LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sdrvgt()

 subroutine sdrvgt ( logical, dimension( * ) DOTYPE, integer NN, integer, dimension( * ) NVAL, integer NRHS, real THRESH, logical TSTERR, real, dimension( * ) A, real, dimension( * ) AF, real, dimension( * ) B, real, dimension( * ) X, real, dimension( * ) XACT, real, dimension( * ) WORK, real, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer NOUT )

SDRVGT

Purpose:
SDRVGT tests SGTSV and -SVX.
Parameters
 [in] DOTYPE DOTYPE is LOGICAL array, dimension (NTYPES) The matrix types to be used for testing. Matrices of type j (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. [in] NN NN is INTEGER The number of values of N contained in the vector NVAL. [in] NVAL NVAL is INTEGER array, dimension (NN) The values of the matrix dimension N. [in] NRHS NRHS is INTEGER The number of right hand sides, NRHS >= 0. [in] THRESH THRESH is REAL The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0. [in] TSTERR TSTERR is LOGICAL Flag that indicates whether error exits are to be tested. [out] A A is REAL array, dimension (NMAX*4) [out] AF AF is REAL array, dimension (NMAX*4) [out] B B is REAL array, dimension (NMAX*NRHS) [out] X X is REAL array, dimension (NMAX*NRHS) [out] XACT XACT is REAL array, dimension (NMAX*NRHS) [out] WORK WORK is REAL array, dimension (NMAX*max(3,NRHS)) [out] RWORK RWORK is REAL array, dimension (max(NMAX,2*NRHS)) [out] IWORK IWORK is INTEGER array, dimension (2*NMAX) [in] NOUT NOUT is INTEGER The unit number for output.

Definition at line 137 of file sdrvgt.f.

139 *
140 * -- LAPACK test routine --
141 * -- LAPACK is a software package provided by Univ. of Tennessee, --
142 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
143 *
144 * .. Scalar Arguments ..
145  LOGICAL TSTERR
146  INTEGER NN, NOUT, NRHS
147  REAL THRESH
148 * ..
149 * .. Array Arguments ..
150  LOGICAL DOTYPE( * )
151  INTEGER IWORK( * ), NVAL( * )
152  REAL A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ),
153  \$ X( * ), XACT( * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  REAL ONE, ZERO
160  parameter( one = 1.0e+0, zero = 0.0e+0 )
161  INTEGER NTYPES
162  parameter( ntypes = 12 )
163  INTEGER NTESTS
164  parameter( ntests = 6 )
165 * ..
166 * .. Local Scalars ..
167  LOGICAL TRFCON, ZEROT
168  CHARACTER DIST, FACT, TRANS, TYPE
169  CHARACTER*3 PATH
170  INTEGER I, IFACT, IMAT, IN, INFO, ITRAN, IX, IZERO, J,
171  \$ K, K1, KL, KOFF, KU, LDA, M, MODE, N, NERRS,
172  \$ NFAIL, NIMAT, NRUN, NT
173  REAL AINVNM, ANORM, ANORMI, ANORMO, COND, RCOND,
174  \$ RCONDC, RCONDI, RCONDO
175 * ..
176 * .. Local Arrays ..
177  CHARACTER TRANSS( 3 )
178  INTEGER ISEED( 4 ), ISEEDY( 4 )
179  REAL RESULT( NTESTS ), Z( 3 )
180 * ..
181 * .. External Functions ..
182  REAL SASUM, SGET06, SLANGT
183  EXTERNAL sasum, sget06, slangt
184 * ..
185 * .. External Subroutines ..
186  EXTERNAL aladhd, alaerh, alasvm, scopy, serrvx, sget04,
189  \$ slatms, sscal
190 * ..
191 * .. Intrinsic Functions ..
192  INTRINSIC max
193 * ..
194 * .. Scalars in Common ..
195  LOGICAL LERR, OK
196  CHARACTER*32 SRNAMT
197  INTEGER INFOT, NUNIT
198 * ..
199 * .. Common blocks ..
200  COMMON / infoc / infot, nunit, ok, lerr
201  COMMON / srnamc / srnamt
202 * ..
