1*> \brief \b ZCHKGK 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE ZCHKGK( NIN, NOUT ) 12* 13* .. Scalar Arguments .. 14* INTEGER NIN, NOUT 15* .. 16* 17* 18*> \par Purpose: 19* ============= 20*> 21*> \verbatim 22*> 23*> ZCHKGK tests ZGGBAK, a routine for backward balancing of 24*> a matrix pair (A, B). 25*> \endverbatim 26* 27* Arguments: 28* ========== 29* 30*> \param[in] NIN 31*> \verbatim 32*> NIN is INTEGER 33*> The logical unit number for input. NIN > 0. 34*> \endverbatim 35*> 36*> \param[in] NOUT 37*> \verbatim 38*> NOUT is INTEGER 39*> The logical unit number for output. NOUT > 0. 40*> \endverbatim 41* 42* Authors: 43* ======== 44* 45*> \author Univ. of Tennessee 46*> \author Univ. of California Berkeley 47*> \author Univ. of Colorado Denver 48*> \author NAG Ltd. 49* 50*> \ingroup complex16_eig 51* 52* ===================================================================== 53 SUBROUTINE ZCHKGK( NIN, NOUT ) 54* 55* -- LAPACK test routine -- 56* -- LAPACK is a software package provided by Univ. of Tennessee, -- 57* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 58* 59* .. Scalar Arguments .. 60 INTEGER NIN, NOUT 61* .. 62* 63* ===================================================================== 64* 65* .. Parameters .. 66 INTEGER LDA, LDB, LDVL, LDVR 67 PARAMETER ( LDA = 50, LDB = 50, LDVL = 50, LDVR = 50 ) 68 INTEGER LDE, LDF, LDWORK, LRWORK 69 PARAMETER ( LDE = 50, LDF = 50, LDWORK = 50, 70 $ LRWORK = 6*50 ) 71 DOUBLE PRECISION ZERO 72 PARAMETER ( ZERO = 0.0D+0 ) 73 COMPLEX*16 CZERO, CONE 74 PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), 75 $ CONE = ( 1.0D+0, 0.0D+0 ) ) 76* .. 77* .. Local Scalars .. 78 INTEGER I, IHI, ILO, INFO, J, KNT, M, N, NINFO 79 DOUBLE PRECISION ANORM, BNORM, EPS, RMAX, VMAX 80 COMPLEX*16 CDUM 81* .. 82* .. Local Arrays .. 83 INTEGER LMAX( 4 ) 84 DOUBLE PRECISION LSCALE( LDA ), RSCALE( LDA ), RWORK( LRWORK ) 85 COMPLEX*16 A( LDA, LDA ), AF( LDA, LDA ), B( LDB, LDB ), 86 $ BF( LDB, LDB ), E( LDE, LDE ), F( LDF, LDF ), 87 $ VL( LDVL, LDVL ), VLF( LDVL, LDVL ), 88 $ VR( LDVR, LDVR ), VRF( LDVR, LDVR ), 89 $ WORK( LDWORK, LDWORK ) 90* .. 91* .. External Functions .. 92 DOUBLE PRECISION DLAMCH, ZLANGE 93 EXTERNAL DLAMCH, ZLANGE 94* .. 95* .. External Subroutines .. 96 EXTERNAL ZGEMM, ZGGBAK, ZGGBAL, ZLACPY 97* .. 98* .. Intrinsic Functions .. 99 INTRINSIC ABS, DBLE, DIMAG, MAX 100* .. 101* .. Statement Functions .. 102 DOUBLE PRECISION CABS1 103* .. 104* .. Statement Function definitions .. 105 CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) ) 106* .. 107* .. Executable Statements .. 108* 109 LMAX( 1 ) = 0 110 LMAX( 2 ) = 0 111 LMAX( 3 ) = 0 112 LMAX( 4 ) = 0 113 NINFO = 0 114 KNT = 0 115 RMAX = ZERO 116* 117 EPS = DLAMCH( 'Precision' ) 118* 119 10 CONTINUE 120 READ( NIN, FMT = * )N, M 121 IF( N.EQ.0 ) 122 $ GO TO 100 123* 124 DO 20 I = 1, N 125 READ( NIN, FMT = * )( A( I, J ), J = 1, N ) 126 20 CONTINUE 127* 128 DO 30 I = 1, N 129 READ( NIN, FMT = * )( B( I, J ), J = 1, N ) 130 30 CONTINUE 131* 132 DO 40 I = 1, N 133 READ( NIN, FMT = * )( VL( I, J ), J = 1, M ) 134 40 CONTINUE 135* 136 DO 50 I = 1, N 137 READ( NIN, FMT = * )( VR( I, J ), J = 1, M ) 138 50 CONTINUE 139* 140 KNT = KNT + 1 141* 142 ANORM = ZLANGE( 