1ZSYTF2(1) LAPACK routine (version 3.2) ZSYTF2(1)
2
6 ZSYTF2 - computes the factorization of a complex symmetric matrix A
7 using the Bunch-Kaufman diagonal pivoting method
8
10 SUBROUTINE ZSYTF2( UPLO, N, A, LDA, IPIV, INFO )
11 CHARACTER UPLO
13 INTEGER INFO, LDA, N
15 INTEGER IPIV( * )
17 COMPLEX*16 A( LDA, * )
19
21 ZSYTF2 computes the factorization of a complex symmetric matrix A using
22 the Bunch-Kaufman diagonal pivoting method:
23 A = U*D*U' or A = L*D*L'
24 where U (or L) is a product of permutation and unit upper (lower) tri‐
25 angular matrices, U' is the transpose of U, and D is symmetric and
26 block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
27 This is the unblocked version of the algorithm, calling Level 2 BLAS.
28
30 UPLO (input) CHARACTER*1
31 Specifies whether the upper or lower triangular part of the
32 symmetric matrix A is stored:
33 = 'U': Upper triangular
34 = 'L': Lower triangular
35 N (input) INTEGER
37 The order of the matrix A. N >= 0.
38 A (input/output) COMPLEX*16 array, dimension (LDA,N)
40 On entry, the symmetric matrix A. If UPLO = 'U', the leading
41 n-by-n upper triangular part of A contains the upper triangular
42 part of the matrix A, and the strictly lower triangular part of
43 A is not referenced. If UPLO = 'L', the leading n-by-n lower
44 triangular part of A contains the lower triangular part of the
45 matrix A, and the strictly upper triangular part of A is not
46 referenced. On exit, the block diagonal matrix D and the mul‐
47 tipliers used to obtain the factor U or L (see below for fur‐
48 ther details).
49 LDA (input) INTEGER
51 The leading dimension of the array A. LDA >= max(1,N).
52 IPIV (output) INTEGER array, dimension (N)
54 Details of the interchanges and the block structure of D. If
55 IPIV(k) > 0, then rows and columns k and IPIV(k) were inter‐
56 changed and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U'
57 and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and
58 -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diag‐
59 onal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then
60 rows and columns k+1 and -IPIV(k) were interchanged and
61 D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
62 INFO (output) INTEGER
64 = 0: successful exit
65 < 0: if INFO = -k, the k-th argument had an illegal value
66 > 0: if INFO = k, D(k,k) is exactly zero. The factorization
67 has been completed, but the block diagonal matrix D is exactly
68 singular, and division by zero will occur if it is used to
69 solve a system of equations.
70
72 09-29-06 - patch from
73 Bobby Cheng, MathWorks
74 Replace l.209 and l.377
75 IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
76 by
77 IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN
78 1-96 - Based on modifications by J. Lewis, Boeing Computer Services
79 Company
80 If UPLO = 'U', then A = U*D*U', where
81 U = P(n)*U(n)* ... *P(k)U(k)* ...,
82 i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1
83 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and
84 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined
85 by IPIV(k), and U(k) is a unit upper triangular matrix, such that if
86 the diagonal block D(k) is of order s (s = 1 or 2), then
87 ( I v 0 ) k-s
88 U(k) = ( 0 I 0 ) s
89 ( 0 0 I ) n-k
90 k-s s n-k
91 If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). If s =
92 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and
93 A(k,k), and v overwrites A(1:k-2,k-1:k).
94 If UPLO = 'L', then A = L*D*L', where
95 L = P(1)*L(1)* ... *P(k)*L(k)* ...,
96 i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n
97 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and
98 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined
99 by IPIV(k), and L(k) is a unit lower triangular matrix, such that if
100 the diagonal block D(k) is of order s (s = 1 or 2), then
101 ( I 0 0 ) k-1
102 L(k) = ( 0 I 0 ) s
103 ( 0 v I ) n-k-s+1
104 k-1 s n-k-s+1
105 If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s =
106 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and
107 A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
108 LAPACK routine (version 3.2) November 2008 ZSYTF2(1)