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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518
|
*> \brief \b DGET31
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGET31( RMAX, LMAX, NINFO, KNT )
*
* .. Scalar Arguments ..
* INTEGER KNT, LMAX
* DOUBLE PRECISION RMAX
* ..
* .. Array Arguments ..
* INTEGER NINFO( 2 )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGET31 tests DLALN2, a routine for solving
*>
*> (ca A - w D)X = sB
*>
*> where A is an NA by NA matrix (NA=1 or 2 only), w is a real (NW=1) or
*> complex (NW=2) constant, ca is a real constant, D is an NA by NA real
*> diagonal matrix, and B is an NA by NW matrix (when NW=2 the second
*> column of B contains the imaginary part of the solution). The code
*> returns X and s, where s is a scale factor, less than or equal to 1,
*> which is chosen to avoid overflow in X.
*>
*> If any singular values of ca A-w D are less than another input
*> parameter SMIN, they are perturbed up to SMIN.
*>
*> The test condition is that the scaled residual
*>
*> norm( (ca A-w D)*X - s*B ) /
*> ( max( ulp*norm(ca A-w D), SMIN )*norm(X) )
*>
*> should be on the order of 1. Here, ulp is the machine precision.
*> Also, it is verified that SCALE is less than or equal to 1, and that
*> XNORM = infinity-norm(X).
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[out] RMAX
*> \verbatim
*> RMAX is DOUBLE PRECISION
*> Value of the largest test ratio.
*> \endverbatim
*>
*> \param[out] LMAX
*> \verbatim
*> LMAX is INTEGER
*> Example number where largest test ratio achieved.
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*> NINFO is INTEGER array, dimension (3)
*> NINFO(1) = number of examples with INFO less than 0
*> NINFO(2) = number of examples with INFO greater than 0
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGET31( RMAX, LMAX, NINFO, KNT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER KNT, LMAX
DOUBLE PRECISION RMAX
* ..
* .. Array Arguments ..
INTEGER NINFO( 2 )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, HALF, ONE
PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
DOUBLE PRECISION TWO, THREE, FOUR
PARAMETER ( TWO = 2.0D0, THREE = 3.0D0, FOUR = 4.0D0 )
DOUBLE PRECISION SEVEN, TEN
PARAMETER ( SEVEN = 7.0D0, TEN = 10.0D0 )
DOUBLE PRECISION TWNONE
PARAMETER ( TWNONE = 21.0D0 )
* ..
* .. Local Scalars ..
INTEGER IA, IB, ICA, ID1, ID2, INFO, ISMIN, ITRANS,
$ IWI, IWR, NA, NW
DOUBLE PRECISION BIGNUM, CA, D1, D2, DEN, EPS, RES, SCALE, SMIN,
$ SMLNUM, TMP, UNFL, WI, WR, XNORM
* ..
* .. Local Arrays ..
LOGICAL LTRANS( 0: 1 )
DOUBLE PRECISION A( 2, 2 ), B( 2, 2 ), VAB( 3 ), VCA( 5 ),
$ VDD( 4 ), VSMIN( 4 ), VWI( 4 ), VWR( 4 ),
$ X( 2, 2 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DLABAD, DLALN2
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, SQRT
* ..
* .. Data statements ..
DATA LTRANS / .FALSE., .TRUE. /
* ..
* .. Executable Statements ..
