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---
:name: zhesv
:md5sum: e745a4fbd2863ca527128103dc22130f
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- a:
:type: doublecomplex
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- ipiv:
:type: integer
:intent: output
:dims:
- n
- b:
:type: doublecomplex
:intent: input/output
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- work:
:type: doublecomplex
:intent: output
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE ZHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZHESV computes the solution to a complex system of linear equations\n\
* A * X = B,\n\
* where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS\n\
* matrices.\n\
*\n\
* The diagonal pivoting method is used to factor A as\n\
* A = U * D * U**H, if UPLO = 'U', or\n\
* A = L * D * L**H, if UPLO = 'L',\n\
* where U (or L) is a product of permutation and unit upper (lower)\n\
* triangular matrices, and D is Hermitian and block diagonal with\n\
* 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then\n\
* used to solve the system of equations A * X = B.\n\
*\n\n\
* Arguments\n\
* =========\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 number of linear equations, i.e., the order of the\n\
* matrix A. N >= 0.\n\
*\n\
* NRHS (input) INTEGER\n\
* The number of right hand sides, i.e., the number of columns\n\
* of the matrix B. NRHS >= 0.\n\
*\n\
* A (input/output) COMPLEX*16 array, dimension (LDA,N)\n\
* On entry, the Hermitian matrix A. If UPLO = 'U', the leading\n\
* N-by-N upper triangular part of A contains the upper\n\
* triangular part of the matrix A, and the strictly lower\n\
* triangular part of A is not referenced. If UPLO = 'L', the\n\
* leading N-by-N lower triangular part of A contains the lower\n\
* triangular part of the matrix A, and the strictly upper\n\
* triangular part of A is not referenced.\n\
*\n\
* On exit, if INFO = 0, the block diagonal matrix D and the\n\
* multipliers used to obtain the factor U or L from the\n\
* factorization A = U*D*U**H or A = L*D*L**H as computed by\n\
* ZHETRF.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* IPIV (output) INTEGER array, dimension (N)\n\
* Details of the interchanges and the block structure of D, as\n\
* determined by ZHETRF. If IPIV(k) > 0, then rows and columns\n\
* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1\n\
* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,\n\
* then rows and columns k-1 and -IPIV(k) were interchanged and\n\
* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and\n\
* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and\n\
* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2\n\
* diagonal block.\n\
*\n\
* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)\n\
* On entry, the N-by-NRHS right hand side matrix B.\n\
* On exit, if INFO = 0, the N-by-NRHS solution matrix X.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* WORK (workspace/output) COMPLEX*16 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 WORK. LWORK >= 1, and for best performance\n\
* LWORK >= max(1,N*NB), where NB is the optimal blocksize for\n\
* ZHETRF.\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: if INFO = i, D(i,i) is exactly zero. The factorization\n\
* has been completed, but the block diagonal matrix D is\n\
* exactly singular, so the solution could not be computed.\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL LQUERY\n INTEGER LWKOPT, NB\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n INTEGER ILAENV\n EXTERNAL LSAME, ILAENV\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL XERBLA, ZHETRF, ZHETRS2\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
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