chbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x
SUBROUTINE CHBGVD(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*) INTEGER N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER IWORK(*) REAL W(*), RWORK(*) SUBROUTINE CHBGVD_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*) INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER*8 IWORK(*) REAL W(*), RWORK(*) F95 INTERFACE SUBROUTINE HBGVD(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: AB, BB, Z INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: W, RWORK SUBROUTINE HBGVD_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: AB, BB, Z INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: W, RWORK C INTERFACE #include <sunperf.h> void chbgvd(char jobz, char uplo, int n, int ka, int kb, complex *ab, int ldab, complex *bb, int ldbb, float *w, complex *z, int ldz, int *info); void chbgvd_64(char jobz, char uplo, long n, long ka, long kb, complex *ab, long ldab, complex *bb, long ldbb, float *w, complex *z, long ldz, long *info);
Oracle Solaris Studio Performance Library chbgvd(3P) NAME chbgvd - compute all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x SYNOPSIS SUBROUTINE CHBGVD(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*) INTEGER N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER IWORK(*) REAL W(*), RWORK(*) SUBROUTINE CHBGVD_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*) INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER*8 IWORK(*) REAL W(*), RWORK(*) F95 INTERFACE SUBROUTINE HBGVD(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: AB, BB, Z INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: W, RWORK SUBROUTINE HBGVD_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: AB, BB, Z INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL, DIMENSION(:) :: W, RWORK C INTERFACE #include <sunperf.h> void chbgvd(char jobz, char uplo, int n, int ka, int kb, complex *ab, int ldab, complex *bb, int ldbb, float *w, complex *z, int ldz, int *info); void chbgvd_64(char jobz, char uplo, long n, long ka, long kb, complex *ab, long ldab, complex *bb, long ldbb, float *w, complex *z, long ldz, long *info); PURPOSE chbgvd computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian and banded, and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm 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 dig- its, but we know of none. 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 Hermitian 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 Hermitian 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**H*S, as returned by CPBSTF. 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**H*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) On exit, if INFO=0, WORK(1) returns the optimal LWORK. LWORK (input) The dimension of the array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= N. If JOBZ = 'V' and N > 1, LWORK >= 2*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. RWORK (workspace) On exit, if INFO=0, RWORK(1) returns the optimal LRWORK. LRWORK (input) The dimension of array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = 'N' and N > 1, LRWORK >= 2*N. If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = -1, then a workspace query is assumed; the rou- tine only calculates the optimal size of the RWORK array, returns this value as the first entry of the RWORK array, and no error message related to LRWORK is issued by XERBLA. IWORK (workspace/output) On exit, if INFO=0, IWORK(1) returns the optimal LIWORK. LIWORK (input) The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK >= 1. If JOBZ = 'V' and N > 1, LIWORK >= 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: 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 CPBSTF returned INFO = i: B is not positive definite. The factor- ization of B could not be completed and no eigenvalues or eigenvectors were computed. FURTHER DETAILS Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 7 Nov 2015 chbgvd(3P)