203 * .. Data statements ..
204  DATA iseedy / 0, 0, 0, 1 / , transs / 'N', 'T',
205  \$ 'C' /
206 * ..
207 * .. Executable Statements ..
208 *
209  path( 1: 1 ) = 'Single precision'
210  path( 2: 3 ) = 'GT'
211  nrun = 0
212  nfail = 0
213  nerrs = 0
214  DO 10 i = 1, 4
215  iseed( i ) = iseedy( i )
216  10 CONTINUE
217 *
218 * Test the error exits
219 *
220  IF( tsterr )
221  \$ CALL serrvx( path, nout )
222  infot = 0
223 *
224  DO 140 in = 1, nn
225 *
226 * Do for each value of N in NVAL.
227 *
228  n = nval( in )
229  m = max( n-1, 0 )
230  lda = max( 1, n )
231  nimat = ntypes
232  IF( n.LE.0 )
233  \$ nimat = 1
234 *
235  DO 130 imat = 1, nimat
236 *
237 * Do the tests only if DOTYPE( IMAT ) is true.
238 *
239  IF( .NOT.dotype( imat ) )
240  \$ GO TO 130
241 *
242 * Set up parameters with SLATB4.
243 *
244  CALL slatb4( path, imat, n, n, TYPE, KL, KU, ANORM, MODE,
245  \$ COND, DIST )
246 *
247  zerot = imat.GE.8 .AND. imat.LE.10
248  IF( imat.LE.6 ) THEN
249 *
250 * Types 1-6: generate matrices of known condition number.
251 *
252  koff = max( 2-ku, 3-max( 1, n ) )
253  srnamt = 'SLATMS'
254  CALL slatms( n, n, dist, iseed, TYPE, RWORK, MODE, COND,
255  \$ ANORM, KL, KU, 'Z', AF( KOFF ), 3, WORK,
256  \$ INFO )
257 *
258 * Check the error code from SLATMS.
259 *
260  IF( info.NE.0 ) THEN
261  CALL alaerh( path, 'SLATMS', info, 0, ' ', n, n, kl,
262  \$ ku, -1, imat, nfail, nerrs, nout )
263  GO TO 130
264  END IF
265  izero = 0
266 *
267  IF( n.GT.1 ) THEN
268  CALL scopy( n-1, af( 4 ), 3, a, 1 )
269  CALL scopy( n-1, af( 3 ), 3, a( n+m+1 ), 1 )
270  END IF
271  CALL scopy( n, af( 2 ), 3, a( m+1 ), 1 )
272  ELSE
273 *
274 * Types 7-12: generate tridiagonal matrices with
275 * unknown condition numbers.
276 *
277  IF( .NOT.zerot .OR. .NOT.dotype( 7 ) ) THEN
278 *
279 * Generate a matrix with elements from [-1,1].
280 *
281  CALL slarnv( 2, iseed, n+2*m, a )
282  IF( anorm.NE.one )
283  \$ CALL sscal( n+2*m, anorm, a, 1 )
284  ELSE IF( izero.GT.0 ) THEN
285 *
286 * Reuse the last matrix by copying back the zeroed out
287 * elements.
288 *
289  IF( izero.EQ.1 ) THEN
290  a( n ) = z( 2 )
291  IF( n.GT.1 )
292  \$ a( 1 ) = z( 3 )
293  ELSE IF( izero.EQ.n ) THEN
294  a( 3*n-2 ) = z( 1 )
295  a( 2*n-1 ) = z( 2 )
296  ELSE
297  a( 2*n-2+izero ) = z( 1 )
298  a( n-1+izero ) = z( 2 )
299  a( izero ) = z( 3 )
300  END IF
301  END IF
302 *
303 * If IMAT > 7, set one column of the matrix to 0.
