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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 simlutaneously
  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, DLABAD, 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. CALL DLABAD( UNFL, OVFL )
  581. ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
  582. ULPINV = ONE / ULP
  583. RTUNFL = SQRT( UNFL )
  584. RTOVFL = SQRT( OVFL )
  585. *
  586. * Loop over sizes, types
  587. *
  588. DO 20 I = 1, 4
  589. ISEED2( I ) = ISEED( I )
  590. ISEED3( I ) = ISEED( I )
  591. 20 CONTINUE
  592. *
  593. NERRS = 0
  594. NMATS = 0
  595. *
  596. *
  597. DO 1740 JSIZE = 1, NSIZES
  598. N = NN( JSIZE )
  599. IF( N.GT.0 ) THEN
  600. LGN = INT( LOG( DBLE( N ) ) / LOG( TWO ) )
  601. IF( 2**LGN.LT.N )
  602. $ LGN = LGN + 1
  603. IF( 2**LGN.LT.N )
  604. $ LGN = LGN + 1
  605. LWEDC = 1 + 4*N + 2*N*LGN + 4*N**2
  606. c LIWEDC = 6 + 6*N + 5*N*LGN
  607. LIWEDC = 3 + 5*N
  608. ELSE
  609. LWEDC = 9
  610. c LIWEDC = 12
  611. LIWEDC = 8
  612. END IF
  613. ANINV = ONE / DBLE( MAX( 1, N ) )
  614. *
  615. IF( NSIZES.NE.1 ) THEN
  616. MTYPES = MIN( MAXTYP, NTYPES )
  617. ELSE
  618. MTYPES = MIN( MAXTYP+1, NTYPES )
  619. END IF
  620. *
  621. DO 1730 JTYPE = 1, MTYPES
  622. *
  623. IF( .NOT.DOTYPE( JTYPE ) )
  624. $ GO TO 1730
  625. NMATS = NMATS + 1
  626. NTEST = 0
  627. *
  628. DO 30 J = 1, 4
  629. IOLDSD( J ) = ISEED( J )
  630. 30 CONTINUE
  631. *
  632. * 2) Compute "A"
  633. *
  634. * Control parameters:
  635. *
  636. * KMAGN KMODE KTYPE
  637. * =1 O(1) clustered 1 zero
  638. * =2 large clustered 2 identity
  639. * =3 small exponential (none)
  640. * =4 arithmetic diagonal, (w/ eigenvalues)
  641. * =5 random log symmetric, w/ eigenvalues
  642. * =6 random (none)
  643. * =7 random diagonal
  644. * =8 random symmetric
  645. * =9 band symmetric, w/ eigenvalues
  646. *
  647. IF( MTYPES.GT.MAXTYP )
  648. $ GO TO 110
  649. *
  650. ITYPE = KTYPE( JTYPE )
  651. IMODE = KMODE( JTYPE )
  652. *
  653. * Compute norm
  654. *
  655. GO TO ( 40, 50, 60 )KMAGN( JTYPE )
  656. *
  657. 40 CONTINUE
  658. ANORM = ONE
  659. GO TO 70
  660. *
  661. 50 CONTINUE
  662. ANORM = ( RTOVFL*ULP )*ANINV
  663. GO TO 70
  664. *
  665. 60 CONTINUE
  666. ANORM = RTUNFL*N*ULPINV
  667. GO TO 70
  668. *
  669. 70 CONTINUE
  670. *
  671. CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
  672. IINFO = 0
  673. COND = ULPINV
  674. *
  675. * Special Matrices -- Identity & Jordan block
  676. *
  677. * Zero
  678. *
  679. IF( ITYPE.EQ.1 ) THEN
  680. IINFO = 0
  681. *
  682. ELSE IF( ITYPE.EQ.2 ) THEN
  683. *
  684. * Identity
  685. *
  686. DO 80 JCOL = 1, N
  687. A( JCOL, JCOL ) = ANORM
  688. 80 CONTINUE
  689. *
  690. ELSE IF( ITYPE.EQ.4 ) THEN
  691. *
  692. * Diagonal Matrix, [Eigen]values Specified
  693. *
  694. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  695. $ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
  696. $ IINFO )
  697. *
  698. ELSE IF( ITYPE.EQ.5 ) THEN
  699. *
  700. * Symmetric, eigenvalues specified
  701. *
  702. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  703. $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
  704. $ IINFO )
  705. *
  706. ELSE IF( ITYPE.EQ.7 ) THEN
  707. *
  708. * Diagonal, random eigenvalues
  709. *
  710. IDUMMA( 1 ) = 1
  711. CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
  712. $ 'T', 'N', WORK( N+1 ), 1, ONE,
  713. $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
  714. $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
  715. *
  716. ELSE IF( ITYPE.EQ.8 ) THEN
  717. *
  718. * Symmetric, random eigenvalues
  719. *
  720. IDUMMA( 1 ) = 1
  721. CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
  722. $ 'T', 'N', WORK( N+1 ), 1, ONE,
  723. $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
  724. $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
  725. *
  726. ELSE IF( ITYPE.EQ.9 ) THEN
  727. *
  728. * Symmetric banded, eigenvalues specified
  729. *
  730. IHBW = INT( ( N-1 )*DLARND( 1, ISEED3 ) )
  731. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  732. $ ANORM, IHBW, IHBW, 'Z', U, LDU, WORK( N+1 ),
  733. $ IINFO )
  734. *
  735. * Store as dense matrix for most routines.
  736. *
  737. CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
  738. DO 100 IDIAG = -IHBW, IHBW
  739. IROW = IHBW - IDIAG + 1
  740. J1 = MAX( 1, IDIAG+1 )
  741. J2 = MIN( N, N+IDIAG )
  742. DO 90 J = J1, J2
  743. I = J - IDIAG
  744. A( I, J ) = U( IROW, J )
  745. 90 CONTINUE
  746. 100 CONTINUE
  747. ELSE
  748. IINFO = 1
  749. END IF
  750. *
  751. IF( IINFO.NE.0 ) THEN
  752. WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
  753. $ IOLDSD
  754. INFO = ABS( IINFO )
  755. RETURN
  756. END IF
  757. *
  758. 110 CONTINUE
  759. *
  760. ABSTOL = UNFL + UNFL
  761. IF( N.LE.1 ) THEN
  762. IL = 1
  763. IU = N
  764. ELSE
  765. IL = 1 + INT( ( N-1 )*DLARND( 1, ISEED2 ) )
  766. IU = 1 + INT( ( N-1 )*DLARND( 1, ISEED2 ) )
  767. IF( IL.GT.IU ) THEN
  768. ITEMP = IL
  769. IL = IU
  770. IU = ITEMP
  771. END IF
  772. END IF
  773. *
  774. * 3) If matrix is tridiagonal, call DSTEV and DSTEVX.
  775. *
  776. IF( JTYPE.LE.7 ) THEN
  777. NTEST = 1
  778. DO 120 I = 1, N
  779. D1( I ) = DBLE( A( I, I ) )
  780. 120 CONTINUE
  781. DO 130 I = 1, N - 1
  782. D2( I ) = DBLE( A( I+1, I ) )
  783. 130 CONTINUE
  784. SRNAMT = 'DSTEV'
  785. CALL DSTEV( 'V', N, D1, D2, Z, LDU, WORK, IINFO )
  786. IF( IINFO.NE.0 ) THEN
  787. WRITE( NOUNIT, FMT = 9999 )'DSTEV(V)', IINFO, N,
  788. $ JTYPE, IOLDSD
  789. INFO = ABS( IINFO )
  790. IF( IINFO.LT.0 ) THEN
  791. RETURN
  792. ELSE
  793. RESULT( 1 ) = ULPINV
  794. RESULT( 2 ) = ULPINV
  795. RESULT( 3 ) = ULPINV
  796. GO TO 180
  797. END IF
  798. END IF
  799. *
  800. * Do tests 1 and 2.
  801. *
  802. DO 140 I = 1, N
  803. D3( I ) = DBLE( A( I, I ) )
  804. 140 CONTINUE
  805. DO 150 I = 1, N - 1
  806. D4( I ) = DBLE( A( I+1, I ) )
  807. 150 CONTINUE
  808. CALL DSTT21( N, 0, D3, D4, D1, D2, Z, LDU, WORK,
  809. $ RESULT( 1 ) )
  810. *
  811. NTEST = 3
  812. DO 160 I = 1, N - 1
  813. D4( I ) = DBLE( A( I+1, I ) )
  814. 160 CONTINUE
  815. SRNAMT = 'DSTEV'
  816. CALL DSTEV( 'N', N, D3, D4, Z, LDU, WORK, IINFO )
  817. IF( IINFO.NE.0 ) THEN
  818. WRITE( NOUNIT, FMT = 9999 )'DSTEV(N)', IINFO, N,
  819. $ JTYPE, IOLDSD
  820. INFO = ABS( IINFO )
  821. IF( IINFO.LT.0 ) THEN
  822. RETURN
  823. ELSE
  824. RESULT( 3 ) = ULPINV
  825. GO TO 180
  826. END IF
  827. END IF
  828. *
  829. * Do test 3.
  830. *
  831. TEMP1 = ZERO
  832. TEMP2 = ZERO
  833. DO 170 J = 1, N
  834. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  835. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  836. 170 CONTINUE
  837. RESULT( 3 ) = TEMP2 / MAX( UNFL,
  838. $ ULP*MAX( TEMP1, TEMP2 ) )
  839. *
  840. 180 CONTINUE
  841. *
  842. NTEST = 4
  843. DO 190 I = 1, N
  844. EVEIGS( I ) = D3( I )
  845. D1( I ) = DBLE( A( I, I ) )
  846. 190 CONTINUE
  847. DO 200 I = 1, N - 1
  848. D2( I ) = DBLE( A( I+1, I ) )
  849. 200 CONTINUE
  850. SRNAMT = 'DSTEVX'
  851. CALL DSTEVX( 'V', 'A', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  852. $ M, WA1, Z, LDU, WORK, IWORK, IWORK( 5*N+1 ),
  853. $ IINFO )
  854. IF( IINFO.NE.0 ) THEN
  855. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,A)', IINFO, N,
  856. $ JTYPE, IOLDSD
  857. INFO = ABS( IINFO )
  858. IF( IINFO.LT.0 ) THEN
  859. RETURN
  860. ELSE
  861. RESULT( 4 ) = ULPINV
  862. RESULT( 5 ) = ULPINV
  863. RESULT( 6 ) = ULPINV
  864. GO TO 250
  865. END IF
  866. END IF
  867. IF( N.GT.0 ) THEN
  868. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  869. ELSE
  870. TEMP3 = ZERO
  871. END IF
  872. *
  873. * Do tests 4 and 5.
