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cdrvst2stg.f 76 kB

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  1. *> \brief \b CDRVST2STG
  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 CDRVST2STG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
  12. * NOUNIT, A, LDA, D1, D2, D3, WA1, WA2, WA3, U,
  13. * LDU, V, TAU, Z, WORK, LWORK, RWORK, LRWORK,
  14. * IWORK, LIWORK, RESULT, INFO )
  15. *
  16. * .. Scalar Arguments ..
  17. * INTEGER INFO, LDA, LDU, LIWORK, LRWORK, LWORK, NOUNIT,
  18. * $ NSIZES, NTYPES
  19. * REAL THRESH
  20. * ..
  21. * .. Array Arguments ..
  22. * LOGICAL DOTYPE( * )
  23. * INTEGER ISEED( 4 ), IWORK( * ), NN( * )
  24. * REAL D1( * ), D2( * ), D3( * ), RESULT( * ),
  25. * $ RWORK( * ), WA1( * ), WA2( * ), WA3( * )
  26. * COMPLEX A( LDA, * ), TAU( * ), U( LDU, * ),
  27. * $ V( LDU, * ), WORK( * ), Z( LDU, * )
  28. * ..
  29. *
  30. *
  31. *> \par Purpose:
  32. * =============
  33. *>
  34. *> \verbatim
  35. *>
  36. *> CDRVST2STG checks the Hermitian eigenvalue problem drivers.
  37. *>
  38. *> CHEEVD computes all eigenvalues and, optionally,
  39. *> eigenvectors of a complex Hermitian matrix,
  40. *> using a divide-and-conquer algorithm.
  41. *>
  42. *> CHEEVX computes selected eigenvalues and, optionally,
  43. *> eigenvectors of a complex Hermitian matrix.
  44. *>
  45. *> CHEEVR computes selected eigenvalues and, optionally,
  46. *> eigenvectors of a complex Hermitian matrix
  47. *> using the Relatively Robust Representation where it can.
  48. *>
  49. *> CHPEVD computes all eigenvalues and, optionally,
  50. *> eigenvectors of a complex Hermitian matrix in packed
  51. *> storage, using a divide-and-conquer algorithm.
  52. *>
  53. *> CHPEVX computes selected eigenvalues and, optionally,
  54. *> eigenvectors of a complex Hermitian matrix in packed
  55. *> storage.
  56. *>
  57. *> CHBEVD computes all eigenvalues and, optionally,
  58. *> eigenvectors of a complex Hermitian band matrix,
  59. *> using a divide-and-conquer algorithm.
  60. *>
  61. *> CHBEVX computes selected eigenvalues and, optionally,
  62. *> eigenvectors of a complex Hermitian band matrix.
  63. *>
  64. *> CHEEV computes all eigenvalues and, optionally,
  65. *> eigenvectors of a complex Hermitian matrix.
  66. *>
  67. *> CHPEV computes all eigenvalues and, optionally,
  68. *> eigenvectors of a complex Hermitian matrix in packed
  69. *> storage.
  70. *>
  71. *> CHBEV computes all eigenvalues and, optionally,
  72. *> eigenvectors of a complex Hermitian band matrix.
  73. *>
  74. *> When CDRVST2STG is called, a number of matrix "sizes" ("n's") and a
  75. *> number of matrix "types" are specified. For each size ("n")
  76. *> and each type of matrix, one matrix will be generated and used
  77. *> to test the appropriate drivers. For each matrix and each
  78. *> driver routine called, the following tests will be performed:
  79. *>
  80. *> (1) | A - Z D Z' | / ( |A| n ulp )
  81. *>
  82. *> (2) | I - Z Z' | / ( n ulp )
  83. *>
  84. *> (3) | D1 - D2 | / ( |D1| ulp )
  85. *>
  86. *> where Z is the matrix of eigenvectors returned when the
  87. *> eigenvector option is given and D1 and D2 are the eigenvalues
  88. *> returned with and without the eigenvector option.
  89. *>
  90. *> The "sizes" are specified by an array NN(1:NSIZES); the value of
  91. *> each element NN(j) specifies one size.
  92. *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
  93. *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
  94. *> Currently, the list of possible types is:
  95. *>
  96. *> (1) The zero matrix.
  97. *> (2) The identity matrix.
  98. *>
  99. *> (3) A diagonal matrix with evenly spaced entries
  100. *> 1, ..., ULP and random signs.
  101. *> (ULP = (first number larger than 1) - 1 )
  102. *> (4) A diagonal matrix with geometrically spaced entries
  103. *> 1, ..., ULP and random signs.
  104. *> (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
  105. *> and random signs.
  106. *>
  107. *> (6) Same as (4), but multiplied by SQRT( overflow threshold )
  108. *> (7) Same as (4), but multiplied by SQRT( underflow threshold )
  109. *>
  110. *> (8) A matrix of the form U* D U, where U is unitary and
  111. *> D has evenly spaced entries 1, ..., ULP with random signs
  112. *> on the diagonal.
  113. *>
  114. *> (9) A matrix of the form U* D U, where U is unitary and
  115. *> D has geometrically spaced entries 1, ..., ULP with random
  116. *> signs on the diagonal.
  117. *>
  118. *> (10) A matrix of the form U* D U, where U is unitary and
  119. *> D has "clustered" entries 1, ULP,..., ULP with random
  120. *> signs on the diagonal.
  121. *>
  122. *> (11) Same as (8), but multiplied by SQRT( overflow threshold )
  123. *> (12) Same as (8), but multiplied by SQRT( underflow threshold )
  124. *>
  125. *> (13) Symmetric matrix with random entries chosen from (-1,1).
  126. *> (14) Same as (13), but multiplied by SQRT( overflow threshold )
  127. *> (15) Same as (13), but multiplied by SQRT( underflow threshold )
  128. *> (16) A band matrix with half bandwidth randomly chosen between
  129. *> 0 and N-1, with evenly spaced eigenvalues 1, ..., ULP
  130. *> with random signs.
  131. *> (17) Same as (16), but multiplied by SQRT( overflow threshold )
  132. *> (18) Same as (16), but multiplied by SQRT( underflow threshold )
  133. *> \endverbatim
  134. *
  135. * Arguments:
  136. * ==========
  137. *
  138. *> \verbatim
  139. *> NSIZES INTEGER
  140. *> The number of sizes of matrices to use. If it is zero,
  141. *> CDRVST2STG does nothing. It must be at least zero.
  142. *> Not modified.
  143. *>
  144. *> NN INTEGER array, dimension (NSIZES)
  145. *> An array containing the sizes to be used for the matrices.
  146. *> Zero values will be skipped. The values must be at least
  147. *> zero.
  148. *> Not modified.
  149. *>
  150. *> NTYPES INTEGER
  151. *> The number of elements in DOTYPE. If it is zero, CDRVST2STG
  152. *> does nothing. It must be at least zero. If it is MAXTYP+1
  153. *> and NSIZES is 1, then an additional type, MAXTYP+1 is
  154. *> defined, which is to use whatever matrix is in A. This
  155. *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
  156. *> DOTYPE(MAXTYP+1) is .TRUE. .
  157. *> Not modified.
  158. *>
  159. *> DOTYPE LOGICAL array, dimension (NTYPES)
  160. *> If DOTYPE(j) is .TRUE., then for each size in NN a
  161. *> matrix of that size and of type j will be generated.
  162. *> If NTYPES is smaller than the maximum number of types
  163. *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
  164. *> MAXTYP will not be generated. If NTYPES is larger
  165. *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
  166. *> will be ignored.
  167. *> Not modified.
  168. *>
  169. *> ISEED INTEGER array, dimension (4)
  170. *> On entry ISEED specifies the seed of the random number
  171. *> generator. The array elements should be between 0 and 4095;
  172. *> if not they will be reduced mod 4096. Also, ISEED(4) must
  173. *> be odd. The random number generator uses a linear
  174. *> congruential sequence limited to small integers, and so
  175. *> should produce machine independent random numbers. The
  176. *> values of ISEED are changed on exit, and can be used in the
  177. *> next call to CDRVST2STG to continue the same random number
  178. *> sequence.
  179. *> Modified.
  180. *>
  181. *> THRESH REAL
  182. *> A test will count as "failed" if the "error", computed as
  183. *> described above, exceeds THRESH. Note that the error
  184. *> is scaled to be O(1), so THRESH should be a reasonably
  185. *> small multiple of 1, e.g., 10 or 100. In particular,
  186. *> it should not depend on the precision (single vs. double)
  187. *> or the size of the matrix. It must be at least zero.
  188. *> Not modified.
  189. *>
  190. *> NOUNIT INTEGER
  191. *> The FORTRAN unit number for printing out error messages
  192. *> (e.g., if a routine returns IINFO not equal to 0.)
  193. *> Not modified.
  194. *>
  195. *> A COMPLEX array, dimension (LDA , max(NN))
  196. *> Used to hold the matrix whose eigenvalues are to be
  197. *> computed. On exit, A contains the last matrix actually
  198. *> used.
  199. *> Modified.
  200. *>
  201. *> LDA INTEGER
  202. *> The leading dimension of A. It must be at
  203. *> least 1 and at least max( NN ).
  204. *> Not modified.
  205. *>
  206. *> D1 REAL array, dimension (max(NN))
  207. *> The eigenvalues of A, as computed by CSTEQR simlutaneously
  208. *> with Z. On exit, the eigenvalues in D1 correspond with the
  209. *> matrix in A.
  210. *> Modified.
  211. *>
  212. *> D2 REAL array, dimension (max(NN))
  213. *> The eigenvalues of A, as computed by CSTEQR if Z is not
  214. *> computed. On exit, the eigenvalues in D2 correspond with
  215. *> the matrix in A.
  216. *> Modified.
  217. *>
  218. *> D3 REAL array, dimension (max(NN))
  219. *> The eigenvalues of A, as computed by SSTERF. On exit, the
  220. *> eigenvalues in D3 correspond with the matrix in A.
  221. *> Modified.
  222. *>
  223. *> WA1 REAL array, dimension
  224. *>
  225. *> WA2 REAL array, dimension
  226. *>
  227. *> WA3 REAL array, dimension
  228. *>
  229. *> U COMPLEX array, dimension (LDU, max(NN))
  230. *> The unitary matrix computed by CHETRD + CUNGC3.
  231. *> Modified.
  232. *>
  233. *> LDU INTEGER
  234. *> The leading dimension of U, Z, and V. It must be at
  235. *> least 1 and at least max( NN ).
  236. *> Not modified.
  237. *>
  238. *> V COMPLEX array, dimension (LDU, max(NN))
  239. *> The Housholder vectors computed by CHETRD in reducing A to
  240. *> tridiagonal form.
  241. *> Modified.
