1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
|
SUBROUTINE SSGT01( ITYPE, UPLO, N, M, A, LDA, B, LDB, Z, LDZ, D,
$ WORK, RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* June 30, 1999
*
* modified August 1997, a new parameter M is added to the calling
* sequence.
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER ITYPE, LDA, LDB, LDZ, M, N
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), D( * ), RESULT( * ),
$ WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* SSGT01 checks a decomposition of the form
*
* A Z = B Z D or
* A B Z = Z D or
* B A Z = Z D
*
* where A is a symmetric matrix, B is
* symmetric positive definite, Z is orthogonal, and D is diagonal.
*
* One of the following test ratios is computed:
*
* ITYPE = 1: RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )
*
* ITYPE = 2: RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )
*
* ITYPE = 3: RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )
*
* Arguments
* =========
*
* ITYPE (input) INTEGER
* The form of the symmetric generalized eigenproblem.
* = 1: A*z = (lambda)*B*z
* = 2: A*B*z = (lambda)*z
* = 3: B*A*z = (lambda)*z
*
* UPLO (input) CHARACTER*1
* Specifies whether the upper or lower triangular part of the
* symmetric matrices A and B is stored.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* M (input) INTEGER
* The number of eigenvalues found. 0 <= M <= N.
*
* A (input) REAL array, dimension (LDA, N)
* The original symmetric matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* B (input) REAL array, dimension (LDB, N)
* The original symmetric positive definite matrix B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* Z (input) REAL array, dimension (LDZ, M)
* The computed eigenvectors of the generalized eigenproblem.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= max(1,N).
*
* D (input) REAL array, dimension (M)
* The computed eigenvalues of the generalized eigenproblem.
*
* WORK (workspace) REAL array, dimension (N*N)
*
* RESULT (output) REAL array, dimension (1)
* The test ratio as described above.
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER I
REAL ANORM, ULP
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE, SLANSY
EXTERNAL SLAMCH, SLANGE, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL SSCAL, SSYMM
* ..
* .. Executable Statements ..
*
RESULT( 1 ) = ZERO
IF( N.LE.0 )
$ RETURN
*
ULP = SLAMCH( 'Epsilon' )
*
* Compute product of 1-norms of A and Z.
*
ANORM = SLANSY( '1', UPLO, N, A, LDA, WORK )*
$ SLANGE( '1', N, M, Z, LDZ, WORK )
IF( ANORM.EQ.ZERO )
$ ANORM = ONE
*
IF( ITYPE.EQ.1 ) THEN
*
* Norm of AZ - BZD
*
CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO,
$ WORK, N )
DO 10 I = 1, M
CALL SSCAL( N, D( I ), Z( 1, I ), 1 )
10 CONTINUE
CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, -ONE,
$ WORK, N )
*
RESULT( 1 ) = ( SLANGE( '1', N, M, WORK, N, WORK ) / ANORM ) /
$ ( N*ULP )
*
ELSE IF( ITYPE.EQ.2 ) THEN
*
* Norm of ABZ - ZD
*
CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, Z, LDZ, ZERO,
$ WORK, N )
DO 20 I = 1, M
CALL SSCAL( N, D( I ), Z( 1, I ), 1 )
20 CONTINUE
CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, WORK, N, -ONE, Z,
$ LDZ )
*
RESULT( 1 ) = ( SLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) /
$ ( N*ULP )
*
ELSE IF( ITYPE.EQ.3 ) THEN
*
* Norm of BAZ - ZD
*
CALL SSYMM( 'Left', UPLO, N, M, ONE, A, LDA, Z, LDZ, ZERO,
$ WORK, N )
DO 30 I = 1, M
CALL SSCAL( N, D( I ), Z( 1, I ), 1 )
30 CONTINUE
CALL SSYMM( 'Left', UPLO, N, M, ONE, B, LDB, WORK, N, -ONE, Z,
$ LDZ )
*
RESULT( 1 ) = ( SLANGE( '1', N, M, Z, LDZ, WORK ) / ANORM ) /
$ ( N*ULP )
END IF
*
RETURN
*
* End of SSGT01
*
END
|
