRF dggbak - form the right or left eigenvectors of a real generalized ei- genvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL dggbal - balance a pair of general real matrices (A,B) dgges - compute for a pair of N-by-N real nonsymmetric matrices (A,B), dggesx - compute for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the real Schur form (S,T), and, optionally, the left and/or right matrices of Schur vectors dggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B) dggevx - compute for a pair of N-by-N real nonsymmetric matrices (A,B), and, optionally, the left and/or right generalized eigenvec- tors dggglm - solve a general Gauss-Markov linear model (GLM) problem dgghrd - reduce a pair of real matrices (A,B) to generalized upper Hes- senberg form using orthogonal transformations, where A is a general matrix and B is upper triangular dgglse - solve the linear equality-constrained least squares (LSE) problem dggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B. dggrqf - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B dggsvd - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B dggsvp - compute orthogonal matrices dgscon - estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SuperLU routine sgstrf. dgsequ - computes row and column scalings intended to equilibrate an M- by-N sparse matrix A and reduce its condition number. dgsrfs - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. It is a SuperLU routine. dgssco - General sparse solver condition number estimate. dgssda - Deallocate working storage for the general sparse solver. dgssfa - General sparse solver numeric factorization. dgssfs - General sparse solver one call interface. dgssin - Initialize the general sparse solver. dgssor - General sparse solver ordering and symbolic factorization. dgssps - Print general sparse solver statics. dgssrp - Return permutation used by the general sparse solver. dgsssl - Solve routine for the general sparse solver. dgssuo - Provide general sparse solvers SPSOLVE and SuperLU a user-sup- plied permutation for ordering. dgssv - solves a system of linear equations A*X=B using the LU factor- ization from sgstrf. dgssvx - solves the system of linear equations A*X=B or A'*X=B, using the LU factorization from sgstrf(). Error bounds on the solu- tion and a condition estimate are also provided. dgstrf - computes an LU factorization of a general sparse m-by-n matrix A using partial pivoting with row interchanges. dgstrs - solves a system of linear equations A*X=B or A'*X=B with A sparse and B dense, using the LU factorization computed by sgstrf. dgsvj0 - pre-processor for the routine sgesvj dgsvj1 - pre-processor for the routine sgesvj, apply Jacobi rotations targeting only particular pivots dgtcon - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF dgthr - Gathers specified elements from y into x. dgthrz - Gather and zero. dgtrfs - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, provide error bounds and backward error estimates for the solution dgtsv - solve the equation A*X=B, where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting dgtsvx - use the LU factorization to compute the solution to a real system of linear equations A*X=B or A**T*X=B, where A is a tridiagonal matrix of order N and X and B are N-by-NRHS matrices dgttrf - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges dgttrs - solve one of the systems of equations A*X=B or A'*X=B, with a tridiagonal matrix A using the LU factorization computed by DGTTRF dgtts2 - solve a system of linear equations with a tridiagonal matrix using the LU factorization computed by dgttrf dhgeqz - implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j) of the equation det( A-w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form dhsein - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H dhseqr - compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decompo- sition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors dinfinite_norm_error - A utility function of the SuperLU solver that computes the infinity-norm of an array of vectors that are approximations to the exact solution vector. djadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack) djadrp - right permutation of a jagged diagonal matrix djadsm - Jagged-diagonal format triangular solve dla_gbamv - perform a matrix-vector operation to calculate error bounds dla_gbrcond - estimate the Skeel condition number for a general banded matrix dla_gbrfsx_extended - improve the computed solution to a system of lin- ear equations for general banded matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution dla_gbrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix dla_geamv - compute a matrix-vector product using a general matrix to calculate error bounds dla_gercond - estimate the Skeel condition number for a general matrix dla_gerfsx_extended - improve the computed solution to a system of lin- ear equations for general matrices by performing extra-pre- cise iterative refinement and provide error bounds and back- ward error estimates for the solution dla_gerpvgrw - compute the reciprocal pivot growth factor using the "max absolute element" norm dla_lin_berr - compute a component-wise relative backward error dla_porcond - estimate the Skeel condition number for a symmetric posi- tive-definite matrix dla_porfsx_extended - improve the computed solution to a system of lin- ear equations for symmetric or Hermitian positive-definite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution dla_porpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-defi- nite matrix dla_syamv - compute a matrix-vector product using a symmetric indefi- nite matrix to calculate error bounds dla_syrcond - estimate the Skeel condition number for a symmetric indefinite matrix dla_syrfsx_extended - improve the computed solution to a system of lin- ear equations for symmetric indefinite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution dla_syrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix dla_wwaddw - add a vector into a doubled-single vector dlaed0 - compute all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Used by dstedc dlaed1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used by dstedc, when the original matrix is tridiagonal dlaed2 - merge eigenvalues and deflates secular equation; used by dst- edc when the original matrix is tridiagonal dlaed3 - find the roots of the secular equation and updates the eigen- vectors; used by dstedc when the original matrix is tridiago- nal dlaed4 - is used by sstedc. Finds a single root of the secular equation dlaed5 - is used by sstedc. Solve the 2-by-2 secular equation dlaed6 - is used by sstedc. Compute one Newton step in solution of the secular equation dlaed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used by dstedc, when the original matrix is dense dlaed8 - merge eigenvalues and deflates secular equation. Used by dst- edc, when the original matrix is dense dlaed9 - is used by sstedc. Find the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense dlaeda - is used by sstedc. Compute the Z vector determining the rank- one modification of the diagonal matrix. Used when the origi- nal matrix is dense dlagtf - factorize the matrix (T-lambda*I), where T is an n by n tridi- agonal matrix and lambda is a scalar, as T-lambda*I = PLU dlals0 - apply back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by dgelsd dlalsa - compute the SVD of the coefficient matrix in compact form. Used by dgelsd dlalsd - use the singular value decomposition of A to solve the least squares problem dlamch - Determines double precision machine parameters. dlamrg - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order dlangs - returns the value of the one-norm, or the Frobenius-norm, or the infinity-norm, or the element with largest absolute value of a general real matrix A in sparse format. dlansf - return the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix in RFP format dlaqgs - a SuperLU function that equilibrates a general sparse M by N matrix A. dlarscl2 - perform reciprocal diagonal scaling on a vector dlartgs - generate a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem dlarz - apply a real elementary reflector H to a real M-by-N matrix C, from either the left or the right dlarzb - apply a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right dlarzt - form the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors dlascl2 - perform diagonal scaling on a vector dlasq1 - compute the singular values of a real square bidiagonal matrix. Used by sbdsqr dlasq2 - compute all the eigenvalues of a real symmetric positive def- inite tridiagonal matrix (high relative accuracy) dlasq3 - check for deflation, computes a shift and calls dqds. Used by dbdsqr dlasq4 - compute an approximation to the smallest eigenvalue using val- ues of d from the previous transform. Used by dbdsqr dlasq5 - compute one dqds transform in ping-pong form. Used by sbdsqr and sstegr dlasq6 - compute one dqd transform in ping-pong form. Used by sbdsqr and sstegr dlasrt - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' ) dlasyf - compute a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method dlasyf_rook - compute a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal piv- oting method dlatrz - factor an upper trapezoidal matrix by means of orthogonal transformations dlatzm - routine is deprecated and has been replaced by routine DORMRZ dnrm2 - Return the Euclidian norm of a vector. dopgtr - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by DSPTRD using packed storage dopmtr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' dorbdb - simultaneously bidiagonalize the blocks of an M-by-M parti- tioned orthogonal matrix dorbdb1 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns dorbdb2 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns dorbdb3 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns dorbdb4 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns dorbdb5 - orthogonalize one column vector with respect to the orthonor- mal columns of another column vector dorbdb6 - orthogonalize one column vector with respect to the orthonor- mal columns of another column vector dorcsd - compute the CS decomposition of an M-by-M partitioned orthogo- nal matrix dorcsd2by1 - compute the CS decomposition of an M-by-Q matrix with orthonormal columns that has been partitioned into a 2-by-1 block structure dorg2l - generate an m by n real matrix Q with orthonormal columns, dorg2r - generate an m by n real matrix Q with orthonormal columns, dorgbr - generate one of the real orthogonal matrices Q or P**T deter- mined by DGEBRD when reducing a real matrix A to bidiagonal form dorghr - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by DGEHRD dorgl2 - generate an m by n real matrix Q with orthonormal rows, dorglq - generate an M-by-N real matrix Q with orthonormal rows, dorgql - generate an M-by-N real matrix Q with orthonormal columns, dorgqr - generate an M-by-N real matrix Q with orthonormal columns, dorgr2 - generate an m by n real matrix Q with orthonormal rows, dorgrq - generate an M-by-N real matrix Q with orthonormal rows, dorgtr - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by DSYTRD dorm2l - multiply a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm) dorm2r - multiply a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm) dormbr - overwrites the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T. dormhr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. dorml2 - multiply a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm) dormlq - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. dormql - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. dormqr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' dormr2 - multiply a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm) dormr3 - multiply a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm) dormrq - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. dormrz - overwrite the general real M-by-N matrix C with Q*C or Q**H*C or C*Q**H or C*Q. dormtr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. dpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF dpbequ - compute row and column scalings intended to equilibrate a sym- metric positive definite band matrix A and reduce its condi- tion number (with respect to the two-norm) dpbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, provide error bounds and backward error estimates for the solution dpbstf - compute a split Cholesky factorization of a real symmetric positive definite band matrix A dpbsv - compute the solution to a real system of linear equations A*X=B, where A is an N-by-N symmetric positive definite band matrix and X and B are N-by-NRHS matrices dpbsvx - use the Cholesky factorization to compute the solution to a real system of linear equations A*X=B, where A is an N-by-N symmetric positive definite band matrix and X and B are N-by- NRHS matrices dpbtf2 - compute the Cholesky factorization of a real symmetric posi- tive definite band matrix A dpbtrf - compute the Cholesky factorization of a real symmetric posi- tive definite band matrix A dpbtrs - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factoriza- tion A = U**T*U or A = L*L**T computed by DPBTRF dpftrf - compute the Cholesky factorization of a real symmetric posi- tive definite matrix A, the block version of the algorithm dpftri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization computed by DPFTRF dpftrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization computed by DPFTRF dpocon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF dpoequ - compute row and column scalings intended to equilibrate a sym- metric positive definite matrix A and reduce its condition number (with respect to the two-norm) dpoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm dporfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, provide error bounds and backward error estimates for the solution dporfsx - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, provide error bounds and backward error estimates for the solution dposv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices dposvx - use the Cholesky factorization to compute the solution to a real system of linear equations A*X = B, where A is an N-by- N symmetric positive definite matrix and X and B are N-by- NRHS matrices dposvxx - compute the solution to a double precision system of linear equations A*X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices dpotf2 - compute the Cholesky factorization of a real symmetric posi- tive definite matrix A dpotrf - compute the Cholesky factorization of a real symmetric posi- tive definite matrix A dpotri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF dpotrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPOTRF dppcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF dppequ - compute row and column scalings intended to equilibrate a sym- metric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) dpprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, provide error bounds and backward error estimates for the solution dppsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite matrix stored in packed format and X and B are N-by-NRHS matrices dppsvx - use the Cholesky factorization to compute the solution to a real system of linear equations A*X = B, where A is an N-by- N symmetric positive definite matrix stored in packed format and X and B are N-by-NRHS matrices dpptrf - compute the Cholesky factorization of a real symmetric posi- tive definite matrix A stored in packed format dpptri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF dpptrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF dpstf2 - compute the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A dpstrf - compute the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A dptcon - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF dpteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first fac- toring the matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor dptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, provide error bounds and backward error estimates for the solution dptsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiago- nal matrix, and X and B are N-by-NRHS matrices dptsvx - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N- by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices dpttrf - compute the L*D*L' factorization of a real symmetric positive definite tridiagonal matrix A dpttrs - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by DPTTRF dptts2 - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by DPTTRF dqdota - compute a double precision constant plus an extended precision constant plus the extended precision dot product of two dou- ble precision vectors x and y. dqdoti - compute a constant plus the extended precision dot product of two double precision vectors x and y. drot - Apply a Given's rotation constructed by SROTG. drotg - Construct a Given's plane rotation droti - Apply an indexed Givens rotation. drotm - Apply a Gentleman's modified Given's rotation constructed by SROTMG. drotmg - Construct a Gentleman's modified Given's plane rotation dsbev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A dsbevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A dsbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A dsbgst - reduce a real symmetric-definite banded generalized eigenprob- lem A*x = lambda*B*x to standard form C*y = lambda*y, dsbgv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x dsbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x dsbgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x dsbmv - perform the matrix-vector operationy := alpha*A*x + beta*y dsbtrd - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation dscal - Compute y := alpha * y dsctr - Scatters elements from x into y dsdot - compute the double precision dot product of two single preci- sion vectors x and y. dsecnd - return the user time for a process in seconds dsfrk - perform a symmetric rank-k operation for matrix in RFP format dsgesv - compute the solution to a real system of linear equations A*X = B dsinqb - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The SINQ operations are unnormalized inverses of themselves, so a call to SINQF followed by a call to SINQB will multiply the input sequence by 4 * N. dsinqf - compute the Fourier coefficients in a sine series representa- tion with only odd wave numbers.The SINQ operations are unnormalized inverses of themselves, so a call to SINQF fol- lowed by a call to SINQB will multiply the input sequence by 4 * N. dsinqi - initialize the array xWSAVE, which is used in both SINQF and SINQB. dsint - compute the discrete Fourier sine transform of an odd sequence. The SINT transforms are unnormalized inverses of themselves, so a call of SINT followed by another call of SINT will mul- tiply the input sequence by 2 * (N+1). dsinti - initialize the array WSAVE, which is used in subroutine SINT. dskymm - Skyline format matrix-matrix multiply dskysm - Skyline format triangular solve dspcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factor- ization A = U*D*U**T or A = L*D*L**T computed by DSPTRF dspev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage dspevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage dspevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage dspgst - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage dspgv - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x dspgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x dspgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x dspmv - perform the matrix-vector operationy := alpha*A*x + beta*y dspr - perform the symmetric rank 1 operation A := alpha*x*x' + A dspr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A dsprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, provides error bounds and backward error estimates for the solution dspsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices dspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices dsptrd - reduce a real symmetric matrix A stored in packed form to sym- metric tridiagonal form T by an orthogonal similarity trans- formation dsptrf - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method dsptri - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF dsptrs - solve a system of linear equations A*X = B with a real symmet- ric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF dstebz - compute the eigenvalues of a symmetric tridiagonal matrix T dstedc - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method dstegr - (a) Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation dstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration dstemr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T dsteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method dsterf - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm dstev - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A dstevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix dstevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T dstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A dstsv - compute the solution to a system of linear equations A * X = B where A is a symmetric tridiagonal matrix dsttrf - compute the factorization of a symmetric tridiagonal matrix A using the Bunch-Kaufman diagonal pivoting method dsttrs - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric tridiagonal matrix and X and B are N-by-NRHS matrices dswap - Exchange vectors x and y dsycon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF dsycon_rook - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF_ROOK dsyconv - convert A given by TRF into L and D and vice-versa dsyequb - compute row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number with respect to the two-norm dsyev - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A dsyevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A dsyevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T dsyevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A dsygs2 - reduce a real symmetric-definite generalized eigenproblem to standard form dsygst - reduce a real symmetric-definite generalized eigenproblem to standard form dsygv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x dsygvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x dsygvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x dsymm - perform one of the matrix-matrix operationsC := alpha*A*B + beta*C or C := alpha*B*A + beta*C dsymv - perform the matrix-vector operationy := alpha*A*x + beta*y dsyr - perform the symmetric rank 1 operation A := alpha*x*x' + A dsyr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A dsyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C dsyrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provide error bounds and backward error estimates for the solution dsyrfsx - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provide error bounds and backward error estimates for the solution dsyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C dsysv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric matrix and X and B are N- by-NRHS matrices dsysv_rook - compute the solution to system of linear equations A*X = B for symmetric matrices. DSYTRF_ROOK is called to compute the factorization of A dsysvx - use the diagonal pivoting factorization to compute the solu- tion to a real system of linear equations A*X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices dsysvxx - compute the solution to real system of linear equations A*X = B for symmetric matrices dsytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation dsytf2 - compute the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algo- rithm) dsytf2_rook - compute the factorization of a real symmetric indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal piv- oting method (unblocked algorithm) dsytrd - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation dsytrf - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method dsytrf_rook - compute the factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm) dsytri - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF dsytri2 - compute the inverse of a DOUBLE PRECISION symmetric indefi- nite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF dsytri2x - compute the inverse of a real symmetric indefinite matrix A using the factorization computed by DSYTRF dsytri_rook - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T com- puted by DSYTRF_ROOK dsytrs - solve a system of linear equations A*X = B with a real symmet- ric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF dsytrs2 - solve a system of linear equations A*X = B with a real sym- metric matrix A using the factorization computed by DSYTRF and converted by DSYCONV dsytrs_rook - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF_ROOK dtbcon - estimate the reciprocal of the condition number of a triangu- lar band matrix A, in either the 1-norm or the infinity-norm dtbmv - perform one of the matrix-vector operationsx := A*x, or x := A'*x dtbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix dtbsv - solve one of the systems of equations A*x = b, or A'*x = b dtbtrs - solve a triangular system of the form A*X = B or A**T*X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix dtfsm - solve a matrix equation (one operand is a triangular matrix in RFP format) dtftri - compute the inverse of a triangular matrix A stored in RFP format dtfttp - copy a triangular matrix from the rectangular full packed for- mat (TF) to the standard packed format (TP) dtfttr - copy a triangular matrix from the rectangular full packed for- mat (TF) to the standard full format (TR) dtgevc - compute the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) that was obtained from the generalized Schur factorization of an orig- inal pair of real nonsymmetric matrices (AO,BO) dtgexc - reorder the generalized Schur decomposition of a real matrix pair using an orthogonal or unitary equivalence transforma- tion dtgsen - reorder the generalized real Schur decomposition of a real matrix pair (A, B), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi- triangular matrix A and the upper triangular B dtgsja - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B dtgsna - estimate reciprocal condition numbers for specified eigenval- ues and/or eigenvectors of a matrix pair (A, B) in general- ized real Schur canonical form (or of any matrix pair (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z' denotes the transpose of Z dtgsyl - solve the generalized Sylvester equation dtpcon - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity- norm dtpmqrt - apply a real orthogonal matrix Q obtained from a "triangular- pentagonal" real block reflector H to a general real matrix C, which consists of two blocks dtpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x dtpqrt - compute a blocked QR factorization of a real "triangular-pen- tagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q dtpqrt2 - compute a QR factorization of a real or complex "triangular- pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q dtprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix dtpsv - solve one of the systems of equations A*x = b, or A'*x = b dtptri - compute the inverse of a real upper or lower triangular matrix A stored in packed format dtptrs - solve a triangular system of the form A*X = B or A**T*X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix dtpttf - copy a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF) dtpttr - copy a triangular matrix from the standard packed format (TP) to the standard full format (TR) dtrans - transpose and scale source matrix dtrcon - estimate the reciprocal of the condition number of a triangu- lar matrix A, in either the 1-norm or the infinity-norm dtrevc - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T dtrexc - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST dtrmm - perform one of the matrix-matrix operationsB := alpha*op( A )*B, or B := alpha*B*op( A ) dtrmv - perform one of the matrix-vector operations x := A*x, or x := A'*x dtrrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix dtrsen - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, dtrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B dtrsna - estimate reciprocal condition numbers for specified eigenval- ues and/or right eigenvectors of a real upper quasi-triangu- lar matrix T (or of any matrix Q*T*Q**T with Q orthogonal) dtrsv - solve one of the systems of equations A*x = b, or A'*x = b dtrsyl - solve the real Sylvester matrix equation dtrti2 - compute the inverse of a real upper or lower triangular matrix dtrtri - compute the inverse of a real upper or lower triangular matrix A dtrtrs - solve a triangular system of the form A*X = B or A**T*X = B, where A is a triangular matrix of order N, and B is an N-by- NRHS matrix dtrttf - copy a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF) dtrttp - copy a triangular matrix from the standard full format (TR) to the standard packed format (TP) dtzrqf - routine is deprecated and has been replaced by routine DTZRZF dtzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations dvbrmm - variable block sparse row format matrix-matrix multiply dvbrsm - variable block sparse row format triangular solve dwiener - perform Wiener deconvolution of two signals dzasum - Return the sum of the absolute values of a vector x. dznrm2 - Return the Euclidian norm of a vector. ezfftb - computes a periodic sequence from its Fourier coefficients. EZFFTB is a simplified but slower version of RFFTB. ezfftf - computes the Fourier coefficients of a periodic sequence. EZFFTF is a simplified but slower version of RFFTF. ezffti - initializes the array WSAVE, which is used in both EZFFTF and EZFFTB. fft - Fast Fourier transform subroutines gen_custom - extract necessary routines from an archive library to cre- ate a purpose-built library. getmsg - Open a catalog file and display the requested message gscon - estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SuperLU routine sgstrf. gsequ - computes row and column scalings intended to equilibrate an M- by-N sparse matrix A and reduce its condition number. gsrfs - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. It is a SuperLU routine. gssv - solves a system of linear equations A*X=B using the LU factor- ization from sgstrf. gssvx - solves the system of linear equations A*X=B or A'*X=B, using the LU factorization from sgstrf(). Error bounds on the solu- tion and a condition estimate are also provided. gstrf - computes an LU factorization of a general sparse m-by-n matrix A using partial pivoting with row interchanges. gstrs - solves a system of linear equations A*X=B or A'*X=B with A sparse and B dense, using the LU factorization computed by sgstrf. icamax - return the index of the element with largest absolute value. idamax - return the index of the element with largest absolute value. iladiag - translated from a character string specifying if a matrix has unit diagonal or not to the relevant BLAST-specified integer constant ilaenv - The name of the calling subroutine, in either upper case or lower case. ilaprec - translate from a character string specifying an intermediate precision to the relevant BLAST-specified integer constant ilatrans - translate from a character string specifying a transposition operation to the relevant BLAST-specified integer constant ilauplo - translate from a character string specifying a upper- or lower-triangular matrix to the relevant BLAST-specified inte- ger constant ilaver - return the Lapack version Arguments infinite_norm_error - A utility function of the SuperLU solver that computes the infinity-norm of an array of vectors that