1CPPTRF(1) LAPACK routine (version 3.2) CPPTRF(1)
2
6 CPPTRF - computes the Cholesky factorization of a complex Hermitian
7 positive definite matrix A stored in packed format
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10 SUBROUTINE CPPTRF( UPLO, N, AP, INFO )
11 CHARACTER UPLO
13 INTEGER INFO, N
15 COMPLEX AP( * )
17
19 CPPTRF computes the Cholesky factorization of a complex Hermitian posi‐
20 tive definite matrix A stored in packed format. The factorization has
21 the form
22 A = U**H * U, if UPLO = 'U', or
23 A = L * L**H, if UPLO = 'L',
24 where U is an upper triangular matrix and L is lower triangular.
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27 UPLO (input) CHARACTER*1
28 = 'U': Upper triangle of A is stored;
29 = 'L': Lower triangle of A is stored.
30 N (input) INTEGER
32 The order of the matrix A. N >= 0.
33 AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
35 On entry, the upper or lower triangle of the Hermitian matrix
36 A, packed columnwise in a linear array. The j-th column of A
37 is stored in the array AP as follows: if UPLO = 'U', AP(i +
38 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
39 (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further
40 details. On exit, if INFO = 0, the triangular factor U or L
41 from the Cholesky factorization A = U**H*U or A = L*L**H, in
42 the same storage format as A.
43 INFO (output) INTEGER
45 = 0: successful exit
46 < 0: if INFO = -i, the i-th argument had an illegal value
47 > 0: if INFO = i, the leading minor of order i is not positive
48 definite, and the factorization could not be completed.
49
51 The packed storage scheme is illustrated by the following example when
52 N = 4, UPLO = 'U':
53 Two-dimensional storage of the Hermitian matrix A:
54 a11 a12 a13 a14
55 a22 a23 a24
56 a33 a34 (aij = conjg(aji))
57 a44
58 Packed storage of the upper triangle of A:
59 AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
60 LAPACK routine (version 3.2) November 2008 CPPTRF(1)