*
* Get machine parameters
*
EPS = DLAMCH( 'P' )
UNFL = DLAMCH( 'U' )
SMLNUM = DLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL DLABAD( SMLNUM, BIGNUM )
*
* Set up test case parameters
*
VSMIN( 1 ) = SMLNUM
VSMIN( 2 ) = EPS
VSMIN( 3 ) = ONE / ( TEN*TEN )
VSMIN( 4 ) = ONE / EPS
VAB( 1 ) = SQRT( SMLNUM )
VAB( 2 ) = ONE
VAB( 3 ) = SQRT( BIGNUM )
VWR( 1 ) = ZERO
VWR( 2 ) = HALF
VWR( 3 ) = TWO
VWR( 4 ) = ONE
VWI( 1 ) = SMLNUM
VWI( 2 ) = EPS
VWI( 3 ) = ONE
VWI( 4 ) = TWO
VDD( 1 ) = SQRT( SMLNUM )
VDD( 2 ) = ONE
VDD( 3 ) = TWO
VDD( 4 ) = SQRT( BIGNUM )
VCA( 1 ) = ZERO
VCA( 2 ) = SQRT( SMLNUM )
VCA( 3 ) = EPS
VCA( 4 ) = HALF
VCA( 5 ) = ONE
*
KNT = 0
NINFO( 1 ) = 0
NINFO( 2 ) = 0
LMAX = 0
RMAX = ZERO
*
* Begin test loop
*
DO 190 ID1 = 1, 4
D1 = VDD( ID1 )
DO 180 ID2 = 1, 4
D2 = VDD( ID2 )
DO 170 ICA = 1, 5
CA = VCA( ICA )
DO 160 ITRANS = 0, 1
DO 150 ISMIN = 1, 4
SMIN = VSMIN( ISMIN )
*
NA = 1
NW = 1
DO 30 IA = 1, 3
A( 1, 1 ) = VAB( IA )
DO 20 IB = 1, 3
B( 1, 1 ) = VAB( IB )
DO 10 IWR = 1, 4
IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND. CA.EQ.
$ ONE ) THEN
WR = VWR( IWR )*A( 1, 1 )
ELSE
WR = VWR( IWR )
END IF
WI = ZERO
CALL DLALN2( LTRANS( ITRANS ), NA, NW,
$ SMIN, CA, A, 2, D1, D2, B, 2,
$ WR, WI, X, 2, SCALE, XNORM,
$ INFO )
IF( INFO.LT.0 )
$ NINFO( 1 ) = NINFO( 1 ) + 1
IF( INFO.GT.0 )
$ NINFO( 2 ) = NINFO( 2 ) + 1
RES = ABS( ( CA*A( 1, 1 )-WR*D1 )*
$ X( 1, 1 )-SCALE*B( 1, 1 ) )
IF( INFO.EQ.0 ) THEN
DEN = MAX( EPS*( ABS( ( CA*A( 1,
$ 1 )-WR*D1 )*X( 1, 1 ) ) ),
$ SMLNUM )
ELSE
DEN = MAX( SMIN*ABS( X( 1, 1 ) ),
$ SMLNUM )
END IF
RES = RES / DEN
IF( ABS( X( 1, 1 ) ).LT.UNFL .AND.
$ ABS( B( 1, 1 ) ).LE.SMLNUM*
$ ABS( CA*A( 1, 1 )-WR*D1 ) )RES = ZERO
IF( SCALE.GT.ONE )
$ RES = RES + ONE / EPS
RES = RES + ABS( XNORM-ABS( X( 1, 1 ) ) )
$ / MAX( SMLNUM, XNORM ) / EPS
IF( INFO.NE.0 .AND. INFO.NE.1 )
$ RES = RES + ONE / EPS
KNT = KNT + 1
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
10 CONTINUE
20 CONTINUE
30 CONTINUE
*
NA = 1
NW = 2
DO 70 IA = 1, 3
A( 1, 1 ) = VAB( IA )
DO 60 IB = 1, 3
B( 1, 1 ) = VAB( IB )
B( 1, 2 ) = -HALF*VAB( IB )
DO 50 IWR = 1, 4
IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND. CA.EQ.
$ ONE ) THEN
WR = VWR( IWR )*A( 1, 1 )
ELSE
WR = VWR( IWR )
END IF
DO 40 IWI = 1, 4
IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND.
