1 SUBROUTINE CLATM6( TYPE, N, A, LDA, B, X, LDX, Y, LDY, ALPHA,
2 $ BETA, WX, WY, S, DIF )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * June 2010
7 *
8 * .. Scalar Arguments ..
9 INTEGER LDA, LDX, LDY, N, TYPE
10 COMPLEX ALPHA, BETA, WX, WY
11 * ..
12 * .. Array Arguments ..
13 REAL DIF( * ), S( * )
14 COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ),
15 $ Y( LDY, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * CLATM6 generates test matrices for the generalized eigenvalue
22 * problem, their corresponding right and left eigenvector matrices,
23 * and also reciprocal condition numbers for all eigenvalues and
24 * the reciprocal condition numbers of eigenvectors corresponding to
25 * the 1th and 5th eigenvalues.
26 *
27 * Test Matrices
28 * =============
29 *
30 * Two kinds of test matrix pairs
31 * (A, B) = inverse(YH) * (Da, Db) * inverse(X)
32 * are used in the tests:
33 *
34 * Type 1:
35 * Da = 1+a 0 0 0 0 Db = 1 0 0 0 0
36 * 0 2+a 0 0 0 0 1 0 0 0
37 * 0 0 3+a 0 0 0 0 1 0 0
38 * 0 0 0 4+a 0 0 0 0 1 0
39 * 0 0 0 0 5+a , 0 0 0 0 1
40 * and Type 2:
41 * Da = 1+i 0 0 0 0 Db = 1 0 0 0 0
42 * 0 1-i 0 0 0 0 1 0 0 0
43 * 0 0 1 0 0 0 0 1 0 0
44 * 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0
45 * 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 .
46 *
47 * In both cases the same inverse(YH) and inverse(X) are used to compute
48 * (A, B), giving the exact eigenvectors to (A,B) as (YH, X):
49 *
50 * YH: = 1 0 -y y -y X = 1 0 -x -x x
51 * 0 1 -y y -y 0 1 x -x -x
52 * 0 0 1 0 0 0 0 1 0 0
53 * 0 0 0 1 0 0 0 0 1 0
54 * 0 0 0 0 1, 0 0 0 0 1 , where
55 *
56 * a, b, x and y will have all values independently of each other.
57 *
58 * Arguments
59 * =========
60 *
61 * TYPE (input) INTEGER
62 * Specifies the problem type (see futher details).
63 *
64 * N (input) INTEGER
65 * Size of the matrices A and B.
66 *
67 * A (output) COMPLEX array, dimension (LDA, N).
68 * On exit A N-by-N is initialized according to TYPE.
69 *
70 * LDA (input) INTEGER
71 * The leading dimension of A and of B.
72 *
73 * B (output) COMPLEX array, dimension (LDA, N).
74 * On exit B N-by-N is initialized according to TYPE.
75 *
76 * X (output) COMPLEX array, dimension (LDX, N).
77 * On exit X is the N-by-N matrix of right eigenvectors.
78 *
79 * LDX (input) INTEGER
80 * The leading dimension of X.
81 *
82 * Y (output) COMPLEX array, dimension (LDY, N).
83 * On exit Y is the N-by-N matrix of left eigenvectors.
84 *
85 * LDY (input) INTEGER
86 * The leading dimension of Y.
87 *
88 * ALPHA (input) COMPLEX
89 *
90 * BETA (input) COMPLEX
91 * Weighting constants for matrix A.
92 *
93 * WX (input) COMPLEX
94 * Constant for right eigenvector matrix.
95 *
96 * WY (input) COMPLEX
97 * Constant for left eigenvector matrix.
98 *
99 * S (output) REAL array, dimension (N)
100 * S(i) is the reciprocal condition number for eigenvalue i.
101 *
102 * DIF (output) REAL array, dimension (N)
103 * DIF(i) is the reciprocal condition number for eigenvector i.
104 *
105 * =====================================================================
106 *
107 * .. Parameters ..
108 REAL RONE, TWO, THREE
109 PARAMETER ( RONE = 1.0E+0, TWO = 2.0E+0, THREE = 3.0E+0 )
110 COMPLEX ZERO, ONE
111 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
112 $ ONE = ( 1.0E+0, 0.0E+0 ) )
113 * ..
114 * .. Local Scalars ..
115 INTEGER I, INFO, J
116 * ..
117 * .. Local Arrays ..
118 REAL RWORK( 50 )
119 COMPLEX WORK( 26 ), Z( 8, 8 )
120 * ..
121 * .. Intrinsic Functions ..
