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---
:name: zhbgv
:md5sum: 53ed0c8a2fa947bd3a711b8a8c2025f0
:category: :subroutine
:arguments:
- jobz:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ka:
:type: integer
:intent: input
- kb:
:type: integer
:intent: input
- ab:
:type: doublecomplex
:intent: input/output
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- bb:
:type: doublecomplex
:intent: input/output
:dims:
- ldbb
- n
- ldbb:
:type: integer
:intent: input
- w:
:type: doublereal
:intent: output
:dims:
- n
- z:
:type: doublecomplex
:intent: output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- work:
:type: doublecomplex
:intent: workspace
:dims:
- n
- rwork:
:type: doublereal
:intent: workspace
:dims:
- 3*n
- info:
:type: integer
:intent: output
:substitutions:
ldz: "lsame_(&jobz,\"V\") ? n : 1"
:fortran_help: " SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZHBGV computes all the eigenvalues, and optionally, the eigenvectors\n\
* of a complex generalized Hermitian-definite banded eigenproblem, of\n\
* the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian\n\
* and banded, and B is also positive definite.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* JOBZ (input) CHARACTER*1\n\
* = 'N': Compute eigenvalues only;\n\
* = 'V': Compute eigenvalues and eigenvectors.\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangles of A and B are stored;\n\
* = 'L': Lower triangles of A and B are stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrices A and B. N >= 0.\n\
*\n\
* KA (input) INTEGER\n\
* The number of superdiagonals of the matrix A if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KA >= 0.\n\
*\n\
* KB (input) INTEGER\n\
* The number of superdiagonals of the matrix B if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KB >= 0.\n\
*\n\
* AB (input/output) COMPLEX*16 array, dimension (LDAB, N)\n\
* On entry, the upper or lower triangle of the Hermitian band\n\
* matrix A, stored in the first ka+1 rows of the array. The\n\
* j-th column of A is stored in the j-th column of the array AB\n\
* as follows:\n\
* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;\n\
* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).\n\
*\n\
* On exit, the contents of AB are destroyed.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KA+1.\n\
*\n\
* BB (input/output) COMPLEX*16 array, dimension (LDBB, N)\n\
* On entry, the upper or lower triangle of the Hermitian band\n\
* matrix B, stored in the first kb+1 rows of the array. The\n\
* j-th column of B is stored in the j-th column of the array BB\n\
* as follows:\n\
* if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;\n\
* if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).\n\
*\n\
* On exit, the factor S from the split Cholesky factorization\n\
* B = S**H*S, as returned by ZPBSTF.\n\
*\n\
* LDBB (input) INTEGER\n\
* The leading dimension of the array BB. LDBB >= KB+1.\n\
*\n\
* W (output) DOUBLE PRECISION array, dimension (N)\n\
* If INFO = 0, the eigenvalues in ascending order.\n\
*\n\
* Z (output) COMPLEX*16 array, dimension (LDZ, N)\n\
* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of\n\
* eigenvectors, with the i-th column of Z holding the\n\
* eigenvector associated with W(i). The eigenvectors are\n\
* normalized so that Z**H*B*Z = I.\n\
* If JOBZ = 'N', then Z is not referenced.\n\
*\n\
* LDZ (input) INTEGER\n\
* The leading dimension of the array Z. LDZ >= 1, and if\n\
* JOBZ = 'V', LDZ >= N.\n\
*\n\
* WORK (workspace) COMPLEX*16 array, dimension (N)\n\
*\n\
* RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: if INFO = i, and i is:\n\
* <= N: the algorithm failed to converge:\n\
* i off-diagonal elements of an intermediate\n\
* tridiagonal form did not converge to zero;\n\
* > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF\n\
* returned INFO = i: B is not positive definite.\n\
* The factorization of B could not be completed and\n\
* no eigenvalues or eigenvectors were computed.\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL UPPER, WANTZ\n CHARACTER VECT\n INTEGER IINFO, INDE, INDWRK\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n EXTERNAL LSAME\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL DSTERF, XERBLA, ZHBGST, ZHBTRD, ZPBSTF, ZSTEQR\n\
* ..\n"
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