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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. *> \date December 2016
  447. *
  448. *> \ingroup double_eig
  449. *
  450. * =====================================================================
  451. SUBROUTINE DDRVST2STG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
  452. $ NOUNIT, A, LDA, D1, D2, D3, D4, EVEIGS, WA1,
  453. $ WA2, WA3, U, LDU, V, TAU, Z, WORK, LWORK,
  454. $ IWORK, LIWORK, RESULT, INFO )
  455. *
  456. * -- LAPACK test routine (version 3.7.0) --
  457. * -- LAPACK is a software package provided by Univ. of Tennessee, --
  458. * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  459. * December 2016
  460. *
  461. * .. Scalar Arguments ..
  462. INTEGER INFO, LDA, LDU, LIWORK, LWORK, NOUNIT, NSIZES,
  463. $ NTYPES
  464. DOUBLE PRECISION THRESH
  465. * ..
  466. * .. Array Arguments ..
  467. LOGICAL DOTYPE( * )
  468. INTEGER ISEED( 4 ), IWORK( * ), NN( * )
  469. DOUBLE PRECISION A( LDA, * ), D1( * ), D2( * ), D3( * ),
  470. $ D4( * ), EVEIGS( * ), RESULT( * ), TAU( * ),
  471. $ U( LDU, * ), V( LDU, * ), WA1( * ), WA2( * ),
  472. $ WA3( * ), WORK( * ), Z( LDU, * )
  473. * ..
  474. *
  475. * =====================================================================
  476. *
  477. * .. Parameters ..
  478. DOUBLE PRECISION ZERO, ONE, TWO, TEN
  479. PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
  480. $ TEN = 10.0D0 )
  481. DOUBLE PRECISION HALF
  482. PARAMETER ( HALF = 0.5D0 )
  483. INTEGER MAXTYP
  484. PARAMETER ( MAXTYP = 18 )
  485. * ..
  486. * .. Local Scalars ..
  487. LOGICAL BADNN
  488. CHARACTER UPLO
  489. INTEGER I, IDIAG, IHBW, IINFO, IL, IMODE, INDX, IROW,
  490. $ ITEMP, ITYPE, IU, IUPLO, J, J1, J2, JCOL,
  491. $ JSIZE, JTYPE, KD, LGN, LIWEDC, LWEDC, M, M2,
  492. $ M3, MTYPES, N, NERRS, NMATS, NMAX, NTEST,
  493. $ NTESTT
  494. DOUBLE PRECISION ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
  495. $ RTUNFL, TEMP1, TEMP2, TEMP3, ULP, ULPINV, UNFL,
  496. $ VL, VU
  497. * ..
  498. * .. Local Arrays ..
  499. INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
  500. $ ISEED3( 4 ), KMAGN( MAXTYP ), KMODE( MAXTYP ),
  501. $ KTYPE( MAXTYP )
  502. * ..
  503. * .. External Functions ..
  504. DOUBLE PRECISION DLAMCH, DLARND, DSXT1
  505. EXTERNAL DLAMCH, DLARND, DSXT1
  506. * ..
  507. * .. External Subroutines ..
  508. EXTERNAL ALASVM, DLABAD, DLACPY, DLAFTS, DLASET, DLATMR,
  509. $ DLATMS, DSBEV, DSBEVD, DSBEVX, DSPEV, DSPEVD,
  510. $ DSPEVX, DSTEV, DSTEVD, DSTEVR, DSTEVX, DSTT21,
  511. $ DSTT22, DSYEV, DSYEVD, DSYEVR, DSYEVX, DSYT21,
  512. $ DSYEVD_2STAGE, DSYEVR_2STAGE, DSYEVX_2STAGE,
  513. $ DSYEV_2STAGE, DSBEV_2STAGE, DSBEVD_2STAGE,
  514. $ DSBEVX_2STAGE, DSYTRD_2STAGE, DSYTRD_SY2SB,
  515. $ DSYTRD_SB2ST, DSYT22, XERBLA
  516. * ..
  517. * .. Scalars in Common ..
  518. CHARACTER*32 SRNAMT
  519. * ..
  520. * .. Common blocks ..
  521. COMMON / SRNAMC / SRNAMT
  522. * ..
  523. * .. Intrinsic Functions ..
  524. INTRINSIC ABS, DBLE, INT, LOG, MAX, MIN, SQRT
  525. * ..
  526. * .. Data statements ..
  527. DATA KTYPE / 1, 2, 5*4, 5*5, 3*8, 3*9 /
  528. DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
  529. $ 2, 3, 1, 2, 3 /
  530. DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
  531. $ 0, 0, 4, 4, 4 /
  532. * ..
  533. * .. Executable Statements ..
  534. *
  535. * Keep ftrnchek happy
  536. *
  537. VL = ZERO
  538. VU = ZERO
  539. *
  540. * 1) Check for errors
  541. *
  542. NTESTT = 0
  543. INFO = 0
  544. *
  545. BADNN = .FALSE.
  546. NMAX = 1
  547. DO 10 J = 1, NSIZES
  548. NMAX = MAX( NMAX, NN( J ) )
  549. IF( NN( J ).LT.0 )
  550. $ BADNN = .TRUE.
  551. 10 CONTINUE
  552. *
  553. * Check for errors
  554. *
  555. IF( NSIZES.LT.0 ) THEN
  556. INFO = -1
  557. ELSE IF( BADNN ) THEN
  558. INFO = -2
  559. ELSE IF( NTYPES.LT.0 ) THEN
  560. INFO = -3
  561. ELSE IF( LDA.LT.NMAX ) THEN
  562. INFO = -9
  563. ELSE IF( LDU.LT.NMAX ) THEN
  564. INFO = -16
  565. ELSE IF( 2*MAX( 2, NMAX )**2.GT.LWORK ) THEN
  566. INFO = -21
  567. END IF
  568. *
  569. IF( INFO.NE.0 ) THEN
  570. CALL XERBLA( 'DDRVST2STG', -INFO )
  571. RETURN
  572. END IF
  573. *
  574. * Quick return if nothing to do
  575. *
  576. IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 )
  577. $ RETURN
  578. *
  579. * More Important constants
  580. *
  581. UNFL = DLAMCH( 'Safe minimum' )
  582. OVFL = DLAMCH( 'Overflow' )
  583. CALL DLABAD( UNFL, OVFL )
  584. ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' )
  585. ULPINV = ONE / ULP
  586. RTUNFL = SQRT( UNFL )
  587. RTOVFL = SQRT( OVFL )
  588. *
  589. * Loop over sizes, types
  590. *
  591. DO 20 I = 1, 4
  592. ISEED2( I ) = ISEED( I )
  593. ISEED3( I ) = ISEED( I )
  594. 20 CONTINUE
  595. *
  596. NERRS = 0
  597. NMATS = 0
  598. *
  599. *
  600. DO 1740 JSIZE = 1, NSIZES
  601. N = NN( JSIZE )
  602. IF( N.GT.0 ) THEN
  603. LGN = INT( LOG( DBLE( N ) ) / LOG( TWO ) )
  604. IF( 2**LGN.LT.N )
  605. $ LGN = LGN + 1
  606. IF( 2**LGN.LT.N )
  607. $ LGN = LGN + 1
  608. LWEDC = 1 + 4*N + 2*N*LGN + 4*N**2
  609. c LIWEDC = 6 + 6*N + 5*N*LGN
  610. LIWEDC = 3 + 5*N
  611. ELSE
  612. LWEDC = 9
  613. c LIWEDC = 12
  614. LIWEDC = 8
  615. END IF
  616. ANINV = ONE / DBLE( MAX( 1, N ) )
  617. *
  618. IF( NSIZES.NE.1 ) THEN
  619. MTYPES = MIN( MAXTYP, NTYPES )
  620. ELSE
  621. MTYPES = MIN( MAXTYP+1, NTYPES )
