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cdrvhe.f 20 kB

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  1. *> \brief \b CDRVHE
  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 CDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
  12. * A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
  13. * NOUT )
  14. *
  15. * .. Scalar Arguments ..
  16. * LOGICAL TSTERR
  17. * INTEGER NMAX, NN, NOUT, NRHS
  18. * REAL THRESH
  19. * ..
  20. * .. Array Arguments ..
  21. * LOGICAL DOTYPE( * )
  22. * INTEGER IWORK( * ), NVAL( * )
  23. * REAL RWORK( * )
  24. * COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
  25. * $ WORK( * ), X( * ), XACT( * )
  26. * ..
  27. *
  28. *
  29. *> \par Purpose:
  30. * =============
  31. *>
  32. *> \verbatim
  33. *>
  34. *> CDRVHE tests the driver routines CHESV and -SVX.
  35. *> \endverbatim
  36. *
  37. * Arguments:
  38. * ==========
  39. *
  40. *> \param[in] DOTYPE
  41. *> \verbatim
  42. *> DOTYPE is LOGICAL array, dimension (NTYPES)
  43. *> The matrix types to be used for testing. Matrices of type j
  44. *> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
  45. *> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
  46. *> \endverbatim
  47. *>
  48. *> \param[in] NN
  49. *> \verbatim
  50. *> NN is INTEGER
  51. *> The number of values of N contained in the vector NVAL.
  52. *> \endverbatim
  53. *>
  54. *> \param[in] NVAL
  55. *> \verbatim
  56. *> NVAL is INTEGER array, dimension (NN)
  57. *> The values of the matrix dimension N.
  58. *> \endverbatim
  59. *>
  60. *> \param[in] NRHS
  61. *> \verbatim
  62. *> NRHS is INTEGER
  63. *> The number of right hand side vectors to be generated for
  64. *> each linear system.
  65. *> \endverbatim
  66. *>
  67. *> \param[in] THRESH
  68. *> \verbatim
  69. *> THRESH is REAL
  70. *> The threshold value for the test ratios. A result is
  71. *> included in the output file if RESULT >= THRESH. To have
  72. *> every test ratio printed, use THRESH = 0.
  73. *> \endverbatim
  74. *>
  75. *> \param[in] TSTERR
  76. *> \verbatim
  77. *> TSTERR is LOGICAL
  78. *> Flag that indicates whether error exits are to be tested.
  79. *> \endverbatim
  80. *>
  81. *> \param[in] NMAX
  82. *> \verbatim
  83. *> NMAX is INTEGER
  84. *> The maximum value permitted for N, used in dimensioning the
  85. *> work arrays.
  86. *> \endverbatim
  87. *>
  88. *> \param[out] A
  89. *> \verbatim
  90. *> A is COMPLEX array, dimension (NMAX*NMAX)
  91. *> \endverbatim
  92. *>
  93. *> \param[out] AFAC
  94. *> \verbatim
  95. *> AFAC is COMPLEX array, dimension (NMAX*NMAX)
  96. *> \endverbatim
  97. *>
  98. *> \param[out] AINV
  99. *> \verbatim
  100. *> AINV is COMPLEX array, dimension (NMAX*NMAX)
  101. *> \endverbatim
  102. *>
  103. *> \param[out] B
  104. *> \verbatim
  105. *> B is COMPLEX array, dimension (NMAX*NRHS)
  106. *> \endverbatim
  107. *>
  108. *> \param[out] X
  109. *> \verbatim
  110. *> X is COMPLEX array, dimension (NMAX*NRHS)
  111. *> \endverbatim
  112. *>
  113. *> \param[out] XACT
  114. *> \verbatim
  115. *> XACT is COMPLEX array, dimension (NMAX*NRHS)
  116. *> \endverbatim
  117. *>
  118. *> \param[out] WORK
  119. *> \verbatim
  120. *> WORK is COMPLEX array, dimension (NMAX*max(2,NRHS))
  121. *> \endverbatim
  122. *>
  123. *> \param[out] RWORK
  124. *> \verbatim
  125. *> RWORK is REAL array, dimension (NMAX+2*NRHS)
  126. *> \endverbatim
  127. *>
  128. *> \param[out] IWORK
  129. *> \verbatim
  130. *> IWORK is INTEGER array, dimension (NMAX)
  131. *> \endverbatim
  132. *>
  133. *> \param[in] NOUT
  134. *> \verbatim
  135. *> NOUT is INTEGER
  136. *> The unit number for output.
