1SLASYF(1) LAPACK routine (version 3.1) SLASYF(1)
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6 SLASYF - a partial factorization of a real symmetric matrix A using the
7 Bunch-Kaufman diagonal pivoting method
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10 SUBROUTINE SLASYF( UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO )
11 CHARACTER UPLO
13 INTEGER INFO, KB, LDA, LDW, N, NB
15 INTEGER IPIV( * )
17 REAL A( LDA, * ), W( LDW, * )
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21 SLASYF computes a partial factorization of a real symmetric matrix A
22 using the Bunch-Kaufman diagonal pivoting method. The partial factor‐
23 ization has the form:
24 A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or:
26 ( 0 U22 ) ( 0 D ) ( U12' U22' )
27 A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L'
29 ( L21 I ) ( 0 A22 ) ( 0 I )
30 where the order of D is at most NB. The actual order is returned in the
32 argument KB, and is either NB or NB-1, or N if N <= NB.
33 SLASYF is an auxiliary routine called by SSYTRF. It uses blocked code
35 (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
36 A22 (if UPLO = 'L').
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40 UPLO (input) CHARACTER*1
41 Specifies whether the upper or lower triangular part of the
42 symmetric matrix A is stored:
43 = 'U': Upper triangular
44 = 'L': Lower triangular
45 N (input) INTEGER
47 The order of the matrix A. N >= 0.
48 NB (input) INTEGER
50 The maximum number of columns of the matrix A that should be
51 factored. NB should be at least 2 to allow for 2-by-2 pivot
52 blocks.
53 KB (output) INTEGER
55 The number of columns of A that were actually factored. KB is
56 either NB-1 or NB, or N if N <= NB.
57 A (input/output) REAL array, dimension (LDA,N)
59 On entry, the symmetric matrix A. If UPLO = 'U', the leading
60 n-by-n upper triangular part of A contains the upper triangular
61 part of the matrix A, and the strictly lower triangular part of
62 A is not referenced. If UPLO = 'L', the leading n-by-n lower
63 triangular part of A contains the lower triangular part of the
64 matrix A, and the strictly upper triangular part of A is not
65 referenced. On exit, A contains details of the partial factor‐
66 ization.
67 LDA (input) INTEGER
69 The leading dimension of the array A. LDA >= max(1,N).
70 IPIV (output) INTEGER array, dimension (N)
72 Details of the interchanges and the block structure of D. If
73 UPLO = 'U', only the last KB elements of IPIV are set; if UPLO
74 = 'L', only the first KB elements are set.
75 If IPIV(k) > 0, then rows and columns k and IPIV(k) were inter‐
77 changed and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U'
78 and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and
79 -IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diag‐
80 onal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then
81 rows and columns k+1 and -IPIV(k) were interchanged and
82 D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
83 W (workspace) REAL array, dimension (LDW,NB)
85 LDW (input) INTEGER
87 The leading dimension of the array W. LDW >= max(1,N).
88 INFO (output) INTEGER
90 = 0: successful exit
91 > 0: if INFO = k, D(k,k) is exactly zero. The factorization
92 has been completed, but the block diagonal matrix D is exactly
93 singular.
94 LAPACK routine (version 3.1) November 2006 SLASYF(1)