  622. END IF
  623. *
  624. DO 1730 JTYPE = 1, MTYPES
  625. *
  626. IF( .NOT.DOTYPE( JTYPE ) )
  627. $ GO TO 1730
  628. NMATS = NMATS + 1
  629. NTEST = 0
  630. *
  631. DO 30 J = 1, 4
  632. IOLDSD( J ) = ISEED( J )
  633. 30 CONTINUE
  634. *
  635. * 2) Compute "A"
  636. *
  637. * Control parameters:
  638. *
  639. * KMAGN KMODE KTYPE
  640. * =1 O(1) clustered 1 zero
  641. * =2 large clustered 2 identity
  642. * =3 small exponential (none)
  643. * =4 arithmetic diagonal, (w/ eigenvalues)
  644. * =5 random log symmetric, w/ eigenvalues
  645. * =6 random (none)
  646. * =7 random diagonal
  647. * =8 random symmetric
  648. * =9 band symmetric, w/ eigenvalues
  649. *
  650. IF( MTYPES.GT.MAXTYP )
  651. $ GO TO 110
  652. *
  653. ITYPE = KTYPE( JTYPE )
  654. IMODE = KMODE( JTYPE )
  655. *
  656. * Compute norm
  657. *
  658. GO TO ( 40, 50, 60 )KMAGN( JTYPE )
  659. *
  660. 40 CONTINUE
  661. ANORM = ONE
  662. GO TO 70
  663. *
  664. 50 CONTINUE
  665. ANORM = ( RTOVFL*ULP )*ANINV
  666. GO TO 70
  667. *
  668. 60 CONTINUE
  669. ANORM = RTUNFL*N*ULPINV
  670. GO TO 70
  671. *
  672. 70 CONTINUE
  673. *
  674. CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
  675. IINFO = 0
  676. COND = ULPINV
  677. *
  678. * Special Matrices -- Identity & Jordan block
  679. *
  680. * Zero
  681. *
  682. IF( ITYPE.EQ.1 ) THEN
  683. IINFO = 0
  684. *
  685. ELSE IF( ITYPE.EQ.2 ) THEN
  686. *
  687. * Identity
  688. *
  689. DO 80 JCOL = 1, N
  690. A( JCOL, JCOL ) = ANORM
  691. 80 CONTINUE
  692. *
  693. ELSE IF( ITYPE.EQ.4 ) THEN
  694. *
  695. * Diagonal Matrix, [Eigen]values Specified
  696. *
  697. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  698. $ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ),
  699. $ IINFO )
  700. *
  701. ELSE IF( ITYPE.EQ.5 ) THEN
  702. *
  703. * Symmetric, eigenvalues specified
  704. *
  705. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  706. $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ),
  707. $ IINFO )
  708. *
  709. ELSE IF( ITYPE.EQ.7 ) THEN
  710. *
  711. * Diagonal, random eigenvalues
  712. *
  713. IDUMMA( 1 ) = 1
  714. CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
  715. $ 'T', 'N', WORK( N+1 ), 1, ONE,
  716. $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0,
  717. $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
  718. *
  719. ELSE IF( ITYPE.EQ.8 ) THEN
  720. *
  721. * Symmetric, random eigenvalues
  722. *
  723. IDUMMA( 1 ) = 1
  724. CALL DLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE,
  725. $ 'T', 'N', WORK( N+1 ), 1, ONE,
  726. $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N,
  727. $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
  728. *
  729. ELSE IF( ITYPE.EQ.9 ) THEN
  730. *
  731. * Symmetric banded, eigenvalues specified
  732. *
  733. IHBW = INT( ( N-1 )*DLARND( 1, ISEED3 ) )
  734. CALL DLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND,
  735. $ ANORM, IHBW, IHBW, 'Z', U, LDU, WORK( N+1 ),
  736. $ IINFO )
  737. *
  738. * Store as dense matrix for most routines.
  739. *
  740. CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
  741. DO 100 IDIAG = -IHBW, IHBW
  742. IROW = IHBW - IDIAG + 1
  743. J1 = MAX( 1, IDIAG+1 )
  744. J2 = MIN( N, N+IDIAG )
  745. DO 90 J = J1, J2
  746. I = J - IDIAG
  747. A( I, J ) = U( IROW, J )
  748. 90 CONTINUE
  749. 100 CONTINUE
  750. ELSE
  751. IINFO = 1
  752. END IF
  753. *
  754. IF( IINFO.NE.0 ) THEN
  755. WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE,
  756. $ IOLDSD
  757. INFO = ABS( IINFO )
  758. RETURN
  759. END IF
  760. *
  761. 110 CONTINUE
  762. *
  763. ABSTOL = UNFL + UNFL
  764. IF( N.LE.1 ) THEN
  765. IL = 1
  766. IU = N
  767. ELSE
  768. IL = 1 + INT( ( N-1 )*DLARND( 1, ISEED2 ) )
  769. IU = 1 + INT( ( N-1 )*DLARND( 1, ISEED2 ) )
  770. IF( IL.GT.IU ) THEN
  771. ITEMP = IL
  772. IL = IU
  773. IU = ITEMP
  774. END IF
  775. END IF
  776. *
  777. * 3) If matrix is tridiagonal, call DSTEV and DSTEVX.
  778. *
  779. IF( JTYPE.LE.7 ) THEN
  780. NTEST = 1
  781. DO 120 I = 1, N
  782. D1( I ) = DBLE( A( I, I ) )
  783. 120 CONTINUE
  784. DO 130 I = 1, N - 1
  785. D2( I ) = DBLE( A( I+1, I ) )
  786. 130 CONTINUE
  787. SRNAMT = 'DSTEV'
  788. CALL DSTEV( 'V', N, D1, D2, Z, LDU, WORK, IINFO )
  789. IF( IINFO.NE.0 ) THEN
  790. WRITE( NOUNIT, FMT = 9999 )'DSTEV(V)', IINFO, N,
  791. $ JTYPE, IOLDSD
  792. INFO = ABS( IINFO )
  793. IF( IINFO.LT.0 ) THEN
  794. RETURN
  795. ELSE
  796. RESULT( 1 ) = ULPINV
  797. RESULT( 2 ) = ULPINV
  798. RESULT( 3 ) = ULPINV
  799. GO TO 180
  800. END IF
  801. END IF
  802. *
  803. * Do tests 1 and 2.
  804. *
  805. DO 140 I = 1, N
  806. D3( I ) = DBLE( A( I, I ) )
  807. 140 CONTINUE
  808. DO 150 I = 1, N - 1
  809. D4( I ) = DBLE( A( I+1, I ) )
  810. 150 CONTINUE
  811. CALL DSTT21( N, 0, D3, D4, D1, D2, Z, LDU, WORK,
  812. $ RESULT( 1 ) )
  813. *
  814. NTEST = 3
  815. DO 160 I = 1, N - 1
  816. D4( I ) = DBLE( A( I+1, I ) )
  817. 160 CONTINUE
  818. SRNAMT = 'DSTEV'
  819. CALL DSTEV( 'N', N, D3, D4, Z, LDU, WORK, IINFO )
  820. IF( IINFO.NE.0 ) THEN
  821. WRITE( NOUNIT, FMT = 9999 )'DSTEV(N)', IINFO, N,
  822. $ JTYPE, IOLDSD
  823. INFO = ABS( IINFO )
  824. IF( IINFO.LT.0 ) THEN
  825. RETURN
  826. ELSE
  827. RESULT( 3 ) = ULPINV
  828. GO TO 180
  829. END IF
  830. END IF
  831. *
  832. * Do test 3.
