dstedc - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
SUBROUTINE DSTEDC(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER*1 COMPZ INTEGER N, LDZ, LWORK, LIWORK, INFO INTEGER IWORK(*) DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*) SUBROUTINE DSTEDC_64(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER*1 COMPZ INTEGER*8 N, LDZ, LWORK, LIWORK, INFO INTEGER*8 IWORK(*) DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE STEDC(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: COMPZ INTEGER :: N, LDZ, LWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: D, E, WORK REAL(8), DIMENSION(:,:) :: Z SUBROUTINE STEDC_64(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: COMPZ INTEGER(8) :: N, LDZ, LWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: D, E, WORK REAL(8), DIMENSION(:,:) :: Z C INTERFACE #include <sunperf.h> void dstedc(char compz, int n, double *d, double *e, double *z, int ldz, int *info); void dstedc_64(char compz, long n, double *d, double *e, double *z, long ldz, long *info);
Oracle Solaris Studio Performance Library dstedc(3P) NAME dstedc - compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method SYNOPSIS SUBROUTINE DSTEDC(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER*1 COMPZ INTEGER N, LDZ, LWORK, LIWORK, INFO INTEGER IWORK(*) DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*) SUBROUTINE DSTEDC_64(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER*1 COMPZ INTEGER*8 N, LDZ, LWORK, LIWORK, INFO INTEGER*8 IWORK(*) DOUBLE PRECISION D(*), E(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE STEDC(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: COMPZ INTEGER :: N, LDZ, LWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: D, E, WORK REAL(8), DIMENSION(:,:) :: Z SUBROUTINE STEDC_64(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: COMPZ INTEGER(8) :: N, LDZ, LWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: D, E, WORK REAL(8), DIMENSION(:,:) :: Z C INTERFACE #include <sunperf.h> void dstedc(char compz, int n, double *d, double *e, double *z, int ldz, int *info); void dstedc_64(char compz, long n, double *d, double *e, double *z, long ldz, long *info); PURPOSE dstedc computes all eigenvalues and, optionally, eigenvectors of a sym- metric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band real symmetric matrix can also be found if SSYTRD or SSPTRD or SSBTRD has been used to reduce this matrix to tridiagonal form. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See DLAED3 for details. ARGUMENTS COMPZ (input) = 'N': Compute eigenvalues only. = 'I': Compute eigenvectors of tridiagonal matrix also. = 'V': Compute eigenvectors of original dense symmetric matrix also. On entry, Z contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. N (input) The dimension of the symmetric tridiagonal matrix. N >= 0. D (input/output) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order. E (input/output) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. Z (input) On entry, if COMPZ = 'V', then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if COMPZ = 'V', Z contains the orthonormal eigenvectors of the original symmetric matrix, and if COMPZ = 'I', Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = 'N', then Z is not refer- enced. LDZ (input) The leading dimension of the array Z. LDZ >= 1. If eigen- vectors are desired, then LDZ >= max(1,N). WORK (workspace) dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) The dimension of the array WORK. If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. If COMPZ = 'V' and N > 1 then LWORK must be at least ( 1 + 3*N + 2*N*lg N + 4*N**2 ), where lg( N ) = smallest integer k such that 2**k >= N. If COMPZ = 'I' and N > 1 then LWORK must be at least ( 1 + 4*N + N**2 ). If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. IWORK (workspace/output) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. LIWORK (input) The dimension of the array IWORK. If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. If COMPZ = 'V' and N > 1 then LIWORK must be at least ( 6 + 6*N + 5*N*lg N ). If COMPZ = 'I' and N > 1 then LIWORK must be at least ( 3 + 5*N ). If LIWORK = -1, then a workspace query is assumed; the rou- tine only calculates the optimal size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA. INFO (output) = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1). FURTHER DETAILS Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA Modified by Francoise Tisseur, University of Tennessee. 7 Nov 2015 dstedc(3P)