  137. *> \endverbatim
  138. *
  139. * Authors:
  140. * ========
  141. *
  142. *> \author Univ. of Tennessee
  143. *> \author Univ. of California Berkeley
  144. *> \author Univ. of Colorado Denver
  145. *> \author NAG Ltd.
  146. *
  147. *> \ingroup complex_lin
  148. *
  149. * =====================================================================
  150. SUBROUTINE CDRVHE( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
  151. $ A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
  152. $ NOUT )
  153. *
  154. * -- LAPACK test routine --
  155. * -- LAPACK is a software package provided by Univ. of Tennessee, --
  156. * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  157. *
  158. * .. Scalar Arguments ..
  159. LOGICAL TSTERR
  160. INTEGER NMAX, NN, NOUT, NRHS
  161. REAL THRESH
  162. * ..
  163. * .. Array Arguments ..
  164. LOGICAL DOTYPE( * )
  165. INTEGER IWORK( * ), NVAL( * )
  166. REAL RWORK( * )
  167. COMPLEX A( * ), AFAC( * ), AINV( * ), B( * ),
  168. $ WORK( * ), X( * ), XACT( * )
  169. * ..
  170. *
  171. * =====================================================================
  172. *
  173. * .. Parameters ..
  174. REAL ONE, ZERO
  175. PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
  176. INTEGER NTYPES, NTESTS
  177. PARAMETER ( NTYPES = 10, NTESTS = 6 )
  178. INTEGER NFACT
  179. PARAMETER ( NFACT = 2 )
  180. * ..
  181. * .. Local Scalars ..
  182. LOGICAL ZEROT
  183. CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
  184. CHARACTER*3 PATH
  185. INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
  186. $ IZERO, J, K, K1, KL, KU, LDA, LWORK, MODE, N,
  187. $ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
  188. REAL AINVNM, ANORM, CNDNUM, RCOND, RCONDC
  189. * ..
  190. * .. Local Arrays ..
  191. CHARACTER FACTS( NFACT ), UPLOS( 2 )
  192. INTEGER ISEED( 4 ), ISEEDY( 4 )
  193. REAL RESULT( NTESTS )
  194. * ..
  195. * .. External Functions ..
  196. REAL CLANHE, SGET06
  197. EXTERNAL CLANHE, SGET06
  198. * ..
  199. * .. External Subroutines ..
  200. EXTERNAL ALADHD, ALAERH, ALASVM, CERRVX, CGET04, CHESV,
  201. $ CHESVX, CHET01, CHETRF, CHETRI2, CLACPY,
  202. $ CLAIPD, CLARHS, CLASET, CLATB4, CLATMS, CPOT02,
  203. $ CPOT05, XLAENV
  204. * ..
  205. * .. Scalars in Common ..
  206. LOGICAL LERR, OK
  207. CHARACTER*32 SRNAMT
  208. INTEGER INFOT, NUNIT
  209. * ..
  210. * .. Common blocks ..
  211. COMMON / INFOC / INFOT, NUNIT, OK, LERR
  212. COMMON / SRNAMC / SRNAMT
  213. * ..
  214. * .. Intrinsic Functions ..
  215. INTRINSIC CMPLX, MAX, MIN
  216. * ..
  217. * .. Data statements ..
  218. DATA ISEEDY / 1988, 1989, 1990, 1991 /
  219. DATA UPLOS / 'U', 'L' / , FACTS / 'F', 'N' /
  220. * ..
  221. * .. Executable Statements ..
  222. *
  223. * Initialize constants and the random number seed.
  224. *
  225. PATH( 1: 1 ) = 'Complex precision'
  226. PATH( 2: 3 ) = 'HE'
  227. NRUN = 0
  228. NFAIL = 0
  229. NERRS = 0
  230. DO 10 I = 1, 4
  231. ISEED( I ) = ISEEDY( I )
  232. 10 CONTINUE
  233. LWORK = MAX( 2*NMAX, NMAX*NRHS )
  234. *
  235. * Test the error exits
  236. *
  237. IF( TSTERR )
  238. $ CALL CERRVX( PATH, NOUT )
  239. INFOT = 0
  240. *
  241. * Set the block size and minimum block size for testing.
