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---
:name: dppsv
:md5sum: 05812066fff4498bbd8b9748ba91010d
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- ap:
:type: doublereal
:intent: input/output
:dims:
- n*(n+1)/2
- b:
:type: doublereal
:intent: input/output
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DPPSV computes the solution to a real system of linear equations\n\
* A * X = B,\n\
* where A is an N-by-N symmetric positive definite matrix stored in\n\
* packed format and X and B are N-by-NRHS matrices.\n\
*\n\
* The Cholesky decomposition is used to factor A as\n\
* A = U**T* U, if UPLO = 'U', or\n\
* A = L * L**T, if UPLO = 'L',\n\
* where U is an upper triangular matrix and L is a lower triangular\n\
* matrix. The factored form of A is then used to solve the system of\n\
* 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) DOUBLE PRECISION array, dimension (N*(N+1)/2)\n\
* On entry, the upper or lower triangle of the symmetric 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, if INFO = 0, the factor U or L from the Cholesky\n\
* factorization A = U**T*U or A = L*L**T, in the same storage\n\
* format as A.\n\
*\n\
* B (input/output) DOUBLE PRECISION 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, the leading minor of order i of A is not\n\
* positive definite, so the factorization could not be\n\
* completed, and the solution has not been 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 symmetric 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 DPPTRF, DPPTRS, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
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