  242. *>
  243. *> TAU COMPLEX array, dimension (max(NN))
  244. *> The Householder factors computed by CHETRD in reducing A
  245. *> to tridiagonal form.
  246. *> Modified.
  247. *>
  248. *> Z COMPLEX array, dimension (LDU, max(NN))
  249. *> The unitary matrix of eigenvectors computed by CHEEVD,
  250. *> CHEEVX, CHPEVD, CHPEVX, CHBEVD, and CHBEVX.
  251. *> Modified.
  252. *>
  253. *> WORK - COMPLEX array of dimension ( LWORK )
  254. *> Workspace.
  255. *> Modified.
  256. *>
  257. *> LWORK - INTEGER
  258. *> The number of entries in WORK. This must be at least
  259. *> 2*max( NN(j), 2 )**2.
  260. *> Not modified.
  261. *>
  262. *> RWORK REAL array, dimension (3*max(NN))
  263. *> Workspace.
  264. *> Modified.
  265. *>
  266. *> LRWORK - INTEGER
  267. *> The number of entries in RWORK.
  268. *>
  269. *> IWORK INTEGER array, dimension (6*max(NN))
  270. *> Workspace.
  271. *> Modified.
  272. *>
  273. *> LIWORK - INTEGER
  274. *> The number of entries in IWORK.
  275. *>
  276. *> RESULT REAL array, dimension (??)
  277. *> The values computed by the tests described above.
  278. *> The values are currently limited to 1/ulp, to avoid
  279. *> overflow.
  280. *> Modified.
  281. *>
  282. *> INFO INTEGER
  283. *> If 0, then everything ran OK.
  284. *> -1: NSIZES < 0
  285. *> -2: Some NN(j) < 0
  286. *> -3: NTYPES < 0
  287. *> -5: THRESH < 0
  288. *> -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
  289. *> -16: LDU < 1 or LDU < NMAX.
  290. *> -21: LWORK too small.
  291. *> If SLATMR, SLATMS, CHETRD, SORGC3, CSTEQR, SSTERF,
  292. *> or SORMC2 returns an error code, the
  293. *> absolute value of it is returned.
  294. *> Modified.
  295. *>
  296. *>-----------------------------------------------------------------------
  297. *>
  298. *> Some Local Variables and Parameters:
  299. *> ---- ----- --------- --- ----------
  300. *> ZERO, ONE Real 0 and 1.
  301. *> MAXTYP The number of types defined.
  302. *> NTEST The number of tests performed, or which can
  303. *> be performed so far, for the current matrix.
  304. *> NTESTT The total number of tests performed so far.
  305. *> NMAX Largest value in NN.
  306. *> NMATS The number of matrices generated so far.
  307. *> NERRS The number of tests which have exceeded THRESH
  308. *> so far (computed by SLAFTS).
  309. *> COND, IMODE Values to be passed to the matrix generators.
  310. *> ANORM Norm of A; passed to matrix generators.
  311. *>
  312. *> OVFL, UNFL Overflow and underflow thresholds.
  313. *> ULP, ULPINV Finest relative precision and its inverse.
  314. *> RTOVFL, RTUNFL Square roots of the previous 2 values.
  315. *> The following four arrays decode JTYPE:
  316. *> KTYPE(j) The general type (1-10) for type "j".
  317. *> KMODE(j) The MODE value to be passed to the matrix
  318. *> generator for type "j".
  319. *> KMAGN(j) The order of magnitude ( O(1),
  320. *> O(overflow^(1/2) ), O(underflow^(1/2) )
  321. *> \endverbatim
  322. *
  323. * Authors:
  324. * ========
  325. *
  326. *> \author Univ. of Tennessee
  327. *> \author Univ. of California Berkeley
  328. *> \author Univ. of Colorado Denver
  329. *> \author NAG Ltd.
  330. *
  331. *> \ingroup complex_eig
  332. *
  333. * =====================================================================
  334. SUBROUTINE CDRVST2STG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
  335. $ NOUNIT, A, LDA, D1, D2, D3, WA1, WA2, WA3, U,
  336. $ LDU, V, TAU, Z, WORK, LWORK, RWORK, LRWORK,
  337. $ IWORK, LIWORK, RESULT, INFO )
  338. *
  339. * -- LAPACK test routine --
  340. * -- LAPACK is a software package provided by Univ. of Tennessee, --
  341. * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  342. *
  343. * .. Scalar Arguments ..
  344. INTEGER INFO, LDA, LDU, LIWORK, LRWORK, LWORK, NOUNIT,
  345. $ NSIZES, NTYPES
  346. REAL THRESH
  347. * ..
  348. * .. Array Arguments ..
  349. LOGICAL DOTYPE( * )
  350. INTEGER ISEED( 4 ), IWORK( * ), NN( * )
  351. REAL D1( * ), D2( * ), D3( * ), RESULT( * ),
  352. $ RWORK( * ), WA1( * ), WA2( * ), WA3( * )
  353. COMPLEX A( LDA, * ), TAU( * ), U( LDU, * ),
  354. $ V( LDU, * ), WORK( * ), Z( LDU, * )
  355. * ..
  356. *
  357. * =====================================================================
  358. *
  359. *
  360. * .. Parameters ..
  361. REAL ZERO, ONE, TWO, TEN
  362. PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0,
  363. $ TEN = 10.0E+0 )
  364. REAL HALF
  365. PARAMETER ( HALF = ONE / TWO )
  366. COMPLEX CZERO, CONE
  367. PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
  368. $ CONE = ( 1.0E+0, 0.0E+0 ) )
  369. INTEGER MAXTYP
  370. PARAMETER ( MAXTYP = 18 )
  371. * ..
  372. * .. Local Scalars ..
  373. LOGICAL BADNN
  374. CHARACTER UPLO
  375. INTEGER I, IDIAG, IHBW, IINFO, IL, IMODE, INDWRK, INDX,
  376. $ IROW, ITEMP, ITYPE, IU, IUPLO, J, J1, J2, JCOL,
  377. $ JSIZE, JTYPE, KD, LGN, LIWEDC, LRWEDC, LWEDC,
  378. $ M, M2, M3, MTYPES, N, NERRS, NMATS, NMAX,
  379. $ NTEST, NTESTT
  380. REAL ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
  381. $ RTUNFL, TEMP1, TEMP2, TEMP3, ULP, ULPINV, UNFL,
  382. $ VL, VU
  383. * ..
  384. * .. Local Arrays ..
  385. INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
  386. $ ISEED3( 4 ), KMAGN( MAXTYP ), KMODE( MAXTYP ),
  387. $ KTYPE( MAXTYP )
  388. * ..
  389. * .. External Functions ..
  390. REAL SLAMCH, SLARND, SSXT1
  391. EXTERNAL SLAMCH, SLARND, SSXT1
  392. * ..
  393. * .. External Subroutines ..
  394. EXTERNAL ALASVM, SLABAD, SLAFTS, XERBLA, CHBEV, CHBEVD,
  395. $ CHBEVX, CHEEV, CHEEVD, CHEEVR, CHEEVX, CHET21,
  396. $ CHET22, CHPEV, CHPEVD, CHPEVX, CLACPY, CLASET,
  397. $ CHEEVD_2STAGE, CHEEVR_2STAGE, CHEEVX_2STAGE,
  398. $ CHEEV_2STAGE, CHBEV_2STAGE, CHBEVD_2STAGE,
  399. $ CHBEVX_2STAGE, CLATMR, CLATMS
  400. * ..
  401. * .. Intrinsic Functions ..
  402. INTRINSIC ABS, REAL, INT, LOG, MAX, MIN, SQRT
  403. * ..
  404. * .. Data statements ..
  405. DATA KTYPE / 1, 2, 5*4, 5*5, 3*8, 3*9 /
  406. DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
  407. $ 2, 3, 1, 2, 3 /
  408. DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
  409. $ 0, 0, 4, 4, 4 /
  410. * ..
  411. * .. Executable Statements ..
  412. *
  413. * 1) Check for errors
  414. *
  415. NTESTT = 0
  416. INFO = 0
  417. *
  418. BADNN = .FALSE.
  419. NMAX = 1
  420. DO 10 J = 1, NSIZES
  421. NMAX = MAX( NMAX, NN( J ) )
  422. IF( NN( J ).LT.0 )
  423. $ BADNN = .TRUE.
