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---
:name: dpptrf
:md5sum: 114d74d68f2338940fdfcbbc9fe314c0
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ap:
:type: doublereal
:intent: input/output
:dims:
- n*(n+1)/2
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DPPTRF( UPLO, N, AP, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DPPTRF computes the Cholesky factorization of a real symmetric\n\
* positive definite matrix A stored in packed format.\n\
*\n\
* The factorization has the form\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 lower triangular.\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 order of the matrix A. N >= 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 triangular factor U or L from the\n\
* Cholesky factorization A = U**T*U or A = L*L**T, in the same\n\
* storage format as A.\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 is not\n\
* positive definite, and the factorization could not be\n\
* completed.\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 = 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"
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