122 INTRINSIC CABS, CMPLX, CONJG, REAL, SQRT
123 * ..
124 * .. External Subroutines ..
125 EXTERNAL CGESVD, CLACPY, CLAKF2
126 * ..
127 * .. Executable Statements ..
128 *
129 * Generate test problem ...
130 * (Da, Db) ...
131 *
132 DO 20 I = 1, N
133 DO 10 J = 1, N
134 *
135 IF( I.EQ.J ) THEN
136 A( I, I ) = CMPLX( I ) + ALPHA
137 B( I, I ) = ONE
138 ELSE
139 A( I, J ) = ZERO
140 B( I, J ) = ZERO
141 END IF
142 *
143 10 CONTINUE
144 20 CONTINUE
145 IF( TYPE.EQ.2 ) THEN
146 A( 1, 1 ) = CMPLX( RONE, RONE )
147 A( 2, 2 ) = CONJG( A( 1, 1 ) )
148 A( 3, 3 ) = ONE
149 A( 4, 4 ) = CMPLX( REAL( ONE+ALPHA ), REAL( ONE+BETA ) )
150 A( 5, 5 ) = CONJG( A( 4, 4 ) )
151 END IF
152 *
153 * Form X and Y
154 *
155 CALL CLACPY( 'F', N, N, B, LDA, Y, LDY )
156 Y( 3, 1 ) = -CONJG( WY )
157 Y( 4, 1 ) = CONJG( WY )
158 Y( 5, 1 ) = -CONJG( WY )
159 Y( 3, 2 ) = -CONJG( WY )
160 Y( 4, 2 ) = CONJG( WY )
161 Y( 5, 2 ) = -CONJG( WY )
162 *
163 CALL CLACPY( 'F', N, N, B, LDA, X, LDX )
164 X( 1, 3 ) = -WX
165 X( 1, 4 ) = -WX
166 X( 1, 5 ) = WX
167 X( 2, 3 ) = WX
168 X( 2, 4 ) = -WX
169 X( 2, 5 ) = -WX
170 *
171 * Form (A, B)
172 *
173 B( 1, 3 ) = WX + WY
174 B( 2, 3 ) = -WX + WY
175 B( 1, 4 ) = WX - WY
176 B( 2, 4 ) = WX - WY
177 B( 1, 5 ) = -WX + WY
178 B( 2, 5 ) = WX + WY
179 A( 1, 3 ) = WX*A( 1, 1 ) + WY*A( 3, 3 )
180 A( 2, 3 ) = -WX*A( 2, 2 ) + WY*A( 3, 3 )
181 A( 1, 4 ) = WX*A( 1, 1 ) - WY*A( 4, 4 )
182 A( 2, 4 ) = WX*A( 2, 2 ) - WY*A( 4, 4 )
183 A( 1, 5 ) = -WX*A( 1, 1 ) + WY*A( 5, 5 )
184 A( 2, 5 ) = WX*A( 2, 2 ) + WY*A( 5, 5 )
185 *
186 * Compute condition numbers
187 *
188 S( 1 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) /
189 $ ( RONE+CABS( A( 1, 1 ) )*CABS( A( 1, 1 ) ) ) )
190 S( 2 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) /
191 $ ( RONE+CABS( A( 2, 2 ) )*CABS( A( 2, 2 ) ) ) )
192 S( 3 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
193 $ ( RONE+CABS( A( 3, 3 ) )*CABS( A( 3, 3 ) ) ) )
194 S( 4 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
195 $ ( RONE+CABS( A( 4, 4 ) )*CABS( A( 4, 4 ) ) ) )
196 S( 5 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
197 $ ( RONE+CABS( A( 5, 5 ) )*CABS( A( 5, 5 ) ) ) )
198 *
199 CALL CLAKF2( 1, 4, A, LDA, A( 2, 2 ), B, B( 2, 2 ), Z, 8 )
200 CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1,
201 $ WORK( 3 ), 24, RWORK( 9 ), INFO )
202 DIF( 1 ) = RWORK( 8 )
203 *
204 CALL CLAKF2( 4, 1, A, LDA, A( 5, 5 ), B, B( 5, 5 ), Z, 8 )
205 CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1,
206 $ WORK( 3 ), 24, RWORK( 9 ), INFO )
207 DIF( 5 ) = RWORK( 8 )
208 *
209 RETURN
210 *
211 * End of CLATM6
212 *
213 END
2 $ BETA, WX, WY, S, DIF )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * June 2010
7 *
8 * .. Scalar Arguments ..
9 INTEGER LDA, LDX, LDY, N, TYPE
10 COMPLEX ALPHA, BETA, WX, WY
11 * ..