$ CA.EQ.ONE ) THEN
WI = VWI( IWI )*A( 1, 1 )
ELSE
WI = VWI( IWI )
END IF
CALL DLALN2( LTRANS( ITRANS ), NA, NW,
$ SMIN, CA, A, 2, D1, D2, B,
$ 2, WR, WI, X, 2, SCALE,
$ XNORM, INFO )
IF( INFO.LT.0 )
$ NINFO( 1 ) = NINFO( 1 ) + 1
IF( INFO.GT.0 )
$ NINFO( 2 ) = NINFO( 2 ) + 1
RES = ABS( ( CA*A( 1, 1 )-WR*D1 )*
$ X( 1, 1 )+( WI*D1 )*X( 1, 2 )-
$ SCALE*B( 1, 1 ) )
RES = RES + ABS( ( -WI*D1 )*X( 1, 1 )+
$ ( CA*A( 1, 1 )-WR*D1 )*X( 1, 2 )-
$ SCALE*B( 1, 2 ) )
IF( INFO.EQ.0 ) THEN
DEN = MAX( EPS*( MAX( ABS( CA*A( 1,
$ 1 )-WR*D1 ), ABS( D1*WI ) )*
$ ( ABS( X( 1, 1 ) )+ABS( X( 1,
$ 2 ) ) ) ), SMLNUM )
ELSE
DEN = MAX( SMIN*( ABS( X( 1,
$ 1 ) )+ABS( X( 1, 2 ) ) ),
$ SMLNUM )
END IF
RES = RES / DEN
IF( ABS( X( 1, 1 ) ).LT.UNFL .AND.
$ ABS( X( 1, 2 ) ).LT.UNFL .AND.
$ ABS( B( 1, 1 ) ).LE.SMLNUM*
$ ABS( CA*A( 1, 1 )-WR*D1 ) )
$ RES = ZERO
IF( SCALE.GT.ONE )
$ RES = RES + ONE / EPS
RES = RES + ABS( XNORM-
$ ABS( X( 1, 1 ) )-
$ ABS( X( 1, 2 ) ) ) /
$ MAX( SMLNUM, XNORM ) / EPS
IF( INFO.NE.0 .AND. INFO.NE.1 )
$ RES = RES + ONE / EPS
KNT = KNT + 1
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
40 CONTINUE
50 CONTINUE
60 CONTINUE
70 CONTINUE
*
NA = 2
NW = 1
DO 100 IA = 1, 3
A( 1, 1 ) = VAB( IA )
A( 1, 2 ) = -THREE*VAB( IA )
A( 2, 1 ) = -SEVEN*VAB( IA )
A( 2, 2 ) = TWNONE*VAB( IA )
DO 90 IB = 1, 3
B( 1, 1 ) = VAB( IB )
B( 2, 1 ) = -TWO*VAB( IB )
DO 80 IWR = 1, 4
IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND. CA.EQ.
$ ONE ) THEN
WR = VWR( IWR )*A( 1, 1 )
ELSE
WR = VWR( IWR )
END IF
WI = ZERO
CALL DLALN2( LTRANS( ITRANS ), NA, NW,
$ SMIN, CA, A, 2, D1, D2, B, 2,
$ WR, WI, X, 2, SCALE, XNORM,
$ INFO )
IF( INFO.LT.0 )
$ NINFO( 1 ) = NINFO( 1 ) + 1
IF( INFO.GT.0 )
$ NINFO( 2 ) = NINFO( 2 ) + 1
IF( ITRANS.EQ.1 ) THEN
TMP = A( 1, 2 )
A( 1, 2 ) = A( 2, 1 )
A( 2, 1 ) = TMP
END IF
RES = ABS( ( CA*A( 1, 1 )-WR*D1 )*
$ X( 1, 1 )+( CA*A( 1, 2 ) )*
$ X( 2, 1 )-SCALE*B( 1, 1 ) )
RES = RES + ABS( ( CA*A( 2, 1 ) )*
$ X( 1, 1 )+( CA*A( 2, 2 )-WR*D2 )*
$ X( 2, 1 )-SCALE*B( 2, 1 ) )
IF( INFO.EQ.0 ) THEN
DEN = MAX( EPS*( MAX( ABS( CA*A( 1,
$ 1 )-WR*D1 )+ABS( CA*A( 1, 2 ) ),
$ ABS( CA*A( 2, 1 ) )+ABS( CA*A( 2,
$ 2 )-WR*D2 ) )*MAX( ABS( X( 1,
$ 1 ) ), ABS( X( 2, 1 ) ) ) ),
$ SMLNUM )
ELSE
DEN = MAX( EPS*( MAX( SMIN / EPS,
$ MAX( ABS( CA*A( 1,
$ 1 )-WR*D1 )+ABS( CA*A( 1, 2 ) ),
$ ABS( CA*A( 2, 1 ) )+ABS( CA*A( 2,
$ 2 )-WR*D2 ) ) )*MAX( ABS( X( 1,
$ 1 ) ), ABS( X( 2, 1 ) ) ) ),
$ SMLNUM )
END IF
RES = RES / DEN
IF( ABS( X( 1, 1 ) ).LT.UNFL .AND.