  424. 10 CONTINUE
  425. *
  426. * Check for errors
  427. *
  428. IF( NSIZES.LT.0 ) THEN
  429. INFO = -1
  430. ELSE IF( BADNN ) THEN
  431. INFO = -2
  432. ELSE IF( NTYPES.LT.0 ) THEN
  433. INFO = -3
  434. ELSE IF( LDA.LT.NMAX ) THEN
  435. INFO = -9
  436. ELSE IF( LDU.LT.NMAX ) THEN
  437. INFO = -16
  438. ELSE IF( 2*MAX( 2, NMAX )**2.GT.LWORK ) THEN
  439. INFO = -22
  440. END IF
  441. *
  442. IF( INFO.NE.0 ) THEN
  443. CALL XERBLA( 'CDRVST2STG', -INFO )
  444. RETURN
  445. END IF
  446. *
  447. * Quick return if nothing to do
  448. *
  449. IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
  450. $ RETURN
  451. *
  452. * More Important constants
  453. *
  454. UNFL = SLAMCH( 'Safe minimum' )
  455. OVFL = SLAMCH( 'Overflow' )
  456. CALL SLABAD( UNFL, OVFL )
  457. ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' )
  458. ULPINV = ONE / ULP
  459. RTUNFL = SQRT( UNFL )
  460. RTOVFL = SQRT( OVFL )
  461. *
  462. * Loop over sizes, types
  463. *
  464. DO 20 I = 1, 4
  465. ISEED2( I ) = ISEED( I )
  466. ISEED3( I ) = ISEED( I )
  467. 20 CONTINUE
  468. *
  469. NERRS = 0
  470. NMATS = 0
  471. *
  472. DO 1220 JSIZE = 1, NSIZES
  473. N = NN( JSIZE )
  474. IF( N.GT.0 ) THEN
  475. LGN = INT( LOG( REAL( N ) ) / LOG( TWO ) )
  476. IF( 2**LGN.LT.N )
  477. $ LGN = LGN + 1
  478. IF( 2**LGN.LT.N )
  479. $ LGN = LGN + 1
  480. LWEDC = MAX( 2*N+N*N, 2*N*N )
  481. LRWEDC = 1 + 4*N + 2*N*LGN + 3*N**2
  482. LIWEDC = 3 + 5*N
  483. ELSE
  484. LWEDC = 2
  485. LRWEDC = 8
  486. LIWEDC = 8
  487. END IF
  488. ANINV = ONE / REAL( MAX( 1, N ) )
  489. *
  490. IF( NSIZES.NE.1 ) THEN
  491. MTYPES = MIN( MAXTYP, NTYPES )
  492. ELSE
  493. MTYPES = MIN( MAXTYP+1, NTYPES )
  494. END IF
  495. *
  496. DO 1210 JTYPE = 1, MTYPES
  497. IF( .NOT.DOTYPE( JTYPE ) )
  498. $ GO TO 1210
  499. NMATS = NMATS + 1
  500. NTEST = 0
  501. *
  502. DO 30 J = 1, 4
  503. IOLDSD( J ) = ISEED( J )
  504. 30 CONTINUE
  505. *
  506. * 2) Compute "A"
  507. *
  508. * Control parameters:
  509. *
  510. * KMAGN KMODE KTYPE
  511. * =1 O(1) clustered 1 zero
  512. * =2 large clustered 2 identity
  513. * =3 small exponential (none)
  514. * =4 arithmetic diagonal, (w/ eigenvalues)
  515. * =5 random log Hermitian, w/ eigenvalues
  516. * =6 random (none)
  517. * =7 random diagonal
  518. * =8 random Hermitian
  519. * =9 band Hermitian, w/ eigenvalues
  520. *
  521. IF( MTYPES.GT.MAXTYP )
  522. $ GO TO 110
  523. *
  524. ITYPE = KTYPE( JTYPE )
  525. IMODE = KMODE( JTYPE )
  526. *
  527. * Compute norm
  528. *
  529. GO TO ( 40, 50, 60 )KMAGN( JTYPE )
  530. *
  531. 40 CONTINUE
  532. ANORM = ONE
  533. GO TO 70
  534. *
  535. 50 CONTINUE
  536. ANORM = ( RTOVFL*ULP )*ANINV
  537. GO TO 70
  538. *
  539. 60 CONTINUE
  540. ANORM = RTUNFL*N*ULPINV
  541. GO TO 70
  542. *
  543. 70 CONTINUE
  544. *
  545. CALL CLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
  546. IINFO = 0
  547. COND = ULPINV
  548. *
  549. * Special Matrices -- Identity & Jordan block
  550. *
  551. * Zero
  552. *
  553. IF( ITYPE.EQ.1 ) THEN
  554. IINFO = 0
  555. *
  556. ELSE IF( ITYPE.EQ.2 ) THEN
  557. *
  558. * Identity
  559. *
  560. DO 80 JCOL = 1, N
  561. A( JCOL, JCOL ) = ANORM
  562. 80 CONTINUE
  563. *
  564. ELSE IF( ITYPE.EQ.4 ) THEN
  565. *
  566. * Diagonal Matrix, [Eigen]values Specified
  567. *
  568. CALL CLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
  569. $ ANORM, 0, 0, 'N', A, LDA, WORK, IINFO )
  570. *
  571. ELSE IF( ITYPE.EQ.5 ) THEN
  572. *
  573. * Hermitian, eigenvalues specified
  574. *
  575. CALL CLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
  576. $ ANORM, N, N, 'N', A, LDA, WORK, IINFO )
  577. *
  578. ELSE IF( ITYPE.EQ.7 ) THEN
  579. *
  580. * Diagonal, random eigenvalues
  581. *
  582. CALL CLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE, CONE,
  583. $ 'T', 'N', WORK( N+1 ), 1, ONE,
  584. $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
  585. $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
  586. *
  587. ELSE IF( ITYPE.EQ.8 ) THEN
  588. *
  589. * Hermitian, random eigenvalues
  590. *
  591. CALL CLATMR( N, N, 'S', ISEED, 'H', WORK, 6, ONE, CONE,
  592. $ 'T', 'N', WORK( N+1 ), 1, ONE,
  593. $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
  594. $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
  595. *
  596. ELSE IF( ITYPE.EQ.9 ) THEN
  597. *
  598. * Hermitian banded, eigenvalues specified
  599. *
  600. IHBW = INT( ( N-1 )*SLARND( 1, ISEED3 ) )
  601. CALL CLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND,
  602. $ ANORM, IHBW, IHBW, 'Z', U, LDU, WORK,
  603. $ IINFO )
  604. *
  605. * Store as dense matrix for most routines.
  606. *
  607. CALL CLASET( 'Full', LDA, N, CZERO, CZERO, A, LDA )
  608. DO 100 IDIAG = -IHBW, IHBW
  609. IROW = IHBW - IDIAG + 1
  610. J1 = MAX( 1, IDIAG+1 )
  611. J2 = MIN( N, N+IDIAG )
  612. DO 90 J = J1, J2
  613. I = J - IDIAG
  614. A( I, J ) = U( IROW, J )
  615. 90 CONTINUE
  616. 100 CONTINUE
  617. ELSE
  618. IINFO = 1
  619. END IF
  620. *
  621. IF( IINFO.NE.0 ) THEN
  622. WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
  623. $ IOLDSD
  624. INFO = ABS( IINFO )
  625. RETURN
  626. END IF
  627. *
  628. 110 CONTINUE
  629. *
  630. ABSTOL = UNFL + UNFL
  631. IF( N.LE.1 ) THEN
  632. IL = 1
  633. IU = N
  634. ELSE
  635. IL = 1 + INT( ( N-1 )*SLARND( 1, ISEED2 ) )
  636. IU = 1 + INT( ( N-1 )*SLARND( 1, ISEED2 ) )
  637. IF( IL.GT.IU ) THEN
  638. ITEMP = IL
  639. IL = IU
  640. IU = ITEMP
  641. END IF
  642. END IF
  643. *
  644. * Perform tests storing upper or lower triangular
  645. * part of matrix.
  646. *
  647. DO 1200 IUPLO = 0, 1
  648. IF( IUPLO.EQ.0 ) THEN
  649. UPLO = 'L'
  650. ELSE
  651. UPLO = 'U'
  652. END IF
  653. *
  654. * Call CHEEVD and CHEEVX.
  655. *
  656. CALL CLACPY( ' ', N, N, A, LDA, V, LDU )
  657. *
  658. NTEST = NTEST + 1
  659. CALL CHEEVD( 'V', UPLO, N, A, LDU, D1, WORK, LWEDC,
  660. $ RWORK, LRWEDC, IWORK, LIWEDC, IINFO )
  661. IF( IINFO.NE.0 ) THEN
  662. WRITE( NOUNIT, FMT = 9999 )'CHEEVD(V,' // UPLO //
  663. $ ')', IINFO, N, JTYPE, IOLDSD
  664. INFO = ABS( IINFO )
  665. IF( IINFO.LT.0 ) THEN
  666. RETURN
  667. ELSE
  668. RESULT( NTEST ) = ULPINV
  669. RESULT( NTEST+1 ) = ULPINV
  670. RESULT( NTEST+2 ) = ULPINV
  671. GO TO 130
  672. END IF
  673. END IF
  674. *
  675. * Do tests 1 and 2.
  676. *
  677. CALL CHET21( 1, UPLO, N, 0, V, LDU, D1, D2, A, LDU, Z,
  678. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  679. *
  680. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  681. *
  682. NTEST = NTEST + 2
  683. CALL CHEEVD_2STAGE( 'N', UPLO, N, A, LDU, D3, WORK,
  684. $ LWORK, RWORK, LRWEDC, IWORK, LIWEDC, IINFO )
  685. IF( IINFO.NE.0 ) THEN
  686. WRITE( NOUNIT, FMT = 9999 )
  687. $ 'CHEEVD_2STAGE(N,' // UPLO //
  688. $ ')', IINFO, N, JTYPE, IOLDSD
  689. INFO = ABS( IINFO )
  690. IF( IINFO.LT.0 ) THEN
  691. RETURN
  692. ELSE
  693. RESULT( NTEST ) = ULPINV
  694. GO TO 130
  695. END IF
  696. END IF
  697. *
  698. * Do test 3.
  699. *
  700. TEMP1 = ZERO
  701. TEMP2 = ZERO
  702. DO 120 J = 1, N
  703. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  704. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  705. 120 CONTINUE
  706. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  707. $ ULP*MAX( TEMP1, TEMP2 ) )
  708. *
  709. 130 CONTINUE
  710. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  711. *
  712. NTEST = NTEST + 1
  713. *
  714. IF( N.GT.0 ) THEN
  715. TEMP3 = MAX( ABS( D1( 1 ) ), ABS( D1( N ) ) )
  716. IF( IL.NE.1 ) THEN
  717. VL = D1( IL ) - MAX( HALF*( D1( IL )-D1( IL-1 ) ),
  718. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  719. ELSE IF( N.GT.0 ) THEN
  720. VL = D1( 1 ) - MAX( HALF*( D1( N )-D1( 1 ) ),
  721. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  722. END IF
  723. IF( IU.NE.N ) THEN
  724. VU = D1( IU ) + MAX( HALF*( D1( IU+1 )-D1( IU ) ),
  725. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  726. ELSE IF( N.GT.0 ) THEN
  727. VU = D1( N ) + MAX( HALF*( D1( N )-D1( 1 ) ),
  728. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  729. END IF
  730. ELSE
  731. TEMP3 = ZERO
  732. VL = ZERO
  733. VU = ONE
  734. END IF
  735. *
  736. CALL CHEEVX( 'V', 'A', UPLO, N, A, LDU, VL, VU, IL, IU,
  737. $ ABSTOL, M, WA1, Z, LDU, WORK, LWORK, RWORK,
  738. $ IWORK, IWORK( 5*N+1 ), IINFO )
  739. IF( IINFO.NE.0 ) THEN
  740. WRITE( NOUNIT, FMT = 9999 )'CHEEVX(V,A,' // UPLO //
  741. $ ')', IINFO, N, JTYPE, IOLDSD
  742. INFO = ABS( IINFO )
  743. IF( IINFO.LT.0 ) THEN
  744. RETURN
  745. ELSE
  746. RESULT( NTEST ) = ULPINV
  747. RESULT( NTEST+1 ) = ULPINV
  748. RESULT( NTEST+2 ) = ULPINV
  749. GO TO 150
  750. END IF
  751. END IF
  752. *
  753. * Do tests 4 and 5.
  754. *
  755. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  756. *
  757. CALL CHET21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  758. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  759. *
  760. NTEST = NTEST + 2
  761. CALL CHEEVX_2STAGE( 'N', 'A', UPLO, N, A, LDU, VL, VU,
  762. $ IL, IU, ABSTOL, M2, WA2, Z, LDU,
  763. $ WORK, LWORK, RWORK, IWORK,
  764. $ IWORK( 5*N+1 ), IINFO )
  765. IF( IINFO.NE.0 ) THEN
  766. WRITE( NOUNIT, FMT = 9999 )
  767. $ 'CHEEVX_2STAGE(N,A,' // UPLO //
  768. $ ')', IINFO, N, JTYPE, IOLDSD
  769. INFO = ABS( IINFO )
  770. IF( IINFO.LT.0 ) THEN
  771. RETURN
  772. ELSE
  773. RESULT( NTEST ) = ULPINV
  774. GO TO 150
  775. END IF
  776. END IF
  777. *
  778. * Do test 6.
