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---
:name: zhpsv
:md5sum: 0713716e5e44cdc4522b3e60e4cd557d
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- ap:
:type: doublecomplex
:intent: input/output
:dims:
- n*(n+1)/2
- ipiv:
:type: integer
:intent: output
:dims:
- n
- b:
:type: doublecomplex
:intent: input/output
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions:
n: ldb
:fortran_help: " SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZHPSV computes the solution to a complex system of linear equations\n\
* A * X = B,\n\
* where A is an N-by-N Hermitian matrix stored in packed format and X\n\
* and B are N-by-NRHS 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, D is Hermitian and block diagonal with 1-by-1\n\
* and 2-by-2 diagonal blocks. The factored form of A is then used to\n\
* 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\
* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)\n\
* On entry, the upper or lower triangle of the Hermitian matrix\n\
* A, packed columnwise in a linear array. The j-th column of A\n\
* is stored in the array AP as follows:\n\
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.\n\
* See below for further details.\n\
*\n\
* On exit, the block diagonal matrix D and the multipliers used\n\
* to obtain the factor U or L from the factorization\n\
* A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as\n\
* a packed triangular matrix in the same storage format as A.\n\
*\n\
* IPIV (output) INTEGER array, dimension (N)\n\
* Details of the interchanges and the block structure of D, as\n\
* determined by ZHPTRF. 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\
* 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\n\
* computed.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The packed storage scheme is illustrated by the following example\n\
* when N = 4, UPLO = 'U':\n\
*\n\
* Two-dimensional storage of the Hermitian matrix A:\n\
*\n\
* a11 a12 a13 a14\n\
* a22 a23 a24\n\
* a33 a34 (aij = conjg(aji))\n\
* a44\n\
*\n\
* Packed storage of the upper triangle of A:\n\
*\n\
* AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]\n\
*\n\
* =====================================================================\n\
*\n\
* .. External Functions ..\n LOGICAL LSAME\n EXTERNAL LSAME\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL XERBLA, ZHPTRF, ZHPTRS\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
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