Mercurial > octave-nkf
annotate libcruft/lapack/ssytrd.f @ 7789:82be108cc558
First attempt at single precision tyeps
* * *
corrections to qrupdate single precision routines
* * *
prefer demotion to single over promotion to double
* * *
Add single precision support to log2 function
* * *
Trivial PROJECT file update
* * *
Cache optimized hermitian/transpose methods
* * *
Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author | David Bateman <dbateman@free.fr> |
---|---|
date | Sun, 27 Apr 2008 22:34:17 +0200 |
parents | |
children |
rev | line source |
---|---|
7789
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
1 SUBROUTINE SSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
2 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
3 * -- LAPACK routine (version 3.1) -- |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
5 * November 2006 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
6 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
7 * .. Scalar Arguments .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
8 CHARACTER UPLO |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
9 INTEGER INFO, LDA, LWORK, N |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
10 * .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
11 * .. Array Arguments .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
12 REAL A( LDA, * ), D( * ), E( * ), TAU( * ), |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
13 $ WORK( * ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
14 * .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
15 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
16 * Purpose |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
17 * ======= |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
18 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
19 * SSYTRD reduces a real symmetric matrix A to real symmetric |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
20 * tridiagonal form T by an orthogonal similarity transformation: |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
21 * Q**T * A * Q = T. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
22 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
23 * Arguments |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
24 * ========= |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
25 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
26 * UPLO (input) CHARACTER*1 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
27 * = 'U': Upper triangle of A is stored; |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
28 * = 'L': Lower triangle of A is stored. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
29 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
30 * N (input) INTEGER |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
31 * The order of the matrix A. N >= 0. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
32 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
33 * A (input/output) REAL array, dimension (LDA,N) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
34 * On entry, the symmetric matrix A. If UPLO = 'U', the leading |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
35 * N-by-N upper triangular part of A contains the upper |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
36 * triangular part of the matrix A, and the strictly lower |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
37 * triangular part of A is not referenced. If UPLO = 'L', the |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
38 * leading N-by-N lower triangular part of A contains the lower |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
39 * triangular part of the matrix A, and the strictly upper |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
40 * triangular part of A is not referenced. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
41 * On exit, if UPLO = 'U', the diagonal and first superdiagonal |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
42 * of A are overwritten by the corresponding elements of the |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
43 * tridiagonal matrix T, and the elements above the first |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
44 * superdiagonal, with the array TAU, represent the orthogonal |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
45 * matrix Q as a product of elementary reflectors; if UPLO |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
46 * = 'L', the diagonal and first subdiagonal of A are over- |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
47 * written by the corresponding elements of the tridiagonal |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
48 * matrix T, and the elements below the first subdiagonal, with |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
49 * the array TAU, represent the orthogonal matrix Q as a product |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
50 * of elementary reflectors. See Further Details. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
51 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
52 * LDA (input) INTEGER |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
53 * The leading dimension of the array A. LDA >= max(1,N). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
54 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
55 * D (output) REAL array, dimension (N) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
56 * The diagonal elements of the tridiagonal matrix T: |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
57 * D(i) = A(i,i). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
58 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
59 * E (output) REAL array, dimension (N-1) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
60 * The off-diagonal elements of the tridiagonal matrix T: |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
61 * E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
62 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
63 * TAU (output) REAL array, dimension (N-1) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
64 * The scalar factors of the elementary reflectors (see Further |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
65 * Details). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
66 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
67 * WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
68 * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
69 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
70 * LWORK (input) INTEGER |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
71 * The dimension of the array WORK. LWORK >= 1. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
72 * For optimum performance LWORK >= N*NB, where NB is the |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
73 * optimal blocksize. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
74 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
75 * If LWORK = -1, then a workspace query is assumed; the routine |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
76 * only calculates the optimal size of the WORK array, returns |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
77 * this value as the first entry of the WORK array, and no error |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
78 * message related to LWORK is issued by XERBLA. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
79 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
80 * INFO (output) INTEGER |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
81 * = 0: successful exit |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
82 * < 0: if INFO = -i, the i-th argument had an illegal value |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
83 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
84 * Further Details |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
85 * =============== |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
86 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
87 * If UPLO = 'U', the matrix Q is represented as a product of elementary |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
88 * reflectors |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
89 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
90 * Q = H(n-1) . . . H(2) H(1). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
91 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
92 * Each H(i) has the form |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
93 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
94 * H(i) = I - tau * v * v' |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
95 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
96 * where tau is a real scalar, and v is a real vector with |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
97 * v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
98 * A(1:i-1,i+1), and tau in TAU(i). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
99 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
100 * If UPLO = 'L', the matrix Q is represented as a product of elementary |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
101 * reflectors |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
102 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
103 * Q = H(1) H(2) . . . H(n-1). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
104 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
105 * Each H(i) has the form |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
106 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
107 * H(i) = I - tau * v * v' |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
108 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
109 * where tau is a real scalar, and v is a real vector with |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
110 * v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
111 * and tau in TAU(i). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
112 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
113 * The contents of A on exit are illustrated by the following examples |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
114 * with n = 5: |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
115 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
116 * if UPLO = 'U': if UPLO = 'L': |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
117 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
118 * ( d e v2 v3 v4 ) ( d ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
119 * ( d e v3 v4 ) ( e d ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
120 * ( d e v4 ) ( v1 e d ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
121 * ( d e ) ( v1 v2 e d ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
122 * ( d ) ( v1 v2 v3 e d ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
123 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
124 * where d and e denote diagonal and off-diagonal elements of T, and vi |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
125 * denotes an element of the vector defining H(i). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
126 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
127 * ===================================================================== |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
128 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
129 * .. Parameters .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
130 REAL ONE |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
131 PARAMETER ( ONE = 1.0E+0 ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
132 * .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
133 * .. Local Scalars .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
134 LOGICAL LQUERY, UPPER |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
135 INTEGER I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB, |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
136 $ NBMIN, NX |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
137 * .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