$ ABS( X( 2, 1 ) ).LT.UNFL .AND.
$ ABS( B( 1, 1 ) )+ABS( B( 2, 1 ) ).LE.
$ SMLNUM*( ABS( CA*A( 1,
$ 1 )-WR*D1 )+ABS( CA*A( 1,
$ 2 ) )+ABS( CA*A( 2,
$ 1 ) )+ABS( CA*A( 2, 2 )-WR*D2 ) ) )
$ RES = ZERO
IF( SCALE.GT.ONE )
$ RES = RES + ONE / EPS
RES = RES + ABS( XNORM-
$ MAX( ABS( X( 1, 1 ) ), ABS( X( 2,
$ 1 ) ) ) ) / MAX( SMLNUM, XNORM ) /
$ EPS
IF( INFO.NE.0 .AND. INFO.NE.1 )
$ RES = RES + ONE / EPS
KNT = KNT + 1
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
80 CONTINUE
90 CONTINUE
100 CONTINUE
*
NA = 2
NW = 2
DO 140 IA = 1, 3
A( 1, 1 ) = VAB( IA )*TWO
A( 1, 2 ) = -THREE*VAB( IA )
A( 2, 1 ) = -SEVEN*VAB( IA )
A( 2, 2 ) = TWNONE*VAB( IA )
DO 130 IB = 1, 3
B( 1, 1 ) = VAB( IB )
B( 2, 1 ) = -TWO*VAB( IB )
B( 1, 2 ) = FOUR*VAB( IB )
B( 2, 2 ) = -SEVEN*VAB( IB )
DO 120 IWR = 1, 4
IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND. CA.EQ.
$ ONE ) THEN
WR = VWR( IWR )*A( 1, 1 )
ELSE
WR = VWR( IWR )
END IF
DO 110 IWI = 1, 4
IF( D1.EQ.ONE .AND. D2.EQ.ONE .AND.
