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ddrvst2stg.f 106 kB

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  1. *> \brief \b DDRVST2STG
  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 DDRVST2STG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
  12. * NOUNIT, A, LDA, D1, D2, D3, D4, EVEIGS, WA1,
  13. * WA2, WA3, U, LDU, V, TAU, Z, WORK, LWORK,
  14. * IWORK, LIWORK, RESULT, INFO )
  15. *
  16. * .. Scalar Arguments ..
  17. * INTEGER INFO, LDA, LDU, LIWORK, LWORK, NOUNIT, NSIZES,
  18. * $ NTYPES
  19. * DOUBLE PRECISION THRESH
  20. * ..
  21. * .. Array Arguments ..
  22. * LOGICAL DOTYPE( * )
  23. * INTEGER ISEED( 4 ), IWORK( * ), NN( * )
  24. * DOUBLE PRECISION A( LDA, * ), D1( * ), D2( * ), D3( * ),
  25. * $ D4( * ), EVEIGS( * ), RESULT( * ), TAU( * ),
  26. * $ U( LDU, * ), V( LDU, * ), WA1( * ), WA2( * ),
  27. * $ WA3( * ), WORK( * ), Z( LDU, * )
  28. * ..
  29. *
  30. *
  31. *> \par Purpose:
  32. * =============
  33. *>
  34. *> \verbatim
  35. *>
  36. *> DDRVST2STG checks the symmetric eigenvalue problem drivers.
  37. *>
  38. *> DSTEV computes all eigenvalues and, optionally,
  39. *> eigenvectors of a real symmetric tridiagonal matrix.
  40. *>
  41. *> DSTEVX computes selected eigenvalues and, optionally,
  42. *> eigenvectors of a real symmetric tridiagonal matrix.
  43. *>
  44. *> DSTEVR computes selected eigenvalues and, optionally,
  45. *> eigenvectors of a real symmetric tridiagonal matrix
  46. *> using the Relatively Robust Representation where it can.
  47. *>
  48. *> DSYEV computes all eigenvalues and, optionally,
  49. *> eigenvectors of a real symmetric matrix.
  50. *>
  51. *> DSYEVX computes selected eigenvalues and, optionally,
  52. *> eigenvectors of a real symmetric matrix.
  53. *>
  54. *> DSYEVR computes selected eigenvalues and, optionally,
  55. *> eigenvectors of a real symmetric matrix
  56. *> using the Relatively Robust Representation where it can.
  57. *>
  58. *> DSPEV computes all eigenvalues and, optionally,
  59. *> eigenvectors of a real symmetric matrix in packed
  60. *> storage.
  61. *>
  62. *> DSPEVX computes selected eigenvalues and, optionally,
  63. *> eigenvectors of a real symmetric matrix in packed
  64. *> storage.
  65. *>
  66. *> DSBEV computes all eigenvalues and, optionally,
  67. *> eigenvectors of a real symmetric band matrix.
  68. *>
  69. *> DSBEVX computes selected eigenvalues and, optionally,
  70. *> eigenvectors of a real symmetric band matrix.
  71. *>
  72. *> DSYEVD computes all eigenvalues and, optionally,
  73. *> eigenvectors of a real symmetric matrix using
  74. *> a divide and conquer algorithm.
  75. *>
  76. *> DSPEVD computes all eigenvalues and, optionally,
  77. *> eigenvectors of a real symmetric matrix in packed
  78. *> storage, using a divide and conquer algorithm.
  79. *>
  80. *> DSBEVD computes all eigenvalues and, optionally,
  81. *> eigenvectors of a real symmetric band matrix,
  82. *> using a divide and conquer algorithm.
  83. *>
  84. *> When DDRVST2STG is called, a number of matrix "sizes" ("n's") and a
  85. *> number of matrix "types" are specified. For each size ("n")
  86. *> and each type of matrix, one matrix will be generated and used
  87. *> to test the appropriate drivers. For each matrix and each
  88. *> driver routine called, the following tests will be performed:
  89. *>
  90. *> (1) | A - Z D Z' | / ( |A| n ulp )
  91. *>
  92. *> (2) | I - Z Z' | / ( n ulp )
  93. *>
  94. *> (3) | D1 - D2 | / ( |D1| ulp )
  95. *>
  96. *> where Z is the matrix of eigenvectors returned when the
  97. *> eigenvector option is given and D1 and D2 are the eigenvalues
  98. *> returned with and without the eigenvector option.
  99. *>
  100. *> The "sizes" are specified by an array NN(1:NSIZES); the value of
  101. *> each element NN(j) specifies one size.
  102. *> The "types" are specified by a logical array DOTYPE( 1:NTYPES );
  103. *> if DOTYPE(j) is .TRUE., then matrix type "j" will be generated.
  104. *> Currently, the list of possible types is:
  105. *>
  106. *> (1) The zero matrix.
  107. *> (2) The identity matrix.
  108. *>
  109. *> (3) A diagonal matrix with evenly spaced eigenvalues
  110. *> 1, ..., ULP and random signs.
  111. *> (ULP = (first number larger than 1) - 1 )
  112. *> (4) A diagonal matrix with geometrically spaced eigenvalues
  113. *> 1, ..., ULP and random signs.
  114. *> (5) A diagonal matrix with "clustered" eigenvalues
  115. *> 1, ULP, ..., ULP and random signs.
  116. *>
  117. *> (6) Same as (4), but multiplied by SQRT( overflow threshold )
  118. *> (7) Same as (4), but multiplied by SQRT( underflow threshold )
  119. *>
  120. *> (8) A matrix of the form U' D U, where U is orthogonal and
  121. *> D has evenly spaced entries 1, ..., ULP with random signs
  122. *> on the diagonal.
  123. *>
  124. *> (9) A matrix of the form U' D U, where U is orthogonal and
  125. *> D has geometrically spaced entries 1, ..., ULP with random
  126. *> signs on the diagonal.
  127. *>
  128. *> (10) A matrix of the form U' D U, where U is orthogonal and
  129. *> D has "clustered" entries 1, ULP,..., ULP with random
  130. *> signs on the diagonal.
  131. *>
  132. *> (11) Same as (8), but multiplied by SQRT( overflow threshold )
  133. *> (12) Same as (8), but multiplied by SQRT( underflow threshold )
  134. *>
  135. *> (13) Symmetric matrix with random entries chosen from (-1,1).
  136. *> (14) Same as (13), but multiplied by SQRT( overflow threshold )
  137. *> (15) Same as (13), but multiplied by SQRT( underflow threshold )
  138. *> (16) A band matrix with half bandwidth randomly chosen between
  139. *> 0 and N-1, with evenly spaced eigenvalues 1, ..., ULP
  140. *> with random signs.
  141. *> (17) Same as (16), but multiplied by SQRT( overflow threshold )
  142. *> (18) Same as (16), but multiplied by SQRT( underflow threshold )
  143. *> \endverbatim
  144. *
  145. * Arguments:
  146. * ==========
  147. *
  148. *> \verbatim
  149. *> NSIZES INTEGER
  150. *> The number of sizes of matrices to use. If it is zero,
  151. *> DDRVST2STG does nothing. It must be at least zero.
  152. *> Not modified.
  153. *>
  154. *> NN INTEGER array, dimension (NSIZES)
  155. *> An array containing the sizes to be used for the matrices.
  156. *> Zero values will be skipped. The values must be at least
  157. *> zero.
  158. *> Not modified.
  159. *>
  160. *> NTYPES INTEGER
  161. *> The number of elements in DOTYPE. If it is zero, DDRVST2STG
  162. *> does nothing. It must be at least zero. If it is MAXTYP+1
  163. *> and NSIZES is 1, then an additional type, MAXTYP+1 is
  164. *> defined, which is to use whatever matrix is in A. This
  165. *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
  166. *> DOTYPE(MAXTYP+1) is .TRUE. .
  167. *> Not modified.
  168. *>
  169. *> DOTYPE LOGICAL array, dimension (NTYPES)
  170. *> If DOTYPE(j) is .TRUE., then for each size in NN a
  171. *> matrix of that size and of type j will be generated.
  172. *> If NTYPES is smaller than the maximum number of types
  173. *> defined (PARAMETER MAXTYP), then types NTYPES+1 through
  174. *> MAXTYP will not be generated. If NTYPES is larger
  175. *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
  176. *> will be ignored.
  177. *> Not modified.
  178. *>
  179. *> ISEED INTEGER array, dimension (4)
  180. *> On entry ISEED specifies the seed of the random number
  181. *> generator. The array elements should be between 0 and 4095;
  182. *> if not they will be reduced mod 4096. Also, ISEED(4) must
  183. *> be odd. The random number generator uses a linear
  184. *> congruential sequence limited to small integers, and so
  185. *> should produce machine independent random numbers. The
  186. *> values of ISEED are changed on exit, and can be used in the
  187. *> next call to DDRVST2STG to continue the same random number
  188. *> sequence.
  189. *> Modified.
  190. *>
  191. *> THRESH DOUBLE PRECISION
  192. *> A test will count as "failed" if the "error", computed as
  193. *> described above, exceeds THRESH. Note that the error
  194. *> is scaled to be O(1), so THRESH should be a reasonably
  195. *> small multiple of 1, e.g., 10 or 100. In particular,
  196. *> it should not depend on the precision (single vs. double)
  197. *> or the size of the matrix. It must be at least zero.
  198. *> Not modified.
  199. *>
  200. *> NOUNIT INTEGER
  201. *> The FORTRAN unit number for printing out error messages
  202. *> (e.g., if a routine returns IINFO not equal to 0.)
  203. *> Not modified.
  204. *>
  205. *> A DOUBLE PRECISION array, dimension (LDA , max(NN))
  206. *> Used to hold the matrix whose eigenvalues are to be
  207. *> computed. On exit, A contains the last matrix actually
  208. *> used.
  209. *> Modified.
  210. *>
  211. *> LDA INTEGER
  212. *> The leading dimension of A. It must be at
  213. *> least 1 and at least max( NN ).
  214. *> Not modified.
  215. *>
  216. *> D1 DOUBLE PRECISION array, dimension (max(NN))
  217. *> The eigenvalues of A, as computed by DSTEQR simultaneously
  218. *> with Z. On exit, the eigenvalues in D1 correspond with the
  219. *> matrix in A.
  220. *> Modified.
  221. *>
  222. *> D2 DOUBLE PRECISION array, dimension (max(NN))
  223. *> The eigenvalues of A, as computed by DSTEQR if Z is not
  224. *> computed. On exit, the eigenvalues in D2 correspond with
  225. *> the matrix in A.
  226. *> Modified.
  227. *>
  228. *> D3 DOUBLE PRECISION array, dimension (max(NN))
  229. *> The eigenvalues of A, as computed by DSTERF. On exit, the
  230. *> eigenvalues in D3 correspond with the matrix in A.
  231. *> Modified.
  232. *>
  233. *> D4 DOUBLE PRECISION array, dimension
  234. *>
  235. *> EVEIGS DOUBLE PRECISION array, dimension (max(NN))
  236. *> The eigenvalues as computed by DSTEV('N', ... )
  237. *> (I reserve the right to change this to the output of
  238. *> whichever algorithm computes the most accurate eigenvalues).
  239. *>
  240. *> WA1 DOUBLE PRECISION array, dimension
  241. *>
  242. *> WA2 DOUBLE PRECISION array, dimension
  243. *>
  244. *> WA3 DOUBLE PRECISION array, dimension
  245. *>
  246. *> U DOUBLE PRECISION array, dimension (LDU, max(NN))
  247. *> The orthogonal matrix computed by DSYTRD + DORGTR.
  248. *> Modified.
  249. *>
  250. *> LDU INTEGER
  251. *> The leading dimension of U, Z, and V. It must be at
  252. *> least 1 and at least max( NN ).
  253. *> Not modified.
  254. *>
  255. *> V DOUBLE PRECISION array, dimension (LDU, max(NN))
  256. *> The Housholder vectors computed by DSYTRD in reducing A to
  257. *> tridiagonal form.
  258. *> Modified.
  259. *>
  260. *> TAU DOUBLE PRECISION array, dimension (max(NN))
  261. *> The Householder factors computed by DSYTRD in reducing A
  262. *> to tridiagonal form.
  263. *> Modified.
  264. *>
  265. *> Z DOUBLE PRECISION array, dimension (LDU, max(NN))
  266. *> The orthogonal matrix of eigenvectors computed by DSTEQR,
  267. *> DPTEQR, and DSTEIN.
  268. *> Modified.
  269. *>
  270. *> WORK DOUBLE PRECISION array, dimension (LWORK)
  271. *> Workspace.
  272. *> Modified.
  273. *>
  274. *> LWORK INTEGER
  275. *> The number of entries in WORK. This must be at least
  276. *> 1 + 4 * Nmax + 2 * Nmax * lg Nmax + 4 * Nmax**2
  277. *> where Nmax = max( NN(j), 2 ) and lg = log base 2.
  278. *> Not modified.
  279. *>
  280. *> IWORK INTEGER array,
  281. *> dimension (6 + 6*Nmax + 5 * Nmax * lg Nmax )
  282. *> where Nmax = max( NN(j), 2 ) and lg = log base 2.
  283. *> Workspace.
  284. *> Modified.
  285. *>
  286. *> RESULT DOUBLE PRECISION array, dimension (105)
  287. *> The values computed by the tests described above.
  288. *> The values are currently limited to 1/ulp, to avoid
  289. *> overflow.
  290. *> Modified.
  291. *>
  292. *> INFO INTEGER
  293. *> If 0, then everything ran OK.
  294. *> -1: NSIZES < 0
  295. *> -2: Some NN(j) < 0
  296. *> -3: NTYPES < 0
  297. *> -5: THRESH < 0
  298. *> -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
  299. *> -16: LDU < 1 or LDU < NMAX.
  300. *> -21: LWORK too small.
  301. *> If DLATMR, DLATMS, DSYTRD, DORGTR, DSTEQR, DSTERF,
  302. *> or DORMTR returns an error code, the
  303. *> absolute value of it is returned.
  304. *> Modified.
  305. *>
  306. *>-----------------------------------------------------------------------
  307. *>
  308. *> Some Local Variables and Parameters:
  309. *> ---- ----- --------- --- ----------
  310. *> ZERO, ONE Real 0 and 1.
  311. *> MAXTYP The number of types defined.
  312. *> NTEST The number of tests performed, or which can
  313. *> be performed so far, for the current matrix.
  314. *> NTESTT The total number of tests performed so far.
  315. *> NMAX Largest value in NN.
  316. *> NMATS The number of matrices generated so far.
  317. *> NERRS The number of tests which have exceeded THRESH
  318. *> so far (computed by DLAFTS).
  319. *> COND, IMODE Values to be passed to the matrix generators.
  320. *> ANORM Norm of A; passed to matrix generators.
  321. *>
  322. *> OVFL, UNFL Overflow and underflow thresholds.
  323. *> ULP, ULPINV Finest relative precision and its inverse.