304 *
305  IF( .NOT.zerot ) THEN
306  izero = 0
307  ELSE IF( imat.EQ.8 ) THEN
308  izero = 1
309  z( 2 ) = a( n )
310  a( n ) = zero
311  IF( n.GT.1 ) THEN
312  z( 3 ) = a( 1 )
313  a( 1 ) = zero
314  END IF
315  ELSE IF( imat.EQ.9 ) THEN
316  izero = n
317  z( 1 ) = a( 3*n-2 )
318  z( 2 ) = a( 2*n-1 )
319  a( 3*n-2 ) = zero
320  a( 2*n-1 ) = zero
321  ELSE
322  izero = ( n+1 ) / 2
323  DO 20 i = izero, n - 1
324  a( 2*n-2+i ) = zero
325  a( n-1+i ) = zero
326  a( i ) = zero
327  20 CONTINUE
328  a( 3*n-2 ) = zero
329  a( 2*n-1 ) = zero
330  END IF
331  END IF
332 *
333  DO 120 ifact = 1, 2
334  IF( ifact.EQ.1 ) THEN
335  fact = 'F'
336  ELSE
337  fact = 'N'
338  END IF
339 *
340 * Compute the condition number for comparison with
341 * the value returned by SGTSVX.
342 *
343  IF( zerot ) THEN
344  IF( ifact.EQ.1 )
345  \$ GO TO 120
346  rcondo = zero
347  rcondi = zero
348 *
349  ELSE IF( ifact.EQ.1 ) THEN
350  CALL scopy( n+2*m, a, 1, af, 1 )
351 *
352 * Compute the 1-norm and infinity-norm of A.
353 *
354  anormo = slangt( '1', n, a, a( m+1 ), a( n+m+1 ) )
355  anormi = slangt( 'I', n, a, a( m+1 ), a( n+m+1 ) )
356 *
357 * Factor the matrix A.
358 *
359  CALL sgttrf( n, af, af( m+1 ), af( n+m+1 ),
360  \$ af( n+2*m+1 ), iwork, info )
361 *
362 * Use SGTTRS to solve for one column at a time of
363 * inv(A), computing the maximum column sum as we go.
364 *
365  ainvnm = zero
366  DO 40 i = 1, n
367  DO 30 j = 1, n
368  x( j ) = zero
369  30 CONTINUE
370  x( i ) = one
371  CALL sgttrs( 'No transpose', n, 1, af, af( m+1 ),
372  \$ af( n+m+1 ), af( n+2*m+1 ), iwork, x,
373  \$ lda, info )
374  ainvnm = max( ainvnm, sasum( n, x, 1 ) )
375  40 CONTINUE
376 *
377 * Compute the 1-norm condition number of A.
378 *
379  IF( anormo.LE.zero .OR. ainvnm.LE.zero ) THEN
380  rcondo = one
381  ELSE
382  rcondo = ( one / anormo ) / ainvnm
383  END IF
384 *
385 * Use SGTTRS to solve for one column at a time of
386 * inv(A'), computing the maximum column sum as we go.
387 *
388  ainvnm = zero
389  DO 60 i = 1, n
390  DO 50 j = 1, n
391  x( j ) = zero
392  50 CONTINUE
393  x( i ) = one
394  CALL sgttrs( 'Transpose', n, 1, af, af( m+1 ),
395  \$ af( n+m+1 ), af( n+2*m+1 ), iwork, x,
396  \$ lda, info )
397  ainvnm = max( ainvnm, sasum( n, x, 1 ) )
398  60 CONTINUE
399 *
400 * Compute the infinity-norm condition number of A.
401 *
402  IF( anormi.LE.zero .OR. ainvnm.LE.zero ) THEN
403  rcondi = one
404  ELSE
405  rcondi = ( one / anormi ) / ainvnm
406  END IF
407  END IF
408 *
409  DO 110 itran = 1, 3
410  trans = transs( itran )
411  IF( itran.EQ.1 ) THEN
412  rcondc = rcondo
413  ELSE
414  rcondc = rcondi
415  END IF
416 *
417 * Generate NRHS random solution vectors.
418 *
419  ix = 1
420  DO 70 j = 1, nrhs
421  CALL slarnv( 2, iseed, n, xact( ix ) )
422  ix = ix + lda
423  70 CONTINUE
424 *
425 * Set the right hand side.