  874. *
  875. DO 210 I = 1, N
  876. D3( I ) = DBLE( A( I, I ) )
  877. 210 CONTINUE
  878. DO 220 I = 1, N - 1
  879. D4( I ) = DBLE( A( I+1, I ) )
  880. 220 CONTINUE
  881. CALL DSTT21( N, 0, D3, D4, WA1, D2, Z, LDU, WORK,
  882. $ RESULT( 4 ) )
  883. *
  884. NTEST = 6
  885. DO 230 I = 1, N - 1
  886. D4( I ) = DBLE( A( I+1, I ) )
  887. 230 CONTINUE
  888. SRNAMT = 'DSTEVX'
  889. CALL DSTEVX( 'N', 'A', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  890. $ M2, WA2, Z, LDU, WORK, IWORK,
  891. $ IWORK( 5*N+1 ), IINFO )
  892. IF( IINFO.NE.0 ) THEN
  893. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,A)', IINFO, N,
  894. $ JTYPE, IOLDSD
  895. INFO = ABS( IINFO )
  896. IF( IINFO.LT.0 ) THEN
  897. RETURN
  898. ELSE
  899. RESULT( 6 ) = ULPINV
  900. GO TO 250
  901. END IF
  902. END IF
  903. *
  904. * Do test 6.
  905. *
  906. TEMP1 = ZERO
  907. TEMP2 = ZERO
  908. DO 240 J = 1, N
  909. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ),
  910. $ ABS( EVEIGS( J ) ) )
  911. TEMP2 = MAX( TEMP2, ABS( WA2( J )-EVEIGS( J ) ) )
  912. 240 CONTINUE
  913. RESULT( 6 ) = TEMP2 / MAX( UNFL,
  914. $ ULP*MAX( TEMP1, TEMP2 ) )
  915. *
  916. 250 CONTINUE
  917. *
  918. NTEST = 7
  919. DO 260 I = 1, N
  920. D1( I ) = DBLE( A( I, I ) )
  921. 260 CONTINUE
  922. DO 270 I = 1, N - 1
  923. D2( I ) = DBLE( A( I+1, I ) )
  924. 270 CONTINUE
  925. SRNAMT = 'DSTEVR'
  926. CALL DSTEVR( 'V', 'A', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  927. $ M, WA1, Z, LDU, IWORK, WORK, LWORK,
  928. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  929. IF( IINFO.NE.0 ) THEN
  930. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,A)', IINFO, N,
  931. $ JTYPE, IOLDSD
  932. INFO = ABS( IINFO )
  933. IF( IINFO.LT.0 ) THEN
  934. RETURN
  935. ELSE
  936. RESULT( 7 ) = ULPINV
  937. RESULT( 8 ) = ULPINV
  938. GO TO 320
  939. END IF
  940. END IF
  941. IF( N.GT.0 ) THEN
  942. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  943. ELSE
  944. TEMP3 = ZERO
  945. END IF
  946. *
  947. * Do tests 7 and 8.
  948. *
  949. DO 280 I = 1, N
  950. D3( I ) = DBLE( A( I, I ) )
  951. 280 CONTINUE
  952. DO 290 I = 1, N - 1
  953. D4( I ) = DBLE( A( I+1, I ) )
  954. 290 CONTINUE
  955. CALL DSTT21( N, 0, D3, D4, WA1, D2, Z, LDU, WORK,
  956. $ RESULT( 7 ) )
  957. *
  958. NTEST = 9
  959. DO 300 I = 1, N - 1
  960. D4( I ) = DBLE( A( I+1, I ) )
  961. 300 CONTINUE
  962. SRNAMT = 'DSTEVR'
  963. CALL DSTEVR( 'N', 'A', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  964. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  965. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  966. IF( IINFO.NE.0 ) THEN
  967. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,A)', IINFO, N,
  968. $ JTYPE, IOLDSD
  969. INFO = ABS( IINFO )
  970. IF( IINFO.LT.0 ) THEN
  971. RETURN
  972. ELSE
  973. RESULT( 9 ) = ULPINV
  974. GO TO 320
  975. END IF
  976. END IF
  977. *
  978. * Do test 9.
  979. *
  980. TEMP1 = ZERO
  981. TEMP2 = ZERO
  982. DO 310 J = 1, N
  983. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ),
  984. $ ABS( EVEIGS( J ) ) )
  985. TEMP2 = MAX( TEMP2, ABS( WA2( J )-EVEIGS( J ) ) )
  986. 310 CONTINUE
  987. RESULT( 9 ) = TEMP2 / MAX( UNFL,
  988. $ ULP*MAX( TEMP1, TEMP2 ) )
  989. *
  990. 320 CONTINUE
  991. *
  992. *
  993. NTEST = 10
  994. DO 330 I = 1, N
  995. D1( I ) = DBLE( A( I, I ) )
  996. 330 CONTINUE
  997. DO 340 I = 1, N - 1
  998. D2( I ) = DBLE( A( I+1, I ) )
  999. 340 CONTINUE
  1000. SRNAMT = 'DSTEVX'
  1001. CALL DSTEVX( 'V', 'I', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1002. $ M2, WA2, Z, LDU, WORK, IWORK,
  1003. $ IWORK( 5*N+1 ), IINFO )
  1004. IF( IINFO.NE.0 ) THEN
  1005. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,I)', IINFO, N,
  1006. $ JTYPE, IOLDSD
  1007. INFO = ABS( IINFO )
  1008. IF( IINFO.LT.0 ) THEN
  1009. RETURN
  1010. ELSE
  1011. RESULT( 10 ) = ULPINV
  1012. RESULT( 11 ) = ULPINV
  1013. RESULT( 12 ) = ULPINV
  1014. GO TO 380
  1015. END IF
  1016. END IF
  1017. *
  1018. * Do tests 10 and 11.
  1019. *
  1020. DO 350 I = 1, N
  1021. D3( I ) = DBLE( A( I, I ) )
  1022. 350 CONTINUE
  1023. DO 360 I = 1, N - 1
  1024. D4( I ) = DBLE( A( I+1, I ) )
  1025. 360 CONTINUE
  1026. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1027. $ MAX( 1, M2 ), RESULT( 10 ) )
  1028. *
  1029. *
  1030. NTEST = 12
  1031. DO 370 I = 1, N - 1
  1032. D4( I ) = DBLE( A( I+1, I ) )
  1033. 370 CONTINUE
  1034. SRNAMT = 'DSTEVX'
  1035. CALL DSTEVX( 'N', 'I', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1036. $ M3, WA3, Z, LDU, WORK, IWORK,
  1037. $ IWORK( 5*N+1 ), IINFO )
  1038. IF( IINFO.NE.0 ) THEN
  1039. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,I)', IINFO, N,
  1040. $ JTYPE, IOLDSD
  1041. INFO = ABS( IINFO )
  1042. IF( IINFO.LT.0 ) THEN
  1043. RETURN
  1044. ELSE
  1045. RESULT( 12 ) = ULPINV
  1046. GO TO 380
  1047. END IF
  1048. END IF
  1049. *
  1050. * Do test 12.
  1051. *
  1052. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1053. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1054. RESULT( 12 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, ULP*TEMP3 )
  1055. *
  1056. 380 CONTINUE
  1057. *
  1058. NTEST = 12
  1059. IF( N.GT.0 ) THEN
  1060. IF( IL.NE.1 ) THEN
  1061. VL = WA1( IL ) - MAX( HALF*
  1062. $ ( WA1( IL )-WA1( IL-1 ) ), TEN*ULP*TEMP3,
  1063. $ TEN*RTUNFL )
  1064. ELSE
  1065. VL = WA1( 1 ) - MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1066. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1067. END IF
  1068. IF( IU.NE.N ) THEN
  1069. VU = WA1( IU ) + MAX( HALF*
  1070. $ ( WA1( IU+1 )-WA1( IU ) ), TEN*ULP*TEMP3,
  1071. $ TEN*RTUNFL )
  1072. ELSE
  1073. VU = WA1( N ) + MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1074. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1075. END IF
  1076. ELSE
  1077. VL = ZERO
  1078. VU = ONE
  1079. END IF
  1080. *
  1081. DO 390 I = 1, N
  1082. D1( I ) = DBLE( A( I, I ) )
  1083. 390 CONTINUE
  1084. DO 400 I = 1, N - 1
  1085. D2( I ) = DBLE( A( I+1, I ) )
  1086. 400 CONTINUE
  1087. SRNAMT = 'DSTEVX'
  1088. CALL DSTEVX( 'V', 'V', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1089. $ M2, WA2, Z, LDU, WORK, IWORK,
  1090. $ IWORK( 5*N+1 ), IINFO )
  1091. IF( IINFO.NE.0 ) THEN
  1092. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,V)', IINFO, N,
  1093. $ JTYPE, IOLDSD
  1094. INFO = ABS( IINFO )
  1095. IF( IINFO.LT.0 ) THEN
  1096. RETURN
  1097. ELSE
  1098. RESULT( 13 ) = ULPINV
  1099. RESULT( 14 ) = ULPINV
  1100. RESULT( 15 ) = ULPINV
  1101. GO TO 440
  1102. END IF
  1103. END IF
  1104. *
  1105. IF( M2.EQ.0 .AND. N.GT.0 ) THEN
  1106. RESULT( 13 ) = ULPINV
  1107. RESULT( 14 ) = ULPINV
  1108. RESULT( 15 ) = ULPINV
  1109. GO TO 440
  1110. END IF
  1111. *
  1112. * Do tests 13 and 14.
  1113. *
  1114. DO 410 I = 1, N
  1115. D3( I ) = DBLE( A( I, I ) )
  1116. 410 CONTINUE
  1117. DO 420 I = 1, N - 1
  1118. D4( I ) = DBLE( A( I+1, I ) )
  1119. 420 CONTINUE
  1120. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1121. $ MAX( 1, M2 ), RESULT( 13 ) )
  1122. *
  1123. NTEST = 15
  1124. DO 430 I = 1, N - 1
  1125. D4( I ) = DBLE( A( I+1, I ) )
  1126. 430 CONTINUE
  1127. SRNAMT = 'DSTEVX'
  1128. CALL DSTEVX( 'N', 'V', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1129. $ M3, WA3, Z, LDU, WORK, IWORK,
  1130. $ IWORK( 5*N+1 ), IINFO )
  1131. IF( IINFO.NE.0 ) THEN
  1132. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,V)', IINFO, N,
  1133. $ JTYPE, IOLDSD
  1134. INFO = ABS( IINFO )
  1135. IF( IINFO.LT.0 ) THEN
  1136. RETURN
  1137. ELSE
  1138. RESULT( 15 ) = ULPINV
  1139. GO TO 440
  1140. END IF
  1141. END IF
  1142. *
  1143. * Do test 15.
  1144. *
  1145. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1146. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1147. RESULT( 15 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, TEMP3*ULP )
  1148. *
  1149. 440 CONTINUE
  1150. *
  1151. NTEST = 16
  1152. DO 450 I = 1, N
  1153. D1( I ) = DBLE( A( I, I ) )
  1154. 450 CONTINUE
  1155. DO 460 I = 1, N - 1
  1156. D2( I ) = DBLE( A( I+1, I ) )
  1157. 460 CONTINUE
  1158. SRNAMT = 'DSTEVD'
  1159. CALL DSTEVD( 'V', N, D1, D2, Z, LDU, WORK, LWEDC, IWORK,
  1160. $ LIWEDC, IINFO )
  1161. IF( IINFO.NE.0 ) THEN
  1162. WRITE( NOUNIT, FMT = 9999 )'DSTEVD(V)', IINFO, N,
  1163. $ JTYPE, IOLDSD
  1164. INFO = ABS( IINFO )
  1165. IF( IINFO.LT.0 ) THEN
  1166. RETURN
  1167. ELSE
  1168. RESULT( 16 ) = ULPINV
  1169. RESULT( 17 ) = ULPINV
  1170. RESULT( 18 ) = ULPINV
  1171. GO TO 510
  1172. END IF
  1173. END IF
  1174. *
  1175. * Do tests 16 and 17.