  324. *> RTOVFL, RTUNFL Square roots of the previous 2 values.
  325. *> The following four arrays decode JTYPE:
  326. *> KTYPE(j) The general type (1-10) for type "j".
  327. *> KMODE(j) The MODE value to be passed to the matrix
  328. *> generator for type "j".
  329. *> KMAGN(j) The order of magnitude ( O(1),
  330. *> O(overflow^(1/2) ), O(underflow^(1/2) )
  331. *>
  332. *> The tests performed are: Routine tested
  333. *> 1= | A - U S U' | / ( |A| n ulp ) DSTEV('V', ... )
  334. *> 2= | I - U U' | / ( n ulp ) DSTEV('V', ... )
  335. *> 3= |D(with Z) - D(w/o Z)| / (|D| ulp) DSTEV('N', ... )
  336. *> 4= | A - U S U' | / ( |A| n ulp ) DSTEVX('V','A', ... )
  337. *> 5= | I - U U' | / ( n ulp ) DSTEVX('V','A', ... )
  338. *> 6= |D(with Z) - EVEIGS| / (|D| ulp) DSTEVX('N','A', ... )
  339. *> 7= | A - U S U' | / ( |A| n ulp ) DSTEVR('V','A', ... )
  340. *> 8= | I - U U' | / ( n ulp ) DSTEVR('V','A', ... )
  341. *> 9= |D(with Z) - EVEIGS| / (|D| ulp) DSTEVR('N','A', ... )
  342. *> 10= | A - U S U' | / ( |A| n ulp ) DSTEVX('V','I', ... )
  343. *> 11= | I - U U' | / ( n ulp ) DSTEVX('V','I', ... )
  344. *> 12= |D(with Z) - D(w/o Z)| / (|D| ulp) DSTEVX('N','I', ... )
  345. *> 13= | A - U S U' | / ( |A| n ulp ) DSTEVX('V','V', ... )
  346. *> 14= | I - U U' | / ( n ulp ) DSTEVX('V','V', ... )
  347. *> 15= |D(with Z) - D(w/o Z)| / (|D| ulp) DSTEVX('N','V', ... )
  348. *> 16= | A - U S U' | / ( |A| n ulp ) DSTEVD('V', ... )
  349. *> 17= | I - U U' | / ( n ulp ) DSTEVD('V', ... )
  350. *> 18= |D(with Z) - EVEIGS| / (|D| ulp) DSTEVD('N', ... )
  351. *> 19= | A - U S U' | / ( |A| n ulp ) DSTEVR('V','I', ... )
  352. *> 20= | I - U U' | / ( n ulp ) DSTEVR('V','I', ... )
  353. *> 21= |D(with Z) - D(w/o Z)| / (|D| ulp) DSTEVR('N','I', ... )
  354. *> 22= | A - U S U' | / ( |A| n ulp ) DSTEVR('V','V', ... )
  355. *> 23= | I - U U' | / ( n ulp ) DSTEVR('V','V', ... )
  356. *> 24= |D(with Z) - D(w/o Z)| / (|D| ulp) DSTEVR('N','V', ... )
  357. *>
  358. *> 25= | A - U S U' | / ( |A| n ulp ) DSYEV('L','V', ... )
  359. *> 26= | I - U U' | / ( n ulp ) DSYEV('L','V', ... )
  360. *> 27= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEV_2STAGE('L','N', ... )
  361. *> 28= | A - U S U' | / ( |A| n ulp ) DSYEVX('L','V','A', ... )
  362. *> 29= | I - U U' | / ( n ulp ) DSYEVX('L','V','A', ... )
  363. *> 30= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEVX_2STAGE('L','N','A', ... )
  364. *> 31= | A - U S U' | / ( |A| n ulp ) DSYEVX('L','V','I', ... )
  365. *> 32= | I - U U' | / ( n ulp ) DSYEVX('L','V','I', ... )
  366. *> 33= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEVX_2STAGE('L','N','I', ... )
  367. *> 34= | A - U S U' | / ( |A| n ulp ) DSYEVX('L','V','V', ... )
  368. *> 35= | I - U U' | / ( n ulp ) DSYEVX('L','V','V', ... )
  369. *> 36= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEVX_2STAGE('L','N','V', ... )
  370. *> 37= | A - U S U' | / ( |A| n ulp ) DSPEV('L','V', ... )
  371. *> 38= | I - U U' | / ( n ulp ) DSPEV('L','V', ... )
  372. *> 39= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEV('L','N', ... )
  373. *> 40= | A - U S U' | / ( |A| n ulp ) DSPEVX('L','V','A', ... )
  374. *> 41= | I - U U' | / ( n ulp ) DSPEVX('L','V','A', ... )
  375. *> 42= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEVX('L','N','A', ... )
  376. *> 43= | A - U S U' | / ( |A| n ulp ) DSPEVX('L','V','I', ... )
  377. *> 44= | I - U U' | / ( n ulp ) DSPEVX('L','V','I', ... )
  378. *> 45= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEVX('L','N','I', ... )
  379. *> 46= | A - U S U' | / ( |A| n ulp ) DSPEVX('L','V','V', ... )
  380. *> 47= | I - U U' | / ( n ulp ) DSPEVX('L','V','V', ... )
  381. *> 48= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEVX('L','N','V', ... )
  382. *> 49= | A - U S U' | / ( |A| n ulp ) DSBEV('L','V', ... )
  383. *> 50= | I - U U' | / ( n ulp ) DSBEV('L','V', ... )
  384. *> 51= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEV_2STAGE('L','N', ... )
  385. *> 52= | A - U S U' | / ( |A| n ulp ) DSBEVX('L','V','A', ... )
  386. *> 53= | I - U U' | / ( n ulp ) DSBEVX('L','V','A', ... )
  387. *> 54= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEVX_2STAGE('L','N','A', ... )
  388. *> 55= | A - U S U' | / ( |A| n ulp ) DSBEVX('L','V','I', ... )
  389. *> 56= | I - U U' | / ( n ulp ) DSBEVX('L','V','I', ... )
  390. *> 57= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEVX_2STAGE('L','N','I', ... )
  391. *> 58= | A - U S U' | / ( |A| n ulp ) DSBEVX('L','V','V', ... )
  392. *> 59= | I - U U' | / ( n ulp ) DSBEVX('L','V','V', ... )
  393. *> 60= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEVX_2STAGE('L','N','V', ... )
  394. *> 61= | A - U S U' | / ( |A| n ulp ) DSYEVD('L','V', ... )
  395. *> 62= | I - U U' | / ( n ulp ) DSYEVD('L','V', ... )
  396. *> 63= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEVD_2STAGE('L','N', ... )
  397. *> 64= | A - U S U' | / ( |A| n ulp ) DSPEVD('L','V', ... )
  398. *> 65= | I - U U' | / ( n ulp ) DSPEVD('L','V', ... )
  399. *> 66= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEVD('L','N', ... )
  400. *> 67= | A - U S U' | / ( |A| n ulp ) DSBEVD('L','V', ... )
  401. *> 68= | I - U U' | / ( n ulp ) DSBEVD('L','V', ... )
  402. *> 69= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEVD_2STAGE('L','N', ... )
  403. *> 70= | A - U S U' | / ( |A| n ulp ) DSYEVR('L','V','A', ... )
  404. *> 71= | I - U U' | / ( n ulp ) DSYEVR('L','V','A', ... )
  405. *> 72= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEVR_2STAGE('L','N','A', ... )
  406. *> 73= | A - U S U' | / ( |A| n ulp ) DSYEVR('L','V','I', ... )
  407. *> 74= | I - U U' | / ( n ulp ) DSYEVR('L','V','I', ... )
  408. *> 75= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEVR_2STAGE('L','N','I', ... )
  409. *> 76= | A - U S U' | / ( |A| n ulp ) DSYEVR('L','V','V', ... )
  410. *> 77= | I - U U' | / ( n ulp ) DSYEVR('L','V','V', ... )
  411. *> 78= |D(with Z) - D(w/o Z)| / (|D| ulp) DSYEVR_2STAGE('L','N','V', ... )
  412. *>
  413. *> Tests 25 through 78 are repeated (as tests 79 through 132)
  414. *> with UPLO='U'
  415. *>
  416. *> To be added in 1999
  417. *>
  418. *> 79= | A - U S U' | / ( |A| n ulp ) DSPEVR('L','V','A', ... )
  419. *> 80= | I - U U' | / ( n ulp ) DSPEVR('L','V','A', ... )
  420. *> 81= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEVR('L','N','A', ... )
  421. *> 82= | A - U S U' | / ( |A| n ulp ) DSPEVR('L','V','I', ... )
  422. *> 83= | I - U U' | / ( n ulp ) DSPEVR('L','V','I', ... )
  423. *> 84= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEVR('L','N','I', ... )
  424. *> 85= | A - U S U' | / ( |A| n ulp ) DSPEVR('L','V','V', ... )
  425. *> 86= | I - U U' | / ( n ulp ) DSPEVR('L','V','V', ... )
  426. *> 87= |D(with Z) - D(w/o Z)| / (|D| ulp) DSPEVR('L','N','V', ... )
  427. *> 88= | A - U S U' | / ( |A| n ulp ) DSBEVR('L','V','A', ... )
  428. *> 89= | I - U U' | / ( n ulp ) DSBEVR('L','V','A', ... )
  429. *> 90= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEVR('L','N','A', ... )
  430. *> 91= | A - U S U' | / ( |A| n ulp ) DSBEVR('L','V','I', ... )
  431. *> 92= | I - U U' | / ( n ulp ) DSBEVR('L','V','I', ... )
  432. *> 93= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEVR('L','N','I', ... )
  433. *> 94= | A - U S U' | / ( |A| n ulp ) DSBEVR('L','V','V', ... )
  434. *> 95= | I - U U' | / ( n ulp ) DSBEVR('L','V','V', ... )
  435. *> 96= |D(with Z) - D(w/o Z)| / (|D| ulp) DSBEVR('L','N','V', ... )
  436. *> \endverbatim
  437. *
  438. * Authors:
  439. * ========
  440. *
  441. *> \author Univ. of Tennessee
  442. *> \author Univ. of California Berkeley
  443. *> \author Univ. of Colorado Denver
  444. *> \author NAG Ltd.
  445. *
  446. *> \ingroup double_eig
  447. *
  448. * =====================================================================
  449. SUBROUTINE DDRVST2STG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
  450. $ NOUNIT, A, LDA, D1, D2, D3, D4, EVEIGS, WA1,
  451. $ WA2, WA3, U, LDU, V, TAU, Z, WORK, LWORK,
  452. $ IWORK, LIWORK, RESULT, INFO )
  453. *
  454. * -- LAPACK test routine --
  455. * -- LAPACK is a software package provided by Univ. of Tennessee, --
  456. * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  457. *
  458. * .. Scalar Arguments ..
  459. INTEGER INFO, LDA, LDU, LIWORK, LWORK, NOUNIT, NSIZES,
  460. $ NTYPES
  461. DOUBLE PRECISION THRESH
  462. * ..
  463. * .. Array Arguments ..
  464. LOGICAL DOTYPE( * )
  465. INTEGER ISEED( 4 ), IWORK( * ), NN( * )
  466. DOUBLE PRECISION A( LDA, * ), D1( * ), D2( * ), D3( * ),
  467. $ D4( * ), EVEIGS( * ), RESULT( * ), TAU( * ),
  468. $ U( LDU, * ), V( LDU, * ), WA1( * ), WA2( * ),
  469. $ WA3( * ), WORK( * ), Z( LDU, * )
  470. * ..
  471. *
  472. * =====================================================================
  473. *
  474. * .. Parameters ..
  475. DOUBLE PRECISION ZERO, ONE, TWO, TEN
  476. PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
  477. $ TEN = 10.0D0 )
  478. DOUBLE PRECISION HALF
  479. PARAMETER ( HALF = 0.5D0 )
  480. INTEGER MAXTYP
  481. PARAMETER ( MAXTYP = 18 )
  482. * ..
  483. * .. Local Scalars ..
  484. LOGICAL BADNN
  485. CHARACTER UPLO
  486. INTEGER I, IDIAG, IHBW, IINFO, IL, IMODE, INDX, IROW,
  487. $ ITEMP, ITYPE, IU, IUPLO, J, J1, J2, JCOL,
  488. $ JSIZE, JTYPE, KD, LGN, LIWEDC, LWEDC, M, M2,
  489. $ M3, MTYPES, N, NERRS, NMATS, NMAX, NTEST,
  490. $ NTESTT
  491. DOUBLE PRECISION ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
  492. $ RTUNFL, TEMP1, TEMP2, TEMP3, ULP, ULPINV, UNFL,
  493. $ VL, VU
  494. * ..
  495. * .. Local Arrays ..
  496. INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
  497. $ ISEED3( 4 ), KMAGN( MAXTYP ), KMODE( MAXTYP ),
  498. $ KTYPE( MAXTYP )
  499. * ..
  500. * .. External Functions ..
  501. DOUBLE PRECISION DLAMCH, DLARND, DSXT1
  502. EXTERNAL DLAMCH, DLARND, DSXT1
  503. * ..
  504. * .. External Subroutines ..
  505. EXTERNAL ALASVM, DLACPY, DLAFTS, DLASET, DLATMR,
  506. $ DLATMS, DSBEV, DSBEVD, DSBEVX, DSPEV, DSPEVD,
  507. $ DSPEVX, DSTEV, DSTEVD, DSTEVR, DSTEVX, DSTT21,
  508. $ DSTT22, DSYEV, DSYEVD, DSYEVR, DSYEVX, DSYT21,
  509. $ DSYEVD_2STAGE, DSYEVR_2STAGE, DSYEVX_2STAGE,
  510. $ DSYEV_2STAGE, DSBEV_2STAGE, DSBEVD_2STAGE,
  511. $ DSBEVX_2STAGE, DSYTRD_2STAGE, DSYTRD_SY2SB,
  512. $ DSYTRD_SB2ST, DSYT22, XERBLA
  513. * ..
  514. * .. Scalars in Common ..
  515. CHARACTER*32 SRNAMT
  516. * ..
  517. * .. Common blocks ..
  518. COMMON / SRNAMC / SRNAMT
  519. * ..
  520. * .. Intrinsic Functions ..
  521. INTRINSIC ABS, DBLE, INT, LOG, MAX, MIN, SQRT
  522. * ..
  523. * .. Data statements ..
  524. DATA KTYPE / 1, 2, 5*4, 5*5, 3*8, 3*9 /
  525. DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
  526. $ 2, 3, 1, 2, 3 /
  527. DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
  528. $ 0, 0, 4, 4, 4 /
  529. * ..
  530. * .. Executable Statements ..
  531. *
  532. * Keep ftrnchek happy
  533. *
  534. VL = ZERO
  535. VU = ZERO
  536. *
  537. * 1) Check for errors
  538. *
  539. NTESTT = 0
  540. INFO = 0
  541. *
  542. BADNN = .FALSE.
  543. NMAX = 1
  544. DO 10 J = 1, NSIZES
  545. NMAX = MAX( NMAX, NN( J ) )
  546. IF( NN( J ).LT.0 )
  547. $ BADNN = .TRUE.
