chbgvx - 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 CHBGVX(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO COMPLEX AB(LDAB,*), BB(LDBB,*), Q(LDQ,*), Z(LDZ,*), WORK(*) INTEGER N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO INTEGER IWORK(*), IFAIL(*) REAL VL, VU, ABSTOL REAL W(*), RWORK(*) SUBROUTINE CHBGVX_64(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO COMPLEX AB(LDAB,*), BB(LDBB,*), Q(LDQ,*), Z(LDZ,*), WORK(*) INTEGER*8 N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO INTEGER*8 IWORK(*), IFAIL(*) REAL VL, VU, ABSTOL REAL W(*), RWORK(*) F95 INTERFACE SUBROUTINE HBGVX(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: AB, BB, Q, Z INTEGER :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK, IFAIL REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: W, RWORK SUBROUTINE HBGVX_64(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: AB, BB, Q, Z INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK, IFAIL REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: W, RWORK C INTERFACE #include <sunperf.h> void chbgvx(char jobz, char range, char uplo, int n, int ka, int kb, complex *ab, int ldab, complex *bb, int ldbb, complex *q, int ldq, float vl, float vu, int il, int iu, float abstol, int *m, float *w, complex *z, int ldz, int *ifail, int *info); void chbgvx_64(char jobz, char range, char uplo, long n, long ka, long kb, complex *ab, long ldab, complex *bb, long ldbb, complex *q, long ldq, float vl, float vu, long il, long iu, float abstol, long *m, float *w, complex *z, long ldz, long *ifail, long *info);
Oracle Solaris Studio Performance Library chbgvx(3P) NAME chbgvx - 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 CHBGVX(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO COMPLEX AB(LDAB,*), BB(LDBB,*), Q(LDQ,*), Z(LDZ,*), WORK(*) INTEGER N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO INTEGER IWORK(*), IFAIL(*) REAL VL, VU, ABSTOL REAL W(*), RWORK(*) SUBROUTINE CHBGVX_64(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO COMPLEX AB(LDAB,*), BB(LDBB,*), Q(LDQ,*), Z(LDZ,*), WORK(*) INTEGER*8 N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO INTEGER*8 IWORK(*), IFAIL(*) REAL VL, VU, ABSTOL REAL W(*), RWORK(*) F95 INTERFACE SUBROUTINE HBGVX(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: AB, BB, Q, Z INTEGER :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO INTEGER, DIMENSION(:) :: IWORK, IFAIL REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: W, RWORK SUBROUTINE HBGVX_64(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: AB, BB, Q, Z INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO INTEGER(8), DIMENSION(:) :: IWORK, IFAIL REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: W, RWORK C INTERFACE #include <sunperf.h> void chbgvx(char jobz, char range, char uplo, int n, int ka, int kb, complex *ab, int ldab, complex *bb, int ldbb, complex *q, int ldq, float vl, float vu, int il, int iu, float abstol, int *m, float *w, complex *z, int ldz, int *ifail, int *info); void chbgvx_64(char jobz, char range, char uplo, long n, long ka, long kb, complex *ab, long ldab, complex *bb, long ldbb, complex *q, long ldq, float vl, float vu, long il, long iu, float abstol, long *m, float *w, complex *z, long ldz, long *ifail, long *info); PURPOSE chbgvx 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. Eigenvalues and eigenvectors can be selected by specifying either all eigenvalues, a range of values or a range of indices for the desired eigenvalues. ARGUMENTS JOBZ (input) = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. RANGE (input) = 'A': all eigenvalues will be found; = 'V': all eigenvalues in the half-open interval (VL,VU] will be found; = 'I': the IL-th through IU-th eigenvalues will be found. 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. Q (output) If JOBZ = 'V', the n-by-n matrix used in the reduction of A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, and consequently C to tridiagonal form. If JOBZ = 'N', the array Q is not referenced. LDQ (input) The leading dimension of the array Q. If JOBZ = 'N', LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N). VL (input) If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. VU (input) If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'. IL (input) If RANGE='I', the indices (in ascending order) of the small- est and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. IU (input) If RANGE='I', the indices (in ascending order) of the small- est and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'. ABSTOL (input) The absolute error tolerance for the eigenvalues. An approx- imate eigenvalue is accepted as converged when it is deter- mined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( |a|,|b| ) , where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing AP to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2*SLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*SLAMCH('S'). M (output) The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+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) dimension(N) RWORK (workspace) dimension(7*N) IWORK (workspace) dimension(5*N) IFAIL (output) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced. 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: then i eigenvectors failed to converge. Their indices are stored in array IFAIL. > 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 chbgvx(3P)