  1176. *
  1177. DO 470 I = 1, N
  1178. D3( I ) = DBLE( A( I, I ) )
  1179. 470 CONTINUE
  1180. DO 480 I = 1, N - 1
  1181. D4( I ) = DBLE( A( I+1, I ) )
  1182. 480 CONTINUE
  1183. CALL DSTT21( N, 0, D3, D4, D1, D2, Z, LDU, WORK,
  1184. $ RESULT( 16 ) )
  1185. *
  1186. NTEST = 18
  1187. DO 490 I = 1, N - 1
  1188. D4( I ) = DBLE( A( I+1, I ) )
  1189. 490 CONTINUE
  1190. SRNAMT = 'DSTEVD'
  1191. CALL DSTEVD( 'N', N, D3, D4, Z, LDU, WORK, LWEDC, IWORK,
  1192. $ LIWEDC, IINFO )
  1193. IF( IINFO.NE.0 ) THEN
  1194. WRITE( NOUNIT, FMT = 9999 )'DSTEVD(N)', IINFO, N,
  1195. $ JTYPE, IOLDSD
  1196. INFO = ABS( IINFO )
  1197. IF( IINFO.LT.0 ) THEN
  1198. RETURN
  1199. ELSE
  1200. RESULT( 18 ) = ULPINV
  1201. GO TO 510
  1202. END IF
  1203. END IF
  1204. *
  1205. * Do test 18.
  1206. *
  1207. TEMP1 = ZERO
  1208. TEMP2 = ZERO
  1209. DO 500 J = 1, N
  1210. TEMP1 = MAX( TEMP1, ABS( EVEIGS( J ) ),
  1211. $ ABS( D3( J ) ) )
  1212. TEMP2 = MAX( TEMP2, ABS( EVEIGS( J )-D3( J ) ) )
  1213. 500 CONTINUE
  1214. RESULT( 18 ) = TEMP2 / MAX( UNFL,
  1215. $ ULP*MAX( TEMP1, TEMP2 ) )
  1216. *
  1217. 510 CONTINUE
  1218. *
  1219. NTEST = 19
  1220. DO 520 I = 1, N
  1221. D1( I ) = DBLE( A( I, I ) )
  1222. 520 CONTINUE
  1223. DO 530 I = 1, N - 1
  1224. D2( I ) = DBLE( A( I+1, I ) )
  1225. 530 CONTINUE
  1226. SRNAMT = 'DSTEVR'
  1227. CALL DSTEVR( 'V', 'I', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1228. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  1229. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1230. IF( IINFO.NE.0 ) THEN
  1231. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,I)', IINFO, N,
  1232. $ JTYPE, IOLDSD
  1233. INFO = ABS( IINFO )
  1234. IF( IINFO.LT.0 ) THEN
  1235. RETURN
  1236. ELSE
  1237. RESULT( 19 ) = ULPINV
  1238. RESULT( 20 ) = ULPINV
  1239. RESULT( 21 ) = ULPINV
  1240. GO TO 570
  1241. END IF
  1242. END IF
  1243. *
  1244. * DO tests 19 and 20.
  1245. *
  1246. DO 540 I = 1, N
  1247. D3( I ) = DBLE( A( I, I ) )
  1248. 540 CONTINUE
  1249. DO 550 I = 1, N - 1
  1250. D4( I ) = DBLE( A( I+1, I ) )
  1251. 550 CONTINUE
  1252. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1253. $ MAX( 1, M2 ), RESULT( 19 ) )
  1254. *
  1255. *
  1256. NTEST = 21
  1257. DO 560 I = 1, N - 1
  1258. D4( I ) = DBLE( A( I+1, I ) )
  1259. 560 CONTINUE
  1260. SRNAMT = 'DSTEVR'
  1261. CALL DSTEVR( 'N', 'I', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1262. $ M3, WA3, Z, LDU, IWORK, WORK, LWORK,
  1263. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1264. IF( IINFO.NE.0 ) THEN
  1265. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,I)', IINFO, N,
  1266. $ JTYPE, IOLDSD
  1267. INFO = ABS( IINFO )
  1268. IF( IINFO.LT.0 ) THEN
  1269. RETURN
  1270. ELSE
  1271. RESULT( 21 ) = ULPINV
  1272. GO TO 570
  1273. END IF
  1274. END IF
  1275. *
  1276. * Do test 21.
  1277. *
  1278. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1279. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1280. RESULT( 21 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, ULP*TEMP3 )
  1281. *
  1282. 570 CONTINUE
  1283. *
  1284. NTEST = 21
  1285. IF( N.GT.0 ) THEN
  1286. IF( IL.NE.1 ) THEN
  1287. VL = WA1( IL ) - MAX( HALF*
  1288. $ ( WA1( IL )-WA1( IL-1 ) ), TEN*ULP*TEMP3,
  1289. $ TEN*RTUNFL )
  1290. ELSE
  1291. VL = WA1( 1 ) - MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1292. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1293. END IF
  1294. IF( IU.NE.N ) THEN
  1295. VU = WA1( IU ) + MAX( HALF*
  1296. $ ( WA1( IU+1 )-WA1( IU ) ), TEN*ULP*TEMP3,
  1297. $ TEN*RTUNFL )
  1298. ELSE
  1299. VU = WA1( N ) + MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1300. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1301. END IF
  1302. ELSE
  1303. VL = ZERO
  1304. VU = ONE
  1305. END IF
  1306. *
  1307. DO 580 I = 1, N
  1308. D1( I ) = DBLE( A( I, I ) )
  1309. 580 CONTINUE
  1310. DO 590 I = 1, N - 1
  1311. D2( I ) = DBLE( A( I+1, I ) )
  1312. 590 CONTINUE
  1313. SRNAMT = 'DSTEVR'
  1314. CALL DSTEVR( 'V', 'V', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1315. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  1316. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1317. IF( IINFO.NE.0 ) THEN
  1318. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,V)', IINFO, N,
  1319. $ JTYPE, IOLDSD
  1320. INFO = ABS( IINFO )
  1321. IF( IINFO.LT.0 ) THEN
  1322. RETURN
  1323. ELSE
  1324. RESULT( 22 ) = ULPINV
  1325. RESULT( 23 ) = ULPINV
  1326. RESULT( 24 ) = ULPINV
  1327. GO TO 630
  1328. END IF
  1329. END IF
  1330. *
  1331. IF( M2.EQ.0 .AND. N.GT.0 ) THEN
  1332. RESULT( 22 ) = ULPINV
  1333. RESULT( 23 ) = ULPINV
  1334. RESULT( 24 ) = ULPINV
  1335. GO TO 630
  1336. END IF
  1337. *
  1338. * Do tests 22 and 23.
  1339. *
  1340. DO 600 I = 1, N
  1341. D3( I ) = DBLE( A( I, I ) )
  1342. 600 CONTINUE
  1343. DO 610 I = 1, N - 1
  1344. D4( I ) = DBLE( A( I+1, I ) )
  1345. 610 CONTINUE
  1346. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1347. $ MAX( 1, M2 ), RESULT( 22 ) )
  1348. *
  1349. NTEST = 24
  1350. DO 620 I = 1, N - 1
  1351. D4( I ) = DBLE( A( I+1, I ) )
  1352. 620 CONTINUE
  1353. SRNAMT = 'DSTEVR'
  1354. CALL DSTEVR( 'N', 'V', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1355. $ M3, WA3, Z, LDU, IWORK, WORK, LWORK,
  1356. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1357. IF( IINFO.NE.0 ) THEN
  1358. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,V)', IINFO, N,
  1359. $ JTYPE, IOLDSD
  1360. INFO = ABS( IINFO )
  1361. IF( IINFO.LT.0 ) THEN
  1362. RETURN
  1363. ELSE
  1364. RESULT( 24 ) = ULPINV
  1365. GO TO 630
  1366. END IF
  1367. END IF
  1368. *
  1369. * Do test 24.
  1370. *
  1371. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1372. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1373. RESULT( 24 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, TEMP3*ULP )
  1374. *
  1375. 630 CONTINUE
  1376. *
  1377. *
  1378. *
  1379. ELSE
  1380. *
  1381. DO 640 I = 1, 24
  1382. RESULT( I ) = ZERO
  1383. 640 CONTINUE
  1384. NTEST = 24
  1385. END IF
  1386. *
  1387. * Perform remaining tests storing upper or lower triangular
  1388. * part of matrix.
  1389. *
  1390. DO 1720 IUPLO = 0, 1
  1391. IF( IUPLO.EQ.0 ) THEN
  1392. UPLO = 'L'
  1393. ELSE
  1394. UPLO = 'U'
  1395. END IF
  1396. *
  1397. * 4) Call DSYEV and DSYEVX.