  548. 10 CONTINUE
  549. *
  550. * Check for errors
  551. *
  552. IF( NSIZES.LT.0 ) THEN
  553. INFO = -1
  554. ELSE IF( BADNN ) THEN
  555. INFO = -2
  556. ELSE IF( NTYPES.LT.0 ) THEN
  557. INFO = -3
  558. ELSE IF( LDA.LT.NMAX ) THEN
  559. INFO = -9
  560. ELSE IF( LDU.LT.NMAX ) THEN
  561. INFO = -16
  562. ELSE IF( 2*MAX( 2, NMAX )**2.GT.LWORK ) THEN
  563. INFO = -21
  564. END IF
  565. *
  566. IF( INFO.NE.0 ) THEN
  567. CALL XERBLA( 'DDRVST2STG', -INFO )
  568. RETURN
  569. END IF
  570. *
  571. * Quick return if nothing to do
  572. *
  573. IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
  574. $ RETURN
  575. *
  576. * More Important constants
  577. *
  578. UNFL = DLAMCH( 'Safe minimum' )
  579. OVFL = DLAMCH( 'Overflow' )
  580. ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
  581. ULPINV = ONE / ULP
  582. RTUNFL = SQRT( UNFL )
  583. RTOVFL = SQRT( OVFL )
  584. *
  585. * Loop over sizes, types
  586. *
  587. DO 20 I = 1, 4
  588. ISEED2( I ) = ISEED( I )
  589. ISEED3( I ) = ISEED( I )
  590. 20 CONTINUE
  591. *
  592. NERRS = 0
  593. NMATS = 0
  594. *
  595. *
  596. DO 1740 JSIZE = 1, NSIZES
  597. N = NN( JSIZE )
  598. IF( N.GT.0 ) THEN
  599. LGN = INT( LOG( DBLE( N ) ) / LOG( TWO ) )
  600. IF( 2**LGN.LT.N )
  601. $ LGN = LGN + 1
  602. IF( 2**LGN.LT.N )
  603. $ LGN = LGN + 1
  604. LWEDC = 1 + 4*N + 2*N*LGN + 4*N**2
  605. c LIWEDC = 6 + 6*N + 5*N*LGN
  606. LIWEDC = 3 + 5*N
  607. ELSE
  608. LWEDC = 9
  609. c LIWEDC = 12
  610. LIWEDC = 8
  611. END IF
  612. ANINV = ONE / DBLE( MAX( 1, N ) )
  613. *
  614. IF( NSIZES.NE.1 ) THEN
  615. MTYPES = MIN( MAXTYP, NTYPES )
  616. ELSE
  617. MTYPES = MIN( MAXTYP+1, NTYPES )
  618. END IF
  619. *
  620. DO 1730 JTYPE = 1, MTYPES
  621. *
  622. IF( .NOT.DOTYPE( JTYPE ) )
  623. $ GO TO 1730
  624. NMATS = NMATS + 1
  625. NTEST = 0
  626. *
  627. DO 30 J = 1, 4
  628. IOLDSD( J ) = ISEED( J )
  629. 30 CONTINUE
  630. *
  631. * 2) Compute "A"
  632. *
  633. * Control parameters:
  634. *
  635. * KMAGN KMODE KTYPE
  636. * =1 O(1) clustered 1 zero
  637. * =2 large clustered 2 identity
  638. * =3 small exponential (none)
  639. * =4 arithmetic diagonal, (w/ eigenvalues)
  640. * =5 random log symmetric, w/ eigenvalues
  641. * =6 random (none)
  642. * =7 random diagonal
  643. * =8 random symmetric
  644. * =9 band symmetric, w/ eigenvalues
  645. *
  646. IF( MTYPES.GT.MAXTYP )
  647. $ GO TO 110
  648. *
  649. ITYPE = KTYPE( JTYPE )
  650. IMODE = KMODE( JTYPE )
  651. *
  652. * Compute norm
  653. *
  654. GO TO ( 40, 50, 60 )KMAGN( JTYPE )
  655. *
  656. 40 CONTINUE
  657. ANORM = ONE
  658. GO TO 70
  659. *
  660. 50 CONTINUE
  661. ANORM = ( RTOVFL*ULP )*ANINV
  662. GO TO 70
  663. *
  664. 60 CONTINUE
  665. ANORM = RTUNFL*N*ULPINV
  666. GO TO 70
  667. *
  668. 70 CONTINUE
  669. *
  670. CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
  671. IINFO = 0
  672. COND = ULPINV
  673. *
  674. * Special Matrices -- Identity & Jordan block
  675. *
  676. * Zero
  677. *
  678. IF( ITYPE.EQ.1 ) THEN
  679. IINFO = 0
  680. *
  681. ELSE IF( ITYPE.EQ.2 ) THEN
  682. *
  683. * Identity
  684. *
  685. DO 80 JCOL = 1, N
  686. A( JCOL, JCOL ) = ANORM
  687. 80 CONTINUE
  688. *
  689. ELSE IF( ITYPE.EQ.4 ) THEN
  690. *
  691. * Diagonal Matrix, [Eigen]values Specified
  692. *
  693. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  694. $ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
  695. $ IINFO )
  696. *
  697. ELSE IF( ITYPE.EQ.5 ) THEN
  698. *
  699. * Symmetric, eigenvalues specified
  700. *
  701. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  702. $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
  703. $ IINFO )
  704. *
  705. ELSE IF( ITYPE.EQ.7 ) THEN
  706. *
  707. * Diagonal, random eigenvalues
  708. *
  709. IDUMMA( 1 ) = 1
  710. CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
  711. $ 'T', 'N', WORK( N+1 ), 1, ONE,
  712. $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
  713. $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
  714. *
  715. ELSE IF( ITYPE.EQ.8 ) THEN
  716. *
  717. * Symmetric, random eigenvalues
  718. *
  719. IDUMMA( 1 ) = 1
  720. CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
  721. $ 'T', 'N', WORK( N+1 ), 1, ONE,
  722. $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
  723. $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
  724. *
  725. ELSE IF( ITYPE.EQ.9 ) THEN
  726. *
  727. * Symmetric banded, eigenvalues specified
  728. *
  729. IHBW = INT( ( N-1 )*DLARND( 1, ISEED3 ) )
  730. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  731. $ ANORM, IHBW, IHBW, 'Z', U, LDU, WORK( N+1 ),
  732. $ IINFO )
  733. *
  734. * Store as dense matrix for most routines.
  735. *
  736. CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
  737. DO 100 IDIAG = -IHBW, IHBW
  738. IROW = IHBW - IDIAG + 1
  739. J1 = MAX( 1, IDIAG+1 )
  740. J2 = MIN( N, N+IDIAG )
  741. DO 90 J = J1, J2
  742. I = J - IDIAG
  743. A( I, J ) = U( IROW, J )
  744. 90 CONTINUE
  745. 100 CONTINUE
  746. ELSE
  747. IINFO = 1
  748. END IF
  749. *
  750. IF( IINFO.NE.0 ) THEN
  751. WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
  752. $ IOLDSD
  753. INFO = ABS( IINFO )
  754. RETURN
  755. END IF
  756. *
  757. 110 CONTINUE
  758. *
  759. ABSTOL = UNFL + UNFL
  760. IF( N.LE.1 ) THEN
  761. IL = 1
  762. IU = N
  763. ELSE
  764. IL = 1 + INT( ( N-1 )*DLARND( 1, ISEED2 ) )
  765. IU = 1 + INT( ( N-1 )*DLARND( 1, ISEED2 ) )
  766. IF( IL.GT.IU ) THEN
  767. ITEMP = IL
  768. IL = IU
  769. IU = ITEMP
  770. END IF
  771. END IF
  772. *
  773. * 3) If matrix is tridiagonal, call DSTEV and DSTEVX.
  774. *
  775. IF( JTYPE.LE.7 ) THEN
  776. NTEST = 1
  777. DO 120 I = 1, N
  778. D1( I ) = DBLE( A( I, I ) )
  779. 120 CONTINUE
  780. DO 130 I = 1, N - 1
  781. D2( I ) = DBLE( A( I+1, I ) )
  782. 130 CONTINUE
  783. SRNAMT = 'DSTEV'
  784. CALL DSTEV( 'V', N, D1, D2, Z, LDU, WORK, IINFO )
  785. IF( IINFO.NE.0 ) THEN
  786. WRITE( NOUNIT, FMT = 9999 )'DSTEV(V)', IINFO, N,
  787. $ JTYPE, IOLDSD
  788. INFO = ABS( IINFO )
  789. IF( IINFO.LT.0 ) THEN
  790. RETURN
  791. ELSE
  792. RESULT( 1 ) = ULPINV
  793. RESULT( 2 ) = ULPINV
  794. RESULT( 3 ) = ULPINV
  795. GO TO 180
  796. END IF
  797. END IF
  798. *
  799. * Do tests 1 and 2.
  800. *
  801. DO 140 I = 1, N
  802. D3( I ) = DBLE( A( I, I ) )
  803. 140 CONTINUE
  804. DO 150 I = 1, N - 1
  805. D4( I ) = DBLE( A( I+1, I ) )
  806. 150 CONTINUE
  807. CALL DSTT21( N, 0, D3, D4, D1, D2, Z, LDU, WORK,
  808. $ RESULT( 1 ) )
  809. *
  810. NTEST = 3
  811. DO 160 I = 1, N - 1
  812. D4( I ) = DBLE( A( I+1, I ) )
  813. 160 CONTINUE
  814. SRNAMT = 'DSTEV'
  815. CALL DSTEV( 'N', N, D3, D4, Z, LDU, WORK, IINFO )
  816. IF( IINFO.NE.0 ) THEN
  817. WRITE( NOUNIT, FMT = 9999 )'DSTEV(N)', IINFO, N,
  818. $ JTYPE, IOLDSD
  819. INFO = ABS( IINFO )
  820. IF( IINFO.LT.0 ) THEN
  821. RETURN
  822. ELSE
  823. RESULT( 3 ) = ULPINV
  824. GO TO 180
  825. END IF
  826. END IF
  827. *
  828. * Do test 3.
  829. *
  830. TEMP1 = ZERO
  831. TEMP2 = ZERO
  832. DO 170 J = 1, N
  833. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  834. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  835. 170 CONTINUE
  836. RESULT( 3 ) = TEMP2 / MAX( UNFL,
  837. $ ULP*MAX( TEMP1, TEMP2 ) )
  838. *
  839. 180 CONTINUE
  840. *
  841. NTEST = 4
  842. DO 190 I = 1, N
  843. EVEIGS( I ) = D3( I )
  844. D1( I ) = DBLE( A( I, I ) )
  845. 190 CONTINUE
  846. DO 200 I = 1, N - 1
  847. D2( I ) = DBLE( A( I+1, I ) )
  848. 200 CONTINUE
  849. SRNAMT = 'DSTEVX'
  850. CALL DSTEVX( 'V', 'A', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  851. $ M, WA1, Z, LDU, WORK, IWORK, IWORK( 5*N+1 ),
  852. $ IINFO )
  853. IF( IINFO.NE.0 ) THEN
  854. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,A)', IINFO, N,
  855. $ JTYPE, IOLDSD
  856. INFO = ABS( IINFO )
  857. IF( IINFO.LT.0 ) THEN
  858. RETURN
  859. ELSE
  860. RESULT( 4 ) = ULPINV
  861. RESULT( 5 ) = ULPINV
  862. RESULT( 6 ) = ULPINV
  863. GO TO 250
  864. END IF
  865. END IF
  866. IF( N.GT.0 ) THEN
  867. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  868. ELSE
  869. TEMP3 = ZERO
  870. END IF
  871. *
  872. * Do tests 4 and 5.
  873. *
  874. DO 210 I = 1, N
  875. D3( I ) = DBLE( A( I, I ) )
  876. 210 CONTINUE
  877. DO 220 I = 1, N - 1
  878. D4( I ) = DBLE( A( I+1, I ) )
  879. 220 CONTINUE
  880. CALL DSTT21( N, 0, D3, D4, WA1, D2, Z, LDU, WORK,
  881. $ RESULT( 4 ) )
  882. *
  883. NTEST = 6
  884. DO 230 I = 1, N - 1
  885. D4( I ) = DBLE( A( I+1, I ) )
  886. 230 CONTINUE
  887. SRNAMT = 'DSTEVX'
  888. CALL DSTEVX( 'N', 'A', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  889. $ M2, WA2, Z, LDU, WORK, IWORK,
  890. $ IWORK( 5*N+1 ), IINFO )
  891. IF( IINFO.NE.0 ) THEN
  892. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,A)', IINFO, N,
  893. $ JTYPE, IOLDSD
  894. INFO = ABS( IINFO )
  895. IF( IINFO.LT.0 ) THEN
  896. RETURN
  897. ELSE
  898. RESULT( 6 ) = ULPINV
  899. GO TO 250
  900. END IF
  901. END IF
  902. *
  903. * Do test 6.
  904. *
  905. TEMP1 = ZERO
  906. TEMP2 = ZERO
  907. DO 240 J = 1, N
  908. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ),
  909. $ ABS( EVEIGS( J ) ) )
  910. TEMP2 = MAX( TEMP2, ABS( WA2( J )-EVEIGS( J ) ) )
  911. 240 CONTINUE
  912. RESULT( 6 ) = TEMP2 / MAX( UNFL,
  913. $ ULP*MAX( TEMP1, TEMP2 ) )
  914. *
  915. 250 CONTINUE
  916. *
  917. NTEST = 7
  918. DO 260 I = 1, N
  919. D1( I ) = DBLE( A( I, I ) )
  920. 260 CONTINUE
  921. DO 270 I = 1, N - 1
  922. D2( I ) = DBLE( A( I+1, I ) )
  923. 270 CONTINUE
  924. SRNAMT = 'DSTEVR'
  925. CALL DSTEVR( 'V', 'A', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  926. $ M, WA1, Z, LDU, IWORK, WORK, LWORK,
  927. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  928. IF( IINFO.NE.0 ) THEN
  929. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,A)', IINFO, N,
  930. $ JTYPE, IOLDSD
  931. INFO = ABS( IINFO )
  932. IF( IINFO.LT.0 ) THEN
  933. RETURN
  934. ELSE
  935. RESULT( 7 ) = ULPINV
  936. RESULT( 8 ) = ULPINV
  937. GO TO 320
  938. END IF
  939. END IF
  940. IF( N.GT.0 ) THEN
  941. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  942. ELSE
  943. TEMP3 = ZERO
  944. END IF
  945. *
  946. * Do tests 7 and 8.
