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
SUBROUTINE SSBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO) CHARACTER*1 JOBZ, UPLO INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO REAL AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*) SUBROUTINE SSBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO) CHARACTER*1 JOBZ, UPLO INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO REAL AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE SBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO REAL, DIMENSION(:) :: W, WORK REAL, DIMENSION(:,:) :: AB, BB, Z SUBROUTINE SBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO REAL, DIMENSION(:) :: W, WORK REAL, DIMENSION(:,:) :: AB, BB, Z C INTERFACE #include <sunperf.h> void ssbgv(char jobz, char uplo, int n, int ka, int kb, float *ab, int ldab, float *bb, int ldbb, float *w, float *z, int ldz, int *info); void ssbgv_64(char jobz, char uplo, long n, long ka, long kb, float *ab, long ldab, float *bb, long ldbb, float *w, float *z, long ldz, long *info);
Oracle Solaris Studio Performance Library ssbgv(3P) NAME 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 SYNOPSIS SUBROUTINE SSBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO) CHARACTER*1 JOBZ, UPLO INTEGER N, KA, KB, LDAB, LDBB, LDZ, INFO REAL AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*) SUBROUTINE SSBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO) CHARACTER*1 JOBZ, UPLO INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, INFO REAL AB(LDAB,*), BB(LDBB,*), W(*), Z(LDZ,*), WORK(*) F95 INTERFACE SUBROUTINE SBGV(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, INFO REAL, DIMENSION(:) :: W, WORK REAL, DIMENSION(:,:) :: AB, BB, Z SUBROUTINE SBGV_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, INFO REAL, DIMENSION(:) :: W, WORK REAL, DIMENSION(:,:) :: AB, BB, Z C INTERFACE #include <sunperf.h> void ssbgv(char jobz, char uplo, int n, int ka, int kb, float *ab, int ldab, float *bb, int ldbb, float *w, float *z, int ldz, int *info); void ssbgv_64(char jobz, char uplo, long n, long ka, long kb, float *ab, long ldab, float *bb, long ldbb, float *w, float *z, long ldz, long *info); PURPOSE ssbgv computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite. ARGUMENTS JOBZ (input) = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. N (input) The order of the matrices A and B. N >= 0. KA (input) The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB (input) The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0. AB (input/output) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array. The j- th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed. LDAB (input) The leading dimension of the array AB. LDAB >= KA+1. BB (input/output) On entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array. The j- th column of B is stored in the j-th column of the array BB as follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by SPBSTF. LDBB (input) The leading dimension of the array BB. LDBB >= KB+1. W (output) If INFO = 0, the eigenvalues in ascending order. Z (output) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvec- tor associated with W(i). The eigenvectors are normalized so that Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced. LDZ (input) The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N. WORK (workspace) dimension(3*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 algorithm failed to converge: i off-diagonal ele- ments of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then SPBSTF returned INFO = i: B is not positive definite. The factor- ization of B could not be completed and no eigenvalues or eigenvectors were computed. 7 Nov 2015 ssbgv(3P)