1 SUBROUTINE ZCHKGK( NIN, NOUT )
2 *
3 * -- LAPACK test routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER NIN, NOUT
9 * ..
10 *
11 * Purpose
12 * =======
13 *
14 * ZCHKGK tests ZGGBAK, a routine for backward balancing of
15 * a matrix pair (A, B).
16 *
17 * Arguments
18 * =========
19 *
20 * NIN (input) INTEGER
21 * The logical unit number for input. NIN > 0.
22 *
23 * NOUT (input) INTEGER
24 * The logical unit number for output. NOUT > 0.
25 *
26 * =====================================================================
27 *
28 * .. Parameters ..
29 INTEGER LDA, LDB, LDVL, LDVR
30 PARAMETER ( LDA = 50, LDB = 50, LDVL = 50, LDVR = 50 )
31 INTEGER LDE, LDF, LDWORK, LRWORK
32 PARAMETER ( LDE = 50, LDF = 50, LDWORK = 50,
33 $ LRWORK = 6*50 )
34 DOUBLE PRECISION ZERO
35 PARAMETER ( ZERO = 0.0D+0 )
36 COMPLEX*16 CZERO, CONE
37 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
38 $ CONE = ( 1.0D+0, 0.0D+0 ) )
39 * ..
40 * .. Local Scalars ..
41 INTEGER I, IHI, ILO, INFO, J, KNT, M, N, NINFO
42 DOUBLE PRECISION ANORM, BNORM, EPS, RMAX, VMAX
43 COMPLEX*16 CDUM
44 * ..
45 * .. Local Arrays ..
46 INTEGER LMAX( 4 )
47 DOUBLE PRECISION LSCALE( LDA ), RSCALE( LDA ), RWORK( LRWORK )
48 COMPLEX*16 A( LDA, LDA ), AF( LDA, LDA ), B( LDB, LDB ),
49 $ BF( LDB, LDB ), E( LDE, LDE ), F( LDF, LDF ),
50 $ VL( LDVL, LDVL ), VLF( LDVL, LDVL ),
51 $ VR( LDVR, LDVR ), VRF( LDVR, LDVR ),
52 $ WORK( LDWORK, LDWORK )
53 * ..
54 * .. External Functions ..
55 DOUBLE PRECISION DLAMCH, ZLANGE
56 EXTERNAL DLAMCH, ZLANGE
57 * ..
58 * .. External Subroutines ..
59 EXTERNAL ZGEMM, ZGGBAK, ZGGBAL, ZLACPY
60 * ..
61 * .. Intrinsic Functions ..
62 INTRINSIC ABS, DBLE, DIMAG, MAX
63 * ..
64 * .. Statement Functions ..
65 DOUBLE PRECISION CABS1
66 * ..
67 * .. Statement Function definitions ..
68 CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
69 * ..
70 * .. Executable Statements ..
71 *
72 LMAX( 1 ) = 0
73 LMAX( 2 ) = 0
74 LMAX( 3 ) = 0
75 LMAX( 4 ) = 0
76 NINFO = 0
77 KNT = 0
78 RMAX = ZERO
79 *
80 EPS = DLAMCH( 'Precision' )
81 *
82 10 CONTINUE
83 READ( NIN, FMT = * )N, M
84 IF( N.EQ.0 )
85 $ GO TO 100
86 *
87 DO 20 I = 1, N
88 READ( NIN, FMT = * )( A( I, J ), J = 1, N )
89 20 CONTINUE
90 *
91 DO 30 I = 1, N
92 READ( NIN, FMT = * )( B( I, J ), J = 1, N )
93 30 CONTINUE
94 *
95 DO 40 I = 1, N
96 READ( NIN, FMT = * )( VL( I, J ), J = 1, M )
97 40 CONTINUE
98 *
99 DO 50 I = 1, N
100 READ( NIN, FMT = * )( VR( I, J ), J = 1, M )
101 50 CONTINUE
102 *
103 KNT = KNT + 1
104 *
105 ANORM = ZLANGE( 'M', N, N, A, LDA, RWORK )
106 BNORM = ZLANGE( 'M', N, N, B, LDB, RWORK )
107 *
108 CALL ZLACPY( 'FULL', N, N, A, LDA, AF, LDA )
109 CALL ZLACPY( 'FULL', N, N, B, LDB, BF, LDB )
110 *
111 CALL ZGGBAL( 'B', N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
112 $ RWORK, INFO )
113 IF( INFO.NE.0 ) THEN
114 NINFO = NINFO + 1
115 LMAX( 1 ) = KNT
116 END IF
117 *
118 CALL ZLACPY( 'FULL', N, M, VL, LDVL, VLF, LDVL )
119 CALL ZLACPY( 'FULL', N, M, VR, LDVR, VRF, LDVR )
120 *
121 CALL ZGGBAK( 'B', 'L', N, ILO, IHI, LSCALE, RSCALE, M, VL, LDVL,
122 $ INFO )
123 IF( INFO.NE.0 ) THEN
124 NINFO = NINFO + 1
125 LMAX( 2 ) = KNT
126 END IF
127 *
128 CALL ZGGBAK( 'B', 'R', N, ILO, IHI, LSCALE, RSCALE, M, VR, LDVR,
129 $ INFO )
130 IF( INFO.NE.0 ) THEN
131 NINFO = NINFO + 1
132 LMAX( 3 ) = KNT
133 END IF
134 *
135 * Test of ZGGBAK
136 *
137 * Check tilde(VL)'*A*tilde(VR) - VL'*tilde(A)*VR
138 * where tilde(A) denotes the transformed matrix.