  947. *
  948. DO 280 I = 1, N
  949. D3( I ) = DBLE( A( I, I ) )
  950. 280 CONTINUE
  951. DO 290 I = 1, N - 1
  952. D4( I ) = DBLE( A( I+1, I ) )
  953. 290 CONTINUE
  954. CALL DSTT21( N, 0, D3, D4, WA1, D2, Z, LDU, WORK,
  955. $ RESULT( 7 ) )
  956. *
  957. NTEST = 9
  958. DO 300 I = 1, N - 1
  959. D4( I ) = DBLE( A( I+1, I ) )
  960. 300 CONTINUE
  961. SRNAMT = 'DSTEVR'
  962. CALL DSTEVR( 'N', 'A', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  963. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  964. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  965. IF( IINFO.NE.0 ) THEN
  966. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,A)', IINFO, N,
  967. $ JTYPE, IOLDSD
  968. INFO = ABS( IINFO )
  969. IF( IINFO.LT.0 ) THEN
  970. RETURN
  971. ELSE
  972. RESULT( 9 ) = ULPINV
  973. GO TO 320
  974. END IF
  975. END IF
  976. *
  977. * Do test 9.
  978. *
  979. TEMP1 = ZERO
  980. TEMP2 = ZERO
  981. DO 310 J = 1, N
  982. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ),
  983. $ ABS( EVEIGS( J ) ) )
  984. TEMP2 = MAX( TEMP2, ABS( WA2( J )-EVEIGS( J ) ) )
  985. 310 CONTINUE
  986. RESULT( 9 ) = TEMP2 / MAX( UNFL,
  987. $ ULP*MAX( TEMP1, TEMP2 ) )
  988. *
  989. 320 CONTINUE
  990. *
  991. *
  992. NTEST = 10
  993. DO 330 I = 1, N
  994. D1( I ) = DBLE( A( I, I ) )
  995. 330 CONTINUE
  996. DO 340 I = 1, N - 1
  997. D2( I ) = DBLE( A( I+1, I ) )
  998. 340 CONTINUE
  999. SRNAMT = 'DSTEVX'
  1000. CALL DSTEVX( 'V', 'I', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1001. $ M2, WA2, Z, LDU, WORK, IWORK,
  1002. $ IWORK( 5*N+1 ), IINFO )
  1003. IF( IINFO.NE.0 ) THEN
  1004. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,I)', IINFO, N,
  1005. $ JTYPE, IOLDSD
  1006. INFO = ABS( IINFO )
  1007. IF( IINFO.LT.0 ) THEN
  1008. RETURN
  1009. ELSE
  1010. RESULT( 10 ) = ULPINV
  1011. RESULT( 11 ) = ULPINV
  1012. RESULT( 12 ) = ULPINV
  1013. GO TO 380
  1014. END IF
  1015. END IF
  1016. *
  1017. * Do tests 10 and 11.
  1018. *
  1019. DO 350 I = 1, N
  1020. D3( I ) = DBLE( A( I, I ) )
  1021. 350 CONTINUE
  1022. DO 360 I = 1, N - 1
  1023. D4( I ) = DBLE( A( I+1, I ) )
  1024. 360 CONTINUE
  1025. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1026. $ MAX( 1, M2 ), RESULT( 10 ) )
  1027. *
  1028. *
  1029. NTEST = 12
  1030. DO 370 I = 1, N - 1
  1031. D4( I ) = DBLE( A( I+1, I ) )
  1032. 370 CONTINUE
  1033. SRNAMT = 'DSTEVX'
  1034. CALL DSTEVX( 'N', 'I', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1035. $ M3, WA3, Z, LDU, WORK, IWORK,
  1036. $ IWORK( 5*N+1 ), IINFO )
  1037. IF( IINFO.NE.0 ) THEN
  1038. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,I)', IINFO, N,
  1039. $ JTYPE, IOLDSD
  1040. INFO = ABS( IINFO )
  1041. IF( IINFO.LT.0 ) THEN
  1042. RETURN
  1043. ELSE
  1044. RESULT( 12 ) = ULPINV
  1045. GO TO 380
  1046. END IF
  1047. END IF
  1048. *
  1049. * Do test 12.
  1050. *
  1051. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1052. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1053. RESULT( 12 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, ULP*TEMP3 )
  1054. *
  1055. 380 CONTINUE
  1056. *
  1057. NTEST = 12
  1058. IF( N.GT.0 ) THEN
  1059. IF( IL.NE.1 ) THEN
  1060. VL = WA1( IL ) - MAX( HALF*
  1061. $ ( WA1( IL )-WA1( IL-1 ) ), TEN*ULP*TEMP3,
  1062. $ TEN*RTUNFL )
  1063. ELSE
  1064. VL = WA1( 1 ) - MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1065. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1066. END IF
  1067. IF( IU.NE.N ) THEN
  1068. VU = WA1( IU ) + MAX( HALF*
  1069. $ ( WA1( IU+1 )-WA1( IU ) ), TEN*ULP*TEMP3,
  1070. $ TEN*RTUNFL )
  1071. ELSE
  1072. VU = WA1( N ) + MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1073. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1074. END IF
  1075. ELSE
  1076. VL = ZERO
  1077. VU = ONE
  1078. END IF
  1079. *
  1080. DO 390 I = 1, N
  1081. D1( I ) = DBLE( A( I, I ) )
  1082. 390 CONTINUE
  1083. DO 400 I = 1, N - 1
  1084. D2( I ) = DBLE( A( I+1, I ) )
  1085. 400 CONTINUE
  1086. SRNAMT = 'DSTEVX'
  1087. CALL DSTEVX( 'V', 'V', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1088. $ M2, WA2, Z, LDU, WORK, IWORK,
  1089. $ IWORK( 5*N+1 ), IINFO )
  1090. IF( IINFO.NE.0 ) THEN
  1091. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,V)', IINFO, N,
  1092. $ JTYPE, IOLDSD
  1093. INFO = ABS( IINFO )
  1094. IF( IINFO.LT.0 ) THEN
  1095. RETURN
  1096. ELSE
  1097. RESULT( 13 ) = ULPINV
  1098. RESULT( 14 ) = ULPINV
  1099. RESULT( 15 ) = ULPINV
  1100. GO TO 440
  1101. END IF
  1102. END IF
  1103. *
  1104. IF( M2.EQ.0 .AND. N.GT.0 ) THEN
  1105. RESULT( 13 ) = ULPINV
  1106. RESULT( 14 ) = ULPINV
  1107. RESULT( 15 ) = ULPINV
  1108. GO TO 440
  1109. END IF
  1110. *
  1111. * Do tests 13 and 14.
  1112. *
  1113. DO 410 I = 1, N
  1114. D3( I ) = DBLE( A( I, I ) )
  1115. 410 CONTINUE
  1116. DO 420 I = 1, N - 1
  1117. D4( I ) = DBLE( A( I+1, I ) )
  1118. 420 CONTINUE
  1119. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1120. $ MAX( 1, M2 ), RESULT( 13 ) )
  1121. *
  1122. NTEST = 15
  1123. DO 430 I = 1, N - 1
  1124. D4( I ) = DBLE( A( I+1, I ) )
  1125. 430 CONTINUE
  1126. SRNAMT = 'DSTEVX'
  1127. CALL DSTEVX( 'N', 'V', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1128. $ M3, WA3, Z, LDU, WORK, IWORK,
  1129. $ IWORK( 5*N+1 ), IINFO )
  1130. IF( IINFO.NE.0 ) THEN
  1131. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,V)', IINFO, N,
  1132. $ JTYPE, IOLDSD
  1133. INFO = ABS( IINFO )
  1134. IF( IINFO.LT.0 ) THEN
  1135. RETURN
  1136. ELSE
  1137. RESULT( 15 ) = ULPINV
  1138. GO TO 440
  1139. END IF
  1140. END IF
  1141. *
  1142. * Do test 15.
  1143. *
  1144. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1145. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1146. RESULT( 15 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, TEMP3*ULP )
  1147. *
  1148. 440 CONTINUE
  1149. *
  1150. NTEST = 16
  1151. DO 450 I = 1, N
  1152. D1( I ) = DBLE( A( I, I ) )
  1153. 450 CONTINUE
  1154. DO 460 I = 1, N - 1
  1155. D2( I ) = DBLE( A( I+1, I ) )
  1156. 460 CONTINUE
  1157. SRNAMT = 'DSTEVD'
  1158. CALL DSTEVD( 'V', N, D1, D2, Z, LDU, WORK, LWEDC, IWORK,
  1159. $ LIWEDC, IINFO )
  1160. IF( IINFO.NE.0 ) THEN
  1161. WRITE( NOUNIT, FMT = 9999 )'DSTEVD(V)', IINFO, N,
  1162. $ JTYPE, IOLDSD
  1163. INFO = ABS( IINFO )
  1164. IF( IINFO.LT.0 ) THEN
  1165. RETURN
  1166. ELSE
  1167. RESULT( 16 ) = ULPINV
  1168. RESULT( 17 ) = ULPINV
  1169. RESULT( 18 ) = ULPINV
  1170. GO TO 510
  1171. END IF
  1172. END IF
  1173. *
  1174. * Do tests 16 and 17.
  1175. *
  1176. DO 470 I = 1, N
  1177. D3( I ) = DBLE( A( I, I ) )
  1178. 470 CONTINUE
  1179. DO 480 I = 1, N - 1
  1180. D4( I ) = DBLE( A( I+1, I ) )
  1181. 480 CONTINUE
  1182. CALL DSTT21( N, 0, D3, D4, D1, D2, Z, LDU, WORK,
  1183. $ RESULT( 16 ) )
  1184. *
  1185. NTEST = 18
  1186. DO 490 I = 1, N - 1
  1187. D4( I ) = DBLE( A( I+1, I ) )
  1188. 490 CONTINUE
  1189. SRNAMT = 'DSTEVD'
  1190. CALL DSTEVD( 'N', N, D3, D4, Z, LDU, WORK, LWEDC, IWORK,
  1191. $ LIWEDC, IINFO )
  1192. IF( IINFO.NE.0 ) THEN
  1193. WRITE( NOUNIT, FMT = 9999 )'DSTEVD(N)', IINFO, N,
  1194. $ JTYPE, IOLDSD
  1195. INFO = ABS( IINFO )
  1196. IF( IINFO.LT.0 ) THEN
  1197. RETURN
  1198. ELSE
  1199. RESULT( 18 ) = ULPINV
  1200. GO TO 510
  1201. END IF
  1202. END IF
  1203. *
  1204. * Do test 18.
  1205. *
  1206. TEMP1 = ZERO
  1207. TEMP2 = ZERO
  1208. DO 500 J = 1, N
  1209. TEMP1 = MAX( TEMP1, ABS( EVEIGS( J ) ),
  1210. $ ABS( D3( J ) ) )
  1211. TEMP2 = MAX( TEMP2, ABS( EVEIGS( J )-D3( J ) ) )
  1212. 500 CONTINUE
  1213. RESULT( 18 ) = TEMP2 / MAX( UNFL,
  1214. $ ULP*MAX( TEMP1, TEMP2 ) )
  1215. *
  1216. 510 CONTINUE
  1217. *
  1218. NTEST = 19
  1219. DO 520 I = 1, N
  1220. D1( I ) = DBLE( A( I, I ) )
  1221. 520 CONTINUE
  1222. DO 530 I = 1, N - 1
  1223. D2( I ) = DBLE( A( I+1, I ) )
  1224. 530 CONTINUE
  1225. SRNAMT = 'DSTEVR'
  1226. CALL DSTEVR( 'V', 'I', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1227. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  1228. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1229. IF( IINFO.NE.0 ) THEN
  1230. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,I)', IINFO, N,
  1231. $ JTYPE, IOLDSD
  1232. INFO = ABS( IINFO )
  1233. IF( IINFO.LT.0 ) THEN
  1234. RETURN
  1235. ELSE
  1236. RESULT( 19 ) = ULPINV
  1237. RESULT( 20 ) = ULPINV
  1238. RESULT( 21 ) = ULPINV
  1239. GO TO 570
  1240. END IF
  1241. END IF
  1242. *
  1243. * DO tests 19 and 20.
  1244. *
  1245. DO 540 I = 1, N
  1246. D3( I ) = DBLE( A( I, I ) )
  1247. 540 CONTINUE
  1248. DO 550 I = 1, N - 1
  1249. D4( I ) = DBLE( A( I+1, I ) )
  1250. 550 CONTINUE
  1251. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1252. $ MAX( 1, M2 ), RESULT( 19 ) )
  1253. *
  1254. *
  1255. NTEST = 21
  1256. DO 560 I = 1, N - 1
  1257. D4( I ) = DBLE( A( I+1, I ) )
  1258. 560 CONTINUE
  1259. SRNAMT = 'DSTEVR'
  1260. CALL DSTEVR( 'N', 'I', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1261. $ M3, WA3, Z, LDU, IWORK, WORK, LWORK,
  1262. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1263. IF( IINFO.NE.0 ) THEN
  1264. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,I)', IINFO, N,
  1265. $ JTYPE, IOLDSD
  1266. INFO = ABS( IINFO )
  1267. IF( IINFO.LT.0 ) THEN
  1268. RETURN
  1269. ELSE
  1270. RESULT( 21 ) = ULPINV
  1271. GO TO 570
  1272. END IF
  1273. END IF
  1274. *
  1275. * Do test 21.
  1276. *
  1277. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1278. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1279. RESULT( 21 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, ULP*TEMP3 )
  1280. *
  1281. 570 CONTINUE
  1282. *
  1283. NTEST = 21
  1284. IF( N.GT.0 ) THEN
  1285. IF( IL.NE.1 ) THEN
  1286. VL = WA1( IL ) - MAX( HALF*
  1287. $ ( WA1( IL )-WA1( IL-1 ) ), TEN*ULP*TEMP3,
  1288. $ TEN*RTUNFL )
  1289. ELSE
  1290. VL = WA1( 1 ) - MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1291. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1292. END IF
  1293. IF( IU.NE.N ) THEN
  1294. VU = WA1( IU ) + MAX( HALF*
  1295. $ ( WA1( IU+1 )-WA1( IU ) ), TEN*ULP*TEMP3,
  1296. $ TEN*RTUNFL )
  1297. ELSE
  1298. VU = WA1( N ) + MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1299. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1300. END IF
  1301. ELSE
  1302. VL = ZERO
  1303. VU = ONE
  1304. END IF
  1305. *
  1306. DO 580 I = 1, N
  1307. D1( I ) = DBLE( A( I, I ) )
  1308. 580 CONTINUE
  1309. DO 590 I = 1, N - 1
  1310. D2( I ) = DBLE( A( I+1, I ) )
  1311. 590 CONTINUE
  1312. SRNAMT = 'DSTEVR'
  1313. CALL DSTEVR( 'V', 'V', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1314. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  1315. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1316. IF( IINFO.NE.0 ) THEN
  1317. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,V)', IINFO, N,
  1318. $ JTYPE, IOLDSD
  1319. INFO = ABS( IINFO )
  1320. IF( IINFO.LT.0 ) THEN
  1321. RETURN
  1322. ELSE
  1323. RESULT( 22 ) = ULPINV
  1324. RESULT( 23 ) = ULPINV
  1325. RESULT( 24 ) = ULPINV
  1326. GO TO 630
  1327. END IF
  1328. END IF
  1329. *
  1330. IF( M2.EQ.0 .AND. N.GT.0 ) THEN
  1331. RESULT( 22 ) = ULPINV
  1332. RESULT( 23 ) = ULPINV
  1333. RESULT( 24 ) = ULPINV
  1334. GO TO 630
  1335. END IF
  1336. *
  1337. * Do tests 22 and 23.