  1398. *
  1399. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  1400. *
  1401. NTEST = NTEST + 1
  1402. SRNAMT = 'DSYEV'
  1403. CALL DSYEV( 'V', UPLO, N, A, LDU, D1, WORK, LWORK,
  1404. $ IINFO )
  1405. IF( IINFO.NE.0 ) THEN
  1406. WRITE( NOUNIT, FMT = 9999 )'DSYEV(V,' // UPLO // ')',
  1407. $ IINFO, N, JTYPE, IOLDSD
  1408. INFO = ABS( IINFO )
  1409. IF( IINFO.LT.0 ) THEN
  1410. RETURN
  1411. ELSE
  1412. RESULT( NTEST ) = ULPINV
  1413. RESULT( NTEST+1 ) = ULPINV
  1414. RESULT( NTEST+2 ) = ULPINV
  1415. GO TO 660
  1416. END IF
  1417. END IF
  1418. *
  1419. * Do tests 25 and 26 (or +54)
  1420. *
  1421. CALL DSYT21( 1, UPLO, N, 0, V, LDU, D1, D2, A, LDU, Z,
  1422. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1423. *
  1424. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1425. *
  1426. NTEST = NTEST + 2
  1427. SRNAMT = 'DSYEV_2STAGE'
  1428. CALL DSYEV_2STAGE( 'N', UPLO, N, A, LDU, D3, WORK, LWORK,
  1429. $ IINFO )
  1430. IF( IINFO.NE.0 ) THEN
  1431. WRITE( NOUNIT, FMT = 9999 )
  1432. $ 'DSYEV_2STAGE(N,' // UPLO // ')',
  1433. $ IINFO, N, JTYPE, IOLDSD
  1434. INFO = ABS( IINFO )
  1435. IF( IINFO.LT.0 ) THEN
  1436. RETURN
  1437. ELSE
  1438. RESULT( NTEST ) = ULPINV
  1439. GO TO 660
  1440. END IF
  1441. END IF
  1442. *
  1443. * Do test 27 (or +54)
  1444. *
  1445. TEMP1 = ZERO
  1446. TEMP2 = ZERO
  1447. DO 650 J = 1, N
  1448. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1449. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1450. 650 CONTINUE
  1451. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1452. $ ULP*MAX( TEMP1, TEMP2 ) )
  1453. *
  1454. 660 CONTINUE
  1455. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1456. *
  1457. NTEST = NTEST + 1
  1458. *
  1459. IF( N.GT.0 ) THEN
  1460. TEMP3 = MAX( ABS( D1( 1 ) ), ABS( D1( N ) ) )
  1461. IF( IL.NE.1 ) THEN
  1462. VL = D1( IL ) - MAX( HALF*( D1( IL )-D1( IL-1 ) ),
  1463. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1464. ELSE IF( N.GT.0 ) THEN
  1465. VL = D1( 1 ) - MAX( HALF*( D1( N )-D1( 1 ) ),
  1466. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1467. END IF
  1468. IF( IU.NE.N ) THEN
  1469. VU = D1( IU ) + MAX( HALF*( D1( IU+1 )-D1( IU ) ),
  1470. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1471. ELSE IF( N.GT.0 ) THEN
  1472. VU = D1( N ) + MAX( HALF*( D1( N )-D1( 1 ) ),
  1473. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1474. END IF
  1475. ELSE
  1476. TEMP3 = ZERO
  1477. VL = ZERO
  1478. VU = ONE
  1479. END IF
  1480. *
  1481. SRNAMT = 'DSYEVX'
  1482. CALL DSYEVX( 'V', 'A', UPLO, N, A, LDU, VL, VU, IL, IU,
  1483. $ ABSTOL, M, WA1, Z, LDU, WORK, LWORK, IWORK,
  1484. $ IWORK( 5*N+1 ), IINFO )
  1485. IF( IINFO.NE.0 ) THEN
  1486. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,A,' // UPLO //
  1487. $ ')', IINFO, N, JTYPE, IOLDSD
  1488. INFO = ABS( IINFO )
  1489. IF( IINFO.LT.0 ) THEN
  1490. RETURN
  1491. ELSE
  1492. RESULT( NTEST ) = ULPINV
  1493. RESULT( NTEST+1 ) = ULPINV
  1494. RESULT( NTEST+2 ) = ULPINV
  1495. GO TO 680
  1496. END IF
  1497. END IF
  1498. *
  1499. * Do tests 28 and 29 (or +54)
  1500. *
  1501. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1502. *
  1503. CALL DSYT21( 1, UPLO, N, 0, A, LDU, D1, D2, Z, LDU, V,
  1504. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1505. *
  1506. NTEST = NTEST + 2
  1507. SRNAMT = 'DSYEVX_2STAGE'
  1508. CALL DSYEVX_2STAGE( 'N', 'A', UPLO, N, A, LDU, VL, VU,
  1509. $ IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  1510. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1511. IF( IINFO.NE.0 ) THEN
  1512. WRITE( NOUNIT, FMT = 9999 )
  1513. $ 'DSYEVX_2STAGE(N,A,' // UPLO //
  1514. $ ')', IINFO, N, JTYPE, IOLDSD
  1515. INFO = ABS( IINFO )
  1516. IF( IINFO.LT.0 ) THEN
  1517. RETURN
  1518. ELSE
  1519. RESULT( NTEST ) = ULPINV
  1520. GO TO 680
  1521. END IF
  1522. END IF
  1523. *
  1524. * Do test 30 (or +54)
  1525. *
  1526. TEMP1 = ZERO
  1527. TEMP2 = ZERO
  1528. DO 670 J = 1, N
  1529. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1530. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1531. 670 CONTINUE
  1532. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1533. $ ULP*MAX( TEMP1, TEMP2 ) )
  1534. *
  1535. 680 CONTINUE
  1536. *
  1537. NTEST = NTEST + 1
  1538. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1539. SRNAMT = 'DSYEVX'
  1540. CALL DSYEVX( 'V', 'I', UPLO, N, A, LDU, VL, VU, IL, IU,
  1541. $ ABSTOL, M2, WA2, Z, LDU, WORK, LWORK, IWORK,
  1542. $ IWORK( 5*N+1 ), IINFO )
  1543. IF( IINFO.NE.0 ) THEN
  1544. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,I,' // UPLO //
  1545. $ ')', IINFO, N, JTYPE, IOLDSD
  1546. INFO = ABS( IINFO )
  1547. IF( IINFO.LT.0 ) THEN
  1548. RETURN
  1549. ELSE
  1550. RESULT( NTEST ) = ULPINV
  1551. RESULT( NTEST+1 ) = ULPINV
  1552. RESULT( NTEST+2 ) = ULPINV
  1553. GO TO 690
  1554. END IF
  1555. END IF
  1556. *
  1557. * Do tests 31 and 32 (or +54)
  1558. *
  1559. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1560. *
  1561. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1562. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1563. *
  1564. NTEST = NTEST + 2
  1565. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1566. SRNAMT = 'DSYEVX_2STAGE'
  1567. CALL DSYEVX_2STAGE( 'N', 'I', UPLO, N, A, LDU, VL, VU,
  1568. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, WORK,
  1569. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1570. IF( IINFO.NE.0 ) THEN
  1571. WRITE( NOUNIT, FMT = 9999 )
  1572. $ 'DSYEVX_2STAGE(N,I,' // UPLO //
  1573. $ ')', IINFO, N, JTYPE, IOLDSD
  1574. INFO = ABS( IINFO )
  1575. IF( IINFO.LT.0 ) THEN
  1576. RETURN
  1577. ELSE
  1578. RESULT( NTEST ) = ULPINV
  1579. GO TO 690
  1580. END IF
  1581. END IF
  1582. *
  1583. * Do test 33 (or +54)
  1584. *
  1585. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1586. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1587. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1588. $ MAX( UNFL, ULP*TEMP3 )
  1589. 690 CONTINUE
  1590. *
  1591. NTEST = NTEST + 1
  1592. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1593. SRNAMT = 'DSYEVX'
  1594. CALL DSYEVX( 'V', 'V', UPLO, N, A, LDU, VL, VU, IL, IU,
  1595. $ ABSTOL, M2, WA2, Z, LDU, WORK, LWORK, IWORK,
  1596. $ IWORK( 5*N+1 ), IINFO )
  1597. IF( IINFO.NE.0 ) THEN
  1598. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,V,' // UPLO //
  1599. $ ')', IINFO, N, JTYPE, IOLDSD
  1600. INFO = ABS( IINFO )
  1601. IF( IINFO.LT.0 ) THEN
  1602. RETURN
  1603. ELSE
  1604. RESULT( NTEST ) = ULPINV
  1605. RESULT( NTEST+1 ) = ULPINV
  1606. RESULT( NTEST+2 ) = ULPINV
  1607. GO TO 700
  1608. END IF
  1609. END IF
  1610. *
  1611. * Do tests 34 and 35 (or +54)
  1612. *
  1613. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1614. *
  1615. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1616. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1617. *
  1618. NTEST = NTEST + 2
  1619. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1620. SRNAMT = 'DSYEVX_2STAGE'
  1621. CALL DSYEVX_2STAGE( 'N', 'V', UPLO, N, A, LDU, VL, VU,
  1622. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, WORK,
  1623. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1624. IF( IINFO.NE.0 ) THEN
  1625. WRITE( NOUNIT, FMT = 9999 )
  1626. $ 'DSYEVX_2STAGE(N,V,' // UPLO //
  1627. $ ')', IINFO, N, JTYPE, IOLDSD
  1628. INFO = ABS( IINFO )
  1629. IF( IINFO.LT.0 ) THEN
  1630. RETURN
  1631. ELSE
  1632. RESULT( NTEST ) = ULPINV
  1633. GO TO 700
  1634. END IF
  1635. END IF
  1636. *
  1637. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  1638. RESULT( NTEST ) = ULPINV
  1639. GO TO 700
  1640. END IF
  1641. *
  1642. * Do test 36 (or +54)
  1643. *
  1644. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1645. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1646. IF( N.GT.0 ) THEN
  1647. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1648. ELSE
  1649. TEMP3 = ZERO
  1650. END IF
  1651. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1652. $ MAX( UNFL, TEMP3*ULP )
  1653. *
  1654. 700 CONTINUE
  1655. *
  1656. * 5) Call DSPEV and DSPEVX.
  1657. *
  1658. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1659. *
  1660. * Load array WORK with the upper or lower triangular
  1661. * part of the matrix in packed form.
  1662. *
  1663. IF( IUPLO.EQ.1 ) THEN
  1664. INDX = 1
  1665. DO 720 J = 1, N
  1666. DO 710 I = 1, J
  1667. WORK( INDX ) = A( I, J )
  1668. INDX = INDX + 1
  1669. 710 CONTINUE
  1670. 720 CONTINUE
  1671. ELSE
  1672. INDX = 1
  1673. DO 740 J = 1, N
  1674. DO 730 I = J, N
  1675. WORK( INDX ) = A( I, J )
  1676. INDX = INDX + 1
  1677. 730 CONTINUE
  1678. 740 CONTINUE
  1679. END IF
  1680. *
  1681. NTEST = NTEST + 1
  1682. SRNAMT = 'DSPEV'
  1683. CALL DSPEV( 'V', UPLO, N, WORK, D1, Z, LDU, V, IINFO )
  1684. IF( IINFO.NE.0 ) THEN
  1685. WRITE( NOUNIT, FMT = 9999 )'DSPEV(V,' // UPLO // ')',
  1686. $ IINFO, N, JTYPE, IOLDSD
  1687. INFO = ABS( IINFO )
  1688. IF( IINFO.LT.0 ) THEN
  1689. RETURN
  1690. ELSE
  1691. RESULT( NTEST ) = ULPINV
  1692. RESULT( NTEST+1 ) = ULPINV
  1693. RESULT( NTEST+2 ) = ULPINV
  1694. GO TO 800
  1695. END IF
  1696. END IF
  1697. *
  1698. * Do tests 37 and 38 (or +54)
  1699. *
  1700. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  1701. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1702. *
  1703. IF( IUPLO.EQ.1 ) THEN
  1704. INDX = 1
  1705. DO 760 J = 1, N
  1706. DO 750 I = 1, J
  1707. WORK( INDX ) = A( I, J )
  1708. INDX = INDX + 1
  1709. 750 CONTINUE
  1710. 760 CONTINUE
  1711. ELSE
  1712. INDX = 1
  1713. DO 780 J = 1, N
  1714. DO 770 I = J, N
  1715. WORK( INDX ) = A( I, J )
  1716. INDX = INDX + 1
  1717. 770 CONTINUE
  1718. 780 CONTINUE
  1719. END IF
  1720. *
  1721. NTEST = NTEST + 2
  1722. SRNAMT = 'DSPEV'
  1723. CALL DSPEV( 'N', UPLO, N, WORK, D3, Z, LDU, V, IINFO )
  1724. IF( IINFO.NE.0 ) THEN
  1725. WRITE( NOUNIT, FMT = 9999 )'DSPEV(N,' // UPLO // ')',
  1726. $ IINFO, N, JTYPE, IOLDSD
  1727. INFO = ABS( IINFO )
  1728. IF( IINFO.LT.0 ) THEN
  1729. RETURN
  1730. ELSE
  1731. RESULT( NTEST ) = ULPINV
  1732. GO TO 800
  1733. END IF
  1734. END IF
  1735. *
  1736. * Do test 39 (or +54)
  1737. *
  1738. TEMP1 = ZERO
  1739. TEMP2 = ZERO
  1740. DO 790 J = 1, N
  1741. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1742. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1743. 790 CONTINUE
  1744. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1745. $ ULP*MAX( TEMP1, TEMP2 ) )
  1746. *
  1747. * Load array WORK with the upper or lower triangular part
  1748. * of the matrix in packed form.