  242. *
  243. NB = 1
  244. NBMIN = 2
  245. CALL XLAENV( 1, NB )
  246. CALL XLAENV( 2, NBMIN )
  247. *
  248. * Do for each value of N in NVAL
  249. *
  250. DO 180 IN = 1, NN
  251. N = NVAL( IN )
  252. LDA = MAX( N, 1 )
  253. XTYPE = 'N'
  254. NIMAT = NTYPES
  255. IF( N.LE.0 )
  256. $ NIMAT = 1
  257. *
  258. DO 170 IMAT = 1, NIMAT
  259. *
  260. * Do the tests only if DOTYPE( IMAT ) is true.
  261. *
  262. IF( .NOT.DOTYPE( IMAT ) )
  263. $ GO TO 170
  264. *
  265. * Skip types 3, 4, 5, or 6 if the matrix size is too small.
  266. *
  267. ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
  268. IF( ZEROT .AND. N.LT.IMAT-2 )
  269. $ GO TO 170
  270. *
  271. * Do first for UPLO = 'U', then for UPLO = 'L'
  272. *
  273. DO 160 IUPLO = 1, 2
  274. UPLO = UPLOS( IUPLO )
  275. *
  276. * Set up parameters with CLATB4 and generate a test matrix
  277. * with CLATMS.
  278. *
  279. CALL CLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
  280. $ CNDNUM, DIST )
  281. *
  282. SRNAMT = 'CLATMS'
  283. CALL CLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
  284. $ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
  285. $ INFO )
  286. *
  287. * Check error code from CLATMS.
  288. *
  289. IF( INFO.NE.0 ) THEN
  290. CALL ALAERH( PATH, 'CLATMS', INFO, 0, UPLO, N, N, -1,
  291. $ -1, -1, IMAT, NFAIL, NERRS, NOUT )
  292. GO TO 160
  293. END IF
  294. *
  295. * For types 3-6, zero one or more rows and columns of the
  296. * matrix to test that INFO is returned correctly.
  297. *
  298. IF( ZEROT ) THEN
  299. IF( IMAT.EQ.3 ) THEN
  300. IZERO = 1
  301. ELSE IF( IMAT.EQ.4 ) THEN
  302. IZERO = N
  303. ELSE
  304. IZERO = N / 2 + 1
  305. END IF
  306. *
  307. IF( IMAT.LT.6 ) THEN
  308. *
  309. * Set row and column IZERO to zero.
  310. *
  311. IF( IUPLO.EQ.1 ) THEN
  312. IOFF = ( IZERO-1 )*LDA
  313. DO 20 I = 1, IZERO - 1
  314. A( IOFF+I ) = ZERO
  315. 20 CONTINUE
  316. IOFF = IOFF + IZERO
  317. DO 30 I = IZERO, N
  318. A( IOFF ) = ZERO
  319. IOFF = IOFF + LDA
  320. 30 CONTINUE
  321. ELSE
  322. IOFF = IZERO
  323. DO 40 I = 1, IZERO - 1
  324. A( IOFF ) = ZERO
  325. IOFF = IOFF + LDA
  326. 40 CONTINUE
  327. IOFF = IOFF - IZERO
  328. DO 50 I = IZERO, N
  329. A( IOFF+I ) = ZERO
  330. 50 CONTINUE
  331. END IF
  332. ELSE
  333. IOFF = 0
  334. IF( IUPLO.EQ.1 ) THEN
  335. *
  336. * Set the first IZERO rows and columns to zero.
  337. *
  338. DO 70 J = 1, N
  339. I2 = MIN( J, IZERO )
  340. DO 60 I = 1, I2
  341. A( IOFF+I ) = ZERO
  342. 60 CONTINUE
  343. IOFF = IOFF + LDA
  344. 70 CONTINUE
  345. ELSE
  346. *
  347. * Set the last IZERO rows and columns to zero.
  348. *
  349. DO 90 J = 1, N
  350. I1 = MAX( J, IZERO )
  351. DO 80 I = I1, N
  352. A( IOFF+I ) = ZERO
  353. 80 CONTINUE
  354. IOFF = IOFF + LDA
  355. 90 CONTINUE
  356. END IF
  357. END IF
  358. ELSE
  359. IZERO = 0
  360. END IF
  361. *
  362. * Set the imaginary part of the diagonals.