  1338. *
  1339. DO 600 I = 1, N
  1340. D3( I ) = DBLE( A( I, I ) )
  1341. 600 CONTINUE
  1342. DO 610 I = 1, N - 1
  1343. D4( I ) = DBLE( A( I+1, I ) )
  1344. 610 CONTINUE
  1345. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1346. $ MAX( 1, M2 ), RESULT( 22 ) )
  1347. *
  1348. NTEST = 24
  1349. DO 620 I = 1, N - 1
  1350. D4( I ) = DBLE( A( I+1, I ) )
  1351. 620 CONTINUE
  1352. SRNAMT = 'DSTEVR'
  1353. CALL DSTEVR( 'N', 'V', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1354. $ M3, WA3, Z, LDU, IWORK, WORK, LWORK,
  1355. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1356. IF( IINFO.NE.0 ) THEN
  1357. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,V)', IINFO, N,
  1358. $ JTYPE, IOLDSD
  1359. INFO = ABS( IINFO )
  1360. IF( IINFO.LT.0 ) THEN
  1361. RETURN
  1362. ELSE
  1363. RESULT( 24 ) = ULPINV
  1364. GO TO 630
  1365. END IF
  1366. END IF
  1367. *
  1368. * Do test 24.
  1369. *
  1370. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1371. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1372. RESULT( 24 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, TEMP3*ULP )
  1373. *
  1374. 630 CONTINUE
  1375. *
  1376. *
  1377. *
  1378. ELSE
  1379. *
  1380. DO 640 I = 1, 24
  1381. RESULT( I ) = ZERO
  1382. 640 CONTINUE
  1383. NTEST = 24
  1384. END IF
  1385. *
  1386. * Perform remaining tests storing upper or lower triangular
  1387. * part of matrix.
  1388. *
  1389. DO 1720 IUPLO = 0, 1
  1390. IF( IUPLO.EQ.0 ) THEN
  1391. UPLO = 'L'
  1392. ELSE
  1393. UPLO = 'U'
  1394. END IF
  1395. *
  1396. * 4) Call DSYEV and DSYEVX.
  1397. *
  1398. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  1399. *
  1400. NTEST = NTEST + 1
  1401. SRNAMT = 'DSYEV'
  1402. CALL DSYEV( 'V', UPLO, N, A, LDU, D1, WORK, LWORK,
  1403. $ IINFO )
  1404. IF( IINFO.NE.0 ) THEN
  1405. WRITE( NOUNIT, FMT = 9999 )'DSYEV(V,' // UPLO // ')',
  1406. $ IINFO, N, JTYPE, IOLDSD
  1407. INFO = ABS( IINFO )
  1408. IF( IINFO.LT.0 ) THEN
  1409. RETURN
  1410. ELSE
  1411. RESULT( NTEST ) = ULPINV
  1412. RESULT( NTEST+1 ) = ULPINV
  1413. RESULT( NTEST+2 ) = ULPINV
  1414. GO TO 660
  1415. END IF
  1416. END IF
  1417. *
  1418. * Do tests 25 and 26 (or +54)
  1419. *
  1420. CALL DSYT21( 1, UPLO, N, 0, V, LDU, D1, D2, A, LDU, Z,
  1421. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1422. *
  1423. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1424. *
  1425. NTEST = NTEST + 2
  1426. SRNAMT = 'DSYEV_2STAGE'
  1427. CALL DSYEV_2STAGE( 'N', UPLO, N, A, LDU, D3, WORK, LWORK,
  1428. $ IINFO )
  1429. IF( IINFO.NE.0 ) THEN
  1430. WRITE( NOUNIT, FMT = 9999 )
  1431. $ 'DSYEV_2STAGE(N,' // UPLO // ')',
  1432. $ IINFO, N, JTYPE, IOLDSD
  1433. INFO = ABS( IINFO )
  1434. IF( IINFO.LT.0 ) THEN
  1435. RETURN
  1436. ELSE
  1437. RESULT( NTEST ) = ULPINV
  1438. GO TO 660
  1439. END IF
  1440. END IF
  1441. *
  1442. * Do test 27 (or +54)
  1443. *
  1444. TEMP1 = ZERO
  1445. TEMP2 = ZERO
  1446. DO 650 J = 1, N
  1447. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1448. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1449. 650 CONTINUE
  1450. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1451. $ ULP*MAX( TEMP1, TEMP2 ) )
  1452. *
  1453. 660 CONTINUE
  1454. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1455. *
  1456. NTEST = NTEST + 1
  1457. *
  1458. IF( N.GT.0 ) THEN
  1459. TEMP3 = MAX( ABS( D1( 1 ) ), ABS( D1( N ) ) )
  1460. IF( IL.NE.1 ) THEN
  1461. VL = D1( IL ) - MAX( HALF*( D1( IL )-D1( IL-1 ) ),
  1462. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1463. ELSE IF( N.GT.0 ) THEN
  1464. VL = D1( 1 ) - MAX( HALF*( D1( N )-D1( 1 ) ),
  1465. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1466. END IF
  1467. IF( IU.NE.N ) THEN
  1468. VU = D1( IU ) + MAX( HALF*( D1( IU+1 )-D1( IU ) ),
  1469. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1470. ELSE IF( N.GT.0 ) THEN
  1471. VU = D1( N ) + MAX( HALF*( D1( N )-D1( 1 ) ),
  1472. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1473. END IF
  1474. ELSE
  1475. TEMP3 = ZERO
  1476. VL = ZERO
  1477. VU = ONE
  1478. END IF
  1479. *
  1480. SRNAMT = 'DSYEVX'
  1481. CALL DSYEVX( 'V', 'A', UPLO, N, A, LDU, VL, VU, IL, IU,
  1482. $ ABSTOL, M, WA1, Z, LDU, WORK, LWORK, IWORK,
  1483. $ IWORK( 5*N+1 ), IINFO )
  1484. IF( IINFO.NE.0 ) THEN
  1485. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,A,' // UPLO //
  1486. $ ')', IINFO, N, JTYPE, IOLDSD
  1487. INFO = ABS( IINFO )
  1488. IF( IINFO.LT.0 ) THEN
  1489. RETURN
  1490. ELSE
  1491. RESULT( NTEST ) = ULPINV
  1492. RESULT( NTEST+1 ) = ULPINV
  1493. RESULT( NTEST+2 ) = ULPINV
  1494. GO TO 680
  1495. END IF
  1496. END IF
  1497. *
  1498. * Do tests 28 and 29 (or +54)
  1499. *
  1500. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1501. *
  1502. CALL DSYT21( 1, UPLO, N, 0, A, LDU, D1, D2, Z, LDU, V,
  1503. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1504. *
  1505. NTEST = NTEST + 2
  1506. SRNAMT = 'DSYEVX_2STAGE'
  1507. CALL DSYEVX_2STAGE( 'N', 'A', UPLO, N, A, LDU, VL, VU,
  1508. $ IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  1509. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1510. IF( IINFO.NE.0 ) THEN
  1511. WRITE( NOUNIT, FMT = 9999 )
  1512. $ 'DSYEVX_2STAGE(N,A,' // UPLO //
  1513. $ ')', IINFO, N, JTYPE, IOLDSD
  1514. INFO = ABS( IINFO )
  1515. IF( IINFO.LT.0 ) THEN
  1516. RETURN
  1517. ELSE
  1518. RESULT( NTEST ) = ULPINV
  1519. GO TO 680
  1520. END IF
  1521. END IF
  1522. *
  1523. * Do test 30 (or +54)
  1524. *
  1525. TEMP1 = ZERO
  1526. TEMP2 = ZERO
  1527. DO 670 J = 1, N
  1528. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1529. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1530. 670 CONTINUE
  1531. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1532. $ ULP*MAX( TEMP1, TEMP2 ) )
  1533. *
  1534. 680 CONTINUE
  1535. *
  1536. NTEST = NTEST + 1
  1537. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1538. SRNAMT = 'DSYEVX'
  1539. CALL DSYEVX( 'V', 'I', UPLO, N, A, LDU, VL, VU, IL, IU,
  1540. $ ABSTOL, M2, WA2, Z, LDU, WORK, LWORK, IWORK,
  1541. $ IWORK( 5*N+1 ), IINFO )
  1542. IF( IINFO.NE.0 ) THEN
  1543. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,I,' // UPLO //
  1544. $ ')', IINFO, N, JTYPE, IOLDSD
  1545. INFO = ABS( IINFO )
  1546. IF( IINFO.LT.0 ) THEN
  1547. RETURN
  1548. ELSE
  1549. RESULT( NTEST ) = ULPINV
  1550. RESULT( NTEST+1 ) = ULPINV
  1551. RESULT( NTEST+2 ) = ULPINV
  1552. GO TO 690
  1553. END IF
  1554. END IF
  1555. *
  1556. * Do tests 31 and 32 (or +54)
  1557. *
  1558. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1559. *
  1560. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1561. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1562. *
  1563. NTEST = NTEST + 2
  1564. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1565. SRNAMT = 'DSYEVX_2STAGE'
  1566. CALL DSYEVX_2STAGE( 'N', 'I', UPLO, N, A, LDU, VL, VU,
  1567. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, WORK,
  1568. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1569. IF( IINFO.NE.0 ) THEN
  1570. WRITE( NOUNIT, FMT = 9999 )
  1571. $ 'DSYEVX_2STAGE(N,I,' // UPLO //
  1572. $ ')', IINFO, N, JTYPE, IOLDSD
  1573. INFO = ABS( IINFO )
  1574. IF( IINFO.LT.0 ) THEN
  1575. RETURN
  1576. ELSE
  1577. RESULT( NTEST ) = ULPINV
  1578. GO TO 690
  1579. END IF
  1580. END IF
  1581. *
  1582. * Do test 33 (or +54)
  1583. *
  1584. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1585. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1586. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1587. $ MAX( UNFL, ULP*TEMP3 )
  1588. 690 CONTINUE
  1589. *
  1590. NTEST = NTEST + 1
  1591. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1592. SRNAMT = 'DSYEVX'
  1593. CALL DSYEVX( 'V', 'V', UPLO, N, A, LDU, VL, VU, IL, IU,
  1594. $ ABSTOL, M2, WA2, Z, LDU, WORK, LWORK, IWORK,
  1595. $ IWORK( 5*N+1 ), IINFO )
  1596. IF( IINFO.NE.0 ) THEN
  1597. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,V,' // UPLO //
  1598. $ ')', IINFO, N, JTYPE, IOLDSD
  1599. INFO = ABS( IINFO )
  1600. IF( IINFO.LT.0 ) THEN
  1601. RETURN
  1602. ELSE
  1603. RESULT( NTEST ) = ULPINV
  1604. RESULT( NTEST+1 ) = ULPINV
  1605. RESULT( NTEST+2 ) = ULPINV
  1606. GO TO 700
  1607. END IF
  1608. END IF
  1609. *
  1610. * Do tests 34 and 35 (or +54)
  1611. *
  1612. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1613. *
  1614. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1615. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1616. *
  1617. NTEST = NTEST + 2
  1618. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1619. SRNAMT = 'DSYEVX_2STAGE'
  1620. CALL DSYEVX_2STAGE( 'N', 'V', UPLO, N, A, LDU, VL, VU,
  1621. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, WORK,
  1622. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1623. IF( IINFO.NE.0 ) THEN
  1624. WRITE( NOUNIT, FMT = 9999 )
  1625. $ 'DSYEVX_2STAGE(N,V,' // UPLO //
  1626. $ ')', IINFO, N, JTYPE, IOLDSD
  1627. INFO = ABS( IINFO )
  1628. IF( IINFO.LT.0 ) THEN
  1629. RETURN
  1630. ELSE
  1631. RESULT( NTEST ) = ULPINV
  1632. GO TO 700
  1633. END IF
  1634. END IF
  1635. *
  1636. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  1637. RESULT( NTEST ) = ULPINV
  1638. GO TO 700
  1639. END IF
  1640. *
  1641. * Do test 36 (or +54)
  1642. *
  1643. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1644. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1645. IF( N.GT.0 ) THEN
  1646. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1647. ELSE
  1648. TEMP3 = ZERO
  1649. END IF
  1650. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1651. $ MAX( UNFL, TEMP3*ULP )
  1652. *
  1653. 700 CONTINUE
  1654. *
  1655. * 5) Call DSPEV and DSPEVX.
  1656. *
  1657. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1658. *
  1659. * Load array WORK with the upper or lower triangular
  1660. * part of the matrix in packed form.
  1661. *
  1662. IF( IUPLO.EQ.1 ) THEN
  1663. INDX = 1
  1664. DO 720 J = 1, N
  1665. DO 710 I = 1, J
  1666. WORK( INDX ) = A( I, J )
  1667. INDX = INDX + 1
  1668. 710 CONTINUE
  1669. 720 CONTINUE
  1670. ELSE
  1671. INDX = 1
  1672. DO 740 J = 1, N
  1673. DO 730 I = J, N
  1674. WORK( INDX ) = A( I, J )
  1675. INDX = INDX + 1
  1676. 730 CONTINUE
  1677. 740 CONTINUE
  1678. END IF
  1679. *
  1680. NTEST = NTEST + 1
  1681. SRNAMT = 'DSPEV'
  1682. CALL DSPEV( 'V', UPLO, N, WORK, D1, Z, LDU, V, IINFO )
  1683. IF( IINFO.NE.0 ) THEN
  1684. WRITE( NOUNIT, FMT = 9999 )'DSPEV(V,' // UPLO // ')',
  1685. $ IINFO, N, JTYPE, IOLDSD
  1686. INFO = ABS( IINFO )
  1687. IF( IINFO.LT.0 ) THEN
  1688. RETURN
  1689. ELSE
  1690. RESULT( NTEST ) = ULPINV
  1691. RESULT( NTEST+1 ) = ULPINV
  1692. RESULT( NTEST+2 ) = ULPINV
  1693. GO TO 800
  1694. END IF
  1695. END IF
  1696. *
  1697. * Do tests 37 and 38 (or +54)
  1698. *
  1699. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  1700. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1701. *
  1702. IF( IUPLO.EQ.1 ) THEN
  1703. INDX = 1
  1704. DO 760 J = 1, N
  1705. DO 750 I = 1, J
  1706. WORK( INDX ) = A( I, J )
  1707. INDX = INDX + 1
  1708. 750 CONTINUE
  1709. 760 CONTINUE
  1710. ELSE
  1711. INDX = 1
  1712. DO 780 J = 1, N
  1713. DO 770 I = J, N
  1714. WORK( INDX ) = A( I, J )
  1715. INDX = INDX + 1
  1716. 770 CONTINUE
  1717. 780 CONTINUE
  1718. END IF
  1719. *
  1720. NTEST = NTEST + 2
  1721. SRNAMT = 'DSPEV'
  1722. CALL DSPEV( 'N', UPLO, N, WORK, D3, Z, LDU, V, IINFO )
  1723. IF( IINFO.NE.0 ) THEN
  1724. WRITE( NOUNIT, FMT = 9999 )'DSPEV(N,' // UPLO // ')',
  1725. $ IINFO, N, JTYPE, IOLDSD
  1726. INFO = ABS( IINFO )
  1727. IF( IINFO.LT.0 ) THEN
  1728. RETURN
  1729. ELSE
  1730. RESULT( NTEST ) = ULPINV
  1731. GO TO 800
  1732. END IF
  1733. END IF
  1734. *
  1735. * Do test 39 (or +54)
  1736. *
  1737. TEMP1 = ZERO
  1738. TEMP2 = ZERO
  1739. DO 790 J = 1, N
  1740. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1741. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1742. 790 CONTINUE
  1743. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1744. $ ULP*MAX( TEMP1, TEMP2 ) )
  1745. *
  1746. * Load array WORK with the upper or lower triangular part
  1747. * of the matrix in packed form.