  833. *
  834. TEMP1 = ZERO
  835. TEMP2 = ZERO
  836. DO 170 J = 1, N
  837. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  838. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  839. 170 CONTINUE
  840. RESULT( 3 ) = TEMP2 / MAX( UNFL,
  841. $ ULP*MAX( TEMP1, TEMP2 ) )
  842. *
  843. 180 CONTINUE
  844. *
  845. NTEST = 4
  846. DO 190 I = 1, N
  847. EVEIGS( I ) = D3( I )
  848. D1( I ) = DBLE( A( I, I ) )
  849. 190 CONTINUE
  850. DO 200 I = 1, N - 1
  851. D2( I ) = DBLE( A( I+1, I ) )
  852. 200 CONTINUE
  853. SRNAMT = 'DSTEVX'
  854. CALL DSTEVX( 'V', 'A', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  855. $ M, WA1, Z, LDU, WORK, IWORK, IWORK( 5*N+1 ),
  856. $ IINFO )
  857. IF( IINFO.NE.0 ) THEN
  858. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,A)', IINFO, N,
  859. $ JTYPE, IOLDSD
  860. INFO = ABS( IINFO )
  861. IF( IINFO.LT.0 ) THEN
  862. RETURN
  863. ELSE
  864. RESULT( 4 ) = ULPINV
  865. RESULT( 5 ) = ULPINV
  866. RESULT( 6 ) = ULPINV
  867. GO TO 250
  868. END IF
  869. END IF
  870. IF( N.GT.0 ) THEN
  871. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  872. ELSE
  873. TEMP3 = ZERO
  874. END IF
  875. *
  876. * Do tests 4 and 5.
  877. *
  878. DO 210 I = 1, N
  879. D3( I ) = DBLE( A( I, I ) )
  880. 210 CONTINUE
  881. DO 220 I = 1, N - 1
  882. D4( I ) = DBLE( A( I+1, I ) )
  883. 220 CONTINUE
  884. CALL DSTT21( N, 0, D3, D4, WA1, D2, Z, LDU, WORK,
  885. $ RESULT( 4 ) )
  886. *
  887. NTEST = 6
  888. DO 230 I = 1, N - 1
  889. D4( I ) = DBLE( A( I+1, I ) )
  890. 230 CONTINUE
  891. SRNAMT = 'DSTEVX'
  892. CALL DSTEVX( 'N', 'A', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  893. $ M2, WA2, Z, LDU, WORK, IWORK,
  894. $ IWORK( 5*N+1 ), IINFO )
  895. IF( IINFO.NE.0 ) THEN
  896. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,A)', IINFO, N,
  897. $ JTYPE, IOLDSD
  898. INFO = ABS( IINFO )
  899. IF( IINFO.LT.0 ) THEN
  900. RETURN
  901. ELSE
  902. RESULT( 6 ) = ULPINV
  903. GO TO 250
  904. END IF
  905. END IF
  906. *
  907. * Do test 6.
  908. *
  909. TEMP1 = ZERO
  910. TEMP2 = ZERO
  911. DO 240 J = 1, N
  912. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ),
  913. $ ABS( EVEIGS( J ) ) )
  914. TEMP2 = MAX( TEMP2, ABS( WA2( J )-EVEIGS( J ) ) )
  915. 240 CONTINUE
  916. RESULT( 6 ) = TEMP2 / MAX( UNFL,
  917. $ ULP*MAX( TEMP1, TEMP2 ) )
  918. *
  919. 250 CONTINUE
  920. *
  921. NTEST = 7
  922. DO 260 I = 1, N
  923. D1( I ) = DBLE( A( I, I ) )
  924. 260 CONTINUE
  925. DO 270 I = 1, N - 1
  926. D2( I ) = DBLE( A( I+1, I ) )
  927. 270 CONTINUE
  928. SRNAMT = 'DSTEVR'
  929. CALL DSTEVR( 'V', 'A', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  930. $ M, WA1, Z, LDU, IWORK, WORK, LWORK,
  931. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  932. IF( IINFO.NE.0 ) THEN
  933. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,A)', IINFO, N,
  934. $ JTYPE, IOLDSD
  935. INFO = ABS( IINFO )
  936. IF( IINFO.LT.0 ) THEN
  937. RETURN
  938. ELSE
  939. RESULT( 7 ) = ULPINV
  940. RESULT( 8 ) = ULPINV
  941. GO TO 320
  942. END IF
  943. END IF
  944. IF( N.GT.0 ) THEN
  945. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  946. ELSE
  947. TEMP3 = ZERO
  948. END IF
  949. *
  950. * Do tests 7 and 8.
  951. *
  952. DO 280 I = 1, N
  953. D3( I ) = DBLE( A( I, I ) )
  954. 280 CONTINUE
  955. DO 290 I = 1, N - 1
  956. D4( I ) = DBLE( A( I+1, I ) )
  957. 290 CONTINUE
  958. CALL DSTT21( N, 0, D3, D4, WA1, D2, Z, LDU, WORK,
  959. $ RESULT( 7 ) )
  960. *
  961. NTEST = 9
  962. DO 300 I = 1, N - 1
  963. D4( I ) = DBLE( A( I+1, I ) )
  964. 300 CONTINUE
  965. SRNAMT = 'DSTEVR'
  966. CALL DSTEVR( 'N', 'A', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  967. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  968. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  969. IF( IINFO.NE.0 ) THEN
  970. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,A)', IINFO, N,
  971. $ JTYPE, IOLDSD
  972. INFO = ABS( IINFO )
  973. IF( IINFO.LT.0 ) THEN
  974. RETURN
  975. ELSE
  976. RESULT( 9 ) = ULPINV
  977. GO TO 320
  978. END IF
  979. END IF
  980. *
  981. * Do test 9.
  982. *
  983. TEMP1 = ZERO
  984. TEMP2 = ZERO
  985. DO 310 J = 1, N
  986. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ),
  987. $ ABS( EVEIGS( J ) ) )
  988. TEMP2 = MAX( TEMP2, ABS( WA2( J )-EVEIGS( J ) ) )
  989. 310 CONTINUE
  990. RESULT( 9 ) = TEMP2 / MAX( UNFL,
  991. $ ULP*MAX( TEMP1, TEMP2 ) )
  992. *
  993. 320 CONTINUE
  994. *
  995. *
  996. NTEST = 10
  997. DO 330 I = 1, N
  998. D1( I ) = DBLE( A( I, I ) )
  999. 330 CONTINUE
  1000. DO 340 I = 1, N - 1
  1001. D2( I ) = DBLE( A( I+1, I ) )
  1002. 340 CONTINUE
  1003. SRNAMT = 'DSTEVX'
  1004. CALL DSTEVX( 'V', 'I', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1005. $ M2, WA2, Z, LDU, WORK, IWORK,
  1006. $ IWORK( 5*N+1 ), IINFO )
  1007. IF( IINFO.NE.0 ) THEN
  1008. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,I)', IINFO, N,
  1009. $ JTYPE, IOLDSD
  1010. INFO = ABS( IINFO )
  1011. IF( IINFO.LT.0 ) THEN
  1012. RETURN
  1013. ELSE
  1014. RESULT( 10 ) = ULPINV
  1015. RESULT( 11 ) = ULPINV
  1016. RESULT( 12 ) = ULPINV
  1017. GO TO 380
  1018. END IF
  1019. END IF
  1020. *
  1021. * Do tests 10 and 11.