are approximations to the exact solution vector. intro - Introduction to Oracle Solaris Studio Performance Library func- tions and subroutines isamax - return the index of the element with largest absolute value. izamax - return the index of the element with largest absolute value. langs - returns the value of the one-norm, or the Frobenius-norm, or the infinity-norm, or the element with largest absolute value of a general real matrix A in sparse format. laqgs - a SuperLU function that equilibrates a general sparse M by N matrix A. libsunperf - Introduction to Oracle Solaris Studio Performance Library functions and subroutines lsame - returns .TRUE. if CA is the same letter as CB regardless of case rfft2b - compute a periodic sequence from its Fourier coefficients. The RFFT operations are unnormalized, so a call of RFFT2F followed by a call of RFFT2B will multiply the input sequence by M*N. rfft2f - compute the Fourier coefficients of a periodic sequence. The RFFT operations are unnormalized, so a call of RFFT2F fol- lowed by a call of RFFT2B will multiply the input sequence by M*N. rfft2i - initialize the array WSAVE, which is used in both the forward and backward transforms. rfft3b - compute a periodic sequence from its Fourier coefficients. The RFFT operations are unnormalized, so a call of RFFT3F fol- lowed by a call of RFFT3B will multiply the input sequence by M*N*K. rfft3f - compute the Fourier coefficients of a real periodic sequence. The RFFT operations are unnormalized, so a call of RFFT3F followed by a call of RFFT3B will multiply the input sequence by M*N*K. rfft3i - initialize the array WSAVE, which is used in both RFFT3F and RFFT3B. rfftb - compute a periodic sequence from its Fourier coefficients. The RFFT operations are unnormalized, so a call of RFFTF followed by a call of RFFTB will multiply the input sequence by N. rfftf - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of RFFTF followed by a call of RFFTB will multiply the input sequence by N. rffti - initialize the array WSAVE, which is used in both RFFTF and RFFTB. rfftopt - compute the length of the closest fast FFT sCopy_CompCol_Matrix - A utility C function in the serial SuperLU solver that copies one SuperMatrix into another. sCreate_CompCol_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse column format (also known as the Harwell-Boeing format). sCreate_CompRow_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse row format. sCreate_Dense_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in dense format. sCreate_SuperNode_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in supernodal format. sPrintPerf - A utility function of the SuperLU solver that prints sta- tistics collected by the computational routines. sQuerySpace - A inquiry function that provides information on the mem- ory statistics of the SuperLU solver. sasum - Return the sum of the absolute values of a vector x. saxpy - compute y := alpha * x + y saxpyi - Compute y := alpha * x + y sbbcsd - compute the CS decomposition of an orthogonal matrix in bidi- agonal-block form sbcomm - block coordinate matrix-matrix multiply sbdimm - block diagonal format matrix-matrix multiply sbdism - block diagonal format triangular solve sbdsdc - compute the singular value decomposition (SVD) of a real N-by- N (upper or lower) bidiagonal matrix B sbdsqr - compute the singular value decomposition (SVD) of a real N-by- N (upper or lower) bidiagonal matrix B sbelmm - block Ellpack format matrix-matrix multiply sbelsm - block Ellpack format triangular solve sbscmm - block sparse column matrix-matrix multiply sbscsm - block sparse column format triangular solve sbsrmm - block sparse row format matrix-matrix multiply sbsrsm - block sparse row format triangular solve scasum - Return the sum of the absolute values of a vector x. scnrm2 - Return the Euclidian norm of a vector. scnvcor - compute the convolution or correlation of real vectors scnvcor2 - compute the convolution or correlation of real matrices scoomm - coordinate matrix-matrix multiply scopy - copy x to y scscmm - compressed sparse column format matrix-matrix multiply scscsm - compressed sparse column format triangular solve scsrmm - compressed sparse row format matrix-matrix multiply scsrsm - compressed sparse row format triangular solve sdiamm - diagonal format matrix-matrix multiply sdiasm - diagonal format triangular solve sdisna - compute the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general m-by-n matrix sdot - compute the dot product of two vectors x and y. sdoti - Compute the indexed dot product. sdsdot - compute a constant plus the double precision dot product of two single precision vectors x and y second - return the user time for a process in seconds sellmm - Ellpack format matrix-matrix multiply sellsm - Ellpack format triangular solve set_default_options - C function that sets to default parameters the options that control the behavior of the serial SuperLU solver. sfftc - initialize the trigonometric weight and factor tables or com- pute the forward Fast Fourier Transform of a real sequence. sfftc2 - initialize the trigonometric weight and factor tables or com- pute the two-dimensional forward Fast Fourier Transform of a two-dimensional real array. sfftc3 - initialize the trigonometric weight and factor tables or com- pute the three-dimensional forward Fast Fourier Transform of a three-dimensional complex array. sfftcm - initialize the trigonometric weight and factor tables or com- pute the one-dimensional forward Fast Fourier Transform of a set of real data sequences stored in a two-dimensional array. sgbbrd - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation sgbcon - estimate the reciprocal of the condition number of a real gen- eral band matrix A, in either the 1-norm or the infinity- norm, using the LU factorization computed by SGBTRF sgbequ - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number sgbequb - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number sgbmv - perform one of the matrix-vector operationsy := alpha*A*x + beta*y or y := alpha*A'*x + beta*y sgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provide error bounds and backward error estimates for the solution sgbrfsx - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution sgbsv - compute the solution to a real system of linear equations A*X=B, where A is a band matrix of order N with KL subdiago- nals and KU superdiagonals, and X and B are N-by-NRHS matri- ces sgbsvx - use the LU factorization to compute the solution to a real system of linear equations A*X=B, A**T*X=B, or A**H*X=B, where A is a band matrix sgbsvxx - compute the solution to system of linear equations A * X = B for genaral band matrices sgbtf2 - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges sgbtrf - compute an LU factorization of a real m-by-n band matrix A using partial pivoting with row interchanges sgbtrs - solve a system of linear equations A*X=B or A'*X=B with a gen- eral band matrix A using the LU factorization computed by SGBTRF sgebak - form the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by SGEBAL sgebal - balance a general real matrix A sgebd2 - reduce a general matrix to bidiagonal form using an unblocked algorithm sgebrd - reduce a general real M-by-N matrix A to upper or lower bidi- agonal form B by an orthogonal transformation sgecon - estimate the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF sgeequ - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number sgeequb - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number sgees - compute for an N-by-N real nonsymmetric matrix A, the eigenval- ues, the real Schur form T, and, optionally, the matrix of Schur vectors Z sgeesx - compute for an N-by-N real nonsymmetric matrix A, the eigen- values, the real Schur form T, and, optionally, the matrix of Schur vectors Z sgeev - compute for an N-by-N real nonsymmetric matrix A, the eigenval- ues and, optionally, the left and/or right eigenvectors sgeevx - compute for an N-by-N real nonsymmetric matrix A, the eigen- values and, optionally, the left and/or right eigenvectors sgegs - routine is deprecated and has been replaced by routine SGGES sgegv - routine is deprecated and has been replaced by routine SGGEV sgehd2 - reduce a general square matrix to upper Hessenberg form using an unblocked algorithm sgehrd - reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation sgejsv - compute the singular value decomposition (SVD) of a real M-by- N matrix A, where M >= N sgelq2 - compute the LQ factorization of a general rectangular matrix using an unblocked algorithm sgelqf - compute an LQ factorization of a real M-by-N matrix A sgels - solve overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A sgelsd - compute the minimum-norm solution to a real linear least squares problem sgelss - compute the minimum norm solution to a real linear least squares problem sgelsx - routine is deprecated and has been replaced by routine SGELSY sgelsy - compute the minimum-norm solution to a real linear least squares problem sgemm - perform one of the matrix-matrix operationsC := alpha*op( A )*op( B ) + beta*C sgemqrt - overwrites the general real M-by-N matrix C with Q C, C Q, Q**T C, or C Q**T depe nding on values of SIDE and TRANS sgemv - perform one of the matrix-vector operationsy := alpha*A*x + beta*y or y := alpha*A'*x + beta*y sgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm sgeqlf - compute a QL factorization of a real M-by-N matrix A sgeqp3 - compute a QR factorization with column pivoting of a matrix A sgeqpf - routine is deprecated and has been replaced by routine SGEQP3 sgeqr2 - computes the QR factorization of a general rectangular matrix using an unblocked algorithm. sgeqr2p - computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algo- rithm. sgeqrf - compute a QR factorization of a real M-by-N matrix A sgeqrfp - compute a QR factorization of a real M-by-N matrix A: A = Q * R sgeqrt - compute a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q sgeqrt2 - compute a QR factorization of a general real matrix using the compact WY representation of Q sgeqrt3 - recursively compute a QR factorization of a general real matrix using the compact WY representation of Q sger - perform the rank 1 operation A := alpha*x*y' + A sgerfs - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution sgerfsx - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution sgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm sgerqf - compute an RQ factorization of a real M-by-N matrix A sgesdd - compute the singular value decomposition (SVD) of a real M-by- N matrix A, optionally computing the left and right singular vectors sgesv - compute the solution to a real system of linear equations A*X=B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices sgesvd - compute the singular value decomposition (SVD) of a real M-by- N matrix A, optionally computing the left and/or right singu- lar vectors sgesvj - compute the singular value decomposition (SVD) of a real M-by- N matrix A, where M >= N sgesvx - use the LU factorization to compute the solution to a real system of linear equations A*X=B, where A is an N-by-N gen- eral matrix sgesvxx - compute the solution to system of linear equations A*X=B for general matrices sgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges sgetrf - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges sgetri - compute the inverse of a matrix using the LU factorization computed by SGETRF sgetrs - solve a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by SGETRF sggbak - form the right or left eigenvectors of a real generalized ei- genvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by SGGBAL sggbal - balance a pair of general real matrices (A,B) sgges - compute for a pair of N-by-N real nonsymmetric matrices (A,B), sggesx - compute for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the real Schur form (S,T), and, and, optionally, the left and/or right matrices of Schur vec- tors sggev - compute for a pair of N-by-N real nonsymmetric matrices (A,B) sggevx - compute for a pair of N-by-N real nonsymmetric matrices (A,B) the generalized eigenvalues, and, optionally, the left and/or right generalized eigenvectors sggglm - solve a general Gauss-Markov linear model (GLM) problem sgghrd - reduce a pair of real matrices (A,B) to generalized upper Hes- senberg form using orthogonal transformations, where A is a general matrix and B is upper triangular sgglse - solve the linear equality-constrained least squares (LSE) problem sggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B. sggrqf - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B sggsvd - compute the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B sggsvp - compute orthogonal matrices sgscon - estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SuperLU routine sgstrf. sgsequ - computes row and column scalings intended to equilibrate an M- by-N sparse matrix A and reduce its condition number. sgsrfs - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. It is a SuperLU routine. sgssco - General sparse solver condition number estimate. sgssda - Deallocate working storage for the general sparse solver. sgssfa - General sparse solver numeric factorization. sgssfs - General sparse solver one call interface. sgssin - Initialize the general sparse solver. sgssor - General sparse solver ordering and symbolic factorization. sgssps - Print general sparse solver statics. sgssrp - Return permutation used by the general sparse solver. sgsssl - Solve routine for the general sparse solver. sgssuo - Provide general sparse solvers SPSOLVE and SuperLU a user- supplied permutation for ordering. sgssv - solves a system of linear equations A*X=B using the LU factor- ization from sgstrf. sgssvx - solves the system of linear equations A*X=B or A'*X=B, using the LU factorization from sgstrf(). Error bounds on the solu- tion and a condition estimate are also provided. sgstrf - computes an LU factorization of a general sparse m-by-n matrix A using partial pivoting with row interchanges. sgstrs - solves a system of linear equations A*X=B or A'*X=B with A sparse and B dense, using the LU factorization computed by sgstrf. sgsvj0 - pre-processor for the routine sgesvj sgsvj1 - pre-processor for the routine sgesvj, apply Jacobi rotations targeting only particular pivots sgtcon - estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF sgthr - Gathers specified elements from y into x. sgthrz - Gather and zero. sgtrfs - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, provide error bounds and backward error estimates for the solution sgtsv - solve the equation A*X=B, where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting sgtsvx - use the LU factorization to compute the solution to a real system of linear equations A*X = B or A**T*X = B, where A is a tridiagonal matrix of order N and X and B are N-by-NRHS matrices sgttrf - compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges sgttrs - solve one of the systems of equations A*X=B or A'*X=B, with a tridiagonal matrix A using the LU factorization computed by SGTTRF sgtts2 - solve a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf shgeqz - implement a single-/double-shift version of the QZ method for finding the generalized eigenvalues w(j)=(ALPHAR(j) + i*ALPHAI(j))/BETAR(j) of the equation det( A-w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form shsein - use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H shseqr - compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decompo- sition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors sinfinite_norm_error - A utility function of the SuperLU solver that computes the infinity-norm of an array of vectors that are approximations to the exact solution vector. sinqb - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The SINQ operations are unnormalized inverses of themselves, so a call to SINQF