slaed0 - compute all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Used by sstedc
SUBROUTINE SLAED0(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ INTEGER IWORK(*) REAL D(*), E(*), Q(LDQ,*), QSTORE(LDQS,*), WORK(*) SUBROUTINE SLAED0_64(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) INTEGER*8 ICOMPQ, INFO, LDQ, LDQS, N, QSIZ INTEGER*8 IWORK(*) REAL D(*), E(*), Q(LDQ,*), QSTORE(LDQS,*), WORK(*) F95 INTERFACE SUBROUTINE LAED0(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) REAL, DIMENSION(:,:) :: Q, QSTORE INTEGER :: ICOMPQ, QSIZ, N, LDQ, LDQS, INFO INTEGER, DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: D, E, WORK SUBROUTINE LAED0_64(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) REAL, DIMENSION(:,:) :: Q, QSTORE INTEGER(8) :: ICOMPQ, QSIZ, N, LDQ, LDQS, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: D, E, WORK C INTERFACE #include <sunperf.h> void slaed0 (int icompq, int qsiz, int n, float *d, float *e, float *q, int ldq, float *qstore, int ldqs, int *info); void slaed0_64 (long icompq, long qsiz, long n, float *d, float *e, float *q, long ldq, float *qstore, long ldqs, long *info);
Oracle Solaris Studio Performance Library slaed0(3P) NAME slaed0 - compute all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. Used by sstedc SYNOPSIS SUBROUTINE SLAED0(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ INTEGER IWORK(*) REAL D(*), E(*), Q(LDQ,*), QSTORE(LDQS,*), WORK(*) SUBROUTINE SLAED0_64(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) INTEGER*8 ICOMPQ, INFO, LDQ, LDQS, N, QSIZ INTEGER*8 IWORK(*) REAL D(*), E(*), Q(LDQ,*), QSTORE(LDQS,*), WORK(*) F95 INTERFACE SUBROUTINE LAED0(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) REAL, DIMENSION(:,:) :: Q, QSTORE INTEGER :: ICOMPQ, QSIZ, N, LDQ, LDQS, INFO INTEGER, DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: D, E, WORK SUBROUTINE LAED0_64(ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK, IWORK, INFO) REAL, DIMENSION(:,:) :: Q, QSTORE INTEGER(8) :: ICOMPQ, QSIZ, N, LDQ, LDQS, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: D, E, WORK C INTERFACE #include <sunperf.h> void slaed0 (int icompq, int qsiz, int n, float *d, float *e, float *q, int ldq, float *qstore, int ldqs, int *info); void slaed0_64 (long icompq, long qsiz, long n, float *d, float *e, float *q, long ldq, float *qstore, long ldqs, long *info); PURPOSE slaed0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. ARGUMENTS ICOMPQ (input) ICOMPQ is INTEGER = 0: Compute eigenvalues only. = 1: Compute eigenvectors of original dense symmetric matrix also. On entry, Q contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. = 2: Compute eigenvalues and eigenvectors of tridiagonal matrix. QSIZ (input) QSIZ is INTEGER The dimension of the orthogonal matrix used to reduce the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. N (input) N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0. D (input/output) D is REAL array, dimension (N) On entry, the main diagonal of the tridiagonal matrix. On exit, its eigenvalues. E (input) E is REAL array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix. On exit, E has been destroyed. Q (input/output) Q is REAL array, dimension (LDQ, N) On entry, Q must contain an N-by-N orthogonal matrix. If ICOMPQ = 0 Q is not referenced. If ICOMPQ = 1 On entry, Q is a subset of the columns of the orthogonal matrix used to reduce the full matrix to tridiagonal form corresponding to the subset of the full matrix which is being decomposed at this time. If ICOMPQ = 2 On entry, Q will be the identity matrix. On exit, Q contains the eigenvectors of the tridiagonal matrix. LDQ (input) LDQ is INTEGER The leading dimension of the array Q. If eigenvectors are desired, then LDQ >= max(1,N). In any case, LDQ >= 1. QSTORE (output) QSTORE is REAL array, dimension (LDQS, N) Referenced only when ICOMPQ = 1. Used to store parts of the eigenvector matrix when the updating matrix multiplies take place. LDQS (input) LDQS is INTEGER The leading dimension of the array QSTORE. If ICOMPQ = 1, then LDQS >= max(1,N). In any case, LDQS >= 1. WORK (output) WORK is REAL array, If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 + 3*N + 2*N*lg N + 3*N**2 ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of WORK must be at least 4*N + N**2. IWORK (output) IWORK is INTEGER array. If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 + 6*N + 5*N*lg N. ( lg( N ) = smallest integer k such that 2^k >= N ) If ICOMPQ = 2, the dimension of IWORK must be at least 3 + 5*N. INFO (output) INFO is INTEGER = 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). 7 Nov 2015 slaed0(3P)