139 *
140 CALL ZGEMM( 'N', 'N', N, M, N, CONE, AF, LDA, VR, LDVR, CZERO,
141 $ WORK, LDWORK )
142 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VL, LDVL, WORK, LDWORK,
143 $ CZERO, E, LDE )
144 *
145 CALL ZGEMM( 'N', 'N', N, M, N, CONE, A, LDA, VRF, LDVR, CZERO,
146 $ WORK, LDWORK )
147 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VLF, LDVL, WORK, LDWORK,
148 $ CZERO, F, LDF )
149 *
150 VMAX = ZERO
151 DO 70 J = 1, M
152 DO 60 I = 1, M
153 VMAX = MAX( VMAX, CABS1( E( I, J )-F( I, J ) ) )
154 60 CONTINUE
155 70 CONTINUE
156 VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )
157 IF( VMAX.GT.RMAX ) THEN
158 LMAX( 4 ) = KNT
159 RMAX = VMAX
160 END IF
161 *
162 * Check tilde(VL)'*B*tilde(VR) - VL'*tilde(B)*VR
163 *
164 CALL ZGEMM( 'N', 'N', N, M, N, CONE, BF, LDB, VR, LDVR, CZERO,
165 $ WORK, LDWORK )
166 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VL, LDVL, WORK, LDWORK,
167 $ CZERO, E, LDE )
168 *
169 CALL ZGEMM( 'n', 'n', N, M, N, CONE, B, LDB, VRF, LDVR, CZERO,
170 $ WORK, LDWORK )
171 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VLF, LDVL, WORK, LDWORK,
172 $ CZERO, F, LDF )
173 *
174 VMAX = ZERO
175 DO 90 J = 1, M
176 DO 80 I = 1, M
177 VMAX = MAX( VMAX, CABS1( E( I, J )-F( I, J ) ) )
178 80 CONTINUE
179 90 CONTINUE
180 VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )
181 IF( VMAX.GT.RMAX ) THEN
182 LMAX( 4 ) = KNT
183 RMAX = VMAX
184 END IF
185 *
186 GO TO 10
187 *
188 100 CONTINUE
189 *
190 WRITE( NOUT, FMT = 9999 )
191 9999 FORMAT( 1X, '.. test output of ZGGBAK .. ' )
192 *
193 WRITE( NOUT, FMT = 9998 )RMAX
194 9998 FORMAT( ' value of largest test error =', D12.3 )
195 WRITE( NOUT, FMT = 9997 )LMAX( 1 )
196 9997 FORMAT( ' example number where ZGGBAL info is not 0 =', I4 )
197 WRITE( NOUT, FMT = 9996 )LMAX( 2 )
198 9996 FORMAT( ' example number where ZGGBAK(L) info is not 0 =', I4 )
199 WRITE( NOUT, FMT = 9995 )LMAX( 3 )
200 9995 FORMAT( ' example number where ZGGBAK(R) info is not 0 =', I4 )
201 WRITE( NOUT, FMT = 9994 )LMAX( 4 )
202 9994 FORMAT( ' example number having largest error =', I4 )
203 WRITE( NOUT, FMT = 9992 )NINFO
204 9992 FORMAT( ' number of examples where info is not 0 =', I4 )
205 WRITE( NOUT, FMT = 9991 )KNT
206 9991 FORMAT( ' total number of examples tested =', I4 )
207 *
208 RETURN
209 *
210 * End of ZCHKGK
211 *
212 END
2 *
3 * -- LAPACK test routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER NIN, NOUT
9 * ..