followed by a call to SINQB will multiply the input sequence by 4 * N. sinqf - compute the Fourier coefficients in a sine series representa- tion with only odd wave numbers.The SINQ operations are unnormalized inverses of themselves, so a call to SINQF fol- lowed by a call to SINQB will multiply the input sequence by 4 * N. sinqi - initialize the array xWSAVE, which is used in both SINQF and SINQB. sint - compute the discrete Fourier sine transform of an odd sequence. The SINT transforms are unnormalized inverses of themselves, so a call of SINT followed by another call of SINT will mul- tiply the input sequence by 2 * (N+1). sinti - initialize the array WSAVE, which is used in subroutine SINT. sjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack) sjadrp - right permutation of a jagged diagonal matrix sjadsm - Jagged-diagonal format triangular solve sla_gbamv - perform a matrix-vector operation to calculate error bounds sla_gbrcond - estimate the Skeel condition number for a general banded matrix sla_gbrfsx_extended - improve the computed solution to a system of lin- ear equations for general banded matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution sla_gbrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix sla_geamv - compute a matrix-vector product using a general matrix to calculate error bounds sla_gercond - estimate the Skeel condition number for a general matrix sla_gerfsx_extended - improve the computed solution to a system of lin- ear equations for general matrices by performing extra-pre- cise iterative refinement and provide error bounds and back- ward error estimates for the solution sla_gerpvgrw - compute the reciprocal pivot growth factor using the "max absolute element" norm sla_lin_berr - compute a component-wise relative backward error sla_porcond - estimate the Skeel condition number for a symmetric posi- tive-definite matrix sla_porfsx_extended - improve the computed solution to a system of lin- ear equations for symmetric or Hermitian positive-definite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution sla_porpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-defi- nite matrix sla_syamv - compute a matrix-vector product using a symmetric indefi- nite matrix to calculate error bounds sla_syrcond - estimate the Skeel condition number for a symmetric indefinite matrix sla_syrfsx_extended - improve the computed solution to a system of lin- ear equations for symmetric indefinite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution sla_syrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix sla_wwaddw - add a vector into a doubled-single vector slaed0 - compute all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Used by sstedc slaed1 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used by sstedc, when the original matrix is tridiagonal slaed2 - merge eigenvalues and deflates secular equation; used by sst- edc when the original matrix is tridiagonal slaed3 - find the roots of the secular equation and updates the eigen- vectors; used by sstedc when the original matrix is tridiago- nal slaed4 - is used by sstedc. Finds a single root of the secular equation slaed5 - is used by sstedc. Solves the 2-by-2 secular equation slaed6 - is used by sstedc. Compute one Newton step in solution of the secular equation slaed7 - compute the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used by sstedc, when the original matrix is dense slaed8 - merge eigenvalues and deflates secular equation. Used by sst- edc, when the original matrix is dense slaed9 - is used by sstedc. Find the roots of the secular equation and updates the eigenvectors. Used when the original matrix is dense slaeda - is used by sstedc. Compute the Z vector determining the rank- one modification of the diagonal matrix. Used when the origi- nal matrix is dense slagtf - factorize the matrix (T-lambda*I), where T is an n by n tridi- agonal matrix and lambda is a scalar, as T-lambda*I = PLU slals0 - apply back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd slalsa - compute the SVD of the coefficient matrix in compact form. Used by sgelsd slalsd - use the singular value decomposition of A to solve the least squares problem slamch - Determines single precision machine parameters. slamrg - will create a permutation list which will merge the elements of A (which is composed of two independently sorted sets) into a single set which is sorted in ascending order slangs - returns the value of the one-norm, or the Frobenius-norm, or the infinity-norm, or the element with largest absolute value of a general real matrix A in sparse format. slansf - return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A in RFP format slaqgs - a SuperLU function that equilibrates a general sparse M by N matrix A. slarscl2 - perform reciprocal diagonal scaling on a vector slartgs - generate a plane rotation designed to introduce a bulge in implicit QR iteration for the bidiagonal SVD problem slarz - apply a real elementary reflector H to a real M-by-N matrix C, from either the left or the right slarzb - apply a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right slarzt - form the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors slascl2 - perform diagonal scaling on a vector slasq1 - compute the singular values of a real square bidiagonal matrix. Used by sbdsqr slasq2 - compute all the eigenvalues of a real symmetric positive defi- nite tridiagonal matrix (high relative accuracy) slasq3 - check for deflation, compute a shift and calls dqds. Used by sbdsqr slasq4 - compute an approximation to the smallest eigenvalue using val- ues of d from the previous transform. Used by sbdsqr slasq5 - compute one dqds transform in ping-pong form. Used by sbdsqr and sstegr slasq6 - compute one dqd transform in ping-pong form. Used by sbdsqr and sstegr slasrt - the numbers in D in increasing order (if ID = 'I') or in decreasing order (if ID = 'D' ) slasyf - compute a partial factorization of a real symmetric matrix, using the Bunch-Kaufman diagonal pivoting method slasyf_rook - compute a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal piv- oting method slatrz - factor an upper trapezoidal matrix by means of orthogonal transformations slatzm - routine is deprecated and has been replaced by routine SORMRZ snrm2 - Return the Euclidian norm of a vector. sopgtr - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by SSPTRD using packed storage sopmtr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' sorbdb - simultaneously bidiagonalize the blocks of an M-by-M parti- tioned orthogonal matrix sorbdb1 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns sorbdb2 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns sorbdb3 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns sorbdb4 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns sorbdb5 - orthogonalize one column vector with respect to the orthonor- mal columns of another column vector sorbdb6 - orthogonalize one column vector with respect to the orthonor- mal columns of another column vector sorcsd - compute the CS decomposition of an M-by-M partitioned orthogo- nal matrix sorcsd2by1 - compute the CS decomposition of an M-by-Q matrix with orthonormal columns that has been partitioned into a 2-by-1 block structure sorg2l - generate an m by n real matrix Q with orthonormal columns, sorg2r - generate an m by n real matrix Q with orthonormal columns, sorgbr - generate one of the real orthogonal matrices Q or P**T deter- mined by SGEBRD when reducing a real matrix A to bidiagonal form sorghr - generate a real orthogonal matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by SGEHRD sorgl2 - generate an m by n real matrix Q with orthonormal rows, sorglq - generate an M-by-N real matrix Q with orthonormal rows, sorgql - generate an M-by-N real matrix Q with orthonormal columns, sorgqr - generate an M-by-N real matrix Q with orthonormal columns, sorgr2 - generate an m by n real matrix Q with orthonormal rows, sorgrq - generate an M-by-N real matrix Q with orthonormal rows, sorgtr - generate a real orthogonal matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by SSYTRD sorm2l - multiply a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm) sorm2r - multiply a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm) sormbr - overwrites the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or C*P**T. sormhr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. sorml2 - multiply a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm) sormlq - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. sormql - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. sormqr - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' sormr2 - multipliy a general matrix by the orthogonal matrix from a RQ factorization determined by sgerqf (unblocked algorithm) sormr3 - multiply a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm) sormrq - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. sormrz - overwrite the general real M-by-N matrix C with Q*C or Q**H*C or C*Q**H or C*Q. sormtr - overwrite the general real M-by-N matrix C with Q*C or Q**T*C or C*Q**T or C*Q. sp_cgemm - a SuperLU routine that performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C where op(X) is one of op(X) = X or op(X) = X' or op(X) = conjg(X'), alpha and beta are scalars, A is a sparse matrix of type SuperMatrix, and B and C are dense matrices, with op( A ) an m by k matrix,op( B ) a k by n matrix and C an m by n matrix. sp_dgemm - a SuperLU routine that performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C where op(X) is one of op(X) = X or op(X) = X' or op(X) = conjg(X'), alpha and beta are scalars, A is a sparse matrix of type SuperMatrix, and B and C are dense matrices, with op( A ) an m by k matrix,op( B ) a k by n matrix and C an m by n matrix. sp_gemm - a SuperLU routine that performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C where op(X) is one of op(X) = X or op(X) = X' or op(X) = conjg(X'), alpha and beta are scalars, A is a sparse matrix of type SuperMatrix, and B and C are dense matrices, with op( A ) an m by k matrix,op( B ) a k by n matrix and C an m by n matrix. sp_ienv - called by SuperLU routines to choose machine dependent param- eters for the local environment. See ISPEC for a description of the parameters. sp_preorder - permutes the columns of the original sparse matrix. sp_sgemm - a SuperLU routine that performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C where op(X) is one of op(X) = X or op(X) = X' or op(X) = conjg(X'), alpha and beta are scalars, A is a sparse matrix of type SuperMatrix, and B and C are dense matrices, with op( A ) an m by k matrix,op( B ) a k by n matrix and C an m by n matrix. sp_zgemm - a SuperLU routine that performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C where op(X) is one of op(X) = X or op(X) = X' or op(X) = conjg(X'), alpha and beta are scalars, A is a sparse matrix of type SuperMatrix, and B and C are dense matrices, with op( A ) an m by k matrix,op( B ) a k by n matrix and C an m by n matrix. spbcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF spbequ - compute row and column scalings intended to equilibrate a sym- metric positive definite band matrix A and reduce its condi- tion number (with respect to the two-norm) spbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and banded, provide error bounds and backward error estimates for the solution spbstf - compute a split Cholesky factorization of a real symmetric positive definite band matrix A spbsv - compute the solution to a real system of linear equations A*X=B, where A is an N-by-N symmetric positive definite band matrix and X and B are N-by-NRHS matrices spbsvx - use the Cholesky factorization to compute the solution to a real system of linear equations A*X=B, where A is an N-by-N symmetric positive definite band matrix and X and B are N-by- NRHS matrices spbtf2 - compute the Cholesky factorization of a real symmetric posi- tive definite band matrix A spbtrf - compute the Cholesky factorization of a real symmetric posi- tive definite band matrix A spbtrs - solve a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factoriza- tion A = U**T*U or A = L*L**T computed by SPBTRF spftrf - compute the Cholesky factorization of a real symmetric posi- tive definite matrix A, the block version of the algorithm spftri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization computed by SPFTRF spftrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization computed by SPFTRF spocon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF spoequ - compute row and column scalings intended to equilibrate a sym- metric positive definite matrix A and reduce its condition number (with respect to the two-norm) spoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm sporfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, provide error bounds and backward error estimates for the solution sporfsx - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, provide error bounds and backward error estimates for the solution sposv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices sposvx - use the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equationsA*X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices sposvxx - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices spotf2 - compute the Cholesky factorization of a real symmetric posi- tive definite matrix A spotrf - compute the Cholesky factorization of a real symmetric posi- tive definite matrix A spotri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF spotrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPOTRF sppcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF sppequ - compute row and column scalings intended to equilibrate a sym- metric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) spprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, provide error bounds and backward error estimates for the solution sppsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite matrix stored in packed format and X and B are N-by-NRHS matrices sppsvx - use the Cholesky factorization to compute the solution to a real system of linear equations A * X = B, where A is an N- by-N symmetric positive definite matrix stored in packed for- mat and X and B are N-by-NRHS matrices spptrf - compute the Cholesky factorization of a real symmetric posi- tive definite matrix A stored in packed format spptri - compute the inverse of a real symmetric positive definite matrix A using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF spptrs - solve a system of linear equations A*X = B with a symmetric positive definite matrix A in packed storage using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF spstf2 - compute the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A spstrf - compute the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A sptcon - compute the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF spteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first fac- toring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor sptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, provide error bounds and backward error estimates for the solution sptsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiago- nal matrix, and X and B are N-by-NRHS matrices sptsvx - use the factorization A = L*D*L**T to compute the solution to a real system of linear equations A*X = B, where A is an N- by-N symmetric positive definite tridiagonal matrix and X and B are N-by-NRHS matrices spttrf - compute the L*D*L' factorization of a real symmetric positive definite tridiagonal matrix A spttrs - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF sptts2 - solve a tridiagonal system of the form A * X = B using the L*D*L' factorization of A computed by SPTTRF srot - Apply a Given's rotation constructed by SROTG srotg - Construct a Given's plane rotation sroti - Apply an