  779. *
  780. TEMP1 = ZERO
  781. TEMP2 = ZERO
  782. DO 140 J = 1, N
  783. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  784. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  785. 140 CONTINUE
  786. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  787. $ ULP*MAX( TEMP1, TEMP2 ) )
  788. *
  789. 150 CONTINUE
  790. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  791. *
  792. NTEST = NTEST + 1
  793. *
  794. CALL CHEEVX( 'V', 'I', UPLO, N, A, LDU, VL, VU, IL, IU,
  795. $ ABSTOL, M2, WA2, Z, LDU, WORK, LWORK, RWORK,
  796. $ IWORK, IWORK( 5*N+1 ), IINFO )
  797. IF( IINFO.NE.0 ) THEN
  798. WRITE( NOUNIT, FMT = 9999 )'CHEEVX(V,I,' // UPLO //
  799. $ ')', IINFO, N, JTYPE, IOLDSD
  800. INFO = ABS( IINFO )
  801. IF( IINFO.LT.0 ) THEN
  802. RETURN
  803. ELSE
  804. RESULT( NTEST ) = ULPINV
  805. GO TO 160
  806. END IF
  807. END IF
  808. *
  809. * Do tests 7 and 8.
  810. *
  811. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  812. *
  813. CALL CHET22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  814. $ V, LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  815. *
  816. NTEST = NTEST + 2
  817. *
  818. CALL CHEEVX_2STAGE( 'N', 'I', UPLO, N, A, LDU, VL, VU,
  819. $ IL, IU, ABSTOL, M3, WA3, Z, LDU,
  820. $ WORK, LWORK, RWORK, IWORK,
  821. $ IWORK( 5*N+1 ), IINFO )
  822. IF( IINFO.NE.0 ) THEN
  823. WRITE( NOUNIT, FMT = 9999 )
  824. $ 'CHEEVX_2STAGE(N,I,' // UPLO //
  825. $ ')', IINFO, N, JTYPE, IOLDSD
  826. INFO = ABS( IINFO )
  827. IF( IINFO.LT.0 ) THEN
  828. RETURN
  829. ELSE
  830. RESULT( NTEST ) = ULPINV
  831. GO TO 160
  832. END IF
  833. END IF
  834. *
  835. * Do test 9.
  836. *
  837. TEMP1 = SSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  838. TEMP2 = SSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  839. IF( N.GT.0 ) THEN
  840. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  841. ELSE
  842. TEMP3 = ZERO
  843. END IF
  844. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  845. $ MAX( UNFL, TEMP3*ULP )
  846. *
  847. 160 CONTINUE
  848. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  849. *
  850. NTEST = NTEST + 1
  851. *
  852. CALL CHEEVX( 'V', 'V', UPLO, N, A, LDU, VL, VU, IL, IU,
  853. $ ABSTOL, M2, WA2, Z, LDU, WORK, LWORK, RWORK,
  854. $ IWORK, IWORK( 5*N+1 ), IINFO )
  855. IF( IINFO.NE.0 ) THEN
  856. WRITE( NOUNIT, FMT = 9999 )'CHEEVX(V,V,' // UPLO //
  857. $ ')', IINFO, N, JTYPE, IOLDSD
  858. INFO = ABS( IINFO )
  859. IF( IINFO.LT.0 ) THEN
  860. RETURN
  861. ELSE
  862. RESULT( NTEST ) = ULPINV
  863. GO TO 170
  864. END IF
  865. END IF
  866. *
  867. * Do tests 10 and 11.
  868. *
  869. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  870. *
  871. CALL CHET22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  872. $ V, LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  873. *
  874. NTEST = NTEST + 2
  875. *
  876. CALL CHEEVX_2STAGE( 'N', 'V', UPLO, N, A, LDU, VL, VU,
  877. $ IL, IU, ABSTOL, M3, WA3, Z, LDU,
  878. $ WORK, LWORK, RWORK, IWORK,
  879. $ IWORK( 5*N+1 ), IINFO )
  880. IF( IINFO.NE.0 ) THEN
  881. WRITE( NOUNIT, FMT = 9999 )
  882. $ 'CHEEVX_2STAGE(N,V,' // UPLO //
  883. $ ')', IINFO, N, JTYPE, IOLDSD
  884. INFO = ABS( IINFO )
  885. IF( IINFO.LT.0 ) THEN
  886. RETURN
  887. ELSE
  888. RESULT( NTEST ) = ULPINV
  889. GO TO 170
  890. END IF
  891. END IF
  892. *
  893. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  894. RESULT( NTEST ) = ULPINV
  895. GO TO 170
  896. END IF
  897. *
  898. * Do test 12.
  899. *
  900. TEMP1 = SSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  901. TEMP2 = SSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  902. IF( N.GT.0 ) THEN
  903. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  904. ELSE
  905. TEMP3 = ZERO
  906. END IF
  907. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  908. $ MAX( UNFL, TEMP3*ULP )
  909. *
  910. 170 CONTINUE
  911. *
  912. * Call CHPEVD and CHPEVX.
  913. *
  914. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  915. *
  916. * Load array WORK with the upper or lower triangular
  917. * part of the matrix in packed form.
  918. *
  919. IF( IUPLO.EQ.1 ) THEN
  920. INDX = 1
  921. DO 190 J = 1, N
  922. DO 180 I = 1, J
  923. WORK( INDX ) = A( I, J )
  924. INDX = INDX + 1
  925. 180 CONTINUE
  926. 190 CONTINUE
  927. ELSE
  928. INDX = 1
  929. DO 210 J = 1, N
  930. DO 200 I = J, N
  931. WORK( INDX ) = A( I, J )
  932. INDX = INDX + 1
  933. 200 CONTINUE
  934. 210 CONTINUE
  935. END IF
  936. *
  937. NTEST = NTEST + 1
  938. INDWRK = N*( N+1 ) / 2 + 1
  939. CALL CHPEVD( 'V', UPLO, N, WORK, D1, Z, LDU,
  940. $ WORK( INDWRK ), LWEDC, RWORK, LRWEDC, IWORK,
  941. $ LIWEDC, IINFO )
  942. IF( IINFO.NE.0 ) THEN
  943. WRITE( NOUNIT, FMT = 9999 )'CHPEVD(V,' // UPLO //
  944. $ ')', IINFO, N, JTYPE, IOLDSD
  945. INFO = ABS( IINFO )
  946. IF( IINFO.LT.0 ) THEN
  947. RETURN
  948. ELSE
  949. RESULT( NTEST ) = ULPINV
  950. RESULT( NTEST+1 ) = ULPINV
  951. RESULT( NTEST+2 ) = ULPINV
  952. GO TO 270
  953. END IF
  954. END IF
  955. *
  956. * Do tests 13 and 14.
  957. *
  958. CALL CHET21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  959. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  960. *
  961. IF( IUPLO.EQ.1 ) THEN
  962. INDX = 1
  963. DO 230 J = 1, N
  964. DO 220 I = 1, J
  965. WORK( INDX ) = A( I, J )
  966. INDX = INDX + 1
  967. 220 CONTINUE
  968. 230 CONTINUE
  969. ELSE
  970. INDX = 1
  971. DO 250 J = 1, N
  972. DO 240 I = J, N
  973. WORK( INDX ) = A( I, J )
  974. INDX = INDX + 1
  975. 240 CONTINUE
  976. 250 CONTINUE
  977. END IF
  978. *
  979. NTEST = NTEST + 2
  980. INDWRK = N*( N+1 ) / 2 + 1
  981. CALL CHPEVD( 'N', UPLO, N, WORK, D3, Z, LDU,
  982. $ WORK( INDWRK ), LWEDC, RWORK, LRWEDC, IWORK,
  983. $ LIWEDC, IINFO )
  984. IF( IINFO.NE.0 ) THEN
  985. WRITE( NOUNIT, FMT = 9999 )'CHPEVD(N,' // UPLO //
  986. $ ')', IINFO, N, JTYPE, IOLDSD
  987. INFO = ABS( IINFO )
  988. IF( IINFO.LT.0 ) THEN
  989. RETURN
  990. ELSE
  991. RESULT( NTEST ) = ULPINV
  992. GO TO 270
  993. END IF
  994. END IF
  995. *
  996. * Do test 15.
  997. *
  998. TEMP1 = ZERO
  999. TEMP2 = ZERO
  1000. DO 260 J = 1, N
  1001. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1002. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1003. 260 CONTINUE
  1004. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1005. $ ULP*MAX( TEMP1, TEMP2 ) )
  1006. *
  1007. * Load array WORK with the upper or lower triangular part
  1008. * of the matrix in packed form.
  1009. *
  1010. 270 CONTINUE
  1011. IF( IUPLO.EQ.1 ) THEN
  1012. INDX = 1
  1013. DO 290 J = 1, N
  1014. DO 280 I = 1, J
  1015. WORK( INDX ) = A( I, J )
  1016. INDX = INDX + 1
  1017. 280 CONTINUE
  1018. 290 CONTINUE
  1019. ELSE
  1020. INDX = 1
  1021. DO 310 J = 1, N
  1022. DO 300 I = J, N
  1023. WORK( INDX ) = A( I, J )
  1024. INDX = INDX + 1
  1025. 300 CONTINUE
  1026. 310 CONTINUE
  1027. END IF
  1028. *
  1029. NTEST = NTEST + 1
  1030. *
  1031. IF( N.GT.0 ) THEN
  1032. TEMP3 = MAX( ABS( D1( 1 ) ), ABS( D1( N ) ) )
  1033. IF( IL.NE.1 ) THEN
  1034. VL = D1( IL ) - MAX( HALF*( D1( IL )-D1( IL-1 ) ),
  1035. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1036. ELSE IF( N.GT.0 ) THEN
  1037. VL = D1( 1 ) - MAX( HALF*( D1( N )-D1( 1 ) ),
  1038. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1039. END IF
  1040. IF( IU.NE.N ) THEN
  1041. VU = D1( IU ) + MAX( HALF*( D1( IU+1 )-D1( IU ) ),
  1042. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1043. ELSE IF( N.GT.0 ) THEN
  1044. VU = D1( N ) + MAX( HALF*( D1( N )-D1( 1 ) ),
  1045. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1046. END IF
  1047. ELSE
  1048. TEMP3 = ZERO
  1049. VL = ZERO
  1050. VU = ONE
  1051. END IF
  1052. *
  1053. CALL CHPEVX( 'V', 'A', UPLO, N, WORK, VL, VU, IL, IU,
  1054. $ ABSTOL, M, WA1, Z, LDU, V, RWORK, IWORK,
  1055. $ IWORK( 5*N+1 ), IINFO )
  1056. IF( IINFO.NE.0 ) THEN
  1057. WRITE( NOUNIT, FMT = 9999 )'CHPEVX(V,A,' // UPLO //
  1058. $ ')', IINFO, N, JTYPE, IOLDSD
  1059. INFO = ABS( IINFO )
  1060. IF( IINFO.LT.0 ) THEN
  1061. RETURN
  1062. ELSE
  1063. RESULT( NTEST ) = ULPINV
  1064. RESULT( NTEST+1 ) = ULPINV
  1065. RESULT( NTEST+2 ) = ULPINV
  1066. GO TO 370
  1067. END IF
  1068. END IF
  1069. *
  1070. * Do tests 16 and 17.