  1022. *
  1023. DO 350 I = 1, N
  1024. D3( I ) = DBLE( A( I, I ) )
  1025. 350 CONTINUE
  1026. DO 360 I = 1, N - 1
  1027. D4( I ) = DBLE( A( I+1, I ) )
  1028. 360 CONTINUE
  1029. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1030. $ MAX( 1, M2 ), RESULT( 10 ) )
  1031. *
  1032. *
  1033. NTEST = 12
  1034. DO 370 I = 1, N - 1
  1035. D4( I ) = DBLE( A( I+1, I ) )
  1036. 370 CONTINUE
  1037. SRNAMT = 'DSTEVX'
  1038. CALL DSTEVX( 'N', 'I', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1039. $ M3, WA3, Z, LDU, WORK, IWORK,
  1040. $ IWORK( 5*N+1 ), IINFO )
  1041. IF( IINFO.NE.0 ) THEN
  1042. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,I)', IINFO, N,
  1043. $ JTYPE, IOLDSD
  1044. INFO = ABS( IINFO )
  1045. IF( IINFO.LT.0 ) THEN
  1046. RETURN
  1047. ELSE
  1048. RESULT( 12 ) = ULPINV
  1049. GO TO 380
  1050. END IF
  1051. END IF
  1052. *
  1053. * Do test 12.
  1054. *
  1055. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1056. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1057. RESULT( 12 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, ULP*TEMP3 )
  1058. *
  1059. 380 CONTINUE
  1060. *
  1061. NTEST = 12
  1062. IF( N.GT.0 ) THEN
  1063. IF( IL.NE.1 ) THEN
  1064. VL = WA1( IL ) - MAX( HALF*
  1065. $ ( WA1( IL )-WA1( IL-1 ) ), TEN*ULP*TEMP3,
  1066. $ TEN*RTUNFL )
  1067. ELSE
  1068. VL = WA1( 1 ) - MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1069. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1070. END IF
  1071. IF( IU.NE.N ) THEN
  1072. VU = WA1( IU ) + MAX( HALF*
  1073. $ ( WA1( IU+1 )-WA1( IU ) ), TEN*ULP*TEMP3,
  1074. $ TEN*RTUNFL )
  1075. ELSE
  1076. VU = WA1( N ) + MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1077. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1078. END IF
  1079. ELSE
  1080. VL = ZERO
  1081. VU = ONE
  1082. END IF
  1083. *
  1084. DO 390 I = 1, N
  1085. D1( I ) = DBLE( A( I, I ) )
  1086. 390 CONTINUE
  1087. DO 400 I = 1, N - 1
  1088. D2( I ) = DBLE( A( I+1, I ) )
  1089. 400 CONTINUE
  1090. SRNAMT = 'DSTEVX'
  1091. CALL DSTEVX( 'V', 'V', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1092. $ M2, WA2, Z, LDU, WORK, IWORK,
  1093. $ IWORK( 5*N+1 ), IINFO )
  1094. IF( IINFO.NE.0 ) THEN
  1095. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(V,V)', IINFO, N,
  1096. $ JTYPE, IOLDSD
  1097. INFO = ABS( IINFO )
  1098. IF( IINFO.LT.0 ) THEN
  1099. RETURN
  1100. ELSE
  1101. RESULT( 13 ) = ULPINV
  1102. RESULT( 14 ) = ULPINV
  1103. RESULT( 15 ) = ULPINV
  1104. GO TO 440
  1105. END IF
  1106. END IF
  1107. *
  1108. IF( M2.EQ.0 .AND. N.GT.0 ) THEN
  1109. RESULT( 13 ) = ULPINV
  1110. RESULT( 14 ) = ULPINV
  1111. RESULT( 15 ) = ULPINV
  1112. GO TO 440
  1113. END IF
  1114. *
  1115. * Do tests 13 and 14.
  1116. *
  1117. DO 410 I = 1, N
  1118. D3( I ) = DBLE( A( I, I ) )
  1119. 410 CONTINUE
  1120. DO 420 I = 1, N - 1
  1121. D4( I ) = DBLE( A( I+1, I ) )
  1122. 420 CONTINUE
  1123. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1124. $ MAX( 1, M2 ), RESULT( 13 ) )
  1125. *
  1126. NTEST = 15
  1127. DO 430 I = 1, N - 1
  1128. D4( I ) = DBLE( A( I+1, I ) )
  1129. 430 CONTINUE
  1130. SRNAMT = 'DSTEVX'
  1131. CALL DSTEVX( 'N', 'V', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1132. $ M3, WA3, Z, LDU, WORK, IWORK,
  1133. $ IWORK( 5*N+1 ), IINFO )
  1134. IF( IINFO.NE.0 ) THEN
  1135. WRITE( NOUNIT, FMT = 9999 )'DSTEVX(N,V)', IINFO, N,
  1136. $ JTYPE, IOLDSD
  1137. INFO = ABS( IINFO )
  1138. IF( IINFO.LT.0 ) THEN
  1139. RETURN
  1140. ELSE
  1141. RESULT( 15 ) = ULPINV
  1142. GO TO 440
  1143. END IF
  1144. END IF
  1145. *
  1146. * Do test 15.
  1147. *
  1148. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1149. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1150. RESULT( 15 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, TEMP3*ULP )
  1151. *
  1152. 440 CONTINUE
  1153. *
  1154. NTEST = 16
  1155. DO 450 I = 1, N
  1156. D1( I ) = DBLE( A( I, I ) )
  1157. 450 CONTINUE
  1158. DO 460 I = 1, N - 1
  1159. D2( I ) = DBLE( A( I+1, I ) )
  1160. 460 CONTINUE
  1161. SRNAMT = 'DSTEVD'
  1162. CALL DSTEVD( 'V', N, D1, D2, Z, LDU, WORK, LWEDC, IWORK,
  1163. $ LIWEDC, IINFO )
  1164. IF( IINFO.NE.0 ) THEN
  1165. WRITE( NOUNIT, FMT = 9999 )'DSTEVD(V)', IINFO, N,
  1166. $ JTYPE, IOLDSD
  1167. INFO = ABS( IINFO )
  1168. IF( IINFO.LT.0 ) THEN
  1169. RETURN
  1170. ELSE
  1171. RESULT( 16 ) = ULPINV
  1172. RESULT( 17 ) = ULPINV
  1173. RESULT( 18 ) = ULPINV
  1174. GO TO 510
  1175. END IF
  1176. END IF
  1177. *
  1178. * Do tests 16 and 17.
  1179. *
  1180. DO 470 I = 1, N
  1181. D3( I ) = DBLE( A( I, I ) )
  1182. 470 CONTINUE
  1183. DO 480 I = 1, N - 1
  1184. D4( I ) = DBLE( A( I+1, I ) )
  1185. 480 CONTINUE
  1186. CALL DSTT21( N, 0, D3, D4, D1, D2, Z, LDU, WORK,
  1187. $ RESULT( 16 ) )
  1188. *
  1189. NTEST = 18
  1190. DO 490 I = 1, N - 1
  1191. D4( I ) = DBLE( A( I+1, I ) )
  1192. 490 CONTINUE
  1193. SRNAMT = 'DSTEVD'
  1194. CALL DSTEVD( 'N', N, D3, D4, Z, LDU, WORK, LWEDC, IWORK,
  1195. $ LIWEDC, IINFO )
  1196. IF( IINFO.NE.0 ) THEN
  1197. WRITE( NOUNIT, FMT = 9999 )'DSTEVD(N)', IINFO, N,
  1198. $ JTYPE, IOLDSD
  1199. INFO = ABS( IINFO )
  1200. IF( IINFO.LT.0 ) THEN
  1201. RETURN
  1202. ELSE
  1203. RESULT( 18 ) = ULPINV
  1204. GO TO 510
  1205. END IF
  1206. END IF
  1207. *
  1208. * Do test 18.