indexed Givens rotation. srotm - Apply a Gentleman's modified Given's rotation constructed by SROTMG. srotmg - Construct a Gentleman's modified Given's plane rotation ssbev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A ssbevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A ssbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A ssbgst - reduce a real symmetric-definite banded generalized eigenprob- lem A*x = lambda*B*x to standard form C*y = lambda*y, ssbgv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x ssbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x ssbgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x ssbmv - perform the matrix-vector operationy := alpha*A*x + beta*y ssbtrd - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation sscal - Compute y := alpha * y ssctr - Scatters elements from x into y ssfrk - perform a symmetric rank-k operation for matrix in RFP format sskymm - Skyline format matrix-matrix multiply sskysm - Skyline format triangular solve sspcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factor- ization A = U*D*U**T or A = L*D*L**T computed by SSPTRF sspev - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage sspevd - compute all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage sspevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage sspgst - reduce a real symmetric-definite generalized eigenproblem to standard form, using packed storage sspgv - compute all the eigenvalues and, optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x sspgvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x sspgvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x sspmv - perform the matrix-vector operationy := alpha*A*x + beta*y sspr - perform the symmetric rank 1 operation A := alpha*x*x' + A sspr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A ssprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, provide error bounds and backward error estimates for the solution sspsv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices sspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices ssptrd - reduce a real symmetric matrix A stored in packed form to sym- metric tridiagonal form T by an orthogonal similarity trans- formation ssptrf - compute the factorization of a real symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal pivoting method ssptri - compute the inverse of a real symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF ssptrs - solve a system of linear equations A*X = B with a real symmet- ric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF sstebz - compute the eigenvalues of a symmetric tridiagonal matrix T sstedc - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method sstegr - (a) Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation sstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration sstemr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T ssteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method ssterf - compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm sstev - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A sstevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix sstevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T sstevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix A sstsv - compute the solution to a system of linear equations A * X = B where A is a symmetric tridiagonal matrix ssttrf - compute the factorization of a symmetric tridiagonal matrix A using the Bunch-Kaufman diagonal pivoting method ssttrs - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric tridiagonal matrix and X and B are N-by-NRHS matrices sswap - Exchange vectors x and y ssycon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF ssycon_rook - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF_ROOK ssyconv - convert A given by TRF into L and D and vice-versa ssyequb - compute row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number with respect to the two-norm ssyev - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A ssyevd - compute all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A ssyevr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T ssyevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A ssygs2 - reduce a real symmetric-definite generalized eigenproblem to standard form ssygst - reduce a real symmetric-definite generalized eigenproblem to standard form ssygv - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x ssygvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x ssygvx - compute selected eigenvalues, and optionally, eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x ssymm - perform one of the matrix-matrix operationsC := alpha*A*B + beta*C or C := alpha*B*A + beta*C ssymv - perform the matrix-vector operationy := alpha*A*x + beta*y ssyr - perform the symmetric rank 1 operation A := alpha*x*x' + A ssyr2 - perform the symmetric rank 2 operation A := alpha*x*y' + alpha*y*x' + A ssyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C ssyrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provide error bounds and backward error estimates for the solution ssyrfsx - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provide error bounds and backward error estimates for the solution ssyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C ssysv - compute the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric matrix and X and B are N- by-NRHS matrices ssysv_rook - compute the solution to system of linear equations A*X = B for symmetric matrices. SSYTRF_ROOK is called to compute the factorization of A ssysvx - use the diagonal pivoting factorization to compute the solu- tion to a real system of linear equations A*X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices ssysvxx - compute the solution to real system of linear equations A*X = B for symmetric matrices ssytd2 - reduce a real symmetric matrix A to symmetric tridiagonal form T by an orthogonal similarity transformation ssytf2 - computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algo- rithm). ssytf2_rook - compute the factorization of a real symmetric indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal piv- oting method (unblocked algorithm) ssytrd - reduce a real symmetric matrix A to real symmetric tridiagonal form T by an orthogonal similarity transformation ssytrf - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method ssytrf_rook - compute the factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm) ssytri - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF ssytri2 - compute the inverse of a REAL symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF ssytri2x - compute the inverse of a real symmetric indefinite matrix A using the factorization computed by SSYTRF ssytri_rook - compute the inverse of a real symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T com- puted by SSYTRF_ROOK ssytrs - solve a system of linear equations A*X = B with a real symmet- ric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF ssytrs2 - solve a system of linear equations A*X = B with a real sym- metric matrix A using the factorization computed by SSYTRF and converted by SSYCONV ssytrs_rook - solve a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF_ROOK stbcon - estimate the reciprocal of the condition number of a triangu- lar band matrix A, in either the 1-norm or the infinity-norm stbmv - perform one of the matrix-vector operationsx := A*x, or x := A'*x stbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix stbsv - solve one of the systems of equations A*x = b, or A'*x = b stbtrs - solve a triangular system of the form A*X = B or A**T*X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix stfsm - solve a matrix equation (one operand is a triangular matrix in RFP format) stftri - compute the inverse of a triangular matrix A stored in RFP format stfttp - copy a triangular matrix from the rectangular full packed for- mat (TF) to the standard packed format (TP) stfttr - copy a triangular matrix from the rectangular full packed for- mat (TF) to the standard full format (TR) stgevc - compute the right and/or left generalized eigenvectors of a pair of real upper triangular matrices (A,B) that was obtained from the generalized Schur factorization of an orig- inal pair of real nonsymmetric matrices (AO,BO) stgexc - reorder the generalized Schur decomposition of a real matrix pair using an orthogonal or unitary equivalence transforma- tion stgsen - reorder the generalized real Schur decomposition of a real matrix pair (A, B), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi- triangular matrix A and the upper triangular B stgsja - compute the generalized singular value decomposition (GSVD) of two real upper triangular (or trapezoidal) matrices A and B stgsna - estimate reciprocal condition numbers for specified eigenval- ues and/or eigenvectors of a matrix pair (A, B) in general- ized real Schur canonical form (or of any matrix pair (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where Z' denotes the transpose of Z stgsyl - solve the generalized Sylvester equation stpcon - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity- norm stpmqrt - apply a real orthogonal matrix Q obtained from a "triangular- pentagonal" real block reflector H to a general real matrix C, which consists of two blocks stpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x stpqrt - compute a blocked QR factorization of a real "triangular-pen- tagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q stpqrt2 - compute a QR factorization of a real or complex "triangular- pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q stprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix stpsv - solve one of the systems of equations A*x = b, or A'*x = b stptri - compute the inverse of a real upper or lower triangular matrix A stored in packed format stptrs - solve a triangular system of the form A*X = B or A**T*X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix stpttf - copy a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF) stpttr - copy a triangular matrix from the standard packed format (TP) to the standard full format (TR) strans - transpose and scale source matrix strcon - estimate the reciprocal of the condition number of a triangu- lar matrix A, in either the 1-norm or the infinity-norm strevc - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T strexc - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST strmm - perform one of the matrix-matrix operationsB := alpha*op( A )*B, or B := alpha*B*op( A ) strmv - perform one of the matrix-vector operations x := A*x, or x := A'*x strrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix strsen - reorder the real Schur factorization of a real matrix A = Q*T*Q**T, so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix T, strsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B strsna - estimate reciprocal condition numbers for specified eigenval- ues and/or right eigenvectors of a real upper quasi-triangu- lar matrix T (or of any matrix Q*T*Q**T with Q orthogonal) strsv - solve one of the systems of equations A*x = b, or A'*x = b strsyl - solve the real Sylvester matrix equation strti2 - compute the inverse of a real upper or lower triangular matrix strtri - compute the inverse of a real upper or lower triangular matrix A strtrs - solve a triangular system of the form A*X = B or A**T*X = B, where A is a triangular matrix of order N, and B is an N-by- NRHS matrix strttf - copy a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF) strttp - copy a triangular matrix from the standard full format (TR) to the standard packed format (TP) stzrqf - routine is deprecated and has been replaced by routine STZRZF stzrzf - reduce the M-by-N ( M<=N ) real upper trapezoidal matrix A to upper triangular form by means of orthogonal transformations sunperf - Introduction to Oracle Solaris Studio Performance Library functions and subroutines sunperf_version - gets library information svbrmm - variable block sparse row format matrix-matrix multiply svbrsm - variable block sparse row format triangular solve swiener - perform Wiener deconvolution of two signals use_threads - Sets the number of threads to use for subsequent parallel regions using_threads - In a parallel environment, if called from a serial region of the master thread it returns the number of threads available for execution (determined by function OMP_GET_NUM_THREADS). Else, if it is called from a thread in the team executing the parallel region it returns a 1. USING_THREADS subroutine vcfftb - compute a periodic sequence from its Fourier coefficients. The VCFFT operations are normalized, so a call of VCFFTF fol- lowed by a call of VCFFTB will return the original sequence. vcfftf - compute the Fourier coefficients of a periodic sequence. The VCFFT operations are normalized, so a call of VCFFTF followed by a call of VCFFTB will return the original sequence. vcffti - initialize the array WSAVE, which is used in both VCFFTF and VCFFTB. vcosqb - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The VCOSQ opera- tions are normalized, so a call of VCOSQF followed by a call of VCOSQB will return the original sequence. vcosqf - compute the Fourier coefficients in a cosine series represen- tation with only odd wave numbers. The VCOSQ operations are normalized, so a call of VCOSQF followed by a call of VCOSQB will return the original sequence. vcosqi - initialize the array WSAVE, which is used in both VCOSQF and VCOSQB. vcost - compute the discrete Fourier cosine transform of an even sequence. The VCOST transform is normalized, so a call of VCOST followed by a call of VCOST will return the original sequence. vcosti - initialize the array WSAVE, which is used in VCOST. vdcosqb - synthesize a Fourier sequence from its representation in terms of a cosine series with odd wave numbers. The VCOSQ operations are normalized, so a call of VCOSQF followed by a call of VCOSQB will return the original sequence. vdcosqf - compute the Fourier coefficients in a cosine series represen- tation with only odd wave numbers. The VCOSQ operations are normalized, so a call of VCOSQF followed by a call of VCOSQB will return the original sequence. vdcosqi - initialize the array WSAVE, which is used in both VCOSQF and VCOSQB. vdcost - compute the discrete Fourier cosine transform of an even sequence. The VCOST transform is normalized, so a call of VCOST followed by a call of VCOST will return the original sequence. vdcosti - initialize the array WSAVE, which is used in VCOST. vdfftb - compute a periodic sequence from its Fourier coefficients. The VDFFT operations are normalized, so a call of VDFFTF fol- lowed by a call of VDFFTB will return the original sequence. vdfftf - compute the Fourier coefficients of a periodic sequence. The VDFFT operations are normalized, so a call of VDFFTF followed by a call of VDFFTB will return the original sequence. vdffti - initialize the array WSAVE, which is used in both VRFFTF and VRFFTB. vdsinqb - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The VSINQ operations are normalized, so a call of VSINQF followed by a call of VSINQB will return the original sequence. vdsinqf - compute the Fourier coefficients in a sine series representa- tion with only odd wave numbers.The VSINQ operations are nor- malized, so a call of VSINQF followed by a call of VSINQB will return the original sequence. vdsinqi - initialize the array WSAVE, which is used in both VSINQF and VSINQB. vdsint - compute the discrete Fourier sine transform of an odd sequence. The VSINT transforms are unnormalized inverses of themselves, so a call of VSINT followed by another call of VSINT will multiply the input sequence by 2 * (N+1). The VSINT transforms are normalized, so a call of VSINT followed by a call of VSINT will return the original sequence. vdsinti - initialize the array WSAVE, which is used in subroutine VSINT. vrfftb - compute a periodic sequence