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---
:name: zhbgst
:md5sum: b25f0a732a0eebdab26f937666828130
:category: :subroutine
:arguments:
- vect:
: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
:dims:
- ldbb
- n
- ldbb:
:type: integer
:intent: input
- x:
:type: doublecomplex
:intent: output
:dims:
- ldx
- n
- ldx:
:type: integer
:intent: input
- work:
:type: doublecomplex
:intent: workspace
:dims:
- n
- rwork:
:type: doublereal
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions:
ldx: "lsame_(&vect,\"V\") ? MAX(1,n) : 1"
:fortran_help: " SUBROUTINE ZHBGST( VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZHBGST reduces a complex Hermitian-definite banded generalized\n\
* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y,\n\
* such that C has the same bandwidth as A.\n\
*\n\
* B must have been previously factorized as S**H*S by ZPBSTF, using a\n\
* split Cholesky factorization. A is overwritten by C = X**H*A*X, where\n\
* X = S**(-1)*Q and Q is a unitary matrix chosen to preserve the\n\
* bandwidth of A.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* VECT (input) CHARACTER*1\n\
* = 'N': do not form the transformation matrix X;\n\
* = 'V': form X.\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of A is stored;\n\
* = 'L': Lower triangle of A is 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'. KA >= 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 transformed matrix X**H*A*X, stored in the same\n\
* format as A.\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KA+1.\n\
*\n\
* BB (input) COMPLEX*16 array, dimension (LDBB,N)\n\
* The banded factor S from the split Cholesky factorization of\n\
* B, as returned by ZPBSTF, stored in the first kb+1 rows of\n\
* the array.\n\
*\n\
* LDBB (input) INTEGER\n\
* The leading dimension of the array BB. LDBB >= KB+1.\n\
*\n\
* X (output) COMPLEX*16 array, dimension (LDX,N)\n\
* If VECT = 'V', the n-by-n matrix X.\n\
* If VECT = 'N', the array X is not referenced.\n\
*\n\
* LDX (input) INTEGER\n\
* The leading dimension of the array X.\n\
* LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise.\n\
*\n\
* WORK (workspace) COMPLEX*16 array, dimension (N)\n\
*\n\
* RWORK (workspace) DOUBLE PRECISION array, dimension (N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value.\n\
*\n\n\
* =====================================================================\n\
*\n"
|