426 *
427  CALL slagtm( trans, n, nrhs, one, a, a( m+1 ),
428  \$ a( n+m+1 ), xact, lda, zero, b, lda )
429 *
430  IF( ifact.EQ.2 .AND. itran.EQ.1 ) THEN
431 *
432 * --- Test SGTSV ---
433 *
434 * Solve the system using Gaussian elimination with
435 * partial pivoting.
436 *
437  CALL scopy( n+2*m, a, 1, af, 1 )
438  CALL slacpy( 'Full', n, nrhs, b, lda, x, lda )
439 *
440  srnamt = 'SGTSV '
441  CALL sgtsv( n, nrhs, af, af( m+1 ), af( n+m+1 ), x,
442  \$ lda, info )
443 *
444 * Check error code from SGTSV .
445 *
446  IF( info.NE.izero )
447  \$ CALL alaerh( path, 'SGTSV ', info, izero, ' ',
448  \$ n, n, 1, 1, nrhs, imat, nfail,
449  \$ nerrs, nout )
450  nt = 1
451  IF( izero.EQ.0 ) THEN
452 *
453 * Check residual of computed solution.
454 *
455  CALL slacpy( 'Full', n, nrhs, b, lda, work,
456  \$ lda )
457  CALL sgtt02( trans, n, nrhs, a, a( m+1 ),
458  \$ a( n+m+1 ), x, lda, work, lda,
459  \$ result( 2 ) )
460 *
461 * Check solution from generated exact solution.
462 *
463  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
464  \$ result( 3 ) )
465  nt = 3
466  END IF
467 *
468 * Print information about the tests that did not pass
469 * the threshold.
470 *
471  DO 80 k = 2, nt
472  IF( result( k ).GE.thresh ) THEN
473  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
474  \$ CALL aladhd( nout, path )
475  WRITE( nout, fmt = 9999 )'SGTSV ', n, imat,
476  \$ k, result( k )
477  nfail = nfail + 1
478  END IF
479  80 CONTINUE
480  nrun = nrun + nt - 1
481  END IF
482 *
483 * --- Test SGTSVX ---
484 *
485  IF( ifact.GT.1 ) THEN
486 *
487 * Initialize AF to zero.
488 *
489  DO 90 i = 1, 3*n - 2
490  af( i ) = zero
491  90 CONTINUE
492  END IF
493  CALL slaset( 'Full', n, nrhs, zero, zero, x, lda )
494 *
495 * Solve the system and compute the condition number and
496 * error bounds using SGTSVX.
497 *
498  srnamt = 'SGTSVX'
499  CALL sgtsvx( fact, trans, n, nrhs, a, a( m+1 ),
500  \$ a( n+m+1 ), af, af( m+1 ), af( n+m+1 ),
501  \$ af( n+2*m+1 ), iwork, b, lda, x, lda,
502  \$ rcond, rwork, rwork( nrhs+1 ), work,
503  \$ iwork( n+1 ), info )
504 *
505 * Check the error code from SGTSVX.
506 *
507  IF( info.NE.izero )
508  \$ CALL alaerh( path, 'SGTSVX', info, izero,
509  \$ fact // trans, n, n, 1, 1, nrhs, imat,
510  \$ nfail, nerrs, nout )
511 *
512  IF( ifact.GE.2 ) THEN
513 *
514 * Reconstruct matrix from factors and compute
515 * residual.
516 *
517  CALL sgtt01( n, a, a( m+1 ), a( n+m+1 ), af,
518  \$ af( m+1 ), af( n+m+1 ), af( n+2*m+1 ),
519  \$ iwork, work, lda, rwork, result( 1 ) )
520  k1 = 1
521  ELSE
522  k1 = 2
523  END IF
524 *
525  IF( info.EQ.0 ) THEN
526  trfcon = .false.
527 *
528 * Check residual of computed solution.
529 *
530  CALL slacpy( 'Full', n, nrhs, b, lda, work, lda )
531  CALL sgtt02( trans, n, nrhs, a, a( m+1 ),
532  \$ a( n+m+1 ), x, lda, work, lda,
533  \$ result( 2 ) )
534 *
535 * Check solution from generated exact solution.
