cpptrf.f (3) - Linux Man Pages
subroutine cpptrf (characterUPLO, integerN, complex, dimension( * )AP, integerINFO)
CPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular.
UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
N is INTEGER The order of the matrix A. N >= 0.
AP is COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A.
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- November 2011
The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U': Two-dimensional storage of the Hermitian matrix A: a11 a12 a13 a14 a22 a23 a24 a33 a34 (aij = conjg(aji)) a44 Packed storage of the upper triangle of A: AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
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