  1071. *
  1072. CALL CHET21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  1073. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1074. *
  1075. NTEST = NTEST + 2
  1076. *
  1077. IF( IUPLO.EQ.1 ) THEN
  1078. INDX = 1
  1079. DO 330 J = 1, N
  1080. DO 320 I = 1, J
  1081. WORK( INDX ) = A( I, J )
  1082. INDX = INDX + 1
  1083. 320 CONTINUE
  1084. 330 CONTINUE
  1085. ELSE
  1086. INDX = 1
  1087. DO 350 J = 1, N
  1088. DO 340 I = J, N
  1089. WORK( INDX ) = A( I, J )
  1090. INDX = INDX + 1
  1091. 340 CONTINUE
  1092. 350 CONTINUE
  1093. END IF
  1094. *
  1095. CALL CHPEVX( 'N', 'A', UPLO, N, WORK, VL, VU, IL, IU,
  1096. $ ABSTOL, M2, WA2, Z, LDU, V, RWORK, IWORK,
  1097. $ IWORK( 5*N+1 ), IINFO )
  1098. IF( IINFO.NE.0 ) THEN
  1099. WRITE( NOUNIT, FMT = 9999 )'CHPEVX(N,A,' // UPLO //
  1100. $ ')', IINFO, N, JTYPE, IOLDSD
  1101. INFO = ABS( IINFO )
  1102. IF( IINFO.LT.0 ) THEN
  1103. RETURN
  1104. ELSE
  1105. RESULT( NTEST ) = ULPINV
  1106. GO TO 370
  1107. END IF
  1108. END IF
  1109. *
  1110. * Do test 18.
  1111. *
  1112. TEMP1 = ZERO
  1113. TEMP2 = ZERO
  1114. DO 360 J = 1, N
  1115. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1116. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1117. 360 CONTINUE
  1118. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1119. $ ULP*MAX( TEMP1, TEMP2 ) )
  1120. *
  1121. 370 CONTINUE
  1122. NTEST = NTEST + 1
  1123. IF( IUPLO.EQ.1 ) THEN
  1124. INDX = 1
  1125. DO 390 J = 1, N
  1126. DO 380 I = 1, J
  1127. WORK( INDX ) = A( I, J )
  1128. INDX = INDX + 1
  1129. 380 CONTINUE
  1130. 390 CONTINUE
  1131. ELSE
  1132. INDX = 1
  1133. DO 410 J = 1, N
  1134. DO 400 I = J, N
  1135. WORK( INDX ) = A( I, J )
  1136. INDX = INDX + 1
  1137. 400 CONTINUE
  1138. 410 CONTINUE
  1139. END IF
  1140. *
  1141. CALL CHPEVX( 'V', 'I', UPLO, N, WORK, VL, VU, IL, IU,
  1142. $ ABSTOL, M2, WA2, Z, LDU, V, RWORK, IWORK,
  1143. $ IWORK( 5*N+1 ), IINFO )
  1144. IF( IINFO.NE.0 ) THEN
  1145. WRITE( NOUNIT, FMT = 9999 )'CHPEVX(V,I,' // UPLO //
  1146. $ ')', IINFO, N, JTYPE, IOLDSD
  1147. INFO = ABS( IINFO )
  1148. IF( IINFO.LT.0 ) THEN
  1149. RETURN
  1150. ELSE
  1151. RESULT( NTEST ) = ULPINV
  1152. RESULT( NTEST+1 ) = ULPINV
  1153. RESULT( NTEST+2 ) = ULPINV
  1154. GO TO 460
  1155. END IF
  1156. END IF
  1157. *
  1158. * Do tests 19 and 20.
  1159. *
  1160. CALL CHET22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1161. $ V, LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1162. *
  1163. NTEST = NTEST + 2
  1164. *
  1165. IF( IUPLO.EQ.1 ) THEN
  1166. INDX = 1
  1167. DO 430 J = 1, N
  1168. DO 420 I = 1, J
  1169. WORK( INDX ) = A( I, J )
  1170. INDX = INDX + 1
  1171. 420 CONTINUE
  1172. 430 CONTINUE
  1173. ELSE
  1174. INDX = 1
  1175. DO 450 J = 1, N
  1176. DO 440 I = J, N
  1177. WORK( INDX ) = A( I, J )
  1178. INDX = INDX + 1
  1179. 440 CONTINUE
  1180. 450 CONTINUE
  1181. END IF
  1182. *
  1183. CALL CHPEVX( 'N', 'I', UPLO, N, WORK, VL, VU, IL, IU,
  1184. $ ABSTOL, M3, WA3, Z, LDU, V, RWORK, IWORK,
  1185. $ IWORK( 5*N+1 ), IINFO )
  1186. IF( IINFO.NE.0 ) THEN
  1187. WRITE( NOUNIT, FMT = 9999 )'CHPEVX(N,I,' // UPLO //
  1188. $ ')', IINFO, N, JTYPE, IOLDSD
  1189. INFO = ABS( IINFO )
  1190. IF( IINFO.LT.0 ) THEN
  1191. RETURN
  1192. ELSE
  1193. RESULT( NTEST ) = ULPINV
  1194. GO TO 460
  1195. END IF
  1196. END IF
  1197. *
  1198. * Do test 21.
  1199. *
  1200. TEMP1 = SSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1201. TEMP2 = SSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1202. IF( N.GT.0 ) THEN
  1203. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1204. ELSE
  1205. TEMP3 = ZERO
  1206. END IF
  1207. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1208. $ MAX( UNFL, TEMP3*ULP )
  1209. *
  1210. 460 CONTINUE
  1211. NTEST = NTEST + 1
  1212. IF( IUPLO.EQ.1 ) THEN
  1213. INDX = 1
  1214. DO 480 J = 1, N
  1215. DO 470 I = 1, J
  1216. WORK( INDX ) = A( I, J )
  1217. INDX = INDX + 1
  1218. 470 CONTINUE
  1219. 480 CONTINUE
  1220. ELSE
  1221. INDX = 1
  1222. DO 500 J = 1, N
  1223. DO 490 I = J, N
  1224. WORK( INDX ) = A( I, J )
  1225. INDX = INDX + 1
  1226. 490 CONTINUE
  1227. 500 CONTINUE
  1228. END IF
  1229. *
  1230. CALL CHPEVX( 'V', 'V', UPLO, N, WORK, VL, VU, IL, IU,
  1231. $ ABSTOL, M2, WA2, Z, LDU, V, RWORK, IWORK,
  1232. $ IWORK( 5*N+1 ), IINFO )
  1233. IF( IINFO.NE.0 ) THEN
  1234. WRITE( NOUNIT, FMT = 9999 )'CHPEVX(V,V,' // UPLO //
  1235. $ ')', IINFO, N, JTYPE, IOLDSD
  1236. INFO = ABS( IINFO )
  1237. IF( IINFO.LT.0 ) THEN
  1238. RETURN
  1239. ELSE
  1240. RESULT( NTEST ) = ULPINV
  1241. RESULT( NTEST+1 ) = ULPINV
  1242. RESULT( NTEST+2 ) = ULPINV
  1243. GO TO 550
  1244. END IF
  1245. END IF
  1246. *
  1247. * Do tests 22 and 23.
  1248. *
  1249. CALL CHET22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1250. $ V, LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1251. *
  1252. NTEST = NTEST + 2
  1253. *
  1254. IF( IUPLO.EQ.1 ) THEN
  1255. INDX = 1
  1256. DO 520 J = 1, N
  1257. DO 510 I = 1, J
  1258. WORK( INDX ) = A( I, J )
  1259. INDX = INDX + 1
  1260. 510 CONTINUE
  1261. 520 CONTINUE
  1262. ELSE
  1263. INDX = 1
  1264. DO 540 J = 1, N
  1265. DO 530 I = J, N
  1266. WORK( INDX ) = A( I, J )
  1267. INDX = INDX + 1
  1268. 530 CONTINUE
  1269. 540 CONTINUE
  1270. END IF
  1271. *
  1272. CALL CHPEVX( 'N', 'V', UPLO, N, WORK, VL, VU, IL, IU,
  1273. $ ABSTOL, M3, WA3, Z, LDU, V, RWORK, IWORK,
  1274. $ IWORK( 5*N+1 ), IINFO )
  1275. IF( IINFO.NE.0 ) THEN
  1276. WRITE( NOUNIT, FMT = 9999 )'CHPEVX(N,V,' // UPLO //
  1277. $ ')', IINFO, N, JTYPE, IOLDSD
  1278. INFO = ABS( IINFO )
  1279. IF( IINFO.LT.0 ) THEN
  1280. RETURN
  1281. ELSE
  1282. RESULT( NTEST ) = ULPINV
  1283. GO TO 550
  1284. END IF
  1285. END IF
  1286. *
  1287. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  1288. RESULT( NTEST ) = ULPINV
  1289. GO TO 550
  1290. END IF
  1291. *
  1292. * Do test 24.
  1293. *
  1294. TEMP1 = SSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1295. TEMP2 = SSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1296. IF( N.GT.0 ) THEN
  1297. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1298. ELSE
  1299. TEMP3 = ZERO
  1300. END IF
  1301. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1302. $ MAX( UNFL, TEMP3*ULP )
  1303. *
  1304. 550 CONTINUE
  1305. *
  1306. * Call CHBEVD and CHBEVX.
  1307. *
  1308. IF( JTYPE.LE.7 ) THEN
  1309. KD = 0
  1310. ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
  1311. KD = MAX( N-1, 0 )
  1312. ELSE
  1313. KD = IHBW
  1314. END IF
  1315. *
  1316. * Load array V with the upper or lower triangular part
  1317. * of the matrix in band form.