from its Fourier coefficients. The VRFFT operations are normalized, so a call of VRFFTF fol- lowed by a call of VRFFTB will return the original sequence. vrfftf - compute the Fourier coefficients of a periodic sequence. The VRFFT operations are normalized, so a call of VRFFTF followed by a call of VRFFTB will return the original sequence. vrffti - initialize the array WSAVE, which is used in both VRFFTF and VRFFTB. vsinqb - synthesize a Fourier sequence from its representation in terms of a sine series with odd wave numbers. The VSINQ operations are normalized, so a call of VSINQF followed by a call of VSINQB will return the original sequence. vsinqf - compute the Fourier coefficients in a sine series representa- tion with only odd wave numbers.The VSINQ operations are nor- malized, so a call of VSINQF followed by a call of VSINQB will return the original sequence. vsinqi - initialize the array WSAVE, which is used in both VSINQF and VSINQB. vsint - compute the discrete Fourier sine transform of an odd sequence. The VSINT transforms are unnormalized inverses of themselves, so a call of VSINT followed by another call of VSINT will multiply the input sequence by 2 * (N+1). The VSINT trans- forms are normalized, so a call of VSINT followed by a call of VSINT will return the original sequence. vsinti - initialize the array WSAVE, which is used in subroutine VSINT. vzfftb - compute a periodic sequence from its Fourier coefficients. The VZFFT operations are normalized, so a call of VZFFTF fol- lowed by a call of VZFFTB will return the original sequence. vzfftf - compute the Fourier coefficients of a periodic sequence. The VZFFT operations are normalized, so a call of VZFFTF followed by a call of VZFFTB will return the original sequence. vzffti - initialize the array WSAVE, which is used in both VZFFTF and VZFFTB. zCopy_CompCol_Matrix - A utility C function in the serial SuperLU solver that copies one SuperMatrix into another. zCreate_CompCol_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse column format (also known as the Harwell-Boeing format). zCreate_CompRow_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in compressed sparse row format. zCreate_Dense_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in dense format. zCreate_SuperNode_Matrix - A utility C function in the serial SuperLU solver that creates a SuperMatrix in supernodal format. zPrintPerf - A utility function of the SuperLU solver that prints sta- tistics collected by the computational routines. zQuerySpace - A inquiry function that provides information on the mem- ory statistics of the SuperLU solver. zaxpy - compute y := alpha * x + y zaxpyi - Compute y := alpha * x + y zbbcsd - compute the CS decomposition of a unitary matrix in bidiago- nal-block form zbcomm - block coordinate matrix-matrix multiply zbdimm - block diagonal format matrix-matrix multiply zbdism - block diagonal format triangular solve zbdsqr - compute the singular value decomposition (SVD) of a real N-by- N (upper or lower) bidiagonal matrix B zbelmm - block Ellpack format matrix-matrix multiply zbelsm - block Ellpack format triangular solve zbscmm - block sparse column matrix-matrix multiply zbscsm - block sparse column format triangular solve zbsrmm - block sparse row format matrix-matrix multiply zbsrsm - block sparse row format triangular solve zcgesv - computes the solution to a complex system of linear equations A * X = B zcnvcor - compute the convolution or correlation of complex vectors zcnvcor2 - compute the convolution or correlation of complex matrices zcoomm - coordinate matrix-matrix multiply zcopy - copy x to y zcposv - computes the solution to system of linear equations A * X = B for PO matrices zcscmm - compressed sparse column format matrix-matrix multiply zcscsm - compressed sparse column format triangular solve zcsrmm - compressed sparse row format matrix-matrix multiply zcsrsm - compressed sparse row format triangular solve zdiamm - diagonal format matrix-matrix multiply. zdiasm - diagonal format triangular solve zdotc - compute the dot product of two vectors conjg(x) and y. zdotci - Compute the complex conjugated indexed dot product. zdotu - compute the dot product of two vectors x and y. zdotui - Compute the complex unconjugated indexed dot product. zdrot - Apply a plane rotation. zdscal - Compute y := alpha * y zellmm - Ellpack format matrix-matrix multiply zellsm - Ellpack format triangular solve zfft2b - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of ZFFT2F fol- lowed by a call of ZFFT2B will multiply the input sequence by M*N. zfft2f - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of ZFFT2F followed by a call of ZFFT2B will multiply the input sequence by M*N. zfft2i - initialize the array WSAVE, which is used in both the forward and backward transforms. zfft3b - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of ZFFT3F fol- lowed by a call of ZFFT3B will multiply the input sequence by M*N*K. zfft3f - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of ZFFT3F followed by a call of ZFFT3B will multiply the input sequence by M*N*K. zfft3i - initialize the array WSAVE, which is used in both ZFFT3F and ZFFT3B. zfftb - compute a periodic sequence from its Fourier coefficients. The FFT operations are unnormalized, so a call of ZFFTF followed by a call of ZFFTB will multiply the input sequence by N. zfftd - initialize the trigonometric weight and factor tables or com- pute the inverse Fast Fourier Transform of a double complex sequence. zfftd2 - initialize the trigonometric weight and factor tables or com- pute the two-dimensional inverse Fast Fourier Transform of a two-dimensional double complex array. zfftd3 - initialize the trigonometric weight and factor tables or com- pute the three-dimensional inverse Fast Fourier Transform of a three-dimensional double complex array. zfftdm - initialize the trigonometric weight and factor tables or com- pute the one-dimensional inverse Fast Fourier Transform of a set of double complex data sequences stored in a two-dimen- sional array. zfftf - compute the Fourier coefficients of a periodic sequence. The FFT operations are unnormalized, so a call of ZFFTF followed by a call of ZFFTB will multiply the input sequence by N. zffti - initialize the array WSAVE, which is used in both ZFFTF and ZFFTB. zfftopt - compute the length of the closest fast FFT zfftz - initialize the trigonometric weight and factor tables or com- pute the Fast Fourier transform (forward or inverse) of a double complex sequence. zfftz2 - initialize the trigonometric weight and factor tables or com- pute the two-dimensional Fast Fourier Transform (forward or inverse) of a two-dimensional double complex array. zfftz3 - initialize the trigonometric weight and factor tables or com- pute the three-dimensional Fast Fourier Transform (forward or inverse) of a three-dimensional double complex array. zfftzm - initialize the trigonometric weight and factor tables or com- pute the one-dimensional Fast Fourier Transform (forward or inverse) of a set of data sequences stored in a two-dimen- sional double complex array. zgbbrd - reduce a complex general m-by-n band matrix A to real upper bidiagonal form B by a unitary transformation zgbcon - estimate the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity- norm, using the LU factorization computed by ZGBTRF zgbequ - compute row and column scalings intended to equilibrate an M- by-N band matrix A and reduce its condition number zgbequb - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number zgbmv - perform one of the matrix-vector operationsy := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y zgbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is banded, and provide error bounds and backward error estimates for the solution zgbrfsx - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution zgbsv - compute the solution to a complex system of linear equations A * X = B, where A is a band matrix of order N with KL subdiag- onals and KU superdiagonals, and X and B are N-by-NRHS matri- ces zgbsvx - use the LU factorization to compute the solution to a complex system of linear equations A*X=B, A**T*X=B, or A**H*X=B, where A is a band matrix zgbsvxx - compute the solution to system of linear equations A * X = B for general band matrices zgbtf2 - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges zgbtrf - compute an LU factorization of a complex m-by-n band matrix A using partial pivoting with row interchanges zgbtrs - solve a system of linear equations A*X=B, A**T*X=B, or A**H*X=B with a general band matrix A using the LU factoriza- tion computed by ZGBTRF zgebak - form the right or left eigenvectors of a complex general matrix by backward transformation on the computed eigenvec- tors of the balanced matrix output by ZGEBAL zgebal - balance a general complex matrix A zgebd2 - reduce a general matrix to bidiagonal form using an unblocked algorithm zgebrd - reduce a general complex M-by-N matrix A to upper or lower bidiagonal form B by a unitary transformation zgecon - estimate the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF zgeequ - compute row and column scalings intended to equilibrate an M- by-N matrix A and reduce its condition number zgeequb - computes row and column scalings intended to equilibrate an M-by-N matrix A and redu ce its condition number zgees - compute for an N-by-N complex nonsymmetric matrix A, the eigen- values, the Schur form T, and, optionally, the matrix of Schur vectors Z zgeesx - compute for an N-by-N complex nonsymmetric matrix A, the ei- genvalues, the Schur form T, and, optionally, the matrix of Schur vectors Z zgeev - compute for an N-by-N complex nonsymmetric matrix A, the eigen- values and, optionally, the left and/or right eigenvectors zgeevx - compute for an N-by-N complex nonsymmetric matrix A, the ei- genvalues and, optionally, the left and/or right eigenvectors zgegs - routine is deprecated and has been replaced by routine ZGGES zgegv - routine is deprecated and has been replaced by routine ZGGEV zgehd2 - reduce a general square matrix to upper Hessenberg form using an unblocked algorithm zgehrd - reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation zgelq2 - compute the LQ factorization of a general rectangular matrix using an unblocked algorithm zgelqf - compute an LQ factorization of a complex M-by-N matrix A zgels - solve overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A zgelsd - compute the minimum-norm solution to a real linear least squares problem zgelss - compute the minimum norm solution to a complex linear least squares problem zgelsx - routine is deprecated and has been replaced by routine ZGELSY zgelsy - compute the minimum-norm solution to a complex linear least squares problem zgemm - perform one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C zgemqrt - overwrite the general complex M-by-N matrix C with Q*C, C*Q, Q**H* C, or C*Q**H depending on values of SIDE and TRANS zgemv - perform one of the matrix-vector operationsy := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or y := alpha*conjg( A' )*x + beta*y zgeql2 - compute the QL factorization of a general rectangular matrix using an unblocked algorithm zgeqlf - compute a QL factorization of a complex M-by-N matrix A zgeqp3 - compute a QR factorization with column pivoting of a matrix A zgeqpf - routine is deprecated and has been replaced by routine ZGEQP3 zgeqr2 - computes the QR factorization of a general rectangular matrix using an unblocked algorithm. zgeqr2p - computes the QR factorization of a general rectangular matrix with non-negative diagonal elements using an unblocked algo- rithm. zgeqrf - compute a QR factorization of a complex M-by-N matrix A zgeqrfp - compute a QR factorization of a complex M-by-N matrix A: A = Q * R zgeqrt - compute a blocked QR factorization of a complex M-by-N matrix A using the compact WY representation of Q zgeqrt2 - compute a QR factorization of a general complex matrix using the compact WY representation of Q zgeqrt3 - recursively computes a QR factorization of a general complex matrix using the compact WY representation of Q zgerc - perform the rank 1 operation A := alpha*x*conjg( y' ) + A zgerfs - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution zgerfsx - improve the computed solution to a system of linear equations and provide error bounds and backward error estimates for the solution zgerq2 - computes the RQ factorization of a general rectangular matrix using an unblocked algorithm zgerqf - compute an RQ factorization of a complex M-by-N matrix A zgeru - perform the rank 1 operation A := alpha*x*y' + A zgesdd - compute the singular value decomposition (SVD) of a complex M- by-N matrix A, optionally computing the left and/or right singular vectors, by using divide-and-conquer method zgesv - compute the solution to a complex system of linear equations A*X=B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices zgesvd - compute the singular value decomposition (SVD) of a complex M- by-N matrix A, optionally computing the left and/or right singular vectors zgesvx - use the LU factorization to compute the solution to a complex system of linear equations A*X=B, where A is an N-by-N gen- eral matrix zgesvxx - compute the solution to system of linear equations A*X=B for general matrices zgetf2 - compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges zgetrf - compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges zgetri - compute the inverse of a matrix using the LU factorization computed by ZGETRF zgetrs - solve a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by ZGETRF zggbak - form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transforma- tion on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL zggbal - balance a pair of general complex matrices (A,B) zgges - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized complex Schur form (S, T), and optionally left and/or right Schur vectors (VSL and VSR) zggesx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, the complex Schur form (S,T), and, optionally, the left and/or right matrices of Schur vectors zggev - compute for a pair of N-by-N complex nonsymmetric matrices (A,B), the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors zggevx - compute for a pair of N-by-N complex nonsymmetric matrices (A,B) the generalized eigenvalues, and, optionally, the left and/or right generalized eigenvectors zggglm - solve a general Gauss-Markov linear model (GLM) problem zgghrd - reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular zgglse - solve the linear equality-constrained least squares (LSE) problem zggqrf - compute a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B. zggrqf - compute a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B zggsvd - compute the generalized singular value decomposition (GSVD) of an M-by-N complex matrix A and P-by-N complex matrix B zggsvp - compute unitary matrices zgscon - estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SuperLU routine sgstrf. zgsequ - computes row and column scalings intended to equilibrate an M- by-N sparse matrix A and reduce its condition number. zgsrfs - improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. It is a SuperLU routine. zgssco - General sparse solver condition number estimate. zgssda - Deallocate working storage for the general sparse solver. zgssfa - General sparse solver numeric factorization. zgssfs - General sparse solver one call interface. zgssin - Initialize the general sparse solver. zgssor - General sparse solver ordering and symbolic factorization. zgssps - Print general sparse solver statics. zgssrp - Return permutation used by the general sparse solver. zgsssl - Solve routine for the general sparse solver. zgssuo - Provide general sparse solvers SPSOLVE and SuperLU a user- supplied permutation for ordering. zgssv - solves a system of linear equations A*X=B using the LU factor- ization from sgstrf. zgssvx - solves the system of linear equations A*X=B or A'*X=B, using the LU factorization from sgstrf(). Error bounds on the solu- tion and a condition estimate are also provided. zgstrf - computes an LU factorization of a general sparse m-by-n matrix A using partial pivoting with row interchanges. zgstrs - solves a system of linear equations A*X=B or A'*X=B with A sparse and B dense, using the LU factorization computed by sgstrf. zgtcon - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF zgthr - Gathers specified elements from y into x. zgthrz - Gather and zero. zgtrfs - improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, provide error bounds and backward error estimates for the solution zgtsv - solve the equation A*X = B, where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting zgtsvx - use the LU factorization to compute the solution to a complex system of linear equations A*X=B, A**T*X=B, or A**H*X=B, where A is a tridiagonal matrix of order N and X and B are N- by-NRHS matrices zgttrf - compute an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges zgttrs - solve one of the systems of equations A*X=B, A**T*X=B, or A**H *X=B, with a tridiagonal matrix A using the LU factorization computed by ZGTTRF zgtts2 - solve a system of linear equations with a tridiagonal matrix using the LU factorization computed by zgttrf zhbev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A zhbevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A zhbevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A zhbgst - reduce a complex Hermitian-definite banded generalized eigen- problem A*x=lambda*B*x to standard form C*y=lambda*y, such that C has the same bandwidth as A zhbgv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenprob- lem, of the form A*x=(lambda)*B*x zhbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenprob- lem, of the form A*x=(lambda)*B*x zhbgvx - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenprob- lem, of the form A*x=(lambda)*B*x zhbmv - perform the matrix-vector operationy := alpha*A*x + beta*y zhbtrd - reduce a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation zhecon - estimate the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF zhecon_rook - estimate the reciprocal of the condition number for Her- mitian matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) zheequb - compute row and column scalings intended to equilibrate a Hermitian matrix A and reduce its condition number (with respect to the two-norm) zheev - compute all eigenvalues and, optionally, eigenvectors of a com- plex Hermitian matrix A zheevd - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A zheevr - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian tridiagonal matrix T zheevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A zhegs2 - reduce a complex Hermitian-definite generalized eigenproblem to standard form zhegst - reduce a complex Hermitian-definite generalized eigenproblem to standard form zhegv - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x zhegvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x zhegvx - compute selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x zhemm - perform one of the matrix-matrix operations C := alpha*A*B + beta*C or C := alpha*B*A + beta*C zhemv - perform the matrix-vector operationy := alpha*A*x + beta*y zher - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A zher2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A zher2k - perform one of the Hermitian rank 2k operations C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C or C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C zherfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and pro- vide error bounds and backward error estimates for the solu- tion zherfsx - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and pro- vide error bounds and backward error estimates for the solu- tion zherk - perform one of the Hermitian rank k operations C := alpha*A*conjg( A' ) + beta*C or C := alpha*conjg( A' )*A + beta*C zhesv - compute the solution to a complex system of linear equations A*X=B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices zhesv_rook - compute the solution to a system of linear equations A*X=B for Hermitian matrices using the bounded Bunch-Kaufman ("rook") diagonal pivoting method zhesvx - use the diagonal pivoting factorization to compute the solu- tion to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices zhesvxx - compute the solution to system of linear equations A*X = B for Hermitian matrices zhetd2 - reduce a Hermitian matrix to real symmetric tridiagonal form by an unitary similarity transformation (unblocked algorithm) zhetf2 - compute the factorization of a complex Hermitian matrix, using the diagonal pivoting method (unblocked algorithm, calling Level 2 BLAS) zhetf2_rook - compute the factorization of a complex Hermitian indefi- nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm) zhetrd - reduce a complex Hermitian matrix A to real symmetric tridiag- onal form T by a unitary similarity transformation zhetrf - compute the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method zhetrf_rook - compute the factorization of a complex Hermitian indefi- nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS) zhetri - compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF zhetri2 - compute the inverse of a COMPLEX*16 Hermitian indefinite matrix A using the factorization A=U*D*U**T or A=L*D*L**T computed by ZHETRF zhetri2x - compute the inverse of a COMPLEX*16 Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF zhetri_rook - compute the inverse of a Hermitian matrix using the fac- torization obtained with the bounded Bunch-Kaufman ("rook") diagonal pivoting method zhetrs - solve a system of linear equations A*X = B with a complex Her- mitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF zhetrs2 - solve a system of linear equations A*X=B with a complex Her- mitian matrix A using the factorization A=U*D*U**H or A=L*D*L**H computed by ZHETRF and converted by ZSYCONV zhetrs_rook - compute the solution to a system of linear equations A*X=B for Hermitian matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) zhfrk - perform a Hermitian rank-k operation for matrix in RFP format zhgeqz - implement a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation det( A-w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both upper triangular) by applying one unitary tranforma- tion (usually called Q) on the left and another (usually called Z) on the right zhpcon - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF zhpev - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage zhpevd - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage zhpevx - compute selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage zhpgst - reduce a complex Hermitian-definite generalized eigenproblem to standard form, using packed storage zhpgv - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x zhpgvd - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x zhpgvx - compute selected eigenvalues and, optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x zhpmv - perform the matrix-vector operationy := alpha*A*x + beta*y zhpr - perform the hermitian rank 1 operation A := alpha*x*conjg( x' ) + A zhpr2 - perform the Hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A zhprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite and packed, and provide error bounds and backward error estimates for the solution zhpsv - compute the solution to a complex system of linear equationsA * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices zhpsvx - use the diagonal pivoting factorization A = U*D*U**H or A = L*D*L**H to compute the solution to a complex system of lin- ear equations A * X = B, where A is an N-by-N Hermitian matrix stored in packed format and X and B are N-by-NRHS matrices zhptrd - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation zhptrf - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method zhptri - compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF zhptrs - solve a system of linear equations A*X = B with a complex Her- mitian matrix A stored in packed format using the factoriza- tion A = U*D*U**H or A = L*D*L**H computed by ZHPTRF zhsein - use inverse iteration to find specified right and/or left eigenvectors of a complex upper Hessenberg matrix H zhseqr - compute the eigenvalues of a complex upper Hessenberg matrix H, and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**H, where T is an upper triangular matrix (the Schur form), and Z is the unitary matrix of Schur vectors zinfinite_norm_error - A utility function of the SuperLU solver that computes the infinity-norm of an array of vectors that are approximations to the exact solution vector. zjadmm - Jagged diagonal matrix-matrix multiply (modified Ellpack) zjadrp - right permutation of a jagged diagonal matrix zjadsm - Jagged-diagonal format triangular solve zla_gbamv - perform a matrix-vector operation to calculate error bounds zla_gbrcond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices zla_gbrcond_x - compute the infinity norm condition number of op(A)*diag(x) for general banded matrices zla_gbrfsx_extended - improve the computed solution to a system of lin- ear equations for general banded matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution zla_gbrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix zla_geamv - compute a matrix-vector product using a general matrix to calculate error bounds zla_gercond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for general matrices zla_gercond_x - compute the infinity norm condition number of op(A)*diag(x) for general matrices zla_gerfsx_extended - improve the computed solution to a system of lin- ear equations by performing extra-precise iterative refine- ment and provide error bounds and backward error estimates for the solution zla_gerpvgrw - compute the reciprocal pivot growth factor using the "max absolute element" norm zla_heamv - compute a matrix-vector product using a Hermitian indefi- nite matrix to calculate error bounds zla_hercond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices zla_hercond_x - compute the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices zla_herfsx_extended - improve the computed solution to a system of lin- ear equations for Hermitian indefinite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution zla_herpvgrw - compute the reciprocal pivot growth factor using the "max absolute element" norm zla_lin_berr - compute a component-wise relative backward error zla_porcond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices zla_porcond_x - compute the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices zla_porfsx_extended - improve the computed solution to a system of lin- ear equations for symmetric or Hermitian positive-definite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution zla_porpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-defi- nite matrix zla_syamv - compute a matrix-vector product using a symmetric indefi- nite matrix to calculate error bounds zla_syrcond_c - compute the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices zla_syrcond_x - compute the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices zla_syrfsx_extended - improve the computed solution to a system of lin- ear equations for symmetric indefinite matrices by performing extra-precise iterative refinement and provide error bounds and backward error estimates for the solution zla_syrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix zla_wwaddw - add a vector into a doubled-single vector zlaed0 - is used by sstedc. Compute all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method zlaed7 - is used by sstedc. Compute the updated eigensystem of a diago- nal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is dense zlaed8 - is used by sstedc. Merge eigenvalues and deflates secular equation. Used when the original matrix is dense zlahef - compute a partial factorization of a complex Hermitian indefi- nite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS) zlahef_rook - compute a partial factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS) zlals0 - apply back multiplying factors in solving the least squares problem using divide and conquer SVD approach. Used by sgelsd zlalsa - compute the SVD of the coefficient matrix in compact form. Used by sgelsd zlalsd - use the singular value decomposition of A to solve the least squares problem zlangs - returns the value of the one-norm, or the Frobenius-norm, or the infinity-norm, or the element with largest absolute value of a general real matrix A in sparse format. zlanhf - return the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian matrix in RFP format zlaqgs - a SuperLU function that equilibrates a general sparse M by N matrix A. zlarscl2 - perform reciprocal diagonal scaling on a vector zlarz - apply a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right zlarzb - apply a complex block reflector H or its transpose H**H to a complex distributed M-by-N C from the left or the right zlarzt - form the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors zlascl2 - perform diagonal scaling on a vector zlasyf - compute a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method zlasyf_rook - compute a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal piv- oting method zlatrz - factor an upper trapezoidal matrix by means of unitary trans- formations zlatzm - routine is deprecated and has been replaced by routine ZUNMRZ zpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF zpbequ - compute row and column scalings intended to equilibrate a Her- mitian positive definite band matrix A and reduce its condi- tion number (with respect to the two-norm) zpbrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, provide error bounds and backward error estimates for the solution zpbstf - compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A zpbsv - compute the solution to a complex system of linear equations A*X=B, where A is an N-by-N Hermitian positive definite band matrix and X and B are N-by-NRHS matrices zpbsvx - use the Cholesky factorization A=U**H*U or A=L*L**H to compute the solution to a complex system of linear equations A*X=B, where A is an N-by-N Hermitian positive definite band matrix and X and B are N-by-NRHS matrices zpbtf2 - compute the Cholesky factorization of a complex Hermitian pos- itive definite band matrix A zpbtrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite band matrix A zpbtrs - solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factoriza- tion A = U**H*U or A = L*L**H computed by ZPBTRF zpftrf - computes the Cholesky factorization of a complex Hermitian positive definite matrix A, the block version of the algo- rithm zpftri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization computed by ZPFTRF zpftrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization computed by ZPFTRF zpocon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF zpoequ - compute row and column scalings intended to equilibrate a Her- mitian positive definite matrix A and reduce its condition number (with respect to the two-norm) zpoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm zporfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, provide error bounds and backward error estimates for the solution zporfsx - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, provide error bounds and backward error estimates for the solution zposv - compute the solution to a complex system of linear equationsA*X = B, where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices zposvx - use the Cholesky factorization to compute the solution to a complex system of linear equations A*X = B, where A is an N- by-N Hermitian positive definite matrix and X and B are N-by- NRHS matri ces zposvxx - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices