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---
:name: dsygv
:md5sum: 1004f5151de1d6f47d819bbd8507eeaa
:category: :subroutine
:arguments:
- itype:
:type: integer
:intent: input
- jobz:
:type: char
:intent: input
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- b:
:type: doublereal
:intent: input/output
:dims:
- ldb
- n
- ldb:
:type: integer
:intent: input
- w:
:type: doublereal
:intent: output
:dims:
- n
- work:
:type: doublereal
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: 3*n-1
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DSYGV computes all the eigenvalues, and optionally, the eigenvectors\n\
* of a real generalized symmetric-definite eigenproblem, of the form\n\
* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.\n\
* Here A and B are assumed to be symmetric and B is also\n\
* positive definite.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* ITYPE (input) INTEGER\n\
* Specifies the problem type to be solved:\n\
* = 1: A*x = (lambda)*B*x\n\
* = 2: A*B*x = (lambda)*x\n\
* = 3: B*A*x = (lambda)*x\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\
* A (input/output) DOUBLE PRECISION array, dimension (LDA, N)\n\
* On entry, the symmetric matrix A. If UPLO = 'U', the\n\
* leading N-by-N upper triangular part of A contains the\n\
* upper triangular part of the matrix A. If UPLO = 'L',\n\
* the leading N-by-N lower triangular part of A contains\n\
* the lower triangular part of the matrix A.\n\
*\n\
* On exit, if JOBZ = 'V', then if INFO = 0, A contains the\n\
* matrix Z of eigenvectors. The eigenvectors are normalized\n\
* as follows:\n\
* if ITYPE = 1 or 2, Z**T*B*Z = I;\n\
* if ITYPE = 3, Z**T*inv(B)*Z = I.\n\
* If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')\n\
* or the lower triangle (if UPLO='L') of A, including the\n\
* diagonal, is destroyed.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* B (input/output) DOUBLE PRECISION array, dimension (LDB, N)\n\
* On entry, the symmetric positive definite matrix B.\n\
* If UPLO = 'U', the leading N-by-N upper triangular part of B\n\
* contains the upper triangular part of the matrix B.\n\
* If UPLO = 'L', the leading N-by-N lower triangular part of B\n\
* contains the lower triangular part of the matrix B.\n\
*\n\
* On exit, if INFO <= N, the part of B containing the matrix is\n\
* overwritten by the triangular factor U or L from the Cholesky\n\
* factorization B = U**T*U or B = L*L**T.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* W (output) DOUBLE PRECISION array, dimension (N)\n\
* If INFO = 0, the eigenvalues in ascending order.\n\
*\n\
* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))\n\
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.\n\
*\n\
* LWORK (input) INTEGER\n\
* The length of the array WORK. LWORK >= max(1,3*N-1).\n\
* For optimal efficiency, LWORK >= (NB+2)*N,\n\
* where NB is the blocksize for DSYTRD returned by ILAENV.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; the routine\n\
* only calculates the optimal size of the WORK array, returns\n\
* this value as the first entry of the WORK array, and no error\n\
* message related to LWORK is issued by XERBLA.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: DPOTRF or DSYEV returned an error code:\n\
* <= N: if INFO = i, DSYEV 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 the leading\n\
* minor of order i of 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"
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