10 *
11 * Purpose
12 * =======
13 *
14 * ZCHKGK tests ZGGBAK, a routine for backward balancing of
15 * a matrix pair (A, B).
16 *
17 * Arguments
18 * =========
19 *
20 * NIN (input) INTEGER
21 * The logical unit number for input. NIN > 0.
22 *
23 * NOUT (input) INTEGER
24 * The logical unit number for output. NOUT > 0.
25 *
26 * =====================================================================
27 *
28 * .. Parameters ..
29 INTEGER LDA, LDB, LDVL, LDVR
30 PARAMETER ( LDA = 50, LDB = 50, LDVL = 50, LDVR = 50 )
31 INTEGER LDE, LDF, LDWORK, LRWORK
32 PARAMETER ( LDE = 50, LDF = 50, LDWORK = 50,
33 $ LRWORK = 6*50 )
34 DOUBLE PRECISION ZERO
35 PARAMETER ( ZERO = 0.0D+0 )
36 COMPLEX*16 CZERO, CONE
37 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
38 $ CONE = ( 1.0D+0, 0.0D+0 ) )
39 * ..
40 * .. Local Scalars ..
41 INTEGER I, IHI, ILO, INFO, J, KNT, M, N, NINFO
42 DOUBLE PRECISION ANORM, BNORM, EPS, RMAX, VMAX
43 COMPLEX*16 CDUM
44 * ..
45 * .. Local Arrays ..
46 INTEGER LMAX( 4 )
47 DOUBLE PRECISION LSCALE( LDA ), RSCALE( LDA ), RWORK( LRWORK )
48 COMPLEX*16 A( LDA, LDA ), AF( LDA, LDA ), B( LDB, LDB ),
49 $ BF( LDB, LDB ), E( LDE, LDE ), F( LDF, LDF ),
50 $ VL( LDVL, LDVL ), VLF( LDVL, LDVL ),
51 $ VR( LDVR, LDVR ), VRF( LDVR, LDVR ),
52 $ WORK( LDWORK, LDWORK )
53 * ..
54 * .. External Functions ..
55 DOUBLE PRECISION DLAMCH, ZLANGE
56 EXTERNAL DLAMCH, ZLANGE
57 * ..
58 * .. External Subroutines ..
59 EXTERNAL ZGEMM, ZGGBAK, ZGGBAL, ZLACPY
60 * ..
61 * .. Intrinsic Functions ..
62 INTRINSIC ABS, DBLE, DIMAG, MAX
63 * ..
64 * .. Statement Functions ..
65 DOUBLE PRECISION CABS1
66 * ..
67 * .. Statement Function definitions ..
68 CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
69 * ..
70 * .. Executable Statements ..
71 *
72 LMAX( 1 ) = 0
73 LMAX( 2 ) = 0
74 LMAX( 3 ) = 0
75 LMAX( 4 ) = 0
76 NINFO = 0
77 KNT = 0
78 RMAX = ZERO
79 *
80 EPS = DLAMCH( 'Precision' )
81 *
82 10 CONTINUE
83 READ( NIN, FMT = * )N, M
84 IF( N.EQ.0 )
85 $ GO TO 100
86 *
87 DO 20 I = 1, N
88 READ( NIN, FMT = * )( A( I, J ), J = 1, N )
89 20 CONTINUE
90 *
91 DO 30 I = 1, N
92 READ( NIN, FMT = * )( B( I, J ), J = 1, N )
93 30 CONTINUE
94 *
95 DO 40 I = 1, N
96 READ( NIN, FMT = * )( VL( I, J ), J = 1, M )
97 40 CONTINUE
98 *
99 DO 50 I = 1, N
100 READ( NIN, FMT = * )( VR( I, J ), J = 1, M )
101 50 CONTINUE
102 *
103 KNT = KNT + 1
104 *
105 ANORM = ZLANGE( 'M', N, N, A, LDA, RWORK )
106 BNORM = ZLANGE( 'M', N, N, B, LDB, RWORK )
107 *
108 CALL ZLACPY( 'FULL', N, N, A, LDA, AF, LDA )
109 CALL ZLACPY( 'FULL', N, N, B, LDB, BF, LDB )
110 *
111 CALL ZGGBAL( 'B', N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
112 $ RWORK, INFO )
113 IF( INFO.NE.0 ) THEN
114 NINFO = NINFO + 1
115 LMAX( 1 ) = KNT
116 END IF
117 *
118 CALL ZLACPY( 'FULL', N, M, VL, LDVL, VLF, LDVL )
119 CALL ZLACPY( 'FULL', N, M, VR, LDVR, VRF, LDVR )
120 *
121 CALL ZGGBAK( 'B', 'L', N, ILO, IHI, LSCALE, RSCALE, M, VL, LDVL,
122 $ INFO )
123 IF( INFO.NE.0 ) THEN
124 NINFO = NINFO + 1
125 LMAX( 2 ) = KNT
126 END IF
127 *
128 CALL ZGGBAK( 'B', 'R', N, ILO, IHI, LSCALE, RSCALE, M, VR, LDVR,
129 $ INFO )
130 IF( INFO.NE.0 ) THEN
131 NINFO = NINFO + 1
132 LMAX( 3 ) = KNT
133 END IF
134 *
135 * Test of ZGGBAK
136 *
137 * Check tilde(VL)'*A*tilde(VR) - VL'*tilde(A)*VR
138 * where tilde(A) denotes the transformed matrix.