  1749. *
  1750. 800 CONTINUE
  1751. IF( IUPLO.EQ.1 ) THEN
  1752. INDX = 1
  1753. DO 820 J = 1, N
  1754. DO 810 I = 1, J
  1755. WORK( INDX ) = A( I, J )
  1756. INDX = INDX + 1
  1757. 810 CONTINUE
  1758. 820 CONTINUE
  1759. ELSE
  1760. INDX = 1
  1761. DO 840 J = 1, N
  1762. DO 830 I = J, N
  1763. WORK( INDX ) = A( I, J )
  1764. INDX = INDX + 1
  1765. 830 CONTINUE
  1766. 840 CONTINUE
  1767. END IF
  1768. *
  1769. NTEST = NTEST + 1
  1770. *
  1771. IF( N.GT.0 ) THEN
  1772. TEMP3 = MAX( ABS( D1( 1 ) ), ABS( D1( N ) ) )
  1773. IF( IL.NE.1 ) THEN
  1774. VL = D1( IL ) - MAX( HALF*( D1( IL )-D1( IL-1 ) ),
  1775. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1776. ELSE IF( N.GT.0 ) THEN
  1777. VL = D1( 1 ) - MAX( HALF*( D1( N )-D1( 1 ) ),
  1778. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1779. END IF
  1780. IF( IU.NE.N ) THEN
  1781. VU = D1( IU ) + MAX( HALF*( D1( IU+1 )-D1( IU ) ),
  1782. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1783. ELSE IF( N.GT.0 ) THEN
  1784. VU = D1( N ) + MAX( HALF*( D1( N )-D1( 1 ) ),
  1785. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1786. END IF
  1787. ELSE
  1788. TEMP3 = ZERO
  1789. VL = ZERO
  1790. VU = ONE
  1791. END IF
  1792. *
  1793. SRNAMT = 'DSPEVX'
  1794. CALL DSPEVX( 'V', 'A', UPLO, N, WORK, VL, VU, IL, IU,
  1795. $ ABSTOL, M, WA1, Z, LDU, V, IWORK,
  1796. $ IWORK( 5*N+1 ), IINFO )
  1797. IF( IINFO.NE.0 ) THEN
  1798. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,A,' // UPLO //
  1799. $ ')', IINFO, N, JTYPE, IOLDSD
  1800. INFO = ABS( IINFO )
  1801. IF( IINFO.LT.0 ) THEN
  1802. RETURN
  1803. ELSE
  1804. RESULT( NTEST ) = ULPINV
  1805. RESULT( NTEST+1 ) = ULPINV
  1806. RESULT( NTEST+2 ) = ULPINV
  1807. GO TO 900
  1808. END IF
  1809. END IF
  1810. *
  1811. * Do tests 40 and 41 (or +54)
  1812. *
  1813. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  1814. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1815. *
  1816. NTEST = NTEST + 2
  1817. *
  1818. IF( IUPLO.EQ.1 ) THEN
  1819. INDX = 1
  1820. DO 860 J = 1, N
  1821. DO 850 I = 1, J
  1822. WORK( INDX ) = A( I, J )
  1823. INDX = INDX + 1
  1824. 850 CONTINUE
  1825. 860 CONTINUE
  1826. ELSE
  1827. INDX = 1
  1828. DO 880 J = 1, N
  1829. DO 870 I = J, N
  1830. WORK( INDX ) = A( I, J )
  1831. INDX = INDX + 1
  1832. 870 CONTINUE
  1833. 880 CONTINUE
  1834. END IF
  1835. *
  1836. SRNAMT = 'DSPEVX'
  1837. CALL DSPEVX( 'N', 'A', UPLO, N, WORK, VL, VU, IL, IU,
  1838. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1839. $ IWORK( 5*N+1 ), IINFO )
  1840. IF( IINFO.NE.0 ) THEN
  1841. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,A,' // UPLO //
  1842. $ ')', IINFO, N, JTYPE, IOLDSD
  1843. INFO = ABS( IINFO )
  1844. IF( IINFO.LT.0 ) THEN
  1845. RETURN
  1846. ELSE
  1847. RESULT( NTEST ) = ULPINV
  1848. GO TO 900
  1849. END IF
  1850. END IF
  1851. *
  1852. * Do test 42 (or +54)
  1853. *
  1854. TEMP1 = ZERO
  1855. TEMP2 = ZERO
  1856. DO 890 J = 1, N
  1857. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1858. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1859. 890 CONTINUE
  1860. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1861. $ ULP*MAX( TEMP1, TEMP2 ) )
  1862. *
  1863. 900 CONTINUE
  1864. IF( IUPLO.EQ.1 ) THEN
  1865. INDX = 1
  1866. DO 920 J = 1, N
  1867. DO 910 I = 1, J
  1868. WORK( INDX ) = A( I, J )
  1869. INDX = INDX + 1
  1870. 910 CONTINUE
  1871. 920 CONTINUE
  1872. ELSE
  1873. INDX = 1
  1874. DO 940 J = 1, N
  1875. DO 930 I = J, N
  1876. WORK( INDX ) = A( I, J )
  1877. INDX = INDX + 1
  1878. 930 CONTINUE
  1879. 940 CONTINUE
  1880. END IF
  1881. *
  1882. NTEST = NTEST + 1
  1883. *
  1884. SRNAMT = 'DSPEVX'
  1885. CALL DSPEVX( 'V', 'I', UPLO, N, WORK, VL, VU, IL, IU,
  1886. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1887. $ IWORK( 5*N+1 ), IINFO )
  1888. IF( IINFO.NE.0 ) THEN
  1889. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,I,' // UPLO //
  1890. $ ')', IINFO, N, JTYPE, IOLDSD
  1891. INFO = ABS( IINFO )
  1892. IF( IINFO.LT.0 ) THEN
  1893. RETURN
  1894. ELSE
  1895. RESULT( NTEST ) = ULPINV
  1896. RESULT( NTEST+1 ) = ULPINV
  1897. RESULT( NTEST+2 ) = ULPINV
  1898. GO TO 990
  1899. END IF
  1900. END IF
  1901. *
  1902. * Do tests 43 and 44 (or +54)
  1903. *
  1904. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1905. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1906. *
  1907. NTEST = NTEST + 2
  1908. *
  1909. IF( IUPLO.EQ.1 ) THEN
  1910. INDX = 1
  1911. DO 960 J = 1, N
  1912. DO 950 I = 1, J
  1913. WORK( INDX ) = A( I, J )
  1914. INDX = INDX + 1
  1915. 950 CONTINUE
  1916. 960 CONTINUE
  1917. ELSE
  1918. INDX = 1
  1919. DO 980 J = 1, N
  1920. DO 970 I = J, N
  1921. WORK( INDX ) = A( I, J )
  1922. INDX = INDX + 1
  1923. 970 CONTINUE
  1924. 980 CONTINUE
  1925. END IF
  1926. *
  1927. SRNAMT = 'DSPEVX'
  1928. CALL DSPEVX( 'N', 'I', UPLO, N, WORK, VL, VU, IL, IU,
  1929. $ ABSTOL, M3, WA3, Z, LDU, V, IWORK,
  1930. $ IWORK( 5*N+1 ), IINFO )
  1931. IF( IINFO.NE.0 ) THEN
  1932. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,I,' // UPLO //
  1933. $ ')', IINFO, N, JTYPE, IOLDSD
  1934. INFO = ABS( IINFO )
  1935. IF( IINFO.LT.0 ) THEN
  1936. RETURN
  1937. ELSE
  1938. RESULT( NTEST ) = ULPINV
  1939. GO TO 990
  1940. END IF
  1941. END IF
  1942. *
  1943. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  1944. RESULT( NTEST ) = ULPINV
  1945. GO TO 990
  1946. END IF
  1947. *
  1948. * Do test 45 (or +54)
  1949. *
  1950. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1951. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1952. IF( N.GT.0 ) THEN
  1953. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1954. ELSE
  1955. TEMP3 = ZERO
  1956. END IF
  1957. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1958. $ MAX( UNFL, TEMP3*ULP )
  1959. *
  1960. 990 CONTINUE
  1961. IF( IUPLO.EQ.1 ) THEN
  1962. INDX = 1
  1963. DO 1010 J = 1, N
  1964. DO 1000 I = 1, J
  1965. WORK( INDX ) = A( I, J )
  1966. INDX = INDX + 1
  1967. 1000 CONTINUE
  1968. 1010 CONTINUE
  1969. ELSE
  1970. INDX = 1
  1971. DO 1030 J = 1, N
  1972. DO 1020 I = J, N
  1973. WORK( INDX ) = A( I, J )
  1974. INDX = INDX + 1
  1975. 1020 CONTINUE
  1976. 1030 CONTINUE
  1977. END IF
  1978. *
  1979. NTEST = NTEST + 1
  1980. *
  1981. SRNAMT = 'DSPEVX'
  1982. CALL DSPEVX( 'V', 'V', UPLO, N, WORK, VL, VU, IL, IU,
  1983. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1984. $ IWORK( 5*N+1 ), IINFO )
  1985. IF( IINFO.NE.0 ) THEN
  1986. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,V,' // UPLO //
  1987. $ ')', IINFO, N, JTYPE, IOLDSD
  1988. INFO = ABS( IINFO )
  1989. IF( IINFO.LT.0 ) THEN
  1990. RETURN
  1991. ELSE
  1992. RESULT( NTEST ) = ULPINV
  1993. RESULT( NTEST+1 ) = ULPINV
  1994. RESULT( NTEST+2 ) = ULPINV
  1995. GO TO 1080
  1996. END IF
  1997. END IF
  1998. *
  1999. * Do tests 46 and 47 (or +54)
  2000. *
  2001. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2002. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2003. *
  2004. NTEST = NTEST + 2
  2005. *
  2006. IF( IUPLO.EQ.1 ) THEN
  2007. INDX = 1
  2008. DO 1050 J = 1, N
  2009. DO 1040 I = 1, J
  2010. WORK( INDX ) = A( I, J )
  2011. INDX = INDX + 1
  2012. 1040 CONTINUE
  2013. 1050 CONTINUE
  2014. ELSE
  2015. INDX = 1
  2016. DO 1070 J = 1, N
  2017. DO 1060 I = J, N
  2018. WORK( INDX ) = A( I, J )
  2019. INDX = INDX + 1
  2020. 1060 CONTINUE
  2021. 1070 CONTINUE
  2022. END IF
  2023. *
  2024. SRNAMT = 'DSPEVX'
  2025. CALL DSPEVX( 'N', 'V', UPLO, N, WORK, VL, VU, IL, IU,
  2026. $ ABSTOL, M3, WA3, Z, LDU, V, IWORK,
  2027. $ IWORK( 5*N+1 ), IINFO )
  2028. IF( IINFO.NE.0 ) THEN
  2029. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,V,' // UPLO //
  2030. $ ')', IINFO, N, JTYPE, IOLDSD
  2031. INFO = ABS( IINFO )
  2032. IF( IINFO.LT.0 ) THEN
  2033. RETURN
  2034. ELSE
  2035. RESULT( NTEST ) = ULPINV
  2036. GO TO 1080
  2037. END IF
  2038. END IF
  2039. *
  2040. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2041. RESULT( NTEST ) = ULPINV
  2042. GO TO 1080
  2043. END IF
  2044. *
  2045. * Do test 48 (or +54)
  2046. *
  2047. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2048. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2049. IF( N.GT.0 ) THEN
  2050. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2051. ELSE
  2052. TEMP3 = ZERO
  2053. END IF
  2054. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2055. $ MAX( UNFL, TEMP3*ULP )
  2056. *
  2057. 1080 CONTINUE
  2058. *
  2059. * 6) Call DSBEV and DSBEVX.
