spteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor
SUBROUTINE SPTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER*1 COMPZ INTEGER N, LDZ, INFO REAL D(*), E(*), Z(LDZ,*), WORK(*) SUBROUTINE SPTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER*1 COMPZ INTEGER*8 N, LDZ, INFO REAL D(*), E(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE PTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER(LEN=1) :: COMPZ INTEGER :: N, LDZ, INFO REAL, DIMENSION(:) :: D, E, WORK REAL, DIMENSION(:,:) :: Z SUBROUTINE PTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER(LEN=1) :: COMPZ INTEGER(8) :: N, LDZ, INFO REAL, DIMENSION(:) :: D, E, WORK REAL, DIMENSION(:,:) :: Z C INTERFACE #include <sunperf.h> void spteqr(char compz, int n, float *d, float *e, float *z, int ldz, int *info); void spteqr_64(char compz, long n, float *d, float *e, float *z, long ldz, long *info);
Oracle Solaris Studio Performance Library spteqr(3P) NAME spteqr - compute all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor SYNOPSIS SUBROUTINE SPTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER*1 COMPZ INTEGER N, LDZ, INFO REAL D(*), E(*), Z(LDZ,*), WORK(*) SUBROUTINE SPTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER*1 COMPZ INTEGER*8 N, LDZ, INFO REAL D(*), E(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE PTEQR(COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER(LEN=1) :: COMPZ INTEGER :: N, LDZ, INFO REAL, DIMENSION(:) :: D, E, WORK REAL, DIMENSION(:,:) :: Z SUBROUTINE PTEQR_64(COMPZ, N, D, E, Z, LDZ, WORK, INFO) CHARACTER(LEN=1) :: COMPZ INTEGER(8) :: N, LDZ, INFO REAL, DIMENSION(:) :: D, E, WORK REAL, DIMENSION(:,:) :: Z C INTERFACE #include <sunperf.h> void spteqr(char compz, int n, float *d, float *e, float *z, int ldz, int *info); void spteqr_64(char compz, long n, float *d, float *e, float *z, long ldz, long *info); PURPOSE spteqr computes all eigenvalues and, optionally, eigenvectors of a sym- metric positive definite tridiagonal matrix by first factoring the matrix using SPTTRF, and then calling SBDSQR to compute the singular values of the bidiagonal factor. This routine computes the eigenvalues of the positive definite tridiag- onal matrix to high relative accuracy. This means that if the eigen- values range over many orders of magnitude in size, then the small ei- genvalues and corresponding eigenvectors will be computed more accu- rately than, for example, with the standard QR method. The eigenvectors of a full or band symmetric positive definite matrix can also be found if SSYTRD, SSPTRD, or SSBTRD has been used to reduce this matrix to tridiagonal form. (The reduction to tridiagonal form, however, may preclude the possibility of obtaining high relative accu- racy in the small eigenvalues of the original matrix, if these eigen- values range over many orders of magnitude.) ARGUMENTS COMPZ (input) = 'N': Compute eigenvalues only. = 'V': Compute eigenvectors of original symmetric matrix also. Array Z contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 'I': Compute eigenvectors of tridiagonal matrix also. N (input) The order of the matrix. N >= 0. D (input/output) On entry, the n diagonal elements of the tridiagonal matrix. On normal exit, D contains the eigenvalues, in descending order. E (input/output) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. Z (input) On entry, if COMPZ = 'V', the orthogonal matrix used in the reduction to tridiagonal form. On exit, if COMPZ = 'V', the orthonormal eigenvectors of the original symmetric matrix; if COMPZ = 'I', the orthonormal eigenvectors of the tridiagonal matrix. If INFO > 0 on exit, Z contains the eigenvectors associated with only the stored eigenvalues. If COMPZ = 'N', then Z is not referenced. LDZ (input) The leading dimension of the array Z. LDZ >= 1, and if COMPZ = 'V' or 'I', LDZ >= max(1,N). WORK (workspace) dimension(4*N) INFO (output) = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, and i is: <= N the Cholesky factorization of the matrix could not be performed because the i-th princi- pal minor was not positive definite. > N the SVD algorithm failed to converge; if INFO = N+i, i off-diagonal elements of the bidiagonal factor did not converge to zero. 7 Nov 2015 spteqr(3P)