138 * .. External Subroutines .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
139 EXTERNAL SLATRD, SSYR2K, SSYTD2, XERBLA |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
140 * .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
141 * .. Intrinsic Functions .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
142 INTRINSIC MAX |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
143 * .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
144 * .. External Functions .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
145 LOGICAL LSAME |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
146 INTEGER ILAENV |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
147 EXTERNAL LSAME, ILAENV |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
148 * .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
149 * .. Executable Statements .. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
150 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
151 * Test the input parameters |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
152 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
153 INFO = 0 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
154 UPPER = LSAME( UPLO, 'U' ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
155 LQUERY = ( LWORK.EQ.-1 ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
156 IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
157 INFO = -1 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
158 ELSE IF( N.LT.0 ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
159 INFO = -2 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
160 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
161 INFO = -4 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
162 ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
163 INFO = -9 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
164 END IF |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
165 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
166 IF( INFO.EQ.0 ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
167 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
168 * Determine the block size. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
169 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
170 NB = ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
171 LWKOPT = N*NB |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
172 WORK( 1 ) = LWKOPT |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
173 END IF |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
174 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
175 IF( INFO.NE.0 ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
176 CALL XERBLA( 'SSYTRD', -INFO ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
177 RETURN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
178 ELSE IF( LQUERY ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
179 RETURN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
180 END IF |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
181 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
182 * Quick return if possible |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
183 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
184 IF( N.EQ.0 ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
185 WORK( 1 ) = 1 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
186 RETURN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
187 END IF |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
188 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
189 NX = N |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
190 IWS = 1 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
191 IF( NB.GT.1 .AND. NB.LT.N ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
192 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
193 * Determine when to cross over from blocked to unblocked code |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
194 * (last block is always handled by unblocked code). |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
195 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
196 NX = MAX( NB, ILAENV( 3, 'SSYTRD', UPLO, N, -1, -1, -1 ) ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
197 IF( NX.LT.N ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
198 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
199 * Determine if workspace is large enough for blocked code. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
200 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
201 LDWORK = N |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
202 IWS = LDWORK*NB |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
203 IF( LWORK.LT.IWS ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
204 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
205 * Not enough workspace to use optimal NB: determine the |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
206 * minimum value of NB, and reduce NB or force use of |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
207 * unblocked code by setting NX = N. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
208 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
209 NB = MAX( LWORK / LDWORK, 1 ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
210 NBMIN = ILAENV( 2, 'SSYTRD', UPLO, N, -1, -1, -1 ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
211 IF( NB.LT.NBMIN ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
212 $ NX = N |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
213 END IF |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
214 ELSE |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
215 NX = N |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
216 END IF |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
217 ELSE |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
218 NB = 1 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
219 END IF |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
220 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
221 IF( UPPER ) THEN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
222 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
223 * Reduce the upper triangle of A. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
224 * Columns 1:kk are handled by the unblocked method. |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
225 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
226 KK = N - ( ( N-NX+NB-1 ) / NB )*NB |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
227 DO 20 I = N - NB + 1, KK + 1, -NB |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
228 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
229 * Reduce columns i:i+nb-1 to tridiagonal form and form the |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
230 * matrix W which is needed to update the unreduced part of |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
231 * the matrix |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
232 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
233 CALL SLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK, |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
234 $ LDWORK ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
235 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
236 * Update the unreduced submatrix A(1:i-1,1:i-1), using an |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
237 * update of the form: A := A - V*W' - W*V' |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
238 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
239 CALL SSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ), |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
240 $ LDA, WORK, LDWORK, ONE, A, LDA ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
241 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
242 * Copy superdiagonal elements back into A, and diagonal |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
243 * elements into D |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
244 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
245 DO 10 J = I, I + NB - 1 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
246 A( J-1, J ) = E( J-1 ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
247 D( J ) = A( J, J ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
248 10 CONTINUE |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
249 20 CONTINUE |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
250 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
251 * Use unblocked code to reduce the last or only block |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
252 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
253 CALL SSYTD2( UPLO, KK, A, LDA, D, E, TAU, IINFO ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
254 ELSE |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
255 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
256 * Reduce the lower triangle of A |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
257 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
258 DO 40 I = 1, N - NX, NB |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
259 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
260 * Reduce columns i:i+nb-1 to tridiagonal form and form the |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
261 * matrix W which is needed to update the unreduced part of |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
262 * the matrix |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
263 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
264 CALL SLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ), |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
265 $ TAU( I ), WORK, LDWORK ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
266 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
267 * Update the unreduced submatrix A(i+ib:n,i+ib:n), using |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
268 * an update of the form: A := A - V*W' - W*V' |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
269 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
270 CALL SSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE, |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
271 $ A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE, |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
272 $ A( I+NB, I+NB ), LDA ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
273 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
274 * Copy subdiagonal elements back into A, and diagonal |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
275 * elements into D |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
276 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
277 DO 30 J = I, I + NB - 1 |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
278 A( J+1, J ) = E( J ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
279 D( J ) = A( J, J ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
280 30 CONTINUE |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
281 40 CONTINUE |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
282 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
283 * Use unblocked code to reduce the last or only block |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
284 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
285 CALL SSYTD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ), |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
286 $ TAU( I ), IINFO ) |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
287 END IF |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
288 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
289 WORK( 1 ) = LWKOPT |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
290 RETURN |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
291 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
292 * End of SSYTRD |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
293 * |
82be108cc558
First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents:
diff
changeset
|
294 END |