'M', N, N, A, LDA, RWORK ) 143 BNORM = ZLANGE( 'M', N, N, B, LDB, RWORK ) 144* 145 CALL ZLACPY( 'FULL', N, N, A, LDA, AF, LDA ) 146 CALL ZLACPY( 'FULL', N, N, B, LDB, BF, LDB ) 147* 148 CALL ZGGBAL( 'B', N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE, 149 $ RWORK, INFO ) 150 IF( INFO.NE.0 ) THEN 151 NINFO = NINFO + 1 152 LMAX( 1 ) = KNT 153 END IF 154* 155 CALL ZLACPY( 'FULL', N, M, VL, LDVL, VLF, LDVL ) 156 CALL ZLACPY( 'FULL', N, M, VR, LDVR, VRF, LDVR ) 157* 158 CALL ZGGBAK( 'B', 'L', N, ILO, IHI, LSCALE, RSCALE, M, VL, LDVL, 159 $ INFO ) 160 IF( INFO.NE.0 ) THEN 161 NINFO = NINFO + 1 162 LMAX( 2 ) = KNT 163 END IF 164* 165 CALL ZGGBAK( 'B', 'R', N, ILO, IHI, LSCALE, RSCALE, M, VR, LDVR, 166 $ INFO ) 167 IF( INFO.NE.0 ) THEN 168 NINFO = NINFO + 1 169 LMAX( 3 ) = KNT 170 END IF 171* 172* Test of ZGGBAK 173* 174* Check tilde(VL)'*A*tilde(VR) - VL'*tilde(A)*VR 175* where tilde(A) denotes the transformed matrix. 176* 177 CALL ZGEMM( 'N', 'N', N, M, N, CONE, AF, LDA, VR, LDVR, CZERO, 178 $ WORK, LDWORK ) 179 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VL, LDVL, WORK, LDWORK, 180 $ CZERO, E, LDE ) 181* 182 CALL ZGEMM( 'N', 'N', N, M, N, CONE, A, LDA, VRF, LDVR, CZERO, 183 $ WORK, LDWORK ) 184 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VLF, LDVL, WORK, LDWORK, 185 $ CZERO, F, LDF ) 186* 187 VMAX = ZERO 188 DO 70 J = 1, M 189 DO 60 I = 1, M 190 VMAX = MAX( VMAX, CABS1( E( I, J )-F( I, J ) ) ) 191 60 CONTINUE 192 70 CONTINUE 193 VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) ) 194 IF( VMAX.GT.RMAX ) THEN 195 LMAX( 4 ) = KNT 196 RMAX = VMAX 197 END IF 198* 199* Check tilde(VL)'*B*tilde(VR) - VL'*tilde(B)*VR 200* 201 CALL ZGEMM( 'N', 'N', N, M, N, CONE, BF, LDB, VR, LDVR, CZERO, 202 $ WORK, LDWORK ) 203 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VL, LDVL, WORK, LDWORK, 204 $ CZERO, E, LDE ) 205* 206 CALL ZGEMM( 'n', 'n', N, M, N, CONE, B, LDB, VRF, LDVR, CZERO, 207 $ WORK, LDWORK ) 208 CALL ZGEMM( 'C', 'N', M, M, N, CONE, VLF, LDVL, WORK, LDWORK, 209 $ CZERO, F, LDF ) 210* 211 VMAX = ZERO 212 DO 90 J = 1, M 213 DO 80 I = 1, M 214 VMAX = MAX( VMAX, CABS1( E( I, J )-F( I, J ) ) ) 215 80 CONTINUE 216 90 CONTINUE 217 VMAX = VMAX / ( EPS*MAX( ANORM, BNORM ) ) 218 IF( VMAX.GT.RMAX ) THEN 219 LMAX( 4 ) = KNT 220 RMAX = VMAX 221 END IF 222* 223 GO TO 10 224* 225 100 CONTINUE 226* 227 WRITE( NOUT, FMT = 9999 ) 228 9999 FORMAT( 1X, '.. test output of ZGGBAK .. ' ) 229* 230 WRITE( NOUT, FMT = 9998 )RMAX 231 9998 FORMAT( ' value of largest test error =', D12.3 ) 232 WRITE( NOUT, FMT = 9997 )LMAX( 1 ) 233 9997 FORMAT( ' example number where ZGGBAL info is not 0 =', I4 ) 234 WRITE( NOUT, FMT = 9996 )LMAX( 2 ) 235 9996 FORMAT( ' example number where ZGGBAK(L) info is not 0 =', I4 ) 236 WRITE( NOUT, FMT = 9995 )LMAX( 3 ) 237 9995 FORMAT( ' example number where ZGGBAK(R) info is not 0 =', I4 ) 238 WRITE( NOUT, FMT = 9994 )LMAX( 4 ) 239 9994 FORMAT( ' example number having largest error =', I4 ) 240 WRITE( NOUT, FMT = 9992 )NINFO 241 9992 FORMAT( ' number of examples where info is not 0 =', I4 ) 242 WRITE( NOUT, FMT = 9991 )KNT 243 9991 FORMAT( ' total number of examples tested =', I4 ) 244* 245 RETURN 246* 247* End of ZCHKGK 248* 249 END 250