  1318. *
  1319. IF( IUPLO.EQ.1 ) THEN
  1320. DO 570 J = 1, N
  1321. DO 560 I = MAX( 1, J-KD ), J
  1322. V( KD+1+I-J, J ) = A( I, J )
  1323. 560 CONTINUE
  1324. 570 CONTINUE
  1325. ELSE
  1326. DO 590 J = 1, N
  1327. DO 580 I = J, MIN( N, J+KD )
  1328. V( 1+I-J, J ) = A( I, J )
  1329. 580 CONTINUE
  1330. 590 CONTINUE
  1331. END IF
  1332. *
  1333. NTEST = NTEST + 1
  1334. CALL CHBEVD( 'V', UPLO, N, KD, V, LDU, D1, Z, LDU, WORK,
  1335. $ LWEDC, RWORK, LRWEDC, IWORK, LIWEDC, IINFO )
  1336. IF( IINFO.NE.0 ) THEN
  1337. WRITE( NOUNIT, FMT = 9998 )'CHBEVD(V,' // UPLO //
  1338. $ ')', IINFO, N, KD, JTYPE, IOLDSD
  1339. INFO = ABS( IINFO )
  1340. IF( IINFO.LT.0 ) THEN
  1341. RETURN
  1342. ELSE
  1343. RESULT( NTEST ) = ULPINV
  1344. RESULT( NTEST+1 ) = ULPINV
  1345. RESULT( NTEST+2 ) = ULPINV
  1346. GO TO 650
  1347. END IF
  1348. END IF
  1349. *
  1350. * Do tests 25 and 26.
  1351. *
  1352. CALL CHET21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  1353. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1354. *
  1355. IF( IUPLO.EQ.1 ) THEN
  1356. DO 610 J = 1, N
  1357. DO 600 I = MAX( 1, J-KD ), J
  1358. V( KD+1+I-J, J ) = A( I, J )
  1359. 600 CONTINUE
  1360. 610 CONTINUE
  1361. ELSE
  1362. DO 630 J = 1, N
  1363. DO 620 I = J, MIN( N, J+KD )
  1364. V( 1+I-J, J ) = A( I, J )
  1365. 620 CONTINUE
  1366. 630 CONTINUE
  1367. END IF
  1368. *
  1369. NTEST = NTEST + 2
  1370. CALL CHBEVD_2STAGE( 'N', UPLO, N, KD, V, LDU, D3,
  1371. $ Z, LDU, WORK, LWORK, RWORK,
  1372. $ LRWEDC, IWORK, LIWEDC, IINFO )
  1373. IF( IINFO.NE.0 ) THEN
  1374. WRITE( NOUNIT, FMT = 9998 )
  1375. $ 'CHBEVD_2STAGE(N,' // UPLO //
  1376. $ ')', IINFO, N, KD, JTYPE, IOLDSD
  1377. INFO = ABS( IINFO )
  1378. IF( IINFO.LT.0 ) THEN
  1379. RETURN
  1380. ELSE
  1381. RESULT( NTEST ) = ULPINV
  1382. GO TO 650
  1383. END IF
  1384. END IF
  1385. *
  1386. * Do test 27.
  1387. *
  1388. TEMP1 = ZERO
  1389. TEMP2 = ZERO
  1390. DO 640 J = 1, N
  1391. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1392. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1393. 640 CONTINUE
  1394. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1395. $ ULP*MAX( TEMP1, TEMP2 ) )
  1396. *
  1397. * Load array V with the upper or lower triangular part
  1398. * of the matrix in band form.
  1399. *
  1400. 650 CONTINUE
  1401. IF( IUPLO.EQ.1 ) THEN
  1402. DO 670 J = 1, N
  1403. DO 660 I = MAX( 1, J-KD ), J
  1404. V( KD+1+I-J, J ) = A( I, J )
  1405. 660 CONTINUE
  1406. 670 CONTINUE
  1407. ELSE
  1408. DO 690 J = 1, N
  1409. DO 680 I = J, MIN( N, J+KD )
  1410. V( 1+I-J, J ) = A( I, J )
  1411. 680 CONTINUE
  1412. 690 CONTINUE
  1413. END IF
  1414. *
  1415. NTEST = NTEST + 1
  1416. CALL CHBEVX( 'V', 'A', UPLO, N, KD, V, LDU, U, LDU, VL,
  1417. $ VU, IL, IU, ABSTOL, M, WA1, Z, LDU, WORK,
  1418. $ RWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1419. IF( IINFO.NE.0 ) THEN
  1420. WRITE( NOUNIT, FMT = 9999 )'CHBEVX(V,A,' // UPLO //
  1421. $ ')', IINFO, N, KD, JTYPE, IOLDSD
  1422. INFO = ABS( IINFO )
  1423. IF( IINFO.LT.0 ) THEN
  1424. RETURN
  1425. ELSE
  1426. RESULT( NTEST ) = ULPINV
  1427. RESULT( NTEST+1 ) = ULPINV
  1428. RESULT( NTEST+2 ) = ULPINV
  1429. GO TO 750
  1430. END IF
  1431. END IF
  1432. *
  1433. * Do tests 28 and 29.
  1434. *
  1435. CALL CHET21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  1436. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1437. *
  1438. NTEST = NTEST + 2
  1439. *
  1440. IF( IUPLO.EQ.1 ) THEN
  1441. DO 710 J = 1, N
  1442. DO 700 I = MAX( 1, J-KD ), J
  1443. V( KD+1+I-J, J ) = A( I, J )
  1444. 700 CONTINUE
  1445. 710 CONTINUE
  1446. ELSE
  1447. DO 730 J = 1, N
  1448. DO 720 I = J, MIN( N, J+KD )
  1449. V( 1+I-J, J ) = A( I, J )
  1450. 720 CONTINUE
  1451. 730 CONTINUE
  1452. END IF
  1453. *
  1454. CALL CHBEVX_2STAGE( 'N', 'A', UPLO, N, KD, V, LDU,
  1455. $ U, LDU, VL, VU, IL, IU, ABSTOL,
  1456. $ M2, WA2, Z, LDU, WORK, LWORK,
  1457. $ RWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1458. IF( IINFO.NE.0 ) THEN
  1459. WRITE( NOUNIT, FMT = 9998 )
  1460. $ 'CHBEVX_2STAGE(N,A,' // UPLO //
  1461. $ ')', IINFO, N, KD, JTYPE, IOLDSD
  1462. INFO = ABS( IINFO )
  1463. IF( IINFO.LT.0 ) THEN
  1464. RETURN
  1465. ELSE
  1466. RESULT( NTEST ) = ULPINV
  1467. GO TO 750
  1468. END IF
  1469. END IF
  1470. *
  1471. * Do test 30.
  1472. *
  1473. TEMP1 = ZERO
  1474. TEMP2 = ZERO
  1475. DO 740 J = 1, N
  1476. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1477. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1478. 740 CONTINUE
  1479. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1480. $ ULP*MAX( TEMP1, TEMP2 ) )
  1481. *
  1482. * Load array V with the upper or lower triangular part
  1483. * of the matrix in band form.
  1484. *
  1485. 750 CONTINUE
  1486. NTEST = NTEST + 1
  1487. IF( IUPLO.EQ.1 ) THEN
  1488. DO 770 J = 1, N
  1489. DO 760 I = MAX( 1, J-KD ), J
  1490. V( KD+1+I-J, J ) = A( I, J )
  1491. 760 CONTINUE
  1492. 770 CONTINUE
  1493. ELSE
  1494. DO 790 J = 1, N
  1495. DO 780 I = J, MIN( N, J+KD )
  1496. V( 1+I-J, J ) = A( I, J )
  1497. 780 CONTINUE
  1498. 790 CONTINUE
  1499. END IF
  1500. *
  1501. CALL CHBEVX( 'V', 'I', UPLO, N, KD, V, LDU, U, LDU, VL,
  1502. $ VU, IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  1503. $ RWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1504. IF( IINFO.NE.0 ) THEN
  1505. WRITE( NOUNIT, FMT = 9998 )'CHBEVX(V,I,' // UPLO //
  1506. $ ')', IINFO, N, KD, JTYPE, IOLDSD
  1507. INFO = ABS( IINFO )
  1508. IF( IINFO.LT.0 ) THEN
  1509. RETURN
  1510. ELSE
  1511. RESULT( NTEST ) = ULPINV
  1512. RESULT( NTEST+1 ) = ULPINV
  1513. RESULT( NTEST+2 ) = ULPINV
  1514. GO TO 840
  1515. END IF
  1516. END IF
  1517. *
  1518. * Do tests 31 and 32.
  1519. *
  1520. CALL CHET22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1521. $ V, LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1522. *
  1523. NTEST = NTEST + 2
  1524. *
  1525. IF( IUPLO.EQ.1 ) THEN
  1526. DO 810 J = 1, N
  1527. DO 800 I = MAX( 1, J-KD ), J
  1528. V( KD+1+I-J, J ) = A( I, J )
  1529. 800 CONTINUE
  1530. 810 CONTINUE
  1531. ELSE
  1532. DO 830 J = 1, N
  1533. DO 820 I = J, MIN( N, J+KD )
  1534. V( 1+I-J, J ) = A( I, J )
  1535. 820 CONTINUE
  1536. 830 CONTINUE
  1537. END IF
  1538. CALL CHBEVX_2STAGE( 'N', 'I', UPLO, N, KD, V, LDU,
  1539. $ U, LDU, VL, VU, IL, IU, ABSTOL,
  1540. $ M3, WA3, Z, LDU, WORK, LWORK,
  1541. $ RWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1542. IF( IINFO.NE.0 ) THEN
  1543. WRITE( NOUNIT, FMT = 9998 )
  1544. $ 'CHBEVX_2STAGE(N,I,' // UPLO //
  1545. $ ')', IINFO, N, KD, JTYPE, IOLDSD
  1546. INFO = ABS( IINFO )
  1547. IF( IINFO.LT.0 ) THEN
  1548. RETURN
  1549. ELSE
  1550. RESULT( NTEST ) = ULPINV
  1551. GO TO 840
  1552. END IF
  1553. END IF
  1554. *
  1555. * Do test 33.
  1556. *
  1557. TEMP1 = SSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1558. TEMP2 = SSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1559. IF( N.GT.0 ) THEN
  1560. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1561. ELSE
  1562. TEMP3 = ZERO
  1563. END IF
  1564. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1565. $ MAX( UNFL, TEMP3*ULP )
  1566. *
  1567. * Load array V with the upper or lower triangular part
  1568. * of the matrix in band form.
  1569. *
  1570. 840 CONTINUE
  1571. NTEST = NTEST + 1
  1572. IF( IUPLO.EQ.1 ) THEN
  1573. DO 860 J = 1, N
  1574. DO 850 I = MAX( 1, J-KD ), J
  1575. V( KD+1+I-J, J ) = A( I, J )
  1576. 850 CONTINUE
  1577. 860 CONTINUE
  1578. ELSE
  1579. DO 880 J = 1, N
  1580. DO 870 I = J, MIN( N, J+KD )
  1581. V( 1+I-J, J ) = A( I, J )
  1582. 870 CONTINUE
  1583. 880 CONTINUE
  1584. END IF
  1585. CALL CHBEVX( 'V', 'V', UPLO, N, KD, V, LDU, U, LDU, VL,
  1586. $ VU, IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  1587. $ RWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1588. IF( IINFO.NE.0 ) THEN
  1589. WRITE( NOUNIT, FMT = 9998 )'CHBEVX(V,V,' // UPLO //
  1590. $ ')', IINFO, N, KD, JTYPE, IOLDSD
  1591. INFO = ABS( IINFO )
  1592. IF( IINFO.LT.0 ) THEN
  1593. RETURN
  1594. ELSE
  1595. RESULT( NTEST ) = ULPINV
  1596. RESULT( NTEST+1 ) = ULPINV
  1597. RESULT( NTEST+2 ) = ULPINV
  1598. GO TO 930
  1599. END IF
  1600. END IF
  1601. *
  1602. * Do tests 34 and 35.