  1748. *
  1749. 800 CONTINUE
  1750. IF( IUPLO.EQ.1 ) THEN
  1751. INDX = 1
  1752. DO 820 J = 1, N
  1753. DO 810 I = 1, J
  1754. WORK( INDX ) = A( I, J )
  1755. INDX = INDX + 1
  1756. 810 CONTINUE
  1757. 820 CONTINUE
  1758. ELSE
  1759. INDX = 1
  1760. DO 840 J = 1, N
  1761. DO 830 I = J, N
  1762. WORK( INDX ) = A( I, J )
  1763. INDX = INDX + 1
  1764. 830 CONTINUE
  1765. 840 CONTINUE
  1766. END IF
  1767. *
  1768. NTEST = NTEST + 1
  1769. *
  1770. IF( N.GT.0 ) THEN
  1771. TEMP3 = MAX( ABS( D1( 1 ) ), ABS( D1( N ) ) )
  1772. IF( IL.NE.1 ) THEN
  1773. VL = D1( IL ) - MAX( HALF*( D1( IL )-D1( IL-1 ) ),
  1774. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1775. ELSE IF( N.GT.0 ) THEN
  1776. VL = D1( 1 ) - MAX( HALF*( D1( N )-D1( 1 ) ),
  1777. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1778. END IF
  1779. IF( IU.NE.N ) THEN
  1780. VU = D1( IU ) + MAX( HALF*( D1( IU+1 )-D1( IU ) ),
  1781. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1782. ELSE IF( N.GT.0 ) THEN
  1783. VU = D1( N ) + MAX( HALF*( D1( N )-D1( 1 ) ),
  1784. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1785. END IF
  1786. ELSE
  1787. TEMP3 = ZERO
  1788. VL = ZERO
  1789. VU = ONE
  1790. END IF
  1791. *
  1792. SRNAMT = 'DSPEVX'
  1793. CALL DSPEVX( 'V', 'A', UPLO, N, WORK, VL, VU, IL, IU,
  1794. $ ABSTOL, M, WA1, Z, LDU, V, IWORK,
  1795. $ IWORK( 5*N+1 ), IINFO )
  1796. IF( IINFO.NE.0 ) THEN
  1797. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,A,' // UPLO //
  1798. $ ')', IINFO, N, JTYPE, IOLDSD
  1799. INFO = ABS( IINFO )
  1800. IF( IINFO.LT.0 ) THEN
  1801. RETURN
  1802. ELSE
  1803. RESULT( NTEST ) = ULPINV
  1804. RESULT( NTEST+1 ) = ULPINV
  1805. RESULT( NTEST+2 ) = ULPINV
  1806. GO TO 900
  1807. END IF
  1808. END IF
  1809. *
  1810. * Do tests 40 and 41 (or +54)
  1811. *
  1812. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  1813. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1814. *
  1815. NTEST = NTEST + 2
  1816. *
  1817. IF( IUPLO.EQ.1 ) THEN
  1818. INDX = 1
  1819. DO 860 J = 1, N
  1820. DO 850 I = 1, J
  1821. WORK( INDX ) = A( I, J )
  1822. INDX = INDX + 1
  1823. 850 CONTINUE
  1824. 860 CONTINUE
  1825. ELSE
  1826. INDX = 1
  1827. DO 880 J = 1, N
  1828. DO 870 I = J, N
  1829. WORK( INDX ) = A( I, J )
  1830. INDX = INDX + 1
  1831. 870 CONTINUE
  1832. 880 CONTINUE
  1833. END IF
  1834. *
  1835. SRNAMT = 'DSPEVX'
  1836. CALL DSPEVX( 'N', 'A', UPLO, N, WORK, VL, VU, IL, IU,
  1837. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1838. $ IWORK( 5*N+1 ), IINFO )
  1839. IF( IINFO.NE.0 ) THEN
  1840. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,A,' // UPLO //
  1841. $ ')', IINFO, N, JTYPE, IOLDSD
  1842. INFO = ABS( IINFO )
  1843. IF( IINFO.LT.0 ) THEN
  1844. RETURN
  1845. ELSE
  1846. RESULT( NTEST ) = ULPINV
  1847. GO TO 900
  1848. END IF
  1849. END IF
  1850. *
  1851. * Do test 42 (or +54)
  1852. *
  1853. TEMP1 = ZERO
  1854. TEMP2 = ZERO
  1855. DO 890 J = 1, N
  1856. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1857. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1858. 890 CONTINUE
  1859. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1860. $ ULP*MAX( TEMP1, TEMP2 ) )
  1861. *
  1862. 900 CONTINUE
  1863. IF( IUPLO.EQ.1 ) THEN
  1864. INDX = 1
  1865. DO 920 J = 1, N
  1866. DO 910 I = 1, J
  1867. WORK( INDX ) = A( I, J )
  1868. INDX = INDX + 1
  1869. 910 CONTINUE
  1870. 920 CONTINUE
  1871. ELSE
  1872. INDX = 1
  1873. DO 940 J = 1, N
  1874. DO 930 I = J, N
  1875. WORK( INDX ) = A( I, J )
  1876. INDX = INDX + 1
  1877. 930 CONTINUE
  1878. 940 CONTINUE
  1879. END IF
  1880. *
  1881. NTEST = NTEST + 1
  1882. *
  1883. SRNAMT = 'DSPEVX'
  1884. CALL DSPEVX( 'V', 'I', UPLO, N, WORK, VL, VU, IL, IU,
  1885. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1886. $ IWORK( 5*N+1 ), IINFO )
  1887. IF( IINFO.NE.0 ) THEN
  1888. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,I,' // UPLO //
  1889. $ ')', IINFO, N, JTYPE, IOLDSD
  1890. INFO = ABS( IINFO )
  1891. IF( IINFO.LT.0 ) THEN
  1892. RETURN
  1893. ELSE
  1894. RESULT( NTEST ) = ULPINV
  1895. RESULT( NTEST+1 ) = ULPINV
  1896. RESULT( NTEST+2 ) = ULPINV
  1897. GO TO 990
  1898. END IF
  1899. END IF
  1900. *
  1901. * Do tests 43 and 44 (or +54)
  1902. *
  1903. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1904. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1905. *
  1906. NTEST = NTEST + 2
  1907. *
  1908. IF( IUPLO.EQ.1 ) THEN
  1909. INDX = 1
  1910. DO 960 J = 1, N
  1911. DO 950 I = 1, J
  1912. WORK( INDX ) = A( I, J )
  1913. INDX = INDX + 1
  1914. 950 CONTINUE
  1915. 960 CONTINUE
  1916. ELSE
  1917. INDX = 1
  1918. DO 980 J = 1, N
  1919. DO 970 I = J, N
  1920. WORK( INDX ) = A( I, J )
  1921. INDX = INDX + 1
  1922. 970 CONTINUE
  1923. 980 CONTINUE
  1924. END IF
  1925. *
  1926. SRNAMT = 'DSPEVX'
  1927. CALL DSPEVX( 'N', 'I', UPLO, N, WORK, VL, VU, IL, IU,
  1928. $ ABSTOL, M3, WA3, Z, LDU, V, IWORK,
  1929. $ IWORK( 5*N+1 ), IINFO )
  1930. IF( IINFO.NE.0 ) THEN
  1931. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,I,' // UPLO //
  1932. $ ')', IINFO, N, JTYPE, IOLDSD
  1933. INFO = ABS( IINFO )
  1934. IF( IINFO.LT.0 ) THEN
  1935. RETURN
  1936. ELSE
  1937. RESULT( NTEST ) = ULPINV
  1938. GO TO 990
  1939. END IF
  1940. END IF
  1941. *
  1942. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  1943. RESULT( NTEST ) = ULPINV
  1944. GO TO 990
  1945. END IF
  1946. *
  1947. * Do test 45 (or +54)
  1948. *
  1949. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1950. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1951. IF( N.GT.0 ) THEN
  1952. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1953. ELSE
  1954. TEMP3 = ZERO
  1955. END IF
  1956. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1957. $ MAX( UNFL, TEMP3*ULP )
  1958. *
  1959. 990 CONTINUE
  1960. IF( IUPLO.EQ.1 ) THEN
  1961. INDX = 1
  1962. DO 1010 J = 1, N
  1963. DO 1000 I = 1, J
  1964. WORK( INDX ) = A( I, J )
  1965. INDX = INDX + 1
  1966. 1000 CONTINUE
  1967. 1010 CONTINUE
  1968. ELSE
  1969. INDX = 1
  1970. DO 1030 J = 1, N
  1971. DO 1020 I = J, N
  1972. WORK( INDX ) = A( I, J )
  1973. INDX = INDX + 1
  1974. 1020 CONTINUE
  1975. 1030 CONTINUE
  1976. END IF
  1977. *
  1978. NTEST = NTEST + 1
  1979. *
  1980. SRNAMT = 'DSPEVX'
  1981. CALL DSPEVX( 'V', 'V', UPLO, N, WORK, VL, VU, IL, IU,
  1982. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1983. $ IWORK( 5*N+1 ), IINFO )
  1984. IF( IINFO.NE.0 ) THEN
  1985. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,V,' // UPLO //
  1986. $ ')', IINFO, N, JTYPE, IOLDSD
  1987. INFO = ABS( IINFO )
  1988. IF( IINFO.LT.0 ) THEN
  1989. RETURN
  1990. ELSE
  1991. RESULT( NTEST ) = ULPINV
  1992. RESULT( NTEST+1 ) = ULPINV
  1993. RESULT( NTEST+2 ) = ULPINV
  1994. GO TO 1080
  1995. END IF
  1996. END IF
  1997. *
  1998. * Do tests 46 and 47 (or +54)
  1999. *
  2000. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2001. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2002. *
  2003. NTEST = NTEST + 2
  2004. *
  2005. IF( IUPLO.EQ.1 ) THEN
  2006. INDX = 1
  2007. DO 1050 J = 1, N
  2008. DO 1040 I = 1, J
  2009. WORK( INDX ) = A( I, J )
  2010. INDX = INDX + 1
  2011. 1040 CONTINUE
  2012. 1050 CONTINUE
  2013. ELSE
  2014. INDX = 1
  2015. DO 1070 J = 1, N
  2016. DO 1060 I = J, N
  2017. WORK( INDX ) = A( I, J )
  2018. INDX = INDX + 1
  2019. 1060 CONTINUE
  2020. 1070 CONTINUE
  2021. END IF
  2022. *
  2023. SRNAMT = 'DSPEVX'
  2024. CALL DSPEVX( 'N', 'V', UPLO, N, WORK, VL, VU, IL, IU,
  2025. $ ABSTOL, M3, WA3, Z, LDU, V, IWORK,
  2026. $ IWORK( 5*N+1 ), IINFO )
  2027. IF( IINFO.NE.0 ) THEN
  2028. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,V,' // UPLO //
  2029. $ ')', IINFO, N, JTYPE, IOLDSD
  2030. INFO = ABS( IINFO )
  2031. IF( IINFO.LT.0 ) THEN
  2032. RETURN
  2033. ELSE
  2034. RESULT( NTEST ) = ULPINV
  2035. GO TO 1080
  2036. END IF
  2037. END IF
  2038. *
  2039. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2040. RESULT( NTEST ) = ULPINV
  2041. GO TO 1080
  2042. END IF
  2043. *
  2044. * Do test 48 (or +54)
  2045. *
  2046. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2047. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2048. IF( N.GT.0 ) THEN
  2049. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2050. ELSE
  2051. TEMP3 = ZERO
  2052. END IF
  2053. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2054. $ MAX( UNFL, TEMP3*ULP )
  2055. *
  2056. 1080 CONTINUE
  2057. *
  2058. * 6) Call DSBEV and DSBEVX.
  2059. *
  2060. IF( JTYPE.LE.7 ) THEN
  2061. KD = 1
  2062. ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
  2063. KD = MAX( N-1, 0 )
  2064. ELSE
  2065. KD = IHBW
  2066. END IF
  2067. *
  2068. * Load array V with the upper or lower triangular part
  2069. * of the matrix in band form.