139 *
140 CALL ZGEMM( 'N', 'N', N, M, N, CONE, AF, LDA, VR, LDVR, CZERO,
141 $ WORK, LDWORK )
142 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VL, LDVL, WORK, LDWORK,
143 $ CZERO, E, LDE )
144 *
145 CALL ZGEMM( 'N', 'N', N, M, N, CONE, A, LDA, VRF, LDVR, CZERO,
146 $ WORK, LDWORK )
147 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VLF, LDVL, WORK, LDWORK,
148 $ CZERO, F, LDF )
149 *
150 VMAX = ZERO
151 DO 70 J = 1, M
152 DO 60 I = 1, M
153 VMAX = MAX( VMAX, CABS1( E( I, J )-F( I, J ) ) )
154 60 CONTINUE
155 70 CONTINUE
156 VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )
157 IF( VMAX.GT.RMAX ) THEN
158 LMAX( 4 ) = KNT
159 RMAX = VMAX
160 END IF
161 *
162 * Check tilde(VL)'*B*tilde(VR) - VL'*tilde(B)*VR
163 *
164 CALL ZGEMM( 'N', 'N', N, M, N, CONE, BF, LDB, VR, LDVR, CZERO,
165 $ WORK, LDWORK )
166 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VL, LDVL, WORK, LDWORK,
167 $ CZERO, E, LDE )
168 *
169 CALL ZGEMM( 'n', 'n', N, M, N, CONE, B, LDB, VRF, LDVR, CZERO,
170 $ WORK, LDWORK )
171 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VLF, LDVL, WORK, LDWORK,
172 $ CZERO, F, LDF )
173 *
174 VMAX = ZERO
175 DO 90 J = 1, M
176 DO 80 I = 1, M
177 VMAX = MAX( VMAX, CABS1( E( I, J )-F( I, J ) ) )
178 80 CONTINUE
179 90 CONTINUE
180 VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) )
181 IF( VMAX.GT.RMAX ) THEN
182 LMAX( 4 ) = KNT
183 RMAX = VMAX
184 END IF
185 *
186 GO TO 10
187 *
188 100 CONTINUE
189 *
190 WRITE( NOUT, FMT = 9999 )
191 9999 FORMAT( 1X, '.. test output of ZGGBAK .. ' )
192 *
193 WRITE( NOUT, FMT = 9998 )RMAX
194 9998 FORMAT( ' value of largest test error =', D12.3 )
195 WRITE( NOUT, FMT = 9997 )LMAX( 1 )
196 9997 FORMAT( ' example number where ZGGBAL info is not 0 =', I4 )
197 WRITE( NOUT, FMT = 9996 )LMAX( 2 )
198 9996 FORMAT( ' example number where ZGGBAK(L) info is not 0 =', I4 )
199 WRITE( NOUT, FMT = 9995 )LMAX( 3 )
200 9995 FORMAT( ' example number where ZGGBAK(R) info is not 0 =', I4 )
201 WRITE( NOUT, FMT = 9994 )LMAX( 4 )
202 9994 FORMAT( ' example number having largest error =', I4 )
203 WRITE( NOUT, FMT = 9992 )NINFO
204 9992 FORMAT( ' number of examples where info is not 0 =', I4 )
205 WRITE( NOUT, FMT = 9991 )KNT
206 9991 FORMAT( ' total number of examples tested =', I4 )
207 *
208 RETURN
209 *
210 * End of ZCHKGK
211 *
212 END