  1603. *
  1604. CALL CHET22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1605. $ V, LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1606. *
  1607. NTEST = NTEST + 2
  1608. *
  1609. IF( IUPLO.EQ.1 ) THEN
  1610. DO 900 J = 1, N
  1611. DO 890 I = MAX( 1, J-KD ), J
  1612. V( KD+1+I-J, J ) = A( I, J )
  1613. 890 CONTINUE
  1614. 900 CONTINUE
  1615. ELSE
  1616. DO 920 J = 1, N
  1617. DO 910 I = J, MIN( N, J+KD )
  1618. V( 1+I-J, J ) = A( I, J )
  1619. 910 CONTINUE
  1620. 920 CONTINUE
  1621. END IF
  1622. CALL CHBEVX_2STAGE( 'N', 'V', UPLO, N, KD, V, LDU,
  1623. $ U, LDU, VL, VU, IL, IU, ABSTOL,
  1624. $ M3, WA3, Z, LDU, WORK, LWORK,
  1625. $ RWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1626. IF( IINFO.NE.0 ) THEN
  1627. WRITE( NOUNIT, FMT = 9998 )
  1628. $ 'CHBEVX_2STAGE(N,V,' // UPLO //
  1629. $ ')', IINFO, N, KD, JTYPE, IOLDSD
  1630. INFO = ABS( IINFO )
  1631. IF( IINFO.LT.0 ) THEN
  1632. RETURN
  1633. ELSE
  1634. RESULT( NTEST ) = ULPINV
  1635. GO TO 930
  1636. END IF
  1637. END IF
  1638. *
  1639. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  1640. RESULT( NTEST ) = ULPINV
  1641. GO TO 930
  1642. END IF
  1643. *
  1644. * Do test 36.
  1645. *
  1646. TEMP1 = SSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1647. TEMP2 = SSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1648. IF( N.GT.0 ) THEN
  1649. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1650. ELSE
  1651. TEMP3 = ZERO
  1652. END IF
  1653. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1654. $ MAX( UNFL, TEMP3*ULP )
  1655. *
  1656. 930 CONTINUE
  1657. *
  1658. * Call CHEEV
  1659. *
  1660. CALL CLACPY( ' ', N, N, A, LDA, V, LDU )
  1661. *
  1662. NTEST = NTEST + 1
  1663. CALL CHEEV( 'V', UPLO, N, A, LDU, D1, WORK, LWORK, RWORK,
  1664. $ IINFO )
  1665. IF( IINFO.NE.0 ) THEN
  1666. WRITE( NOUNIT, FMT = 9999 )'CHEEV(V,' // UPLO // ')',
  1667. $ IINFO, N, JTYPE, IOLDSD
  1668. INFO = ABS( IINFO )
  1669. IF( IINFO.LT.0 ) THEN
  1670. RETURN
  1671. ELSE
  1672. RESULT( NTEST ) = ULPINV
  1673. RESULT( NTEST+1 ) = ULPINV
  1674. RESULT( NTEST+2 ) = ULPINV
  1675. GO TO 950
  1676. END IF
  1677. END IF
  1678. *
  1679. * Do tests 37 and 38
  1680. *
  1681. CALL CHET21( 1, UPLO, N, 0, V, LDU, D1, D2, A, LDU, Z,
  1682. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1683. *
  1684. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  1685. *
  1686. NTEST = NTEST + 2
  1687. CALL CHEEV_2STAGE( 'N', UPLO, N, A, LDU, D3,
  1688. $ WORK, LWORK, RWORK, IINFO )
  1689. IF( IINFO.NE.0 ) THEN
  1690. WRITE( NOUNIT, FMT = 9999 )
  1691. $ 'CHEEV_2STAGE(N,' // UPLO // ')',
  1692. $ IINFO, N, JTYPE, IOLDSD
  1693. INFO = ABS( IINFO )
  1694. IF( IINFO.LT.0 ) THEN
  1695. RETURN
  1696. ELSE
  1697. RESULT( NTEST ) = ULPINV
  1698. GO TO 950
  1699. END IF
  1700. END IF
  1701. *
  1702. * Do test 39
  1703. *
  1704. TEMP1 = ZERO
  1705. TEMP2 = ZERO
  1706. DO 940 J = 1, N
  1707. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1708. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1709. 940 CONTINUE
  1710. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1711. $ ULP*MAX( TEMP1, TEMP2 ) )
  1712. *
  1713. 950 CONTINUE
  1714. *
  1715. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  1716. *
  1717. * Call CHPEV
  1718. *
  1719. * Load array WORK with the upper or lower triangular
  1720. * part of the matrix in packed form.
  1721. *
  1722. IF( IUPLO.EQ.1 ) THEN
  1723. INDX = 1
  1724. DO 970 J = 1, N
  1725. DO 960 I = 1, J
  1726. WORK( INDX ) = A( I, J )
  1727. INDX = INDX + 1
  1728. 960 CONTINUE
  1729. 970 CONTINUE
  1730. ELSE
  1731. INDX = 1
  1732. DO 990 J = 1, N
  1733. DO 980 I = J, N
  1734. WORK( INDX ) = A( I, J )
  1735. INDX = INDX + 1
  1736. 980 CONTINUE
  1737. 990 CONTINUE
  1738. END IF
  1739. *
  1740. NTEST = NTEST + 1
  1741. INDWRK = N*( N+1 ) / 2 + 1
  1742. CALL CHPEV( 'V', UPLO, N, WORK, D1, Z, LDU,
  1743. $ WORK( INDWRK ), RWORK, IINFO )
  1744. IF( IINFO.NE.0 ) THEN
  1745. WRITE( NOUNIT, FMT = 9999 )'CHPEV(V,' // UPLO // ')',
  1746. $ IINFO, N, JTYPE, IOLDSD
  1747. INFO = ABS( IINFO )
  1748. IF( IINFO.LT.0 ) THEN
  1749. RETURN
  1750. ELSE
  1751. RESULT( NTEST ) = ULPINV
  1752. RESULT( NTEST+1 ) = ULPINV
  1753. RESULT( NTEST+2 ) = ULPINV
  1754. GO TO 1050
  1755. END IF
  1756. END IF
  1757. *
  1758. * Do tests 40 and 41.
  1759. *
  1760. CALL CHET21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  1761. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1762. *
  1763. IF( IUPLO.EQ.1 ) THEN
  1764. INDX = 1
  1765. DO 1010 J = 1, N
  1766. DO 1000 I = 1, J
  1767. WORK( INDX ) = A( I, J )
  1768. INDX = INDX + 1
  1769. 1000 CONTINUE
  1770. 1010 CONTINUE
  1771. ELSE
  1772. INDX = 1
  1773. DO 1030 J = 1, N
  1774. DO 1020 I = J, N
  1775. WORK( INDX ) = A( I, J )
  1776. INDX = INDX + 1
  1777. 1020 CONTINUE
  1778. 1030 CONTINUE
  1779. END IF
  1780. *
  1781. NTEST = NTEST + 2
  1782. INDWRK = N*( N+1 ) / 2 + 1
  1783. CALL CHPEV( 'N', UPLO, N, WORK, D3, Z, LDU,
  1784. $ WORK( INDWRK ), RWORK, IINFO )
  1785. IF( IINFO.NE.0 ) THEN
  1786. WRITE( NOUNIT, FMT = 9999 )'CHPEV(N,' // UPLO // ')',
  1787. $ IINFO, N, JTYPE, IOLDSD
  1788. INFO = ABS( IINFO )
  1789. IF( IINFO.LT.0 ) THEN
  1790. RETURN
  1791. ELSE
  1792. RESULT( NTEST ) = ULPINV
  1793. GO TO 1050
  1794. END IF
  1795. END IF
  1796. *
  1797. * Do test 42
  1798. *
  1799. TEMP1 = ZERO
  1800. TEMP2 = ZERO
  1801. DO 1040 J = 1, N
  1802. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1803. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1804. 1040 CONTINUE
  1805. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1806. $ ULP*MAX( TEMP1, TEMP2 ) )
  1807. *
  1808. 1050 CONTINUE
  1809. *
  1810. * Call CHBEV
  1811. *
  1812. IF( JTYPE.LE.7 ) THEN
  1813. KD = 0
  1814. ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
  1815. KD = MAX( N-1, 0 )
  1816. ELSE
  1817. KD = IHBW
  1818. END IF
  1819. *
  1820. * Load array V with the upper or lower triangular part
  1821. * of the matrix in band form.
  1822. *
  1823. IF( IUPLO.EQ.1 ) THEN
  1824. DO 1070 J = 1, N
  1825. DO 1060 I = MAX( 1, J-KD ), J
  1826. V( KD+1+I-J, J ) = A( I, J )
  1827. 1060 CONTINUE
  1828. 1070 CONTINUE
  1829. ELSE
  1830. DO 1090 J = 1, N
  1831. DO 1080 I = J, MIN( N, J+KD )
  1832. V( 1+I-J, J ) = A( I, J )
  1833. 1080 CONTINUE
  1834. 1090 CONTINUE
  1835. END IF
  1836. *
  1837. NTEST = NTEST + 1
  1838. CALL CHBEV( 'V', UPLO, N, KD, V, LDU, D1, Z, LDU, WORK,
  1839. $ RWORK, IINFO )
  1840. IF( IINFO.NE.0 ) THEN
  1841. WRITE( NOUNIT, FMT = 9998 )'CHBEV(V,' // UPLO // ')',
  1842. $ IINFO, N, KD, JTYPE, IOLDSD
  1843. INFO = ABS( IINFO )
  1844. IF( IINFO.LT.0 ) THEN
  1845. RETURN
  1846. ELSE
  1847. RESULT( NTEST ) = ULPINV
  1848. RESULT( NTEST+1 ) = ULPINV
  1849. RESULT( NTEST+2 ) = ULPINV
  1850. GO TO 1140
  1851. END IF
  1852. END IF
  1853. *
  1854. * Do tests 43 and 44.