  363. *
  364. CALL CLAIPD( N, A, LDA+1, 0 )
  365. *
  366. DO 150 IFACT = 1, NFACT
  367. *
  368. * Do first for FACT = 'F', then for other values.
  369. *
  370. FACT = FACTS( IFACT )
  371. *
  372. * Compute the condition number for comparison with
  373. * the value returned by CHESVX.
  374. *
  375. IF( ZEROT ) THEN
  376. IF( IFACT.EQ.1 )
  377. $ GO TO 150
  378. RCONDC = ZERO
  379. *
  380. ELSE IF( IFACT.EQ.1 ) THEN
  381. *
  382. * Compute the 1-norm of A.
  383. *
  384. ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK )
  385. *
  386. * Factor the matrix A.
  387. *
  388. CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
  389. CALL CHETRF( UPLO, N, AFAC, LDA, IWORK, WORK,
  390. $ LWORK, INFO )
  391. *
  392. * Compute inv(A) and take its norm.
  393. *
  394. CALL CLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
  395. LWORK = (N+NB+1)*(NB+3)
  396. CALL CHETRI2( UPLO, N, AINV, LDA, IWORK, WORK,
  397. $ LWORK, INFO )
  398. AINVNM = CLANHE( '1', UPLO, N, AINV, LDA, RWORK )
  399. *
  400. * Compute the 1-norm condition number of A.
  401. *
  402. IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
  403. RCONDC = ONE
  404. ELSE
  405. RCONDC = ( ONE / ANORM ) / AINVNM
  406. END IF
  407. END IF
  408. *
  409. * Form an exact solution and set the right hand side.
  410. *
  411. SRNAMT = 'CLARHS'
  412. CALL CLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
  413. $ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
  414. $ INFO )
  415. XTYPE = 'C'
  416. *
  417. * --- Test CHESV ---
  418. *
  419. IF( IFACT.EQ.2 ) THEN
  420. CALL CLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
  421. CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
  422. *
  423. * Factor the matrix and solve the system using CHESV.
  424. *
  425. SRNAMT = 'CHESV '
  426. CALL CHESV( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
  427. $ LDA, WORK, LWORK, INFO )
  428. *
  429. * Adjust the expected value of INFO to account for
  430. * pivoting.
  431. *
  432. K = IZERO
  433. IF( K.GT.0 ) THEN
  434. 100 CONTINUE
  435. IF( IWORK( K ).LT.0 ) THEN
  436. IF( IWORK( K ).NE.-K ) THEN
  437. K = -IWORK( K )
  438. GO TO 100
  439. END IF
  440. ELSE IF( IWORK( K ).NE.K ) THEN
  441. K = IWORK( K )
  442. GO TO 100
  443. END IF
  444. END IF
  445. *
  446. * Check error code from CHESV .
  447. *
  448. IF( INFO.NE.K ) THEN
  449. CALL ALAERH( PATH, 'CHESV ', INFO, K, UPLO, N,
  450. $ N, -1, -1, NRHS, IMAT, NFAIL,
  451. $ NERRS, NOUT )
  452. GO TO 120
  453. ELSE IF( INFO.NE.0 ) THEN
  454. GO TO 120
  455. END IF
  456. *
  457. * Reconstruct matrix from factors and compute
  458. * residual.
  459. *
  460. CALL CHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
  461. $ AINV, LDA, RWORK, RESULT( 1 ) )
  462. *
  463. * Compute residual of the computed solution.
  464. *
  465. CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
  466. CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
  467. $ LDA, RWORK, RESULT( 2 ) )
  468. *
  469. * Check solution from generated exact solution.
  470. *
  471. CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
  472. $ RESULT( 3 ) )
  473. NT = 3
  474. *
  475. * Print information about the tests that did not pass
  476. * the threshold.
