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LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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subroutine chpgvd | ( | integer | itype, |
character | jobz, | ||
character | uplo, | ||
integer | n, | ||
complex, dimension( * ) | ap, | ||
complex, dimension( * ) | bp, | ||
real, dimension( * ) | w, | ||
complex, dimension( ldz, * ) | z, | ||
integer | ldz, | ||
complex, dimension( * ) | work, | ||
integer | lwork, | ||
real, dimension( * ) | rwork, | ||
integer | lrwork, | ||
integer, dimension( * ) | iwork, | ||
integer | liwork, | ||
integer | info ) |
CHPGVD
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!> !> CHPGVD 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. !> !>
[in] | ITYPE | !> ITYPE is 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 !> |
[in] | JOBZ | !> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !> |
[in] | UPLO | !> UPLO is CHARACTER*1 !> = 'U': Upper triangles of A and B are stored; !> = 'L': Lower triangles of A and B are stored. !> |
[in] | N | !> N is INTEGER !> The order of the matrices A and B. N >= 0. !> |
[in,out] | AP | !> AP is COMPLEX 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. !> |
[in,out] | BP | !> BP is COMPLEX 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 !> factorization B = U**H*U or B = L*L**H, in the same storage !> format as B. !> |
[out] | W | !> W is REAL array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !> |
[out] | Z | !> Z is COMPLEX 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. !> |
[in] | LDZ | !> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1, and if !> JOBZ = 'V', LDZ >= max(1,N). !> |
[out] | WORK | !> WORK is COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the required LWORK. !> |
[in] | LWORK | !> LWORK is INTEGER !> 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 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. !> |
[out] | RWORK | !> RWORK is REAL array, dimension (MAX(1,LRWORK)) !> On exit, if INFO = 0, RWORK(1) returns the required LRWORK. !> |
[in] | LRWORK | !> LRWORK is INTEGER !> 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 !> 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. !> |
[out] | IWORK | !> IWORK is INTEGER array, dimension (MAX(1,LIWORK)) !> On exit, if INFO = 0, IWORK(1) returns the required LIWORK. !> |
[in] | LIWORK | !> LIWORK is INTEGER !> 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 !> 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. !> |
[out] | INFO | !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: CPPTRF or CHPEVD returned an error code: !> <= N: if INFO = i, CHPEVD failed to converge; !> i off-diagonal elements of an intermediate !> tridiagonal form did not convergeto zero; !> > N: if INFO = N + i, for 1 <= i <= n, then the leading !> principal minor of order i of B is not positive. !> The factorization of B could not be completed and !> no eigenvalues or eigenvectors were computed. !> |
Definition at line 221 of file chpgvd.f.