12 * .. Array Arguments ..
13 REAL DIF( * ), S( * )
14 COMPLEX A( LDA, * ), B( LDA, * ), X( LDX, * ),
15 $ Y( LDY, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * CLATM6 generates test matrices for the generalized eigenvalue
22 * problem, their corresponding right and left eigenvector matrices,
23 * and also reciprocal condition numbers for all eigenvalues and
24 * the reciprocal condition numbers of eigenvectors corresponding to
25 * the 1th and 5th eigenvalues.
26 *
27 * Test Matrices
28 * =============
29 *
30 * Two kinds of test matrix pairs
31 * (A, B) = inverse(YH) * (Da, Db) * inverse(X)
32 * are used in the tests:
33 *
34 * Type 1:
35 * Da = 1+a 0 0 0 0 Db = 1 0 0 0 0
36 * 0 2+a 0 0 0 0 1 0 0 0
37 * 0 0 3+a 0 0 0 0 1 0 0
38 * 0 0 0 4+a 0 0 0 0 1 0
39 * 0 0 0 0 5+a , 0 0 0 0 1
40 * and Type 2:
41 * Da = 1+i 0 0 0 0 Db = 1 0 0 0 0
42 * 0 1-i 0 0 0 0 1 0 0 0
43 * 0 0 1 0 0 0 0 1 0 0
44 * 0 0 0 (1+a)+(1+b)i 0 0 0 0 1 0
45 * 0 0 0 0 (1+a)-(1+b)i, 0 0 0 0 1 .
46 *
47 * In both cases the same inverse(YH) and inverse(X) are used to compute
48 * (A, B), giving the exact eigenvectors to (A,B) as (YH, X):
49 *
50 * YH: = 1 0 -y y -y X = 1 0 -x -x x
51 * 0 1 -y y -y 0 1 x -x -x
52 * 0 0 1 0 0 0 0 1 0 0
53 * 0 0 0 1 0 0 0 0 1 0
54 * 0 0 0 0 1, 0 0 0 0 1 , where
55 *
56 * a, b, x and y will have all values independently of each other.
57 *
58 * Arguments
59 * =========
60 *
61 * TYPE (input) INTEGER
62 * Specifies the problem type (see futher details).
63 *
64 * N (input) INTEGER
65 * Size of the matrices A and B.
66 *
67 * A (output) COMPLEX array, dimension (LDA, N).
68 * On exit A N-by-N is initialized according to TYPE.
69 *
70 * LDA (input) INTEGER
71 * The leading dimension of A and of B.
72 *
73 * B (output) COMPLEX array, dimension (LDA, N).
74 * On exit B N-by-N is initialized according to TYPE.
75 *
76 * X (output) COMPLEX array, dimension (LDX, N).
77 * On exit X is the N-by-N matrix of right eigenvectors.
78 *
79 * LDX (input) INTEGER
80 * The leading dimension of X.
81 *
82 * Y (output) COMPLEX array, dimension (LDY, N).
83 * On exit Y is the N-by-N matrix of left eigenvectors.
84 *
85 * LDY (input) INTEGER
86 * The leading dimension of Y.
87 *
88 * ALPHA (input) COMPLEX
89 *
90 * BETA (input) COMPLEX
91 * Weighting constants for matrix A.
92 *
93 * WX (input) COMPLEX
94 * Constant for right eigenvector matrix.
95 *
96 * WY (input) COMPLEX
97 * Constant for left eigenvector matrix.
98 *
99 * S (output) REAL array, dimension (N)
100 * S(i) is the reciprocal condition number for eigenvalue i.
101 *
102 * DIF (output) REAL array, dimension (N)
103 * DIF(i) is the reciprocal condition number for eigenvector i.
104 *
105 * =====================================================================
106 *
107 * .. Parameters ..
108 REAL RONE, TWO, THREE
109 PARAMETER ( RONE = 1.0E+0, TWO = 2.0E+0, THREE = 3.0E+0 )
110 COMPLEX ZERO, ONE
111 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
112 $ ONE = ( 1.0E+0, 0.0E+0 ) )
113 * ..
114 * .. Local Scalars ..
115 INTEGER I, INFO, J
116 * ..
117 * .. Local Arrays ..
118 REAL RWORK( 50 )
119 COMPLEX WORK( 26 ), Z( 8, 8 )
120 * ..
121 * .. Intrinsic Functions ..
122 INTRINSIC CABS, CMPLX, CONJG, REAL, SQRT
123 * ..
124 * .. External Subroutines ..