  2070. *
  2071. IF( IUPLO.EQ.1 ) THEN
  2072. DO 1100 J = 1, N
  2073. DO 1090 I = MAX( 1, J-KD ), J
  2074. V( KD+1+I-J, J ) = A( I, J )
  2075. 1090 CONTINUE
  2076. 1100 CONTINUE
  2077. ELSE
  2078. DO 1120 J = 1, N
  2079. DO 1110 I = J, MIN( N, J+KD )
  2080. V( 1+I-J, J ) = A( I, J )
  2081. 1110 CONTINUE
  2082. 1120 CONTINUE
  2083. END IF
  2084. *
  2085. NTEST = NTEST + 1
  2086. SRNAMT = 'DSBEV'
  2087. CALL DSBEV( 'V', UPLO, N, KD, V, LDU, D1, Z, LDU, WORK,
  2088. $ IINFO )
  2089. IF( IINFO.NE.0 ) THEN
  2090. WRITE( NOUNIT, FMT = 9999 )'DSBEV(V,' // UPLO // ')',
  2091. $ IINFO, N, JTYPE, IOLDSD
  2092. INFO = ABS( IINFO )
  2093. IF( IINFO.LT.0 ) THEN
  2094. RETURN
  2095. ELSE
  2096. RESULT( NTEST ) = ULPINV
  2097. RESULT( NTEST+1 ) = ULPINV
  2098. RESULT( NTEST+2 ) = ULPINV
  2099. GO TO 1180
  2100. END IF
  2101. END IF
  2102. *
  2103. * Do tests 49 and 50 (or ... )
  2104. *
  2105. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2106. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2107. *
  2108. IF( IUPLO.EQ.1 ) THEN
  2109. DO 1140 J = 1, N
  2110. DO 1130 I = MAX( 1, J-KD ), J
  2111. V( KD+1+I-J, J ) = A( I, J )
  2112. 1130 CONTINUE
  2113. 1140 CONTINUE
  2114. ELSE
  2115. DO 1160 J = 1, N
  2116. DO 1150 I = J, MIN( N, J+KD )
  2117. V( 1+I-J, J ) = A( I, J )
  2118. 1150 CONTINUE
  2119. 1160 CONTINUE
  2120. END IF
  2121. *
  2122. NTEST = NTEST + 2
  2123. SRNAMT = 'DSBEV_2STAGE'
  2124. CALL DSBEV_2STAGE( 'N', UPLO, N, KD, V, LDU, D3, Z, LDU,
  2125. $ WORK, LWORK, IINFO )
  2126. IF( IINFO.NE.0 ) THEN
  2127. WRITE( NOUNIT, FMT = 9999 )
  2128. $ 'DSBEV_2STAGE(N,' // UPLO // ')',
  2129. $ IINFO, N, JTYPE, IOLDSD
  2130. INFO = ABS( IINFO )
  2131. IF( IINFO.LT.0 ) THEN
  2132. RETURN
  2133. ELSE
  2134. RESULT( NTEST ) = ULPINV
  2135. GO TO 1180
  2136. END IF
  2137. END IF
  2138. *
  2139. * Do test 51 (or +54)
  2140. *
  2141. TEMP1 = ZERO
  2142. TEMP2 = ZERO
  2143. DO 1170 J = 1, N
  2144. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2145. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2146. 1170 CONTINUE
  2147. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2148. $ ULP*MAX( TEMP1, TEMP2 ) )
  2149. *
  2150. * Load array V with the upper or lower triangular part
  2151. * of the matrix in band form.
  2152. *
  2153. 1180 CONTINUE
  2154. IF( IUPLO.EQ.1 ) THEN
  2155. DO 1200 J = 1, N
  2156. DO 1190 I = MAX( 1, J-KD ), J
  2157. V( KD+1+I-J, J ) = A( I, J )
  2158. 1190 CONTINUE
  2159. 1200 CONTINUE
  2160. ELSE
  2161. DO 1220 J = 1, N
  2162. DO 1210 I = J, MIN( N, J+KD )
  2163. V( 1+I-J, J ) = A( I, J )
  2164. 1210 CONTINUE
  2165. 1220 CONTINUE
  2166. END IF
  2167. *
  2168. NTEST = NTEST + 1
  2169. SRNAMT = 'DSBEVX'
  2170. CALL DSBEVX( 'V', 'A', UPLO, N, KD, V, LDU, U, LDU, VL,
  2171. $ VU, IL, IU, ABSTOL, M, WA2, Z, LDU, WORK,
  2172. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2173. IF( IINFO.NE.0 ) THEN
  2174. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,A,' // UPLO //
  2175. $ ')', IINFO, N, JTYPE, IOLDSD
  2176. INFO = ABS( IINFO )
  2177. IF( IINFO.LT.0 ) THEN
  2178. RETURN
  2179. ELSE
  2180. RESULT( NTEST ) = ULPINV
  2181. RESULT( NTEST+1 ) = ULPINV
  2182. RESULT( NTEST+2 ) = ULPINV
  2183. GO TO 1280
  2184. END IF
  2185. END IF
  2186. *
  2187. * Do tests 52 and 53 (or +54)
  2188. *
  2189. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA2, D2, Z, LDU, V,
  2190. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2191. *
  2192. NTEST = NTEST + 2
  2193. *
  2194. IF( IUPLO.EQ.1 ) THEN
  2195. DO 1240 J = 1, N
  2196. DO 1230 I = MAX( 1, J-KD ), J
  2197. V( KD+1+I-J, J ) = A( I, J )
  2198. 1230 CONTINUE
  2199. 1240 CONTINUE
  2200. ELSE
  2201. DO 1260 J = 1, N
  2202. DO 1250 I = J, MIN( N, J+KD )
  2203. V( 1+I-J, J ) = A( I, J )
  2204. 1250 CONTINUE
  2205. 1260 CONTINUE
  2206. END IF
  2207. *
  2208. SRNAMT = 'DSBEVX_2STAGE'
  2209. CALL DSBEVX_2STAGE( 'N', 'A', UPLO, N, KD, V, LDU,
  2210. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2211. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2212. $ IINFO )
  2213. IF( IINFO.NE.0 ) THEN
  2214. WRITE( NOUNIT, FMT = 9999 )
  2215. $ 'DSBEVX_2STAGE(N,A,' // UPLO //
  2216. $ ')', IINFO, N, JTYPE, IOLDSD
  2217. INFO = ABS( IINFO )
  2218. IF( IINFO.LT.0 ) THEN
  2219. RETURN
  2220. ELSE
  2221. RESULT( NTEST ) = ULPINV
  2222. GO TO 1280
  2223. END IF
  2224. END IF
  2225. *
  2226. * Do test 54 (or +54)
  2227. *
  2228. TEMP1 = ZERO
  2229. TEMP2 = ZERO
  2230. DO 1270 J = 1, N
  2231. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ), ABS( WA3( J ) ) )
  2232. TEMP2 = MAX( TEMP2, ABS( WA2( J )-WA3( J ) ) )
  2233. 1270 CONTINUE
  2234. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2235. $ ULP*MAX( TEMP1, TEMP2 ) )
  2236. *
  2237. 1280 CONTINUE
  2238. NTEST = NTEST + 1
  2239. IF( IUPLO.EQ.1 ) THEN
  2240. DO 1300 J = 1, N
  2241. DO 1290 I = MAX( 1, J-KD ), J
  2242. V( KD+1+I-J, J ) = A( I, J )
  2243. 1290 CONTINUE
  2244. 1300 CONTINUE
  2245. ELSE
  2246. DO 1320 J = 1, N
  2247. DO 1310 I = J, MIN( N, J+KD )
  2248. V( 1+I-J, J ) = A( I, J )
  2249. 1310 CONTINUE
  2250. 1320 CONTINUE
  2251. END IF
  2252. *
  2253. SRNAMT = 'DSBEVX'
  2254. CALL DSBEVX( 'V', 'I', UPLO, N, KD, V, LDU, U, LDU, VL,
  2255. $ VU, IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  2256. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2257. IF( IINFO.NE.0 ) THEN
  2258. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,I,' // UPLO //
  2259. $ ')', IINFO, N, JTYPE, IOLDSD
  2260. INFO = ABS( IINFO )
  2261. IF( IINFO.LT.0 ) THEN
  2262. RETURN
  2263. ELSE
  2264. RESULT( NTEST ) = ULPINV
  2265. RESULT( NTEST+1 ) = ULPINV
  2266. RESULT( NTEST+2 ) = ULPINV
  2267. GO TO 1370
  2268. END IF
  2269. END IF
  2270. *
  2271. * Do tests 55 and 56 (or +54)
  2272. *
  2273. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2274. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2275. *
  2276. NTEST = NTEST + 2
  2277. *
  2278. IF( IUPLO.EQ.1 ) THEN
  2279. DO 1340 J = 1, N
  2280. DO 1330 I = MAX( 1, J-KD ), J
  2281. V( KD+1+I-J, J ) = A( I, J )
  2282. 1330 CONTINUE
  2283. 1340 CONTINUE
  2284. ELSE
  2285. DO 1360 J = 1, N
  2286. DO 1350 I = J, MIN( N, J+KD )
  2287. V( 1+I-J, J ) = A( I, J )
  2288. 1350 CONTINUE
  2289. 1360 CONTINUE
  2290. END IF
  2291. *
  2292. SRNAMT = 'DSBEVX_2STAGE'
  2293. CALL DSBEVX_2STAGE( 'N', 'I', UPLO, N, KD, V, LDU,
  2294. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2295. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2296. $ IINFO )
  2297. IF( IINFO.NE.0 ) THEN
  2298. WRITE( NOUNIT, FMT = 9999 )
  2299. $ 'DSBEVX_2STAGE(N,I,' // UPLO //
  2300. $ ')', IINFO, N, JTYPE, IOLDSD
  2301. INFO = ABS( IINFO )
  2302. IF( IINFO.LT.0 ) THEN
  2303. RETURN
  2304. ELSE
  2305. RESULT( NTEST ) = ULPINV
  2306. GO TO 1370
  2307. END IF
  2308. END IF
  2309. *
  2310. * Do test 57 (or +54)
  2311. *
  2312. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2313. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2314. IF( N.GT.0 ) THEN
  2315. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2316. ELSE
  2317. TEMP3 = ZERO
  2318. END IF
  2319. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2320. $ MAX( UNFL, TEMP3*ULP )
  2321. *
  2322. 1370 CONTINUE
  2323. NTEST = NTEST + 1
  2324. IF( IUPLO.EQ.1 ) THEN
  2325. DO 1390 J = 1, N
  2326. DO 1380 I = MAX( 1, J-KD ), J
  2327. V( KD+1+I-J, J ) = A( I, J )
  2328. 1380 CONTINUE
  2329. 1390 CONTINUE
  2330. ELSE
  2331. DO 1410 J = 1, N
  2332. DO 1400 I = J, MIN( N, J+KD )
  2333. V( 1+I-J, J ) = A( I, J )
  2334. 1400 CONTINUE
  2335. 1410 CONTINUE
  2336. END IF
  2337. *
  2338. SRNAMT = 'DSBEVX'
  2339. CALL DSBEVX( 'V', 'V', UPLO, N, KD, V, LDU, U, LDU, VL,
  2340. $ VU, IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  2341. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2342. IF( IINFO.NE.0 ) THEN
  2343. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,V,' // UPLO //
  2344. $ ')', IINFO, N, JTYPE, IOLDSD
  2345. INFO = ABS( IINFO )
  2346. IF( IINFO.LT.0 ) THEN
  2347. RETURN
  2348. ELSE
  2349. RESULT( NTEST ) = ULPINV
  2350. RESULT( NTEST+1 ) = ULPINV
  2351. RESULT( NTEST+2 ) = ULPINV
  2352. GO TO 1460
  2353. END IF
  2354. END IF
  2355. *
  2356. * Do tests 58 and 59 (or +54)
  2357. *
  2358. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2359. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2360. *
  2361. NTEST = NTEST + 2
  2362. *
  2363. IF( IUPLO.EQ.1 ) THEN
  2364. DO 1430 J = 1, N
  2365. DO 1420 I = MAX( 1, J-KD ), J
  2366. V( KD+1+I-J, J ) = A( I, J )
  2367. 1420 CONTINUE
  2368. 1430 CONTINUE
  2369. ELSE
  2370. DO 1450 J = 1, N
  2371. DO 1440 I = J, MIN( N, J+KD )
  2372. V( 1+I-J, J ) = A( I, J )
  2373. 1440 CONTINUE
  2374. 1450 CONTINUE
  2375. END IF
  2376. *
  2377. SRNAMT = 'DSBEVX_2STAGE'
  2378. CALL DSBEVX_2STAGE( 'N', 'V', UPLO, N, KD, V, LDU,
  2379. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2380. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2381. $ IINFO )
  2382. IF( IINFO.NE.0 ) THEN
  2383. WRITE( NOUNIT, FMT = 9999 )
  2384. $ 'DSBEVX_2STAGE(N,V,' // UPLO //
  2385. $ ')', IINFO, N, JTYPE, IOLDSD
  2386. INFO = ABS( IINFO )
  2387. IF( IINFO.LT.0 ) THEN
  2388. RETURN
  2389. ELSE
  2390. RESULT( NTEST ) = ULPINV
  2391. GO TO 1460
  2392. END IF
  2393. END IF
  2394. *
  2395. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2396. RESULT( NTEST ) = ULPINV
  2397. GO TO 1460
  2398. END IF
  2399. *
  2400. * Do test 60 (or +54)
  2401. *
  2402. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2403. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2404. IF( N.GT.0 ) THEN
  2405. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2406. ELSE
  2407. TEMP3 = ZERO
  2408. END IF
  2409. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2410. $ MAX( UNFL, TEMP3*ULP )
  2411. *
  2412. 1460 CONTINUE
  2413. *
  2414. * 7) Call DSYEVD
  2415. *
  2416. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  2417. *
  2418. NTEST = NTEST + 1
  2419. SRNAMT = 'DSYEVD'
  2420. CALL DSYEVD( 'V', UPLO, N, A, LDU, D1, WORK, LWEDC,
  2421. $ IWORK, LIWEDC, IINFO )
  2422. IF( IINFO.NE.0 ) THEN
  2423. WRITE( NOUNIT, FMT = 9999 )'DSYEVD(V,' // UPLO //
  2424. $ ')', IINFO, N, JTYPE, IOLDSD
  2425. INFO = ABS( IINFO )
  2426. IF( IINFO.LT.0 ) THEN
  2427. RETURN
  2428. ELSE
  2429. RESULT( NTEST ) = ULPINV
  2430. RESULT( NTEST+1 ) = ULPINV
  2431. RESULT( NTEST+2 ) = ULPINV
  2432. GO TO 1480
  2433. END IF
  2434. END IF
  2435. *
  2436. * Do tests 61 and 62 (or +54)
  2437. *
  2438. CALL DSYT21( 1, UPLO, N, 0, V, LDU, D1, D2, A, LDU, Z,
  2439. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2440. *
  2441. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2442. *
  2443. NTEST = NTEST + 2
  2444. SRNAMT = 'DSYEVD_2STAGE'
  2445. CALL DSYEVD_2STAGE( 'N', UPLO, N, A, LDU, D3, WORK,
  2446. $ LWORK, IWORK, LIWEDC, IINFO )
  2447. IF( IINFO.NE.0 ) THEN
  2448. WRITE( NOUNIT, FMT = 9999 )
  2449. $ 'DSYEVD_2STAGE(N,' // UPLO //
  2450. $ ')', IINFO, N, JTYPE, IOLDSD
  2451. INFO = ABS( IINFO )
  2452. IF( IINFO.LT.0 ) THEN
  2453. RETURN
  2454. ELSE
  2455. RESULT( NTEST ) = ULPINV
  2456. GO TO 1480
  2457. END IF
  2458. END IF
  2459. *
  2460. * Do test 63 (or +54)
  2461. *
  2462. TEMP1 = ZERO
  2463. TEMP2 = ZERO
  2464. DO 1470 J = 1, N
  2465. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2466. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2467. 1470 CONTINUE
  2468. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2469. $ ULP*MAX( TEMP1, TEMP2 ) )
  2470. *
  2471. 1480 CONTINUE
  2472. *
  2473. * 8) Call DSPEVD.
  2474. *
  2475. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2476. *
  2477. * Load array WORK with the upper or lower triangular
  2478. * part of the matrix in packed form.