  1209. *
  1210. TEMP1 = ZERO
  1211. TEMP2 = ZERO
  1212. DO 500 J = 1, N
  1213. TEMP1 = MAX( TEMP1, ABS( EVEIGS( J ) ),
  1214. $ ABS( D3( J ) ) )
  1215. TEMP2 = MAX( TEMP2, ABS( EVEIGS( J )-D3( J ) ) )
  1216. 500 CONTINUE
  1217. RESULT( 18 ) = TEMP2 / MAX( UNFL,
  1218. $ ULP*MAX( TEMP1, TEMP2 ) )
  1219. *
  1220. 510 CONTINUE
  1221. *
  1222. NTEST = 19
  1223. DO 520 I = 1, N
  1224. D1( I ) = DBLE( A( I, I ) )
  1225. 520 CONTINUE
  1226. DO 530 I = 1, N - 1
  1227. D2( I ) = DBLE( A( I+1, I ) )
  1228. 530 CONTINUE
  1229. SRNAMT = 'DSTEVR'
  1230. CALL DSTEVR( 'V', 'I', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1231. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  1232. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1233. IF( IINFO.NE.0 ) THEN
  1234. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,I)', IINFO, N,
  1235. $ JTYPE, IOLDSD
  1236. INFO = ABS( IINFO )
  1237. IF( IINFO.LT.0 ) THEN
  1238. RETURN
  1239. ELSE
  1240. RESULT( 19 ) = ULPINV
  1241. RESULT( 20 ) = ULPINV
  1242. RESULT( 21 ) = ULPINV
  1243. GO TO 570
  1244. END IF
  1245. END IF
  1246. *
  1247. * DO tests 19 and 20.
  1248. *
  1249. DO 540 I = 1, N
  1250. D3( I ) = DBLE( A( I, I ) )
  1251. 540 CONTINUE
  1252. DO 550 I = 1, N - 1
  1253. D4( I ) = DBLE( A( I+1, I ) )
  1254. 550 CONTINUE
  1255. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1256. $ MAX( 1, M2 ), RESULT( 19 ) )
  1257. *
  1258. *
  1259. NTEST = 21
  1260. DO 560 I = 1, N - 1
  1261. D4( I ) = DBLE( A( I+1, I ) )
  1262. 560 CONTINUE
  1263. SRNAMT = 'DSTEVR'
  1264. CALL DSTEVR( 'N', 'I', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1265. $ M3, WA3, Z, LDU, IWORK, WORK, LWORK,
  1266. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1267. IF( IINFO.NE.0 ) THEN
  1268. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,I)', IINFO, N,
  1269. $ JTYPE, IOLDSD
  1270. INFO = ABS( IINFO )
  1271. IF( IINFO.LT.0 ) THEN
  1272. RETURN
  1273. ELSE
  1274. RESULT( 21 ) = ULPINV
  1275. GO TO 570
  1276. END IF
  1277. END IF
  1278. *
  1279. * Do test 21.
  1280. *
  1281. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1282. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1283. RESULT( 21 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, ULP*TEMP3 )
  1284. *
  1285. 570 CONTINUE
  1286. *
  1287. NTEST = 21
  1288. IF( N.GT.0 ) THEN
  1289. IF( IL.NE.1 ) THEN
  1290. VL = WA1( IL ) - MAX( HALF*
  1291. $ ( WA1( IL )-WA1( IL-1 ) ), TEN*ULP*TEMP3,
  1292. $ TEN*RTUNFL )
  1293. ELSE
  1294. VL = WA1( 1 ) - MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1295. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1296. END IF
  1297. IF( IU.NE.N ) THEN
  1298. VU = WA1( IU ) + MAX( HALF*
  1299. $ ( WA1( IU+1 )-WA1( IU ) ), TEN*ULP*TEMP3,
  1300. $ TEN*RTUNFL )
  1301. ELSE
  1302. VU = WA1( N ) + MAX( HALF*( WA1( N )-WA1( 1 ) ),
  1303. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1304. END IF
  1305. ELSE
  1306. VL = ZERO
  1307. VU = ONE
  1308. END IF
  1309. *
  1310. DO 580 I = 1, N
  1311. D1( I ) = DBLE( A( I, I ) )
  1312. 580 CONTINUE
  1313. DO 590 I = 1, N - 1
  1314. D2( I ) = DBLE( A( I+1, I ) )
  1315. 590 CONTINUE
  1316. SRNAMT = 'DSTEVR'
  1317. CALL DSTEVR( 'V', 'V', N, D1, D2, VL, VU, IL, IU, ABSTOL,
  1318. $ M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  1319. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1320. IF( IINFO.NE.0 ) THEN
  1321. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(V,V)', IINFO, N,
  1322. $ JTYPE, IOLDSD
  1323. INFO = ABS( IINFO )
  1324. IF( IINFO.LT.0 ) THEN
  1325. RETURN
  1326. ELSE
  1327. RESULT( 22 ) = ULPINV
  1328. RESULT( 23 ) = ULPINV
  1329. RESULT( 24 ) = ULPINV
  1330. GO TO 630
  1331. END IF
  1332. END IF
  1333. *
  1334. IF( M2.EQ.0 .AND. N.GT.0 ) THEN
  1335. RESULT( 22 ) = ULPINV
  1336. RESULT( 23 ) = ULPINV
  1337. RESULT( 24 ) = ULPINV
  1338. GO TO 630
  1339. END IF
  1340. *
  1341. * Do tests 22 and 23.
  1342. *
  1343. DO 600 I = 1, N
  1344. D3( I ) = DBLE( A( I, I ) )
  1345. 600 CONTINUE
  1346. DO 610 I = 1, N - 1
  1347. D4( I ) = DBLE( A( I+1, I ) )
  1348. 610 CONTINUE
  1349. CALL DSTT22( N, M2, 0, D3, D4, WA2, D2, Z, LDU, WORK,
  1350. $ MAX( 1, M2 ), RESULT( 22 ) )
  1351. *
  1352. NTEST = 24
  1353. DO 620 I = 1, N - 1
  1354. D4( I ) = DBLE( A( I+1, I ) )
  1355. 620 CONTINUE
  1356. SRNAMT = 'DSTEVR'
  1357. CALL DSTEVR( 'N', 'V', N, D3, D4, VL, VU, IL, IU, ABSTOL,
  1358. $ M3, WA3, Z, LDU, IWORK, WORK, LWORK,
  1359. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  1360. IF( IINFO.NE.0 ) THEN
  1361. WRITE( NOUNIT, FMT = 9999 )'DSTEVR(N,V)', IINFO, N,
  1362. $ JTYPE, IOLDSD
  1363. INFO = ABS( IINFO )
  1364. IF( IINFO.LT.0 ) THEN
  1365. RETURN
  1366. ELSE
  1367. RESULT( 24 ) = ULPINV
  1368. GO TO 630
  1369. END IF
  1370. END IF
  1371. *
  1372. * Do test 24.