  2060. *
  2061. IF( JTYPE.LE.7 ) THEN
  2062. KD = 1
  2063. ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
  2064. KD = MAX( N-1, 0 )
  2065. ELSE
  2066. KD = IHBW
  2067. END IF
  2068. *
  2069. * Load array V with the upper or lower triangular part
  2070. * of the matrix in band form.
  2071. *
  2072. IF( IUPLO.EQ.1 ) THEN
  2073. DO 1100 J = 1, N
  2074. DO 1090 I = MAX( 1, J-KD ), J
  2075. V( KD+1+I-J, J ) = A( I, J )
  2076. 1090 CONTINUE
  2077. 1100 CONTINUE
  2078. ELSE
  2079. DO 1120 J = 1, N
  2080. DO 1110 I = J, MIN( N, J+KD )
  2081. V( 1+I-J, J ) = A( I, J )
  2082. 1110 CONTINUE
  2083. 1120 CONTINUE
  2084. END IF
  2085. *
  2086. NTEST = NTEST + 1
  2087. SRNAMT = 'DSBEV'
  2088. CALL DSBEV( 'V', UPLO, N, KD, V, LDU, D1, Z, LDU, WORK,
  2089. $ IINFO )
  2090. IF( IINFO.NE.0 ) THEN
  2091. WRITE( NOUNIT, FMT = 9999 )'DSBEV(V,' // UPLO // ')',
  2092. $ IINFO, N, JTYPE, IOLDSD
  2093. INFO = ABS( IINFO )
  2094. IF( IINFO.LT.0 ) THEN
  2095. RETURN
  2096. ELSE
  2097. RESULT( NTEST ) = ULPINV
  2098. RESULT( NTEST+1 ) = ULPINV
  2099. RESULT( NTEST+2 ) = ULPINV
  2100. GO TO 1180
  2101. END IF
  2102. END IF
  2103. *
  2104. * Do tests 49 and 50 (or ... )
  2105. *
  2106. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2107. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2108. *
  2109. IF( IUPLO.EQ.1 ) THEN
  2110. DO 1140 J = 1, N
  2111. DO 1130 I = MAX( 1, J-KD ), J
  2112. V( KD+1+I-J, J ) = A( I, J )
  2113. 1130 CONTINUE
  2114. 1140 CONTINUE
  2115. ELSE
  2116. DO 1160 J = 1, N
  2117. DO 1150 I = J, MIN( N, J+KD )
  2118. V( 1+I-J, J ) = A( I, J )
  2119. 1150 CONTINUE
  2120. 1160 CONTINUE
  2121. END IF
  2122. *
  2123. NTEST = NTEST + 2
  2124. SRNAMT = 'DSBEV_2STAGE'
  2125. CALL DSBEV_2STAGE( 'N', UPLO, N, KD, V, LDU, D3, Z, LDU,
  2126. $ WORK, LWORK, IINFO )
  2127. IF( IINFO.NE.0 ) THEN
  2128. WRITE( NOUNIT, FMT = 9999 )
  2129. $ 'DSBEV_2STAGE(N,' // UPLO // ')',
  2130. $ IINFO, N, JTYPE, IOLDSD
  2131. INFO = ABS( IINFO )
  2132. IF( IINFO.LT.0 ) THEN
  2133. RETURN
  2134. ELSE
  2135. RESULT( NTEST ) = ULPINV
  2136. GO TO 1180
  2137. END IF
  2138. END IF
  2139. *
  2140. * Do test 51 (or +54)
  2141. *
  2142. TEMP1 = ZERO
  2143. TEMP2 = ZERO
  2144. DO 1170 J = 1, N
  2145. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2146. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2147. 1170 CONTINUE
  2148. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2149. $ ULP*MAX( TEMP1, TEMP2 ) )
  2150. *
  2151. * Load array V with the upper or lower triangular part
  2152. * of the matrix in band form.
  2153. *
  2154. 1180 CONTINUE
  2155. IF( IUPLO.EQ.1 ) THEN
  2156. DO 1200 J = 1, N
  2157. DO 1190 I = MAX( 1, J-KD ), J
  2158. V( KD+1+I-J, J ) = A( I, J )
  2159. 1190 CONTINUE
  2160. 1200 CONTINUE
  2161. ELSE
  2162. DO 1220 J = 1, N
  2163. DO 1210 I = J, MIN( N, J+KD )
  2164. V( 1+I-J, J ) = A( I, J )
  2165. 1210 CONTINUE
  2166. 1220 CONTINUE
  2167. END IF
  2168. *
  2169. NTEST = NTEST + 1
  2170. SRNAMT = 'DSBEVX'
  2171. CALL DSBEVX( 'V', 'A', UPLO, N, KD, V, LDU, U, LDU, VL,
  2172. $ VU, IL, IU, ABSTOL, M, WA2, Z, LDU, WORK,
  2173. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2174. IF( IINFO.NE.0 ) THEN
  2175. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,A,' // UPLO //
  2176. $ ')', IINFO, N, JTYPE, IOLDSD
  2177. INFO = ABS( IINFO )
  2178. IF( IINFO.LT.0 ) THEN
  2179. RETURN
  2180. ELSE
  2181. RESULT( NTEST ) = ULPINV
  2182. RESULT( NTEST+1 ) = ULPINV
  2183. RESULT( NTEST+2 ) = ULPINV
  2184. GO TO 1280
  2185. END IF
  2186. END IF
  2187. *
  2188. * Do tests 52 and 53 (or +54)
  2189. *
  2190. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA2, D2, Z, LDU, V,
  2191. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2192. *
  2193. NTEST = NTEST + 2
  2194. *
  2195. IF( IUPLO.EQ.1 ) THEN
  2196. DO 1240 J = 1, N
  2197. DO 1230 I = MAX( 1, J-KD ), J
  2198. V( KD+1+I-J, J ) = A( I, J )
  2199. 1230 CONTINUE
  2200. 1240 CONTINUE
  2201. ELSE
  2202. DO 1260 J = 1, N
  2203. DO 1250 I = J, MIN( N, J+KD )
  2204. V( 1+I-J, J ) = A( I, J )
  2205. 1250 CONTINUE
  2206. 1260 CONTINUE
  2207. END IF
  2208. *
  2209. SRNAMT = 'DSBEVX_2STAGE'
  2210. CALL DSBEVX_2STAGE( 'N', 'A', UPLO, N, KD, V, LDU,
  2211. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2212. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2213. $ IINFO )
  2214. IF( IINFO.NE.0 ) THEN
  2215. WRITE( NOUNIT, FMT = 9999 )
  2216. $ 'DSBEVX_2STAGE(N,A,' // UPLO //
  2217. $ ')', IINFO, N, JTYPE, IOLDSD
  2218. INFO = ABS( IINFO )
  2219. IF( IINFO.LT.0 ) THEN
  2220. RETURN
  2221. ELSE
  2222. RESULT( NTEST ) = ULPINV
  2223. GO TO 1280
  2224. END IF
  2225. END IF
  2226. *
  2227. * Do test 54 (or +54)
  2228. *
  2229. TEMP1 = ZERO
  2230. TEMP2 = ZERO
  2231. DO 1270 J = 1, N
  2232. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ), ABS( WA3( J ) ) )
  2233. TEMP2 = MAX( TEMP2, ABS( WA2( J )-WA3( J ) ) )
  2234. 1270 CONTINUE
  2235. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2236. $ ULP*MAX( TEMP1, TEMP2 ) )
  2237. *
  2238. 1280 CONTINUE
  2239. NTEST = NTEST + 1
  2240. IF( IUPLO.EQ.1 ) THEN
  2241. DO 1300 J = 1, N
  2242. DO 1290 I = MAX( 1, J-KD ), J
  2243. V( KD+1+I-J, J ) = A( I, J )
  2244. 1290 CONTINUE
  2245. 1300 CONTINUE
  2246. ELSE
  2247. DO 1320 J = 1, N
  2248. DO 1310 I = J, MIN( N, J+KD )
  2249. V( 1+I-J, J ) = A( I, J )
  2250. 1310 CONTINUE
  2251. 1320 CONTINUE
  2252. END IF
  2253. *
  2254. SRNAMT = 'DSBEVX'
  2255. CALL DSBEVX( 'V', 'I', UPLO, N, KD, V, LDU, U, LDU, VL,
  2256. $ VU, IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  2257. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2258. IF( IINFO.NE.0 ) THEN
  2259. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,I,' // UPLO //
  2260. $ ')', IINFO, N, JTYPE, IOLDSD
  2261. INFO = ABS( IINFO )
  2262. IF( IINFO.LT.0 ) THEN
  2263. RETURN
  2264. ELSE
  2265. RESULT( NTEST ) = ULPINV
  2266. RESULT( NTEST+1 ) = ULPINV
  2267. RESULT( NTEST+2 ) = ULPINV
  2268. GO TO 1370
  2269. END IF
  2270. END IF
  2271. *
  2272. * Do tests 55 and 56 (or +54)
  2273. *
  2274. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2275. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2276. *
  2277. NTEST = NTEST + 2
  2278. *
  2279. IF( IUPLO.EQ.1 ) THEN
  2280. DO 1340 J = 1, N
  2281. DO 1330 I = MAX( 1, J-KD ), J
  2282. V( KD+1+I-J, J ) = A( I, J )
  2283. 1330 CONTINUE
  2284. 1340 CONTINUE
  2285. ELSE
  2286. DO 1360 J = 1, N
  2287. DO 1350 I = J, MIN( N, J+KD )
  2288. V( 1+I-J, J ) = A( I, J )
  2289. 1350 CONTINUE
  2290. 1360 CONTINUE
  2291. END IF
  2292. *
  2293. SRNAMT = 'DSBEVX_2STAGE'
  2294. CALL DSBEVX_2STAGE( 'N', 'I', UPLO, N, KD, V, LDU,
  2295. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2296. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2297. $ IINFO )
  2298. IF( IINFO.NE.0 ) THEN
  2299. WRITE( NOUNIT, FMT = 9999 )
  2300. $ 'DSBEVX_2STAGE(N,I,' // UPLO //
  2301. $ ')', IINFO, N, JTYPE, IOLDSD
  2302. INFO = ABS( IINFO )
  2303. IF( IINFO.LT.0 ) THEN
  2304. RETURN
  2305. ELSE
  2306. RESULT( NTEST ) = ULPINV
  2307. GO TO 1370
  2308. END IF
  2309. END IF
  2310. *
  2311. * Do test 57 (or +54)
  2312. *
  2313. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2314. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2315. IF( N.GT.0 ) THEN
  2316. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2317. ELSE
