zhpgvd (l)  Linux Manuals
zhpgvd: computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
NAME
ZHPGVD  computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*xSYNOPSIS
 SUBROUTINE ZHPGVD(
 ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
 CHARACTER JOBZ, UPLO
 INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
 INTEGER IWORK( * )
 DOUBLE PRECISION RWORK( * ), W( * )
 COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
PURPOSE
ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors of a complex generalized Hermitiandefinite 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 XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.
ARGUMENTS
 ITYPE (input) INTEGER

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) CHARACTER*1

= aqNaq: Compute eigenvalues only;
= aqVaq: Compute eigenvalues and eigenvectors.  UPLO (input) CHARACTER*1

= aqUaq: Upper triangles of A and B are stored;
= aqLaq: Lower triangles of A and B are stored.  N (input) INTEGER
 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 jth column of A is stored in the array AP as follows: if UPLO = aqUaq, AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, AP(i + (j1)*(2*nj)/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 jth column of B is stored in the array BP as follows: if UPLO = aqUaq, BP(i + (j1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = aqLaq, BP(i + (j1)*(2*nj)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H, in the same storage format 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 = aqVaq, 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 = aqNaq, then Z is not referenced.
 LDZ (input) INTEGER
 The leading dimension of the array Z. LDZ >= 1, and if JOBZ = aqVaq, LDZ >= max(1,N).
 WORK (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
 On exit, if INFO = 0, WORK(1) returns the required LWORK.
 LWORK (input) INTEGER
 The dimension of array WORK. If N <= 1, LWORK >= 1. If JOBZ = aqNaq and N > 1, LWORK >= N. If JOBZ = aqVaq and N > 1, LWORK >= 2*N. If LWORK = 1, then a workspace query is assumed; the routine only calculates the required sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
 RWORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
 On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
 LRWORK (input) INTEGER
 The dimension of array RWORK. If N <= 1, LRWORK >= 1. If JOBZ = aqNaq and N > 1, LRWORK >= N. If JOBZ = aqVaq and N > 1, LRWORK >= 1 + 5*N + 2*N**2. If LRWORK = 1, then a workspace query is assumed; the routine only calculates the required sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
 IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
 On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
 LIWORK (input) INTEGER
 The dimension of array IWORK. If JOBZ = aqNaq or N <= 1, LIWORK >= 1. If JOBZ = aqVaq and N > 1, LIWORK >= 3 + 5*N. If LIWORK = 1, then a workspace query is assumed; the routine only calculates the required sizes of the WORK, RWORK and IWORK arrays, returns these values as the first entries of the WORK, RWORK and IWORK arrays, and no error message related to LWORK or LRWORK or LIWORK is issued by XERBLA.
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: ZPPTRF or ZHPEVD returned an error code:
<= N: if INFO = i, ZHPEVD failed to converge; i offdiagonal elements of an intermediate tridiagonal form did not convergeto 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 eigenvalues or eigenvectors were computed.
FURTHER DETAILS
Based on contributions byMark Fahey, Department of Mathematics, Univ. of Kentucky, USA