  1855. *
  1856. CALL CHET21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  1857. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1858. *
  1859. IF( IUPLO.EQ.1 ) THEN
  1860. DO 1110 J = 1, N
  1861. DO 1100 I = MAX( 1, J-KD ), J
  1862. V( KD+1+I-J, J ) = A( I, J )
  1863. 1100 CONTINUE
  1864. 1110 CONTINUE
  1865. ELSE
  1866. DO 1130 J = 1, N
  1867. DO 1120 I = J, MIN( N, J+KD )
  1868. V( 1+I-J, J ) = A( I, J )
  1869. 1120 CONTINUE
  1870. 1130 CONTINUE
  1871. END IF
  1872. *
  1873. NTEST = NTEST + 2
  1874. CALL CHBEV_2STAGE( 'N', UPLO, N, KD, V, LDU, D3, Z, LDU,
  1875. $ WORK, LWORK, RWORK, IINFO )
  1876. IF( IINFO.NE.0 ) THEN
  1877. WRITE( NOUNIT, FMT = 9998 )
  1878. $ 'CHBEV_2STAGE(N,' // UPLO // ')',
  1879. $ IINFO, N, KD, JTYPE, IOLDSD
  1880. INFO = ABS( IINFO )
  1881. IF( IINFO.LT.0 ) THEN
  1882. RETURN
  1883. ELSE
  1884. RESULT( NTEST ) = ULPINV
  1885. GO TO 1140
  1886. END IF
  1887. END IF
  1888. *
  1889. 1140 CONTINUE
  1890. *
  1891. * Do test 45.
  1892. *
  1893. TEMP1 = ZERO
  1894. TEMP2 = ZERO
  1895. DO 1150 J = 1, N
  1896. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1897. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1898. 1150 CONTINUE
  1899. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1900. $ ULP*MAX( TEMP1, TEMP2 ) )
  1901. *
  1902. CALL CLACPY( ' ', N, N, A, LDA, V, LDU )
  1903. NTEST = NTEST + 1
  1904. CALL CHEEVR( 'V', 'A', UPLO, N, A, LDU, VL, VU, IL, IU,
  1905. $ ABSTOL, M, WA1, Z, LDU, IWORK, WORK, LWORK,
  1906. $ RWORK, LRWORK, IWORK( 2*N+1 ), LIWORK-2*N,
  1907. $ IINFO )
  1908. IF( IINFO.NE.0 ) THEN
  1909. WRITE( NOUNIT, FMT = 9999 )'CHEEVR(V,A,' // UPLO //
  1910. $ ')', IINFO, N, JTYPE, IOLDSD
  1911. INFO = ABS( IINFO )
  1912. IF( IINFO.LT.0 ) THEN
  1913. RETURN
  1914. ELSE
  1915. RESULT( NTEST ) = ULPINV
  1916. RESULT( NTEST+1 ) = ULPINV
  1917. RESULT( NTEST+2 ) = ULPINV
  1918. GO TO 1170
  1919. END IF
  1920. END IF
  1921. *
  1922. * Do tests 45 and 46 (or ... )
  1923. *
  1924. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  1925. *
  1926. CALL CHET21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  1927. $ LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1928. *
  1929. NTEST = NTEST + 2
  1930. CALL CHEEVR_2STAGE( 'N', 'A', UPLO, N, A, LDU, VL, VU,
  1931. $ IL, IU, ABSTOL, M2, WA2, Z, LDU,
  1932. $ IWORK, WORK, LWORK, RWORK, LRWORK,
  1933. $ IWORK( 2*N+1 ), LIWORK-2*N, IINFO )
  1934. IF( IINFO.NE.0 ) THEN
  1935. WRITE( NOUNIT, FMT = 9999 )
  1936. $ 'CHEEVR_2STAGE(N,A,' // UPLO //
  1937. $ ')', IINFO, N, JTYPE, IOLDSD
  1938. INFO = ABS( IINFO )
  1939. IF( IINFO.LT.0 ) THEN
  1940. RETURN
  1941. ELSE
  1942. RESULT( NTEST ) = ULPINV
  1943. GO TO 1170
  1944. END IF
  1945. END IF
  1946. *
  1947. * Do test 47 (or ... )
  1948. *
  1949. TEMP1 = ZERO
  1950. TEMP2 = ZERO
  1951. DO 1160 J = 1, N
  1952. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1953. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1954. 1160 CONTINUE
  1955. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1956. $ ULP*MAX( TEMP1, TEMP2 ) )
  1957. *
  1958. 1170 CONTINUE
  1959. *
  1960. NTEST = NTEST + 1
  1961. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  1962. CALL CHEEVR( 'V', 'I', UPLO, N, A, LDU, VL, VU, IL, IU,
  1963. $ ABSTOL, M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  1964. $ RWORK, LRWORK, IWORK( 2*N+1 ), LIWORK-2*N,
  1965. $ IINFO )
  1966. IF( IINFO.NE.0 ) THEN
  1967. WRITE( NOUNIT, FMT = 9999 )'CHEEVR(V,I,' // UPLO //
  1968. $ ')', IINFO, N, JTYPE, IOLDSD
  1969. INFO = ABS( IINFO )
  1970. IF( IINFO.LT.0 ) THEN
  1971. RETURN
  1972. ELSE
  1973. RESULT( NTEST ) = ULPINV
  1974. RESULT( NTEST+1 ) = ULPINV
  1975. RESULT( NTEST+2 ) = ULPINV
  1976. GO TO 1180
  1977. END IF
  1978. END IF
  1979. *
  1980. * Do tests 48 and 49 (or +??)
  1981. *
  1982. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  1983. *
  1984. CALL CHET22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1985. $ V, LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  1986. *
  1987. NTEST = NTEST + 2
  1988. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  1989. CALL CHEEVR_2STAGE( 'N', 'I', UPLO, N, A, LDU, VL, VU,
  1990. $ IL, IU, ABSTOL, M3, WA3, Z, LDU,
  1991. $ IWORK, WORK, LWORK, RWORK, LRWORK,
  1992. $ IWORK( 2*N+1 ), LIWORK-2*N, IINFO )
  1993. IF( IINFO.NE.0 ) THEN
  1994. WRITE( NOUNIT, FMT = 9999 )
  1995. $ 'CHEEVR_2STAGE(N,I,' // UPLO //
  1996. $ ')', IINFO, N, JTYPE, IOLDSD
  1997. INFO = ABS( IINFO )
  1998. IF( IINFO.LT.0 ) THEN
  1999. RETURN
  2000. ELSE
  2001. RESULT( NTEST ) = ULPINV
  2002. GO TO 1180
  2003. END IF
  2004. END IF
  2005. *
  2006. * Do test 50 (or +??)
  2007. *
  2008. TEMP1 = SSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2009. TEMP2 = SSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2010. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2011. $ MAX( UNFL, ULP*TEMP3 )
  2012. 1180 CONTINUE
  2013. *
  2014. NTEST = NTEST + 1
  2015. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  2016. CALL CHEEVR( 'V', 'V', UPLO, N, A, LDU, VL, VU, IL, IU,
  2017. $ ABSTOL, M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  2018. $ RWORK, LRWORK, IWORK( 2*N+1 ), LIWORK-2*N,
  2019. $ IINFO )
  2020. IF( IINFO.NE.0 ) THEN
  2021. WRITE( NOUNIT, FMT = 9999 )'CHEEVR(V,V,' // UPLO //
  2022. $ ')', IINFO, N, JTYPE, IOLDSD
  2023. INFO = ABS( IINFO )
  2024. IF( IINFO.LT.0 ) THEN
  2025. RETURN
  2026. ELSE
  2027. RESULT( NTEST ) = ULPINV
  2028. RESULT( NTEST+1 ) = ULPINV
  2029. RESULT( NTEST+2 ) = ULPINV
  2030. GO TO 1190
  2031. END IF
  2032. END IF
  2033. *
  2034. * Do tests 51 and 52 (or +??)
  2035. *
  2036. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  2037. *
  2038. CALL CHET22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2039. $ V, LDU, TAU, WORK, RWORK, RESULT( NTEST ) )
  2040. *
  2041. NTEST = NTEST + 2
  2042. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  2043. CALL CHEEVR_2STAGE( 'N', 'V', UPLO, N, A, LDU, VL, VU,
  2044. $ IL, IU, ABSTOL, M3, WA3, Z, LDU,
  2045. $ IWORK, WORK, LWORK, RWORK, LRWORK,
  2046. $ IWORK( 2*N+1 ), LIWORK-2*N, IINFO )
  2047. IF( IINFO.NE.0 ) THEN
  2048. WRITE( NOUNIT, FMT = 9999 )
  2049. $ 'CHEEVR_2STAGE(N,V,' // UPLO //
  2050. $ ')', IINFO, N, JTYPE, IOLDSD
  2051. INFO = ABS( IINFO )
  2052. IF( IINFO.LT.0 ) THEN
  2053. RETURN
  2054. ELSE
  2055. RESULT( NTEST ) = ULPINV
  2056. GO TO 1190
  2057. END IF
  2058. END IF
  2059. *
  2060. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2061. RESULT( NTEST ) = ULPINV
  2062. GO TO 1190
  2063. END IF
  2064. *
  2065. * Do test 52 (or +??)
  2066. *
  2067. TEMP1 = SSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2068. TEMP2 = SSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2069. IF( N.GT.0 ) THEN
  2070. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2071. ELSE
  2072. TEMP3 = ZERO
  2073. END IF
  2074. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2075. $ MAX( UNFL, TEMP3*ULP )
  2076. *
  2077. CALL CLACPY( ' ', N, N, V, LDU, A, LDA )
  2078. *
  2079. *
  2080. *
  2081. *
  2082. * Load array V with the upper or lower triangular part
  2083. * of the matrix in band form.
  2084. *
  2085. 1190 CONTINUE
  2086. *
  2087. 1200 CONTINUE
  2088. *
  2089. * End of Loop -- Check for RESULT(j) > THRESH
  2090. *
  2091. NTESTT = NTESTT + NTEST
  2092. CALL SLAFTS( 'CST', N, N, JTYPE, NTEST, RESULT, IOLDSD,
  2093. $ THRESH, NOUNIT, NERRS )
  2094. *
  2095. 1210 CONTINUE
  2096. 1220 CONTINUE
  2097. *
  2098. * Summary
  2099. *
  2100. CALL ALASVM( 'CST', NOUNIT, NERRS, NTESTT, 0 )
  2101. *
  2102. 9999 FORMAT( ' CDRVST2STG: ', A, ' returned INFO=', I6, / 9X, 'N=', I6,
  2103. $ ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
  2104. 9998 FORMAT( ' CDRVST2STG: ', A, ' returned INFO=', I6, / 9X, 'N=', I6,
  2105. $ ', KD=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5,
  2106. $ ')' )
  2107. *
  2108. RETURN
  2109. *
  2110. * End of CDRVST2STG
  2111. *
  2112. END