zhbgst - problem A*x=lambda*B*x to standard form C*y=lambda*y, such that C has the same bandwidth as A
SUBROUTINE ZHBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO) CHARACTER*1 VECT, UPLO DOUBLE COMPLEX AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*) INTEGER N, KA, KB, LDAB, LDBB, LDX, INFO DOUBLE PRECISION RWORK(*) SUBROUTINE ZHBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO) CHARACTER*1 VECT, UPLO DOUBLE COMPLEX AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*) INTEGER*8 N, KA, KB, LDAB, LDBB, LDX, INFO DOUBLE PRECISION RWORK(*) F95 INTERFACE SUBROUTINE HBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO) CHARACTER(LEN=1) :: VECT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: AB, BB, X INTEGER :: N, KA, KB, LDAB, LDBB, LDX, INFO REAL(8), DIMENSION(:) :: RWORK SUBROUTINE HBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO) CHARACTER(LEN=1) :: VECT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: AB, BB, X INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDX, INFO REAL(8), DIMENSION(:) :: RWORK C INTERFACE #include <sunperf.h> void zhbgst(char vect, char uplo, int n, int ka, int kb, doublecomplex *ab, int ldab, doublecomplex *bb, int ldbb, doublecomplex *x, int ldx, int *info); void zhbgst_64(char vect, char uplo, long n, long ka, long kb, double- complex *ab, long ldab, doublecomplex *bb, long ldbb, double- complex *x, long ldx, long *info);
Oracle Solaris Studio Performance Library zhbgst(3P) NAME zhbgst - reduce a complex Hermitian-definite banded generalized eigen- problem A*x=lambda*B*x to standard form C*y=lambda*y, such that C has the same bandwidth as A SYNOPSIS SUBROUTINE ZHBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO) CHARACTER*1 VECT, UPLO DOUBLE COMPLEX AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*) INTEGER N, KA, KB, LDAB, LDBB, LDX, INFO DOUBLE PRECISION RWORK(*) SUBROUTINE ZHBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO) CHARACTER*1 VECT, UPLO DOUBLE COMPLEX AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*) INTEGER*8 N, KA, KB, LDAB, LDBB, LDX, INFO DOUBLE PRECISION RWORK(*) F95 INTERFACE SUBROUTINE HBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO) CHARACTER(LEN=1) :: VECT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: AB, BB, X INTEGER :: N, KA, KB, LDAB, LDBB, LDX, INFO REAL(8), DIMENSION(:) :: RWORK SUBROUTINE HBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO) CHARACTER(LEN=1) :: VECT, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: AB, BB, X INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDX, INFO REAL(8), DIMENSION(:) :: RWORK C INTERFACE #include <sunperf.h> void zhbgst(char vect, char uplo, int n, int ka, int kb, doublecomplex *ab, int ldab, doublecomplex *bb, int ldbb, doublecomplex *x, int ldx, int *info); void zhbgst_64(char vect, char uplo, long n, long ka, long kb, double- complex *ab, long ldab, doublecomplex *bb, long ldbb, double- complex *x, long ldx, long *info); PURPOSE zhbgst reduces a complex Hermitian-definite banded generalized eigen- problem A*x = lambda*B*x to standard form C*y = lambda*y, such that C has the same bandwidth as A. B must have been previously factorized as S**H*S by CPBSTF, using a split Cholesky factorization. A is overwritten by C = X**H*A*X, where X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the bandwidth of A. ARGUMENTS VECT (input) = 'N': do not form the transformation matrix X; = 'V': form X. UPLO (input) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is 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'. KA >= 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 transformed matrix X**H*A*X, stored in the same format as A. LDAB (input) The leading dimension of the array AB. LDAB >= KA+1. BB (input) The banded factor S from the split Cholesky factorization of B, as returned by CPBSTF, stored in the first kb+1 rows of the array. LDBB (input) The leading dimension of the array BB. LDBB >= KB+1. X (output) If VECT = 'V', the n-by-n matrix X. If VECT = 'N', the array X is not referenced. LDX (input) The leading dimension of the array X. LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. WORK (workspace) dimension(N) RWORK (workspace) dimension(N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. 7 Nov 2015 zhbgst(3P)