zhpgvd - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SUBROUTINE ZHPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO DOUBLE COMPLEX AP(*), BP(*), Z(LDZ,*), WORK(*) INTEGER ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER IWORK(*) DOUBLE PRECISION W(*), RWORK(*) SUBROUTINE ZHPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO DOUBLE COMPLEX AP(*), BP(*), Z(LDZ,*), WORK(*) INTEGER*8 ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER*8 IWORK(*) DOUBLE PRECISION W(*), RWORK(*) F95 INTERFACE SUBROUTINE HPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX(8), DIMENSION(:) :: AP, BP, WORK COMPLEX(8), DIMENSION(:,:) :: Z INTEGER :: ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: W, RWORK SUBROUTINE HPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX(8), DIMENSION(:) :: AP, BP, WORK COMPLEX(8), DIMENSION(:,:) :: Z INTEGER(8) :: ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: W, RWORK C INTERFACE #include <sunperf.h> void zhpgvd(int itype, char jobz, char uplo, int n, doublecomplex *ap, doublecomplex *bp, double *w, doublecomplex *z, int ldz, int *info); void zhpgvd_64(long itype, char jobz, char uplo, long n, doublecomplex *ap, doublecomplex *bp, double *w, doublecomplex *z, long ldz, long *info);
Oracle Solaris Studio Performance Library zhpgvd(3P) NAME zhpgvd - compute all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x SYNOPSIS SUBROUTINE ZHPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO DOUBLE COMPLEX AP(*), BP(*), Z(LDZ,*), WORK(*) INTEGER ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER IWORK(*) DOUBLE PRECISION W(*), RWORK(*) SUBROUTINE ZHPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER*1 JOBZ, UPLO DOUBLE COMPLEX AP(*), BP(*), Z(LDZ,*), WORK(*) INTEGER*8 ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER*8 IWORK(*) DOUBLE PRECISION W(*), RWORK(*) F95 INTERFACE SUBROUTINE HPGVD(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX(8), DIMENSION(:) :: AP, BP, WORK COMPLEX(8), DIMENSION(:,:) :: Z INTEGER :: ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: W, RWORK SUBROUTINE HPGVD_64(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX(8), DIMENSION(:) :: AP, BP, WORK COMPLEX(8), DIMENSION(:,:) :: Z INTEGER(8) :: ITYPE, N, LDZ, LWORK, LRWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: W, RWORK C INTERFACE #include <sunperf.h> void zhpgvd(int itype, char jobz, char uplo, int n, doublecomplex *ap, doublecomplex *bp, double *w, doublecomplex *z, int ldz, int *info); void zhpgvd_64(long itype, char jobz, char uplo, long n, doublecomplex *ap, doublecomplex *bp, double *w, doublecomplex *z, long ldz, long *info); PURPOSE zhpgvd computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian, stored in packed format, 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 ITYPE (input) Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x 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. AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, the contents of AP are destroyed. BP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky fac- torization B = U**H*U or B = L*L**H, in the same storage for- mat as B. W (output) DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z (output) COMPLEX*16 array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(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 >= max(1,N). WORK (workspace) COMPLEX*16 array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) The dimension of array WORK. If N <= 1, LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= N. If JOBZ = 'V' and N > 1, LWORK >= 2*N. 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) DOUBLE PRECISION array, dimension (LRWORK) 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 >= 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) INTEGER array, dimension (LIWORK) 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: CPPTRF or ZHPEVD returned an error code: <= N: if INFO = i, ZHPEVD failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not con- vergeto zero; > N: if INFO = N + i, for 1 <= i <= n, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigen- values or eigenvectors were computed. FURTHER DETAILS Based on contributions by Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 7 Nov 2015 zhpgvd(3P)