$ CA.EQ.ONE ) THEN
WI = VWI( IWI )*A( 1, 1 )
ELSE
WI = VWI( IWI )
END IF
CALL DLALN2( LTRANS( ITRANS ), NA, NW,
$ SMIN, CA, A, 2, D1, D2, B,
$ 2, WR, WI, X, 2, SCALE,
$ XNORM, INFO )
IF( INFO.LT.0 )
$ NINFO( 1 ) = NINFO( 1 ) + 1
IF( INFO.GT.0 )
$ NINFO( 2 ) = NINFO( 2 ) + 1
IF( ITRANS.EQ.1 ) THEN
TMP = A( 1, 2 )
A( 1, 2 ) = A( 2, 1 )
A( 2, 1 ) = TMP
END IF
RES = ABS( ( CA*A( 1, 1 )-WR*D1 )*
$ X( 1, 1 )+( CA*A( 1, 2 ) )*
$ X( 2, 1 )+( WI*D1 )*X( 1, 2 )-
$ SCALE*B( 1, 1 ) )
RES = RES + ABS( ( CA*A( 1,
$ 1 )-WR*D1 )*X( 1, 2 )+
$ ( CA*A( 1, 2 ) )*X( 2, 2 )-
$ ( WI*D1 )*X( 1, 1 )-SCALE*
$ B( 1, 2 ) )
RES = RES + ABS( ( CA*A( 2, 1 ) )*
$ X( 1, 1 )+( CA*A( 2, 2 )-WR*D2 )*
$ X( 2, 1 )+( WI*D2 )*X( 2, 2 )-
$ SCALE*B( 2, 1 ) )
RES = RES + ABS( ( CA*A( 2, 1 ) )*
$ X( 1, 2 )+( CA*A( 2, 2 )-WR*D2 )*
$ X( 2, 2 )-( WI*D2 )*X( 2, 1 )-
$ SCALE*B( 2, 2 ) )
IF( INFO.EQ.0 ) THEN
DEN = MAX( EPS*( MAX( ABS( CA*A( 1,
$ 1 )-WR*D1 )+ABS( CA*A( 1,
$ 2 ) )+ABS( WI*D1 ),
$ ABS( CA*A( 2,
$ 1 ) )+ABS( CA*A( 2,
$ 2 )-WR*D2 )+ABS( WI*D2 ) )*
$ MAX( ABS( X( 1,
$ 1 ) )+ABS( X( 2, 1 ) ),
$ ABS( X( 1, 2 ) )+ABS( X( 2,
$ 2 ) ) ) ), SMLNUM )
ELSE
DEN = MAX( EPS*( MAX( SMIN / EPS,
$ MAX( ABS( CA*A( 1,
$ 1 )-WR*D1 )+ABS( CA*A( 1,
$ 2 ) )+ABS( WI*D1 ),
$ ABS( CA*A( 2,
$ 1 ) )+ABS( CA*A( 2,
$ 2 )-WR*D2 )+ABS( WI*D2 ) ) )*
$ MAX( ABS( X( 1,
$ 1 ) )+ABS( X( 2, 1 ) ),
$ ABS( X( 1, 2 ) )+ABS( X( 2,
$ 2 ) ) ) ), SMLNUM )
END IF
RES = RES / DEN
IF( ABS( X( 1, 1 ) ).LT.UNFL .AND.
$ ABS( X( 2, 1 ) ).LT.UNFL .AND.
$ ABS( X( 1, 2 ) ).LT.UNFL .AND.
$ ABS( X( 2, 2 ) ).LT.UNFL .AND.
$ ABS( B( 1, 1 ) )+
$ ABS( B( 2, 1 ) ).LE.SMLNUM*
$ ( ABS( CA*A( 1, 1 )-WR*D1 )+
$ ABS( CA*A( 1, 2 ) )+ABS( CA*A( 2,
$ 1 ) )+ABS( CA*A( 2,
$ 2 )-WR*D2 )+ABS( WI*D2 )+ABS( WI*
$ D1 ) ) )RES = ZERO
IF( SCALE.GT.ONE )
$ RES = RES + ONE / EPS
RES = RES + ABS( XNORM-
$ MAX( ABS( X( 1, 1 ) )+ABS( X( 1,
$ 2 ) ), ABS( X( 2,
$ 1 ) )+ABS( X( 2, 2 ) ) ) ) /
$ MAX( SMLNUM, XNORM ) / EPS
IF( INFO.NE.0 .AND. INFO.NE.1 )
$ RES = RES + ONE / EPS
KNT = KNT + 1
IF( RES.GT.RMAX ) THEN
LMAX = KNT
RMAX = RES
END IF
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
160 CONTINUE
170 CONTINUE
180 CONTINUE
190 CONTINUE
*
RETURN
*
* End of DGET31
*
END
|