125 EXTERNAL CGESVD, CLACPY, CLAKF2
126 * ..
127 * .. Executable Statements ..
128 *
129 * Generate test problem ...
130 * (Da, Db) ...
131 *
132 DO 20 I = 1, N
133 DO 10 J = 1, N
134 *
135 IF( I.EQ.J ) THEN
136 A( I, I ) = CMPLX( I ) + ALPHA
137 B( I, I ) = ONE
138 ELSE
139 A( I, J ) = ZERO
140 B( I, J ) = ZERO
141 END IF
142 *
143 10 CONTINUE
144 20 CONTINUE
145 IF( TYPE.EQ.2 ) THEN
146 A( 1, 1 ) = CMPLX( RONE, RONE )
147 A( 2, 2 ) = CONJG( A( 1, 1 ) )
148 A( 3, 3 ) = ONE
149 A( 4, 4 ) = CMPLX( REAL( ONE+ALPHA ), REAL( ONE+BETA ) )
150 A( 5, 5 ) = CONJG( A( 4, 4 ) )
151 END IF
152 *
153 * Form X and Y
154 *
155 CALL CLACPY( 'F', N, N, B, LDA, Y, LDY )
156 Y( 3, 1 ) = -CONJG( WY )
157 Y( 4, 1 ) = CONJG( WY )
158 Y( 5, 1 ) = -CONJG( WY )
159 Y( 3, 2 ) = -CONJG( WY )
160 Y( 4, 2 ) = CONJG( WY )
161 Y( 5, 2 ) = -CONJG( WY )
162 *
163 CALL CLACPY( 'F', N, N, B, LDA, X, LDX )
164 X( 1, 3 ) = -WX
165 X( 1, 4 ) = -WX
166 X( 1, 5 ) = WX
167 X( 2, 3 ) = WX
168 X( 2, 4 ) = -WX
169 X( 2, 5 ) = -WX
170 *
171 * Form (A, B)
172 *
173 B( 1, 3 ) = WX + WY
174 B( 2, 3 ) = -WX + WY
175 B( 1, 4 ) = WX - WY
176 B( 2, 4 ) = WX - WY
177 B( 1, 5 ) = -WX + WY
178 B( 2, 5 ) = WX + WY
179 A( 1, 3 ) = WX*A( 1, 1 ) + WY*A( 3, 3 )
180 A( 2, 3 ) = -WX*A( 2, 2 ) + WY*A( 3, 3 )
181 A( 1, 4 ) = WX*A( 1, 1 ) - WY*A( 4, 4 )
182 A( 2, 4 ) = WX*A( 2, 2 ) - WY*A( 4, 4 )
183 A( 1, 5 ) = -WX*A( 1, 1 ) + WY*A( 5, 5 )
184 A( 2, 5 ) = WX*A( 2, 2 ) + WY*A( 5, 5 )
185 *
186 * Compute condition numbers
187 *
188 S( 1 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) /
189 $ ( RONE+CABS( A( 1, 1 ) )*CABS( A( 1, 1 ) ) ) )
190 S( 2 ) = RONE / SQRT( ( RONE+THREE*CABS( WY )*CABS( WY ) ) /
191 $ ( RONE+CABS( A( 2, 2 ) )*CABS( A( 2, 2 ) ) ) )
192 S( 3 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
193 $ ( RONE+CABS( A( 3, 3 ) )*CABS( A( 3, 3 ) ) ) )
194 S( 4 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
195 $ ( RONE+CABS( A( 4, 4 ) )*CABS( A( 4, 4 ) ) ) )
196 S( 5 ) = RONE / SQRT( ( RONE+TWO*CABS( WX )*CABS( WX ) ) /
197 $ ( RONE+CABS( A( 5, 5 ) )*CABS( A( 5, 5 ) ) ) )
198 *
199 CALL CLAKF2( 1, 4, A, LDA, A( 2, 2 ), B, B( 2, 2 ), Z, 8 )
200 CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1,
201 $ WORK( 3 ), 24, RWORK( 9 ), INFO )
202 DIF( 1 ) = RWORK( 8 )
203 *
204 CALL CLAKF2( 4, 1, A, LDA, A( 5, 5 ), B, B( 5, 5 ), Z, 8 )
205 CALL CGESVD( 'N', 'N', 8, 8, Z, 8, RWORK, WORK, 1, WORK( 2 ), 1,
206 $ WORK( 3 ), 24, RWORK( 9 ), INFO )
207 DIF( 5 ) = RWORK( 8 )
208 *
209 RETURN
210 *
211 * End of CLATM6
212 *
213 END