  1373. *
  1374. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1375. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1376. RESULT( 24 ) = ( TEMP1+TEMP2 ) / MAX( UNFL, TEMP3*ULP )
  1377. *
  1378. 630 CONTINUE
  1379. *
  1380. *
  1381. *
  1382. ELSE
  1383. *
  1384. DO 640 I = 1, 24
  1385. RESULT( I ) = ZERO
  1386. 640 CONTINUE
  1387. NTEST = 24
  1388. END IF
  1389. *
  1390. * Perform remaining tests storing upper or lower triangular
  1391. * part of matrix.
  1392. *
  1393. DO 1720 IUPLO = 0, 1
  1394. IF( IUPLO.EQ.0 ) THEN
  1395. UPLO = 'L'
  1396. ELSE
  1397. UPLO = 'U'
  1398. END IF
  1399. *
  1400. * 4) Call DSYEV and DSYEVX.
  1401. *
  1402. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  1403. *
  1404. NTEST = NTEST + 1
  1405. SRNAMT = 'DSYEV'
  1406. CALL DSYEV( 'V', UPLO, N, A, LDU, D1, WORK, LWORK,
  1407. $ IINFO )
  1408. IF( IINFO.NE.0 ) THEN
  1409. WRITE( NOUNIT, FMT = 9999 )'DSYEV(V,' // UPLO // ')',
  1410. $ IINFO, N, JTYPE, IOLDSD
  1411. INFO = ABS( IINFO )
  1412. IF( IINFO.LT.0 ) THEN
  1413. RETURN
  1414. ELSE
  1415. RESULT( NTEST ) = ULPINV
  1416. RESULT( NTEST+1 ) = ULPINV
  1417. RESULT( NTEST+2 ) = ULPINV
  1418. GO TO 660
  1419. END IF
  1420. END IF
  1421. *
  1422. * Do tests 25 and 26 (or +54)
  1423. *
  1424. CALL DSYT21( 1, UPLO, N, 0, V, LDU, D1, D2, A, LDU, Z,
  1425. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1426. *
  1427. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1428. *
  1429. NTEST = NTEST + 2
  1430. SRNAMT = 'DSYEV_2STAGE'
  1431. CALL DSYEV_2STAGE( 'N', UPLO, N, A, LDU, D3, WORK, LWORK,
  1432. $ IINFO )
  1433. IF( IINFO.NE.0 ) THEN
  1434. WRITE( NOUNIT, FMT = 9999 )
  1435. $ 'DSYEV_2STAGE(N,' // UPLO // ')',
  1436. $ IINFO, N, JTYPE, IOLDSD
  1437. INFO = ABS( IINFO )
  1438. IF( IINFO.LT.0 ) THEN
  1439. RETURN
  1440. ELSE
  1441. RESULT( NTEST ) = ULPINV
  1442. GO TO 660
  1443. END IF
  1444. END IF
  1445. *
  1446. * Do test 27 (or +54)
  1447. *
  1448. TEMP1 = ZERO
  1449. TEMP2 = ZERO
  1450. DO 650 J = 1, N
  1451. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1452. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1453. 650 CONTINUE
  1454. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1455. $ ULP*MAX( TEMP1, TEMP2 ) )
  1456. *
  1457. 660 CONTINUE
  1458. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1459. *
  1460. NTEST = NTEST + 1
  1461. *
  1462. IF( N.GT.0 ) THEN
  1463. TEMP3 = MAX( ABS( D1( 1 ) ), ABS( D1( N ) ) )
  1464. IF( IL.NE.1 ) THEN
  1465. VL = D1( IL ) - MAX( HALF*( D1( IL )-D1( IL-1 ) ),
  1466. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1467. ELSE IF( N.GT.0 ) THEN
  1468. VL = D1( 1 ) - MAX( HALF*( D1( N )-D1( 1 ) ),
  1469. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1470. END IF
  1471. IF( IU.NE.N ) THEN
  1472. VU = D1( IU ) + MAX( HALF*( D1( IU+1 )-D1( IU ) ),
  1473. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1474. ELSE IF( N.GT.0 ) THEN
  1475. VU = D1( N ) + MAX( HALF*( D1( N )-D1( 1 ) ),
  1476. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1477. END IF
  1478. ELSE
  1479. TEMP3 = ZERO
  1480. VL = ZERO
  1481. VU = ONE
  1482. END IF
  1483. *
  1484. SRNAMT = 'DSYEVX'
  1485. CALL DSYEVX( 'V', 'A', UPLO, N, A, LDU, VL, VU, IL, IU,
  1486. $ ABSTOL, M, WA1, Z, LDU, WORK, LWORK, IWORK,
  1487. $ IWORK( 5*N+1 ), IINFO )
  1488. IF( IINFO.NE.0 ) THEN
  1489. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,A,' // UPLO //
  1490. $ ')', IINFO, N, JTYPE, IOLDSD
  1491. INFO = ABS( IINFO )
  1492. IF( IINFO.LT.0 ) THEN
  1493. RETURN
  1494. ELSE
  1495. RESULT( NTEST ) = ULPINV
  1496. RESULT( NTEST+1 ) = ULPINV
  1497. RESULT( NTEST+2 ) = ULPINV
  1498. GO TO 680
  1499. END IF
  1500. END IF
  1501. *
  1502. * Do tests 28 and 29 (or +54)
  1503. *
  1504. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1505. *
  1506. CALL DSYT21( 1, UPLO, N, 0, A, LDU, D1, D2, Z, LDU, V,
  1507. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1508. *
  1509. NTEST = NTEST + 2
  1510. SRNAMT = 'DSYEVX_2STAGE'
  1511. CALL DSYEVX_2STAGE( 'N', 'A', UPLO, N, A, LDU, VL, VU,
  1512. $ IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  1513. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1514. IF( IINFO.NE.0 ) THEN
  1515. WRITE( NOUNIT, FMT = 9999 )
  1516. $ 'DSYEVX_2STAGE(N,A,' // UPLO //
  1517. $ ')', IINFO, N, JTYPE, IOLDSD
  1518. INFO = ABS( IINFO )
  1519. IF( IINFO.LT.0 ) THEN
  1520. RETURN
  1521. ELSE
  1522. RESULT( NTEST ) = ULPINV
  1523. GO TO 680
  1524. END IF
  1525. END IF
  1526. *
  1527. * Do test 30 (or +54)
  1528. *
  1529. TEMP1 = ZERO
  1530. TEMP2 = ZERO
  1531. DO 670 J = 1, N
  1532. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1533. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1534. 670 CONTINUE
  1535. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1536. $ ULP*MAX( TEMP1, TEMP2 ) )
  1537. *
  1538. 680 CONTINUE
  1539. *
  1540. NTEST = NTEST + 1
  1541. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1542. SRNAMT = 'DSYEVX'
  1543. CALL DSYEVX( 'V', 'I', UPLO, N, A, LDU, VL, VU, IL, IU,
  1544. $ ABSTOL, M2, WA2, Z, LDU, WORK, LWORK, IWORK,
  1545. $ IWORK( 5*N+1 ), IINFO )
  1546. IF( IINFO.NE.0 ) THEN
  1547. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,I,' // UPLO //
  1548. $ ')', IINFO, N, JTYPE, IOLDSD
  1549. INFO = ABS( IINFO )
  1550. IF( IINFO.LT.0 ) THEN
  1551. RETURN
  1552. ELSE
  1553. RESULT( NTEST ) = ULPINV
  1554. RESULT( NTEST+1 ) = ULPINV
  1555. RESULT( NTEST+2 ) = ULPINV
  1556. GO TO 690
  1557. END IF
  1558. END IF
  1559. *
  1560. * Do tests 31 and 32 (or +54)
  1561. *