  477. *
  478. DO 110 K = 1, NT
  479. IF( RESULT( K ).GE.THRESH ) THEN
  480. IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
  481. $ CALL ALADHD( NOUT, PATH )
  482. WRITE( NOUT, FMT = 9999 )'CHESV ', UPLO, N,
  483. $ IMAT, K, RESULT( K )
  484. NFAIL = NFAIL + 1
  485. END IF
  486. 110 CONTINUE
  487. NRUN = NRUN + NT
  488. 120 CONTINUE
  489. END IF
  490. *
  491. * --- Test CHESVX ---
  492. *
  493. IF( IFACT.EQ.2 )
  494. $ CALL CLASET( UPLO, N, N, CMPLX( ZERO ),
  495. $ CMPLX( ZERO ), AFAC, LDA )
  496. CALL CLASET( 'Full', N, NRHS, CMPLX( ZERO ),
  497. $ CMPLX( ZERO ), X, LDA )
  498. *
  499. * Solve the system and compute the condition number and
  500. * error bounds using CHESVX.
  501. *
  502. SRNAMT = 'CHESVX'
  503. CALL CHESVX( FACT, UPLO, N, NRHS, A, LDA, AFAC, LDA,
  504. $ IWORK, B, LDA, X, LDA, RCOND, RWORK,
  505. $ RWORK( NRHS+1 ), WORK, LWORK,
  506. $ RWORK( 2*NRHS+1 ), INFO )
  507. *
  508. * Adjust the expected value of INFO to account for
  509. * pivoting.
  510. *
  511. K = IZERO
  512. IF( K.GT.0 ) THEN
  513. 130 CONTINUE
  514. IF( IWORK( K ).LT.0 ) THEN
  515. IF( IWORK( K ).NE.-K ) THEN
  516. K = -IWORK( K )
  517. GO TO 130
  518. END IF
  519. ELSE IF( IWORK( K ).NE.K ) THEN
  520. K = IWORK( K )
  521. GO TO 130
  522. END IF
  523. END IF
  524. *
  525. * Check the error code from CHESVX.
  526. *
  527. IF( INFO.NE.K ) THEN
  528. CALL ALAERH( PATH, 'CHESVX', INFO, K, FACT // UPLO,
  529. $ N, N, -1, -1, NRHS, IMAT, NFAIL,
  530. $ NERRS, NOUT )
  531. GO TO 150
  532. END IF
  533. *
  534. IF( INFO.EQ.0 ) THEN
  535. IF( IFACT.GE.2 ) THEN
  536. *
  537. * Reconstruct matrix from factors and compute
  538. * residual.
  539. *
  540. CALL CHET01( UPLO, N, A, LDA, AFAC, LDA, IWORK,
  541. $ AINV, LDA, RWORK( 2*NRHS+1 ),
  542. $ RESULT( 1 ) )
  543. K1 = 1
  544. ELSE
  545. K1 = 2
  546. END IF
  547. *
  548. * Compute residual of the computed solution.
  549. *
  550. CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
  551. CALL CPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
  552. $ LDA, RWORK( 2*NRHS+1 ), RESULT( 2 ) )
  553. *
  554. * Check solution from generated exact solution.
  555. *
  556. CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
  557. $ RESULT( 3 ) )
  558. *
  559. * Check the error bounds from iterative refinement.
  560. *
  561. CALL CPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
  562. $ XACT, LDA, RWORK, RWORK( NRHS+1 ),
  563. $ RESULT( 4 ) )
  564. ELSE
  565. K1 = 6
  566. END IF
  567. *
  568. * Compare RCOND from CHESVX with the computed value
  569. * in RCONDC.
  570. *
  571. RESULT( 6 ) = SGET06( RCOND, RCONDC )
  572. *
  573. * Print information about the tests that did not pass
  574. * the threshold.
  575. *
  576. DO 140 K = K1, 6
  577. IF( RESULT( K ).GE.THRESH ) THEN
  578. IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
  579. $ CALL ALADHD( NOUT, PATH )
  580. WRITE( NOUT, FMT = 9998 )'CHESVX', FACT, UPLO,
  581. $ N, IMAT, K, RESULT( K )
  582. NFAIL = NFAIL + 1
  583. END IF
  584. 140 CONTINUE
  585. NRUN = NRUN + 7 - K1
  586. *
  587. 150 CONTINUE
  588. *
  589. 160 CONTINUE
  590. 170 CONTINUE
  591. 180 CONTINUE
  592. *
  593. * Print a summary of the results.
  594. *
  595. CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
  596. *
  597. 9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
  598. $ ', test ', I2, ', ratio =', G12.5 )
  599. 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
  600. $ ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
  601. RETURN
  602. *
  603. * End of CDRVHE
  604. *
  605. END