  2318. TEMP3 = ZERO
  2319. END IF
  2320. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2321. $ MAX( UNFL, TEMP3*ULP )
  2322. *
  2323. 1370 CONTINUE
  2324. NTEST = NTEST + 1
  2325. IF( IUPLO.EQ.1 ) THEN
  2326. DO 1390 J = 1, N
  2327. DO 1380 I = MAX( 1, J-KD ), J
  2328. V( KD+1+I-J, J ) = A( I, J )
  2329. 1380 CONTINUE
  2330. 1390 CONTINUE
  2331. ELSE
  2332. DO 1410 J = 1, N
  2333. DO 1400 I = J, MIN( N, J+KD )
  2334. V( 1+I-J, J ) = A( I, J )
  2335. 1400 CONTINUE
  2336. 1410 CONTINUE
  2337. END IF
  2338. *
  2339. SRNAMT = 'DSBEVX'
  2340. CALL DSBEVX( 'V', 'V', UPLO, N, KD, V, LDU, U, LDU, VL,
  2341. $ VU, IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  2342. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2343. IF( IINFO.NE.0 ) THEN
  2344. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,V,' // UPLO //
  2345. $ ')', IINFO, N, JTYPE, IOLDSD
  2346. INFO = ABS( IINFO )
  2347. IF( IINFO.LT.0 ) THEN
  2348. RETURN
  2349. ELSE
  2350. RESULT( NTEST ) = ULPINV
  2351. RESULT( NTEST+1 ) = ULPINV
  2352. RESULT( NTEST+2 ) = ULPINV
  2353. GO TO 1460
  2354. END IF
  2355. END IF
  2356. *
  2357. * Do tests 58 and 59 (or +54)
  2358. *
  2359. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2360. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2361. *
  2362. NTEST = NTEST + 2
  2363. *
  2364. IF( IUPLO.EQ.1 ) THEN
  2365. DO 1430 J = 1, N
  2366. DO 1420 I = MAX( 1, J-KD ), J
  2367. V( KD+1+I-J, J ) = A( I, J )
  2368. 1420 CONTINUE
  2369. 1430 CONTINUE
  2370. ELSE
  2371. DO 1450 J = 1, N
  2372. DO 1440 I = J, MIN( N, J+KD )
  2373. V( 1+I-J, J ) = A( I, J )
  2374. 1440 CONTINUE
  2375. 1450 CONTINUE
  2376. END IF
  2377. *
  2378. SRNAMT = 'DSBEVX_2STAGE'
  2379. CALL DSBEVX_2STAGE( 'N', 'V', UPLO, N, KD, V, LDU,
  2380. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2381. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2382. $ IINFO )
  2383. IF( IINFO.NE.0 ) THEN
  2384. WRITE( NOUNIT, FMT = 9999 )
  2385. $ 'DSBEVX_2STAGE(N,V,' // UPLO //
  2386. $ ')', IINFO, N, JTYPE, IOLDSD
  2387. INFO = ABS( IINFO )
  2388. IF( IINFO.LT.0 ) THEN
  2389. RETURN
  2390. ELSE
  2391. RESULT( NTEST ) = ULPINV
  2392. GO TO 1460
  2393. END IF
  2394. END IF
  2395. *
  2396. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2397. RESULT( NTEST ) = ULPINV
  2398. GO TO 1460
  2399. END IF
  2400. *
  2401. * Do test 60 (or +54)
  2402. *
  2403. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2404. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2405. IF( N.GT.0 ) THEN
  2406. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2407. ELSE
  2408. TEMP3 = ZERO
  2409. END IF
  2410. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2411. $ MAX( UNFL, TEMP3*ULP )
  2412. *
  2413. 1460 CONTINUE
  2414. *
  2415. * 7) Call DSYEVD
  2416. *
  2417. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  2418. *
  2419. NTEST = NTEST + 1
  2420. SRNAMT = 'DSYEVD'
  2421. CALL DSYEVD( 'V', UPLO, N, A, LDU, D1, WORK, LWEDC,
  2422. $ IWORK, LIWEDC, IINFO )
  2423. IF( IINFO.NE.0 ) THEN
  2424. WRITE( NOUNIT, FMT = 9999 )'DSYEVD(V,' // UPLO //
  2425. $ ')', IINFO, N, JTYPE, IOLDSD
  2426. INFO = ABS( IINFO )
  2427. IF( IINFO.LT.0 ) THEN
  2428. RETURN
  2429. ELSE
  2430. RESULT( NTEST ) = ULPINV
  2431. RESULT( NTEST+1 ) = ULPINV
  2432. RESULT( NTEST+2 ) = ULPINV
  2433. GO TO 1480
  2434. END IF
  2435. END IF
  2436. *
  2437. * Do tests 61 and 62 (or +54)
  2438. *
  2439. CALL DSYT21( 1, UPLO, N, 0, V, LDU, D1, D2, A, LDU, Z,
  2440. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2441. *
  2442. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2443. *
  2444. NTEST = NTEST + 2
  2445. SRNAMT = 'DSYEVD_2STAGE'
  2446. CALL DSYEVD_2STAGE( 'N', UPLO, N, A, LDU, D3, WORK,
  2447. $ LWORK, IWORK, LIWEDC, IINFO )
  2448. IF( IINFO.NE.0 ) THEN
  2449. WRITE( NOUNIT, FMT = 9999 )
  2450. $ 'DSYEVD_2STAGE(N,' // UPLO //
  2451. $ ')', IINFO, N, JTYPE, IOLDSD
  2452. INFO = ABS( IINFO )
  2453. IF( IINFO.LT.0 ) THEN
  2454. RETURN
  2455. ELSE
  2456. RESULT( NTEST ) = ULPINV
  2457. GO TO 1480
  2458. END IF
  2459. END IF
  2460. *
  2461. * Do test 63 (or +54)
  2462. *
  2463. TEMP1 = ZERO
  2464. TEMP2 = ZERO
  2465. DO 1470 J = 1, N
  2466. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2467. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2468. 1470 CONTINUE
  2469. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2470. $ ULP*MAX( TEMP1, TEMP2 ) )
  2471. *
  2472. 1480 CONTINUE
  2473. *
  2474. * 8) Call DSPEVD.
  2475. *
  2476. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2477. *
  2478. * Load array WORK with the upper or lower triangular
  2479. * part of the matrix in packed form.
  2480. *
  2481. IF( IUPLO.EQ.1 ) THEN
  2482. INDX = 1
  2483. DO 1500 J = 1, N
  2484. DO 1490 I = 1, J
  2485. WORK( INDX ) = A( I, J )
  2486. INDX = INDX + 1
  2487. 1490 CONTINUE
  2488. 1500 CONTINUE
  2489. ELSE
  2490. INDX = 1
  2491. DO 1520 J = 1, N
  2492. DO 1510 I = J, N
  2493. WORK( INDX ) = A( I, J )
  2494. INDX = INDX + 1
  2495. 1510 CONTINUE
  2496. 1520 CONTINUE
  2497. END IF
  2498. *
  2499. NTEST = NTEST + 1
  2500. SRNAMT = 'DSPEVD'
  2501. CALL DSPEVD( 'V', UPLO, N, WORK, D1, Z, LDU,
  2502. $ WORK( INDX ), LWEDC-INDX+1, IWORK, LIWEDC,
  2503. $ IINFO )
  2504. IF( IINFO.NE.0 ) THEN
  2505. WRITE( NOUNIT, FMT = 9999 )'DSPEVD(V,' // UPLO //
  2506. $ ')', IINFO, N, JTYPE, IOLDSD
  2507. INFO = ABS( IINFO )
  2508. IF( IINFO.LT.0 ) THEN
  2509. RETURN
  2510. ELSE
  2511. RESULT( NTEST ) = ULPINV
  2512. RESULT( NTEST+1 ) = ULPINV
  2513. RESULT( NTEST+2 ) = ULPINV
  2514. GO TO 1580
  2515. END IF
  2516. END IF
  2517. *
  2518. * Do tests 64 and 65 (or +54)
  2519. *
  2520. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2521. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2522. *
  2523. IF( IUPLO.EQ.1 ) THEN
  2524. INDX = 1
  2525. DO 1540 J = 1, N
  2526. DO 1530 I = 1, J
  2527. *
  2528. WORK( INDX ) = A( I, J )
  2529. INDX = INDX + 1
  2530. 1530 CONTINUE
  2531. 1540 CONTINUE
  2532. ELSE
  2533. INDX = 1
  2534. DO 1560 J = 1, N
  2535. DO 1550 I = J, N
  2536. WORK( INDX ) = A( I, J )
  2537. INDX = INDX + 1
  2538. 1550 CONTINUE
  2539. 1560 CONTINUE
  2540. END IF
  2541. *
  2542. NTEST = NTEST + 2
  2543. SRNAMT = 'DSPEVD'
  2544. CALL DSPEVD( 'N', UPLO, N, WORK, D3, Z, LDU,
  2545. $ WORK( INDX ), LWEDC-INDX+1, IWORK, LIWEDC,
  2546. $ IINFO )
  2547. IF( IINFO.NE.0 ) THEN
  2548. WRITE( NOUNIT, FMT = 9999 )'DSPEVD(N,' // UPLO //
  2549. $ ')', IINFO, N, JTYPE, IOLDSD
  2550. INFO = ABS( IINFO )
  2551. IF( IINFO.LT.0 ) THEN
  2552. RETURN
  2553. ELSE
  2554. RESULT( NTEST ) = ULPINV
  2555. GO TO 1580
  2556. END IF
  2557. END IF
  2558. *
  2559. * Do test 66 (or +54)
  2560. *
  2561. TEMP1 = ZERO
  2562. TEMP2 = ZERO
  2563. DO 1570 J = 1, N
  2564. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2565. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2566. 1570 CONTINUE
  2567. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2568. $ ULP*MAX( TEMP1, TEMP2 ) )
  2569. 1580 CONTINUE
  2570. *
  2571. * 9) Call DSBEVD.
  2572. *
  2573. IF( JTYPE.LE.7 ) THEN
  2574. KD = 1
  2575. ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
  2576. KD = MAX( N-1, 0 )
  2577. ELSE
  2578. KD = IHBW
  2579. END IF
  2580. *
  2581. * Load array V with the upper or lower triangular part
  2582. * of the matrix in band form.