  1562. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1563. *
  1564. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1565. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1566. *
  1567. NTEST = NTEST + 2
  1568. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1569. SRNAMT = 'DSYEVX_2STAGE'
  1570. CALL DSYEVX_2STAGE( 'N', 'I', UPLO, N, A, LDU, VL, VU,
  1571. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, WORK,
  1572. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1573. IF( IINFO.NE.0 ) THEN
  1574. WRITE( NOUNIT, FMT = 9999 )
  1575. $ 'DSYEVX_2STAGE(N,I,' // UPLO //
  1576. $ ')', IINFO, N, JTYPE, IOLDSD
  1577. INFO = ABS( IINFO )
  1578. IF( IINFO.LT.0 ) THEN
  1579. RETURN
  1580. ELSE
  1581. RESULT( NTEST ) = ULPINV
  1582. GO TO 690
  1583. END IF
  1584. END IF
  1585. *
  1586. * Do test 33 (or +54)
  1587. *
  1588. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1589. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1590. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1591. $ MAX( UNFL, ULP*TEMP3 )
  1592. 690 CONTINUE
  1593. *
  1594. NTEST = NTEST + 1
  1595. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1596. SRNAMT = 'DSYEVX'
  1597. CALL DSYEVX( 'V', 'V', UPLO, N, A, LDU, VL, VU, IL, IU,
  1598. $ ABSTOL, M2, WA2, Z, LDU, WORK, LWORK, IWORK,
  1599. $ IWORK( 5*N+1 ), IINFO )
  1600. IF( IINFO.NE.0 ) THEN
  1601. WRITE( NOUNIT, FMT = 9999 )'DSYEVX(V,V,' // UPLO //
  1602. $ ')', IINFO, N, JTYPE, IOLDSD
  1603. INFO = ABS( IINFO )
  1604. IF( IINFO.LT.0 ) THEN
  1605. RETURN
  1606. ELSE
  1607. RESULT( NTEST ) = ULPINV
  1608. RESULT( NTEST+1 ) = ULPINV
  1609. RESULT( NTEST+2 ) = ULPINV
  1610. GO TO 700
  1611. END IF
  1612. END IF
  1613. *
  1614. * Do tests 34 and 35 (or +54)
  1615. *
  1616. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1617. *
  1618. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1619. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1620. *
  1621. NTEST = NTEST + 2
  1622. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1623. SRNAMT = 'DSYEVX_2STAGE'
  1624. CALL DSYEVX_2STAGE( 'N', 'V', UPLO, N, A, LDU, VL, VU,
  1625. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, WORK,
  1626. $ LWORK, IWORK, IWORK( 5*N+1 ), IINFO )
  1627. IF( IINFO.NE.0 ) THEN
  1628. WRITE( NOUNIT, FMT = 9999 )
  1629. $ 'DSYEVX_2STAGE(N,V,' // UPLO //
  1630. $ ')', IINFO, N, JTYPE, IOLDSD
  1631. INFO = ABS( IINFO )
  1632. IF( IINFO.LT.0 ) THEN
  1633. RETURN
  1634. ELSE
  1635. RESULT( NTEST ) = ULPINV
  1636. GO TO 700
  1637. END IF
  1638. END IF
  1639. *
  1640. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  1641. RESULT( NTEST ) = ULPINV
  1642. GO TO 700
  1643. END IF
  1644. *
  1645. * Do test 36 (or +54)
  1646. *
  1647. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1648. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1649. IF( N.GT.0 ) THEN
  1650. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1651. ELSE
  1652. TEMP3 = ZERO
  1653. END IF
  1654. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1655. $ MAX( UNFL, TEMP3*ULP )
  1656. *
  1657. 700 CONTINUE
  1658. *
  1659. * 5) Call DSPEV and DSPEVX.
  1660. *
  1661. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  1662. *
  1663. * Load array WORK with the upper or lower triangular
  1664. * part of the matrix in packed form.
  1665. *
  1666. IF( IUPLO.EQ.1 ) THEN
  1667. INDX = 1
  1668. DO 720 J = 1, N
  1669. DO 710 I = 1, J
  1670. WORK( INDX ) = A( I, J )
  1671. INDX = INDX + 1
  1672. 710 CONTINUE
  1673. 720 CONTINUE
  1674. ELSE
  1675. INDX = 1
  1676. DO 740 J = 1, N
  1677. DO 730 I = J, N
  1678. WORK( INDX ) = A( I, J )
  1679. INDX = INDX + 1
  1680. 730 CONTINUE
  1681. 740 CONTINUE
  1682. END IF
  1683. *
  1684. NTEST = NTEST + 1
  1685. SRNAMT = 'DSPEV'
  1686. CALL DSPEV( 'V', UPLO, N, WORK, D1, Z, LDU, V, IINFO )
  1687. IF( IINFO.NE.0 ) THEN
  1688. WRITE( NOUNIT, FMT = 9999 )'DSPEV(V,' // UPLO // ')',
  1689. $ IINFO, N, JTYPE, IOLDSD
  1690. INFO = ABS( IINFO )
  1691. IF( IINFO.LT.0 ) THEN
  1692. RETURN
  1693. ELSE
  1694. RESULT( NTEST ) = ULPINV
  1695. RESULT( NTEST+1 ) = ULPINV
  1696. RESULT( NTEST+2 ) = ULPINV
  1697. GO TO 800
  1698. END IF
  1699. END IF
  1700. *
  1701. * Do tests 37 and 38 (or +54)
  1702. *
  1703. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  1704. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1705. *
  1706. IF( IUPLO.EQ.1 ) THEN
  1707. INDX = 1
  1708. DO 760 J = 1, N
  1709. DO 750 I = 1, J
  1710. WORK( INDX ) = A( I, J )
  1711. INDX = INDX + 1
  1712. 750 CONTINUE
  1713. 760 CONTINUE
  1714. ELSE
  1715. INDX = 1
  1716. DO 780 J = 1, N
  1717. DO 770 I = J, N
  1718. WORK( INDX ) = A( I, J )
  1719. INDX = INDX + 1
  1720. 770 CONTINUE
  1721. 780 CONTINUE
  1722. END IF
  1723. *
  1724. NTEST = NTEST + 2
  1725. SRNAMT = 'DSPEV'
  1726. CALL DSPEV( 'N', UPLO, N, WORK, D3, Z, LDU, V, IINFO )
  1727. IF( IINFO.NE.0 ) THEN
  1728. WRITE( NOUNIT, FMT = 9999 )'DSPEV(N,' // UPLO // ')',
  1729. $ IINFO, N, JTYPE, IOLDSD
  1730. INFO = ABS( IINFO )
  1731. IF( IINFO.LT.0 ) THEN
  1732. RETURN
  1733. ELSE
  1734. RESULT( NTEST ) = ULPINV
  1735. GO TO 800
  1736. END IF
  1737. END IF
  1738. *
  1739. * Do test 39 (or +54)
  1740. *
  1741. TEMP1 = ZERO
  1742. TEMP2 = ZERO
  1743. DO 790 J = 1, N
  1744. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  1745. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  1746. 790 CONTINUE
  1747. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1748. $ ULP*MAX( TEMP1, TEMP2 ) )
  1749. *
  1750. * Load array WORK with the upper or lower triangular part
  1751. * of the matrix in packed form.