536 *
537  CALL sget04( n, nrhs, x, lda, xact, lda, rcondc,
538  \$ result( 3 ) )
539 *
540 * Check the error bounds from iterative refinement.
541 *
542  CALL sgtt05( trans, n, nrhs, a, a( m+1 ),
543  \$ a( n+m+1 ), b, lda, x, lda, xact, lda,
544  \$ rwork, rwork( nrhs+1 ), result( 4 ) )
545  nt = 5
546  END IF
547 *
548 * Print information about the tests that did not pass
549 * the threshold.
550 *
551  DO 100 k = k1, nt
552  IF( result( k ).GE.thresh ) THEN
553  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
554  \$ CALL aladhd( nout, path )
555  WRITE( nout, fmt = 9998 )'SGTSVX', fact, trans,
556  \$ n, imat, k, result( k )
557  nfail = nfail + 1
558  END IF
559  100 CONTINUE
560 *
561 * Check the reciprocal of the condition number.
562 *
563  result( 6 ) = sget06( rcond, rcondc )
564  IF( result( 6 ).GE.thresh ) THEN
565  IF( nfail.EQ.0 .AND. nerrs.EQ.0 )
566  \$ CALL aladhd( nout, path )
567  WRITE( nout, fmt = 9998 )'SGTSVX', fact, trans, n,
568  \$ imat, k, result( k )
569  nfail = nfail + 1
570  END IF
571  nrun = nrun + nt - k1 + 2
572 *
573  110 CONTINUE
574  120 CONTINUE
575  130 CONTINUE
576  140 CONTINUE
577 *
578 * Print a summary of the results.
579 *
580  CALL alasvm( path, nout, nfail, nrun, nerrs )
581 *
582  9999 FORMAT( 1x, a, ', N =', i5, ', type ', i2, ', test ', i2,
583  \$ ', ratio = ', g12.5 )
584  9998 FORMAT( 1x, a, ', FACT=''', a1, ''', TRANS=''', a1, ''', N =',
585  \$ i5, ', type ', i2, ', test ', i2, ', ratio = ', g12.5 )
586  RETURN
587 *
588 * End of SDRVGT
589 *
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:97
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
subroutine alasvm(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASVM
Definition: alasvm.f:73
subroutine alaerh(PATH, SUBNAM, INFO, INFOE, OPTS, M, N, KL, KU, N5, IMAT, NFAIL, NERRS, NOUT)
ALAERH
Definition: alaerh.f:147
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine sgttrf(N, DL, D, DU, DU2, IPIV, INFO)
SGTTRF
Definition: sgttrf.f:124
subroutine sgttrs(TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, INFO)
SGTTRS
Definition: sgttrs.f:138
subroutine sgtsvx(FACT, TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, IWORK, INFO)
SGTSVX computes the solution to system of linear equations A * X = B for GT matrices
Definition: sgtsvx.f:293
subroutine sgtsv(N, NRHS, DL, D, DU, B, LDB, INFO)
SGTSV computes the solution to system of linear equations A * X = B for GT matrices
Definition: sgtsv.f:127
real function slangt(NORM, N, DL, D, DU)
SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slangt.f:106
subroutine slagtm(TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix,...
Definition: slagtm.f:145
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
real function sasum(N, SX, INCX)
SASUM
Definition: sasum.f:72
subroutine slatb4(PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE, CNDNUM, DIST)
SLATB4
Definition: slatb4.f:120
subroutine sgtt02(TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
SGTT02
Definition: sgtt02.f:125
subroutine sgtt05(TRANS, N, NRHS, DL, D, DU, B, LDB, X, LDX, XACT, LDXACT, FERR, BERR, RESLTS)
SGTT05
Definition: sgtt05.f:165
subroutine serrvx(PATH, NUNIT)
SERRVX
Definition: serrvx.f:55
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:102
subroutine sgtt01(N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK, LDWORK, RWORK, RESID)
SGTT01
Definition: sgtt01.f:134
real function sget06(RCOND, RCONDC)
SGET06
Definition: sget06.f:55
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