  2583. *
  2584. IF( IUPLO.EQ.1 ) THEN
  2585. DO 1600 J = 1, N
  2586. DO 1590 I = MAX( 1, J-KD ), J
  2587. V( KD+1+I-J, J ) = A( I, J )
  2588. 1590 CONTINUE
  2589. 1600 CONTINUE
  2590. ELSE
  2591. DO 1620 J = 1, N
  2592. DO 1610 I = J, MIN( N, J+KD )
  2593. V( 1+I-J, J ) = A( I, J )
  2594. 1610 CONTINUE
  2595. 1620 CONTINUE
  2596. END IF
  2597. *
  2598. NTEST = NTEST + 1
  2599. SRNAMT = 'DSBEVD'
  2600. CALL DSBEVD( 'V', UPLO, N, KD, V, LDU, D1, Z, LDU, WORK,
  2601. $ LWEDC, IWORK, LIWEDC, IINFO )
  2602. IF( IINFO.NE.0 ) THEN
  2603. WRITE( NOUNIT, FMT = 9999 )'DSBEVD(V,' // UPLO //
  2604. $ ')', IINFO, N, JTYPE, IOLDSD
  2605. INFO = ABS( IINFO )
  2606. IF( IINFO.LT.0 ) THEN
  2607. RETURN
  2608. ELSE
  2609. RESULT( NTEST ) = ULPINV
  2610. RESULT( NTEST+1 ) = ULPINV
  2611. RESULT( NTEST+2 ) = ULPINV
  2612. GO TO 1680
  2613. END IF
  2614. END IF
  2615. *
  2616. * Do tests 67 and 68 (or +54)
  2617. *
  2618. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2619. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2620. *
  2621. IF( IUPLO.EQ.1 ) THEN
  2622. DO 1640 J = 1, N
  2623. DO 1630 I = MAX( 1, J-KD ), J
  2624. V( KD+1+I-J, J ) = A( I, J )
  2625. 1630 CONTINUE
  2626. 1640 CONTINUE
  2627. ELSE
  2628. DO 1660 J = 1, N
  2629. DO 1650 I = J, MIN( N, J+KD )
  2630. V( 1+I-J, J ) = A( I, J )
  2631. 1650 CONTINUE
  2632. 1660 CONTINUE
  2633. END IF
  2634. *
  2635. NTEST = NTEST + 2
  2636. SRNAMT = 'DSBEVD_2STAGE'
  2637. CALL DSBEVD_2STAGE( 'N', UPLO, N, KD, V, LDU, D3, Z, LDU,
  2638. $ WORK, LWORK, IWORK, LIWEDC, IINFO )
  2639. IF( IINFO.NE.0 ) THEN
  2640. WRITE( NOUNIT, FMT = 9999 )
  2641. $ 'DSBEVD_2STAGE(N,' // UPLO //
  2642. $ ')', IINFO, N, JTYPE, IOLDSD
  2643. INFO = ABS( IINFO )
  2644. IF( IINFO.LT.0 ) THEN
  2645. RETURN
  2646. ELSE
  2647. RESULT( NTEST ) = ULPINV
  2648. GO TO 1680
  2649. END IF
  2650. END IF
  2651. *
  2652. * Do test 69 (or +54)
  2653. *
  2654. TEMP1 = ZERO
  2655. TEMP2 = ZERO
  2656. DO 1670 J = 1, N
  2657. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2658. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2659. 1670 CONTINUE
  2660. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2661. $ ULP*MAX( TEMP1, TEMP2 ) )
  2662. *
  2663. 1680 CONTINUE
  2664. *
  2665. *
  2666. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  2667. NTEST = NTEST + 1
  2668. SRNAMT = 'DSYEVR'
  2669. CALL DSYEVR( 'V', 'A', UPLO, N, A, LDU, VL, VU, IL, IU,
  2670. $ ABSTOL, M, WA1, Z, LDU, IWORK, WORK, LWORK,
  2671. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2672. IF( IINFO.NE.0 ) THEN
  2673. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,A,' // UPLO //
  2674. $ ')', IINFO, N, JTYPE, IOLDSD
  2675. INFO = ABS( IINFO )
  2676. IF( IINFO.LT.0 ) THEN
  2677. RETURN
  2678. ELSE
  2679. RESULT( NTEST ) = ULPINV
  2680. RESULT( NTEST+1 ) = ULPINV
  2681. RESULT( NTEST+2 ) = ULPINV
  2682. GO TO 1700
  2683. END IF
  2684. END IF
  2685. *
  2686. * Do tests 70 and 71 (or ... )
  2687. *
  2688. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2689. *
  2690. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  2691. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2692. *
  2693. NTEST = NTEST + 2
  2694. SRNAMT = 'DSYEVR_2STAGE'
  2695. CALL DSYEVR_2STAGE( 'N', 'A', UPLO, N, A, LDU, VL, VU,
  2696. $ IL, IU, ABSTOL, M2, WA2, Z, LDU, IWORK,
  2697. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2698. $ IINFO )
  2699. IF( IINFO.NE.0 ) THEN
  2700. WRITE( NOUNIT, FMT = 9999 )
  2701. $ 'DSYEVR_2STAGE(N,A,' // UPLO //
  2702. $ ')', IINFO, N, JTYPE, IOLDSD
  2703. INFO = ABS( IINFO )
  2704. IF( IINFO.LT.0 ) THEN
  2705. RETURN
  2706. ELSE
  2707. RESULT( NTEST ) = ULPINV
  2708. GO TO 1700
  2709. END IF
  2710. END IF
  2711. *
  2712. * Do test 72 (or ... )
  2713. *
  2714. TEMP1 = ZERO
  2715. TEMP2 = ZERO
  2716. DO 1690 J = 1, N
  2717. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  2718. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  2719. 1690 CONTINUE
  2720. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2721. $ ULP*MAX( TEMP1, TEMP2 ) )
  2722. *
  2723. 1700 CONTINUE
  2724. *
  2725. NTEST = NTEST + 1
  2726. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2727. SRNAMT = 'DSYEVR'
  2728. CALL DSYEVR( 'V', 'I', UPLO, N, A, LDU, VL, VU, IL, IU,
  2729. $ ABSTOL, M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  2730. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2731. IF( IINFO.NE.0 ) THEN
  2732. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,I,' // UPLO //
  2733. $ ')', IINFO, N, JTYPE, IOLDSD
  2734. INFO = ABS( IINFO )
  2735. IF( IINFO.LT.0 ) THEN
  2736. RETURN
  2737. ELSE
  2738. RESULT( NTEST ) = ULPINV
  2739. RESULT( NTEST+1 ) = ULPINV
  2740. RESULT( NTEST+2 ) = ULPINV
  2741. GO TO 1710
  2742. END IF
  2743. END IF
  2744. *
  2745. * Do tests 73 and 74 (or +54)
  2746. *
  2747. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2748. *
  2749. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2750. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2751. *
  2752. NTEST = NTEST + 2
  2753. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2754. SRNAMT = 'DSYEVR_2STAGE'
  2755. CALL DSYEVR_2STAGE( 'N', 'I', UPLO, N, A, LDU, VL, VU,
  2756. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, IWORK,
  2757. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2758. $ IINFO )
  2759. IF( IINFO.NE.0 ) THEN
  2760. WRITE( NOUNIT, FMT = 9999 )
  2761. $ 'DSYEVR_2STAGE(N,I,' // UPLO //
  2762. $ ')', IINFO, N, JTYPE, IOLDSD
  2763. INFO = ABS( IINFO )
  2764. IF( IINFO.LT.0 ) THEN
  2765. RETURN
  2766. ELSE
  2767. RESULT( NTEST ) = ULPINV
  2768. GO TO 1710
  2769. END IF
  2770. END IF
  2771. *
  2772. * Do test 75 (or +54)
  2773. *
  2774. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2775. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2776. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2777. $ MAX( UNFL, ULP*TEMP3 )
  2778. 1710 CONTINUE
  2779. *
  2780. NTEST = NTEST + 1
  2781. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2782. SRNAMT = 'DSYEVR'
  2783. CALL DSYEVR( 'V', 'V', UPLO, N, A, LDU, VL, VU, IL, IU,
  2784. $ ABSTOL, M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  2785. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2786. IF( IINFO.NE.0 ) THEN
  2787. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,V,' // UPLO //
  2788. $ ')', IINFO, N, JTYPE, IOLDSD
  2789. INFO = ABS( IINFO )
  2790. IF( IINFO.LT.0 ) THEN
  2791. RETURN
  2792. ELSE
  2793. RESULT( NTEST ) = ULPINV
  2794. RESULT( NTEST+1 ) = ULPINV
  2795. RESULT( NTEST+2 ) = ULPINV
  2796. GO TO 1720
  2797. END IF
  2798. END IF
  2799. *
  2800. * Do tests 76 and 77 (or +54)
  2801. *
  2802. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2803. *
  2804. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2805. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2806. *
  2807. NTEST = NTEST + 2
  2808. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2809. SRNAMT = 'DSYEVR_2STAGE'
  2810. CALL DSYEVR_2STAGE( 'N', 'V', UPLO, N, A, LDU, VL, VU,
  2811. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, IWORK,
  2812. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2813. $ IINFO )
  2814. IF( IINFO.NE.0 ) THEN
  2815. WRITE( NOUNIT, FMT = 9999 )
  2816. $ 'DSYEVR_2STAGE(N,V,' // UPLO //
  2817. $ ')', IINFO, N, JTYPE, IOLDSD
  2818. INFO = ABS( IINFO )
  2819. IF( IINFO.LT.0 ) THEN
  2820. RETURN
  2821. ELSE
  2822. RESULT( NTEST ) = ULPINV
  2823. GO TO 1720
  2824. END IF
  2825. END IF
  2826. *
  2827. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2828. RESULT( NTEST ) = ULPINV
  2829. GO TO 1720
  2830. END IF
  2831. *
  2832. * Do test 78 (or +54)
  2833. *
  2834. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2835. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2836. IF( N.GT.0 ) THEN
  2837. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2838. ELSE
  2839. TEMP3 = ZERO
  2840. END IF
  2841. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2842. $ MAX( UNFL, TEMP3*ULP )
  2843. *
  2844. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2845. *
  2846. 1720 CONTINUE
  2847. *
  2848. * End of Loop -- Check for RESULT(j) > THRESH
  2849. *
  2850. NTESTT = NTESTT + NTEST
  2851. *
  2852. CALL DLAFTS( 'DST', N, N, JTYPE, NTEST, RESULT, IOLDSD,
  2853. $ THRESH, NOUNIT, NERRS )
  2854. *
  2855. 1730 CONTINUE
  2856. 1740 CONTINUE
  2857. *
  2858. * Summary
  2859. *
  2860. CALL ALASVM( 'DST', NOUNIT, NERRS, NTESTT, 0 )
  2861. *
  2862. 9999 FORMAT( ' DDRVST2STG: ', A, ' returned INFO=', I6, '.', / 9X,
  2863. $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
  2864. *
  2865. RETURN
  2866. *
  2867. * End of DDRVST2STG
  2868. *
  2869. END