1ZPBTF2(1) LAPACK routine (version 3.2) ZPBTF2(1)
2
6 ZPBTF2 - computes the Cholesky factorization of a complex Hermitian
7 positive definite band matrix A
8
10 SUBROUTINE ZPBTF2( UPLO, N, KD, AB, LDAB, INFO )
11 CHARACTER UPLO
13 INTEGER INFO, KD, LDAB, N
15 COMPLEX*16 AB( LDAB, * )
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19 ZPBTF2 computes the Cholesky factorization of a complex Hermitian posi‐
20 tive definite band matrix A. The factorization has the form
21 A = U' * U , if UPLO = 'U', or
22 A = L * L', if UPLO = 'L',
23 where U is an upper triangular matrix, U' is the conjugate transpose of
24 U, and L is lower triangular.
25 This is the unblocked version of the algorithm, calling Level 2 BLAS.
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28 UPLO (input) CHARACTER*1
29 Specifies whether the upper or lower triangular part of the
30 Hermitian matrix A is stored:
31 = 'U': Upper triangular
32 = 'L': Lower triangular
33 N (input) INTEGER
35 The order of the matrix A. N >= 0.
36 KD (input) INTEGER
38 The number of super-diagonals of the matrix A if UPLO = 'U', or
39 the number of sub-diagonals if UPLO = 'L'. KD >= 0.
40 AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
42 On entry, the upper or lower triangle of the Hermitian band
43 matrix A, stored in the first KD+1 rows of the array. The j-th
44 column of A is stored in the j-th column of the array AB as
45 follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
46 kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
47 j<=i<=min(n,j+kd). On exit, if INFO = 0, the triangular factor
48 U or L from the Cholesky factorization A = U'*U or A = L*L' of
49 the band matrix A, in the same storage format as A.
50 LDAB (input) INTEGER
52 The leading dimension of the array AB. LDAB >= KD+1.
53 INFO (output) INTEGER
55 = 0: successful exit
56 < 0: if INFO = -k, the k-th argument had an illegal value
57 > 0: if INFO = k, the leading minor of order k is not positive
58 definite, and the factorization could not be completed.
59
61 The band storage scheme is illustrated by the following example, when N
62 = 6, KD = 2, and UPLO = 'U':
63 On entry: On exit:
64 * * a13 a24 a35 a46 * * u13 u24 u35 u46
65 * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
66 a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 Simi‐
67 larly, if UPLO = 'L' the format of A is as follows:
68 On entry: On exit:
69 a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66
70 a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 *
71 a31 a42 a53 a64 * * l31 l42 l53 l64 * * Array
72 elements marked * are not used by the routine.
73 LAPACK routine (version 3.2) November 2008 ZPBTF2(1)