zpotf2 - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A zpotrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A zpotri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF zpotrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF zppcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF zppequ - compute row and column scalings intended to equilibrate a Her- mitian positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm) zpprfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and packed, provide error bounds and backward error estimates for the solution zppsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite matrix stored in packed format and X and B are N-by-NRHS matrices zppsvx - use the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B, zpptrf - compute the Cholesky factorization of a complex Hermitian pos- itive definite matrix A stored in packed format zpptri - compute the inverse of a complex Hermitian positive definite matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF zpptrs - solve a system of linear equations A*X = B with a Hermitian positive definite matrix A in packed storage using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF zpstf2 - compute the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A zpstrf - compute the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix A zptcon - compute the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF zpteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first fac- toring the matrix using SPTTRF and then calling CBDSQR to compute the singular values of the bidiagonal factor zptrfs - improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and tridiagonal, provide error bounds and backward error estimates for the solution zptsv - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices zptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices zpttrf - compute the L*D*L' factorization of a complex Hermitian posi- tive definite tridiagonal matrix A zpttrs - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF zptts2 - solve a tridiagonal system of the form A * X = B using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF zrot - apply a plane rotation, where the cos (C) is real and the sin (S) is complex, and the vectors X and Y are complex zrotg - Construct a Given's plane rotation zscal - Compute y := alpha * y zsctr - Scatters elements from x into y zskymm - Skyline format matrix-matrix multiply zskysm - Skyline format triangular solve zspcon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the fac- torization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF zsprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, provide error bounds and backward error estimates for the solution zspsv - compute the solution to a complex system of linear equationsA*X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices zspsvx - use the diagonal pivoting factorization A = U*D*U**T or A = L*D*L**T to compute the solution to a complex system of lin- ear equations A * X = B, where A is an N-by-N symmetric matrix stored in packed format and X and B are N-by-NRHS matrices zsptrf - compute the factorization of a complex symmetric matrix A stored in packed format using the Bunch-Kaufman diagonal piv- oting method zsptri - compute the inverse of a complex symmetric indefinite matrix A in packed storage using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF zsptrs - solve a system of linear equations A*X = B with a complex sym- metric matrix A stored in packed format using the factoriza- tion A = U*D*U**T or A = L*D*L**T computed by ZSPTRF zstedc - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method zstegr - Compute T-sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T is a relatively robust representation zstein - compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration zstemr - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix T zsteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method zstsv - compute the solution to a complex system of linear equations A * X = B where A is a symmetric tridiagonal matrix zsttrf - compute the factorization of a complex symmetric tridiagonal matrix A using the Bunch-Kaufman diagonal pivoting method zsttrs - compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N symmetric tridiagonal matrix and X and B are N-by-NRHS matrices zswap - Exchange vectors x and y zsycon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factoriza- tion A = U*D*U**T or A = L*D*L**T computed by ZSYTRF zsycon_rook - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK zsyconv - converts A given by ZHETRF into L and D or vice-versa zsyequb - compute row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number with respect to the two-norm zsymm - perform one of the matrix-matrix operationsC := alpha*A*B + beta*C or C := alpha*B*A + beta*C zsyr2k - perform one of the symmetric rank 2k operations C := alpha*A*B' + alpha*B*A' + beta*C or C := alpha*A'*B + alpha*B'*A + beta*C zsyrfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provide error bounds and backward error estimates for the solution zsyrfsx - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, provides error bounds and backward error estimates for the solution zsyrk - perform one of the symmetric rank k operations C := alpha*A*A' + beta*C or C := alpha*A'*A + beta*C zsysv - compute the solution to a complex system of linear equationsA*X = B, where A is an N-by-N symmetric matrix and X and B are N- by-NRHS matrices zsysv_rook - compute the solution to system of linear equations A*X = B for symmetric matrices. ZSYTRF_ROOK is called to compute the factorization of A zsysvx - use the diagonal pivoting factorization to compute the solu- tion to a complex system of linear equations A*X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices zsysvxx - compute the solution to complex system of linear equations A*X = B for symmetric matrices zsytf2 - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method zsytf2_rook - compute the factorization of a complex symmetric indefi- nite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm) zsytrf - compute the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method zsytrf_rook - compute the factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm) zsytri - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF zsytri2 - compute the inverse of a COMPLEX*16 symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF zsytri2x - compute the inverse of a complex symmetric indefinite matrix A using the factorization computed by ZSYTRF zsytri_rook - compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK zsytrs - solve a system of linear equations A*X = B with a complex sym- metric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF zsytrs2 - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization computed by ZSYTRF and converted by ZSYCONV zsytrs_rook - solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK ztbcon - estimate the reciprocal of the condition number of a triangu- lar band matrix A, in either the 1-norm or the infinity-norm ztbmv - perform one of the matrix-vector operationsx := A*x, or x := A'*x, or x := conjg( A' )*x ztbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix ztbsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b ztbtrs - solve a triangular system of the form A*X = B, A**T*X = B, or A**H*X = B, where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix ztfsm - solve a matrix equation (one operand is a triangular matrix in RFP format) ztftri - compute the inverse of a triangular matrix A stored in RFP format ztfttp - copy a triangular matrix from the rectangular full packed for- mat (TF) to the standard packed format (TP) ztfttr - copy a triangular matrix from the rectangular full packed for- mat (TF) to the standard full format (TR) ztgevc - compute the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices with real diagonal elements (A,B) obtained from the generalized Schur factoriza- tion of an original pair of complex nonsymmetric matrices (AO,BO) ztgexc - reorder the generalized Schur decomposition of a complex matrix pair (A,B), using an unitary equivalence transforma- tion (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with row index IFST is moved to row ILST ztgsen - reorder the generalized Schur decomposition of a complex matrix pair (A, B), so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the pair (A,B) ztgsja - compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B ztgsna - estimate reciprocal condition numbers for specified eigenval- ues and/or eigenvectors of a matrix pair (A, B) ztgsyl - solve the generalized Sylvester equation ztpcon - estimate the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity- norm ztpmqrt - apply a complex orthogonal matrix Q obtained from a "triangu- lar-pentagonal" complex block reflector H to a general com- plex matrix C, which consists of two blocks ztpmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x ztpqrt - compute a blocked QR factorization of a complex "triangular- pentagonal" matrix C, which is composed of a triangular block A and pentagonal block B, using the compact WY representation for Q ztpqrt2 - compute a QR factorization of a real or complex "triangular- pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q ztprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix ztpsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b ztptri - compute the inverse of a complex upper or lower triangular matrix A stored in packed format ztptrs - solve a triangular system of the form A*X = B, A**T*X = B, or A**H*X = B, where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix ztpttf - copy a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF) ztpttr - copy a triangular matrix from the standard packed format (TP) to the standard full format (TR) ztrans - transpose and scale source matrix ztrcon - estimate the reciprocal of the condition number of a triangu- lar matrix A, in either the 1-norm or the infinity-norm ztrevc - compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T ztrexc - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST ztrmm - perform one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower tri- angular matrix and op( A ) is one of op( A ) = A or op( A ) = A' or op( A ) = conjg( A' ) ztrmv - perform one of the matrix-vector operations x := A*x, or x := A'*x, or x := conjg( A' )*x ztrrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix ztrsen - reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper trian- gular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant sub- space ztrsm - solve one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B ztrsna - estimate reciprocal condition numbers for specified eigenval- ues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary) ztrsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg(A')*x = b ztrsyl - solve the complex Sylvester matrix equation ztrti2 - compute the inverse of a complex upper or lower triangular matrix ztrtri - compute the inverse of a complex upper or lower triangular matrix A ztrtrs - solve a triangular system of the form A*X = B, A**T*X = B, or A**H*X = B, where A is a triangular matrix of order N, and B is an N-by-NRHS matrix ztrttf - copy a triangular matrix from the standard full format (TR) to the rectangular full packed format (TF) ztrttp - copy a triangular matrix from the standard full format (TR) to the standard packed format (TP) ztzrqf - routine is deprecated and has been replaced by routine ZTZRZF ztzrzf - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations zunbdb - simultaneously bidiagonalize the blocks of an M-by-M parti- tioned unitary matrix zunbdb1 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns zunbdb2 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns zunbdb3 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns zunbdb4 - simultaneously bidiagonalize the blocks of a tall and skinny matrix with orthonomal columns zunbdb5 - orthogonalize one column vector with respect to the orthonor- mal columns of another column vector zunbdb6 - orthogonalize one column vector with respect to the orthonor- mal columns of another column vector zuncsd - compute the CS decomposition of an M-by-M partitioned unitary matrix zuncsd2by1 - compute the CS decomposition of an M-by-Q matrix with orthonormal columns that has been partitioned into a 2-by-1 block structure zung2l - generate all or part of the unitary matrix Q from a QL factor- ization determined by cgeqlf (unblocked algorithm) zung2r - generate an M-by-N complex matrix Q with orthonormal columns, which is defined as the first N columns of a product of N elementary reflectors of order M zungbr - generate one of the complex unitary matrices Q or P**H deter- mined by ZGEBRD when reducing a complex matrix A to bidiago- nal form zunghr - generate a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD zungl2 - generate all or part of the unitary matrix Q from an LQ fac- torization determined by zgelqf (unblocked algorithm) zunglq - generate an M-by-N complex matrix Q with orthonormal rows, which is defined as the first M rows of a product of K ele- mentary reflectors of order N zungql - generate an M-by-N complex matrix Q with orthonormal columns, which is defined as the last N columns of a product of K ele- mentary reflectors of order M zungqr - generate an M-by-N complex matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M zungr2 - generate all or part of the unitary matrix Q from an RQ fac- torization determined by cgerqf (unblocked algorithm) zungrq - generate an M-by-N complex matrix Q with orthonormal rows, which is defined as the last M rows of a product of K elemen- tary reflectors of order N zungtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by CHETRD zunm2l - multiply a general matrix by the unitary matrix from a QL fac- torization determined by cgeqlf (unblocked algorithm) zunm2r - multipliy a general matrix by the unitary matrix from a QR factorization determined by cgeqrf (unblocked algorithm) zunmbr - overwrite the general complex M-by-N matrix C Q*C or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H zunmhr - overwrite the general complex M-by-N matrix C with Q*C or Q**H*C or C*Q**H or C*Q zunml2 - multiply a general matrix by the unitary matrix from a LQ fac- torization determined by cgelqf (unblocked algorithm) zunmlq - overwrite the general complex M-by-N matrix C with Q*C, or Q**H*C, or C*Q**H, or C*Q, where Q is a complex unitary matrix defined as the product of K elementary reflectors zunmql - overwrite the general complex M-by-N matrix C with Q*C, or Q**H*C, or C*Q**H, or C*Q, where Q is a complex unitary matrix defined as the product of K elementary reflectors zunmqr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' zunmr2 - multiply a general matrix by the unitary matrix from a RQ fac- torization determined by zgerqf (unblocked algorithm) zunmr3 - multiply a general matrix by the unitary matrix from a RZ fac- torization determined by ctzrzf (unblocked algorithm) zunmrq - overwrite the general complex M-by-N matrix C with Q*C, or Q**H*C, or C*Q**H, or C*Q, where Q is a complex unitary matrix defined as the product of K elementary reflectors zunmrz - overwrite the general complex M-by-N matrix C with Q*C or Q**H*C or C*Q**H or C*Q. zunmtr - overwrite the general complex M-by-N matrix C with Q*C, or Q**H*C, or C*Q**H, or C*Q, where Q is defined as the product of elementary reflectors, as returned by ZHETRD zupgtr - generate a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors H(i) of order n, as returned by CHPTRD using packed storage zupmtr - overwrite the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N' zvbrmm - variable block sparse row format matrix-matrix multiply zvbrsm - variable block sparse row format triangular solve zvmul - compute the scaled product of complex vectors 7 Nov 2015 intro(3P)