  2479. *
  2480. IF( IUPLO.EQ.1 ) THEN
  2481. INDX = 1
  2482. DO 1500 J = 1, N
  2483. DO 1490 I = 1, J
  2484. WORK( INDX ) = A( I, J )
  2485. INDX = INDX + 1
  2486. 1490 CONTINUE
  2487. 1500 CONTINUE
  2488. ELSE
  2489. INDX = 1
  2490. DO 1520 J = 1, N
  2491. DO 1510 I = J, N
  2492. WORK( INDX ) = A( I, J )
  2493. INDX = INDX + 1
  2494. 1510 CONTINUE
  2495. 1520 CONTINUE
  2496. END IF
  2497. *
  2498. NTEST = NTEST + 1
  2499. SRNAMT = 'DSPEVD'
  2500. CALL DSPEVD( 'V', UPLO, N, WORK, D1, Z, LDU,
  2501. $ WORK( INDX ), LWEDC-INDX+1, IWORK, LIWEDC,
  2502. $ IINFO )
  2503. IF( IINFO.NE.0 ) THEN
  2504. WRITE( NOUNIT, FMT = 9999 )'DSPEVD(V,' // UPLO //
  2505. $ ')', IINFO, N, JTYPE, IOLDSD
  2506. INFO = ABS( IINFO )
  2507. IF( IINFO.LT.0 ) THEN
  2508. RETURN
  2509. ELSE
  2510. RESULT( NTEST ) = ULPINV
  2511. RESULT( NTEST+1 ) = ULPINV
  2512. RESULT( NTEST+2 ) = ULPINV
  2513. GO TO 1580
  2514. END IF
  2515. END IF
  2516. *
  2517. * Do tests 64 and 65 (or +54)
  2518. *
  2519. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2520. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2521. *
  2522. IF( IUPLO.EQ.1 ) THEN
  2523. INDX = 1
  2524. DO 1540 J = 1, N
  2525. DO 1530 I = 1, J
  2526. *
  2527. WORK( INDX ) = A( I, J )
  2528. INDX = INDX + 1
  2529. 1530 CONTINUE
  2530. 1540 CONTINUE
  2531. ELSE
  2532. INDX = 1
  2533. DO 1560 J = 1, N
  2534. DO 1550 I = J, N
  2535. WORK( INDX ) = A( I, J )
  2536. INDX = INDX + 1
  2537. 1550 CONTINUE
  2538. 1560 CONTINUE
  2539. END IF
  2540. *
  2541. NTEST = NTEST + 2
  2542. SRNAMT = 'DSPEVD'
  2543. CALL DSPEVD( 'N', UPLO, N, WORK, D3, Z, LDU,
  2544. $ WORK( INDX ), LWEDC-INDX+1, IWORK, LIWEDC,
  2545. $ IINFO )
  2546. IF( IINFO.NE.0 ) THEN
  2547. WRITE( NOUNIT, FMT = 9999 )'DSPEVD(N,' // UPLO //
  2548. $ ')', IINFO, N, JTYPE, IOLDSD
  2549. INFO = ABS( IINFO )
  2550. IF( IINFO.LT.0 ) THEN
  2551. RETURN
  2552. ELSE
  2553. RESULT( NTEST ) = ULPINV
  2554. GO TO 1580
  2555. END IF
  2556. END IF
  2557. *
  2558. * Do test 66 (or +54)
  2559. *
  2560. TEMP1 = ZERO
  2561. TEMP2 = ZERO
  2562. DO 1570 J = 1, N
  2563. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2564. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2565. 1570 CONTINUE
  2566. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2567. $ ULP*MAX( TEMP1, TEMP2 ) )
  2568. 1580 CONTINUE
  2569. *
  2570. * 9) Call DSBEVD.
  2571. *
  2572. IF( JTYPE.LE.7 ) THEN
  2573. KD = 1
  2574. ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
  2575. KD = MAX( N-1, 0 )
  2576. ELSE
  2577. KD = IHBW
  2578. END IF
  2579. *
  2580. * Load array V with the upper or lower triangular part
  2581. * of the matrix in band form.
  2582. *
  2583. IF( IUPLO.EQ.1 ) THEN
  2584. DO 1600 J = 1, N
  2585. DO 1590 I = MAX( 1, J-KD ), J
  2586. V( KD+1+I-J, J ) = A( I, J )
  2587. 1590 CONTINUE
  2588. 1600 CONTINUE
  2589. ELSE
  2590. DO 1620 J = 1, N
  2591. DO 1610 I = J, MIN( N, J+KD )
  2592. V( 1+I-J, J ) = A( I, J )
  2593. 1610 CONTINUE
  2594. 1620 CONTINUE
  2595. END IF
  2596. *
  2597. NTEST = NTEST + 1
  2598. SRNAMT = 'DSBEVD'
  2599. CALL DSBEVD( 'V', UPLO, N, KD, V, LDU, D1, Z, LDU, WORK,
  2600. $ LWEDC, IWORK, LIWEDC, IINFO )
  2601. IF( IINFO.NE.0 ) THEN
  2602. WRITE( NOUNIT, FMT = 9999 )'DSBEVD(V,' // UPLO //
  2603. $ ')', IINFO, N, JTYPE, IOLDSD
  2604. INFO = ABS( IINFO )
  2605. IF( IINFO.LT.0 ) THEN
  2606. RETURN
  2607. ELSE
  2608. RESULT( NTEST ) = ULPINV
  2609. RESULT( NTEST+1 ) = ULPINV
  2610. RESULT( NTEST+2 ) = ULPINV
  2611. GO TO 1680
  2612. END IF
  2613. END IF
  2614. *
  2615. * Do tests 67 and 68 (or +54)
  2616. *
  2617. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2618. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2619. *
  2620. IF( IUPLO.EQ.1 ) THEN
  2621. DO 1640 J = 1, N
  2622. DO 1630 I = MAX( 1, J-KD ), J
  2623. V( KD+1+I-J, J ) = A( I, J )
  2624. 1630 CONTINUE
  2625. 1640 CONTINUE
  2626. ELSE
  2627. DO 1660 J = 1, N
  2628. DO 1650 I = J, MIN( N, J+KD )
  2629. V( 1+I-J, J ) = A( I, J )
  2630. 1650 CONTINUE
  2631. 1660 CONTINUE
  2632. END IF
  2633. *
  2634. NTEST = NTEST + 2
  2635. SRNAMT = 'DSBEVD_2STAGE'
  2636. CALL DSBEVD_2STAGE( 'N', UPLO, N, KD, V, LDU, D3, Z, LDU,
  2637. $ WORK, LWORK, IWORK, LIWEDC, IINFO )
  2638. IF( IINFO.NE.0 ) THEN
  2639. WRITE( NOUNIT, FMT = 9999 )
  2640. $ 'DSBEVD_2STAGE(N,' // UPLO //
  2641. $ ')', IINFO, N, JTYPE, IOLDSD
  2642. INFO = ABS( IINFO )
  2643. IF( IINFO.LT.0 ) THEN
  2644. RETURN
  2645. ELSE
  2646. RESULT( NTEST ) = ULPINV
  2647. GO TO 1680
  2648. END IF
  2649. END IF
  2650. *
  2651. * Do test 69 (or +54)
  2652. *
  2653. TEMP1 = ZERO
  2654. TEMP2 = ZERO
  2655. DO 1670 J = 1, N
  2656. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2657. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2658. 1670 CONTINUE
  2659. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2660. $ ULP*MAX( TEMP1, TEMP2 ) )
  2661. *
  2662. 1680 CONTINUE
  2663. *
  2664. *
  2665. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  2666. NTEST = NTEST + 1
  2667. SRNAMT = 'DSYEVR'
  2668. CALL DSYEVR( 'V', 'A', UPLO, N, A, LDU, VL, VU, IL, IU,
  2669. $ ABSTOL, M, WA1, Z, LDU, IWORK, WORK, LWORK,
  2670. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2671. IF( IINFO.NE.0 ) THEN
  2672. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,A,' // UPLO //
  2673. $ ')', IINFO, N, JTYPE, IOLDSD
  2674. INFO = ABS( IINFO )
  2675. IF( IINFO.LT.0 ) THEN
  2676. RETURN
  2677. ELSE
  2678. RESULT( NTEST ) = ULPINV
  2679. RESULT( NTEST+1 ) = ULPINV
  2680. RESULT( NTEST+2 ) = ULPINV
  2681. GO TO 1700
  2682. END IF
  2683. END IF
  2684. *
  2685. * Do tests 70 and 71 (or ... )
  2686. *
  2687. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2688. *
  2689. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  2690. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2691. *
  2692. NTEST = NTEST + 2
  2693. SRNAMT = 'DSYEVR_2STAGE'
  2694. CALL DSYEVR_2STAGE( 'N', 'A', UPLO, N, A, LDU, VL, VU,
  2695. $ IL, IU, ABSTOL, M2, WA2, Z, LDU, IWORK,
  2696. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2697. $ IINFO )
  2698. IF( IINFO.NE.0 ) THEN
  2699. WRITE( NOUNIT, FMT = 9999 )
  2700. $ 'DSYEVR_2STAGE(N,A,' // UPLO //
  2701. $ ')', IINFO, N, JTYPE, IOLDSD
  2702. INFO = ABS( IINFO )
  2703. IF( IINFO.LT.0 ) THEN
  2704. RETURN
  2705. ELSE
  2706. RESULT( NTEST ) = ULPINV
  2707. GO TO 1700
  2708. END IF
  2709. END IF
  2710. *
  2711. * Do test 72 (or ... )
  2712. *
  2713. TEMP1 = ZERO
  2714. TEMP2 = ZERO
  2715. DO 1690 J = 1, N
  2716. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  2717. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  2718. 1690 CONTINUE
  2719. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2720. $ ULP*MAX( TEMP1, TEMP2 ) )
  2721. *
  2722. 1700 CONTINUE
  2723. *
  2724. NTEST = NTEST + 1
  2725. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2726. SRNAMT = 'DSYEVR'
  2727. CALL DSYEVR( 'V', 'I', UPLO, N, A, LDU, VL, VU, IL, IU,
  2728. $ ABSTOL, M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  2729. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2730. IF( IINFO.NE.0 ) THEN
  2731. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,I,' // UPLO //
  2732. $ ')', IINFO, N, JTYPE, IOLDSD
  2733. INFO = ABS( IINFO )
  2734. IF( IINFO.LT.0 ) THEN
  2735. RETURN
  2736. ELSE
  2737. RESULT( NTEST ) = ULPINV
  2738. RESULT( NTEST+1 ) = ULPINV
  2739. RESULT( NTEST+2 ) = ULPINV
  2740. GO TO 1710
  2741. END IF
  2742. END IF
  2743. *
  2744. * Do tests 73 and 74 (or +54)
  2745. *
  2746. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2747. *
  2748. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2749. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2750. *
  2751. NTEST = NTEST + 2
  2752. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2753. SRNAMT = 'DSYEVR_2STAGE'
  2754. CALL DSYEVR_2STAGE( 'N', 'I', UPLO, N, A, LDU, VL, VU,
  2755. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, IWORK,
  2756. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2757. $ IINFO )
  2758. IF( IINFO.NE.0 ) THEN
  2759. WRITE( NOUNIT, FMT = 9999 )
  2760. $ 'DSYEVR_2STAGE(N,I,' // UPLO //
  2761. $ ')', IINFO, N, JTYPE, IOLDSD
  2762. INFO = ABS( IINFO )
  2763. IF( IINFO.LT.0 ) THEN
  2764. RETURN
  2765. ELSE
  2766. RESULT( NTEST ) = ULPINV
  2767. GO TO 1710
  2768. END IF
  2769. END IF
  2770. *
  2771. * Do test 75 (or +54)
  2772. *
  2773. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2774. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2775. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2776. $ MAX( UNFL, ULP*TEMP3 )
  2777. 1710 CONTINUE
  2778. *
  2779. NTEST = NTEST + 1
  2780. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2781. SRNAMT = 'DSYEVR'
  2782. CALL DSYEVR( 'V', 'V', UPLO, N, A, LDU, VL, VU, IL, IU,
  2783. $ ABSTOL, M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  2784. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2785. IF( IINFO.NE.0 ) THEN
  2786. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,V,' // UPLO //
  2787. $ ')', IINFO, N, JTYPE, IOLDSD
  2788. INFO = ABS( IINFO )
  2789. IF( IINFO.LT.0 ) THEN
  2790. RETURN
  2791. ELSE
  2792. RESULT( NTEST ) = ULPINV
  2793. RESULT( NTEST+1 ) = ULPINV
  2794. RESULT( NTEST+2 ) = ULPINV
  2795. GO TO 1720
  2796. END IF
  2797. END IF
  2798. *
  2799. * Do tests 76 and 77 (or +54)
  2800. *
  2801. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2802. *
  2803. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2804. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2805. *
  2806. NTEST = NTEST + 2
  2807. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2808. SRNAMT = 'DSYEVR_2STAGE'
  2809. CALL DSYEVR_2STAGE( 'N', 'V', UPLO, N, A, LDU, VL, VU,
  2810. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, IWORK,
  2811. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2812. $ IINFO )
  2813. IF( IINFO.NE.0 ) THEN
  2814. WRITE( NOUNIT, FMT = 9999 )
  2815. $ 'DSYEVR_2STAGE(N,V,' // UPLO //
  2816. $ ')', IINFO, N, JTYPE, IOLDSD
  2817. INFO = ABS( IINFO )
  2818. IF( IINFO.LT.0 ) THEN
  2819. RETURN
  2820. ELSE
  2821. RESULT( NTEST ) = ULPINV
  2822. GO TO 1720
  2823. END IF
  2824. END IF
  2825. *
  2826. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2827. RESULT( NTEST ) = ULPINV
  2828. GO TO 1720
  2829. END IF
  2830. *
  2831. * Do test 78 (or +54)
  2832. *
  2833. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2834. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2835. IF( N.GT.0 ) THEN
  2836. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2837. ELSE
  2838. TEMP3 = ZERO
  2839. END IF
  2840. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2841. $ MAX( UNFL, TEMP3*ULP )
  2842. *
  2843. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2844. *
  2845. 1720 CONTINUE
  2846. *
  2847. * End of Loop -- Check for RESULT(j) > THRESH
  2848. *
  2849. NTESTT = NTESTT + NTEST
  2850. *
  2851. CALL DLAFTS( 'DST', N, N, JTYPE, NTEST, RESULT, IOLDSD,
  2852. $ THRESH, NOUNIT, NERRS )
  2853. *
  2854. 1730 CONTINUE
  2855. 1740 CONTINUE
  2856. *
  2857. * Summary
  2858. *
  2859. CALL ALASVM( 'DST', NOUNIT, NERRS, NTESTT, 0 )
  2860. *
  2861. 9999 FORMAT( ' DDRVST2STG: ', A, ' returned INFO=', I6, '.', / 9X,
  2862. $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
  2863. *
  2864. RETURN
  2865. *
  2866. * End of DDRVST2STG
  2867. *
  2868. END