  1752. *
  1753. 800 CONTINUE
  1754. IF( IUPLO.EQ.1 ) THEN
  1755. INDX = 1
  1756. DO 820 J = 1, N
  1757. DO 810 I = 1, J
  1758. WORK( INDX ) = A( I, J )
  1759. INDX = INDX + 1
  1760. 810 CONTINUE
  1761. 820 CONTINUE
  1762. ELSE
  1763. INDX = 1
  1764. DO 840 J = 1, N
  1765. DO 830 I = J, N
  1766. WORK( INDX ) = A( I, J )
  1767. INDX = INDX + 1
  1768. 830 CONTINUE
  1769. 840 CONTINUE
  1770. END IF
  1771. *
  1772. NTEST = NTEST + 1
  1773. *
  1774. IF( N.GT.0 ) THEN
  1775. TEMP3 = MAX( ABS( D1( 1 ) ), ABS( D1( N ) ) )
  1776. IF( IL.NE.1 ) THEN
  1777. VL = D1( IL ) - MAX( HALF*( D1( IL )-D1( IL-1 ) ),
  1778. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1779. ELSE IF( N.GT.0 ) THEN
  1780. VL = D1( 1 ) - MAX( HALF*( D1( N )-D1( 1 ) ),
  1781. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1782. END IF
  1783. IF( IU.NE.N ) THEN
  1784. VU = D1( IU ) + MAX( HALF*( D1( IU+1 )-D1( IU ) ),
  1785. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1786. ELSE IF( N.GT.0 ) THEN
  1787. VU = D1( N ) + MAX( HALF*( D1( N )-D1( 1 ) ),
  1788. $ TEN*ULP*TEMP3, TEN*RTUNFL )
  1789. END IF
  1790. ELSE
  1791. TEMP3 = ZERO
  1792. VL = ZERO
  1793. VU = ONE
  1794. END IF
  1795. *
  1796. SRNAMT = 'DSPEVX'
  1797. CALL DSPEVX( 'V', 'A', UPLO, N, WORK, VL, VU, IL, IU,
  1798. $ ABSTOL, M, WA1, Z, LDU, V, IWORK,
  1799. $ IWORK( 5*N+1 ), IINFO )
  1800. IF( IINFO.NE.0 ) THEN
  1801. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,A,' // UPLO //
  1802. $ ')', IINFO, N, JTYPE, IOLDSD
  1803. INFO = ABS( IINFO )
  1804. IF( IINFO.LT.0 ) THEN
  1805. RETURN
  1806. ELSE
  1807. RESULT( NTEST ) = ULPINV
  1808. RESULT( NTEST+1 ) = ULPINV
  1809. RESULT( NTEST+2 ) = ULPINV
  1810. GO TO 900
  1811. END IF
  1812. END IF
  1813. *
  1814. * Do tests 40 and 41 (or +54)
  1815. *
  1816. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  1817. $ LDU, TAU, WORK, RESULT( NTEST ) )
  1818. *
  1819. NTEST = NTEST + 2
  1820. *
  1821. IF( IUPLO.EQ.1 ) THEN
  1822. INDX = 1
  1823. DO 860 J = 1, N
  1824. DO 850 I = 1, J
  1825. WORK( INDX ) = A( I, J )
  1826. INDX = INDX + 1
  1827. 850 CONTINUE
  1828. 860 CONTINUE
  1829. ELSE
  1830. INDX = 1
  1831. DO 880 J = 1, N
  1832. DO 870 I = J, N
  1833. WORK( INDX ) = A( I, J )
  1834. INDX = INDX + 1
  1835. 870 CONTINUE
  1836. 880 CONTINUE
  1837. END IF
  1838. *
  1839. SRNAMT = 'DSPEVX'
  1840. CALL DSPEVX( 'N', 'A', UPLO, N, WORK, VL, VU, IL, IU,
  1841. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1842. $ IWORK( 5*N+1 ), IINFO )
  1843. IF( IINFO.NE.0 ) THEN
  1844. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,A,' // UPLO //
  1845. $ ')', IINFO, N, JTYPE, IOLDSD
  1846. INFO = ABS( IINFO )
  1847. IF( IINFO.LT.0 ) THEN
  1848. RETURN
  1849. ELSE
  1850. RESULT( NTEST ) = ULPINV
  1851. GO TO 900
  1852. END IF
  1853. END IF
  1854. *
  1855. * Do test 42 (or +54)
  1856. *
  1857. TEMP1 = ZERO
  1858. TEMP2 = ZERO
  1859. DO 890 J = 1, N
  1860. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  1861. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  1862. 890 CONTINUE
  1863. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  1864. $ ULP*MAX( TEMP1, TEMP2 ) )
  1865. *
  1866. 900 CONTINUE
  1867. IF( IUPLO.EQ.1 ) THEN
  1868. INDX = 1
  1869. DO 920 J = 1, N
  1870. DO 910 I = 1, J
  1871. WORK( INDX ) = A( I, J )
  1872. INDX = INDX + 1
  1873. 910 CONTINUE
  1874. 920 CONTINUE
  1875. ELSE
  1876. INDX = 1
  1877. DO 940 J = 1, N
  1878. DO 930 I = J, N
  1879. WORK( INDX ) = A( I, J )
  1880. INDX = INDX + 1
  1881. 930 CONTINUE
  1882. 940 CONTINUE
  1883. END IF
  1884. *
  1885. NTEST = NTEST + 1
  1886. *
  1887. SRNAMT = 'DSPEVX'
  1888. CALL DSPEVX( 'V', 'I', UPLO, N, WORK, VL, VU, IL, IU,
  1889. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1890. $ IWORK( 5*N+1 ), IINFO )
  1891. IF( IINFO.NE.0 ) THEN
  1892. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,I,' // UPLO //
  1893. $ ')', IINFO, N, JTYPE, IOLDSD
  1894. INFO = ABS( IINFO )
  1895. IF( IINFO.LT.0 ) THEN
  1896. RETURN
  1897. ELSE
  1898. RESULT( NTEST ) = ULPINV
  1899. RESULT( NTEST+1 ) = ULPINV
  1900. RESULT( NTEST+2 ) = ULPINV
  1901. GO TO 990
  1902. END IF
  1903. END IF
  1904. *
  1905. * Do tests 43 and 44 (or +54)
  1906. *
  1907. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  1908. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  1909. *
  1910. NTEST = NTEST + 2
  1911. *
  1912. IF( IUPLO.EQ.1 ) THEN
  1913. INDX = 1
  1914. DO 960 J = 1, N
  1915. DO 950 I = 1, J
  1916. WORK( INDX ) = A( I, J )
  1917. INDX = INDX + 1
  1918. 950 CONTINUE
  1919. 960 CONTINUE
  1920. ELSE
  1921. INDX = 1
  1922. DO 980 J = 1, N
  1923. DO 970 I = J, N
  1924. WORK( INDX ) = A( I, J )
  1925. INDX = INDX + 1
  1926. 970 CONTINUE
  1927. 980 CONTINUE
  1928. END IF
  1929. *
  1930. SRNAMT = 'DSPEVX'
  1931. CALL DSPEVX( 'N', 'I', UPLO, N, WORK, VL, VU, IL, IU,
  1932. $ ABSTOL, M3, WA3, Z, LDU, V, IWORK,
  1933. $ IWORK( 5*N+1 ), IINFO )
  1934. IF( IINFO.NE.0 ) THEN
  1935. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,I,' // UPLO //
  1936. $ ')', IINFO, N, JTYPE, IOLDSD
  1937. INFO = ABS( IINFO )
  1938. IF( IINFO.LT.0 ) THEN
  1939. RETURN
  1940. ELSE
  1941. RESULT( NTEST ) = ULPINV
  1942. GO TO 990
  1943. END IF
  1944. END IF
  1945. *
  1946. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  1947. RESULT( NTEST ) = ULPINV
  1948. GO TO 990
  1949. END IF
  1950. *
  1951. * Do test 45 (or +54)
  1952. *
  1953. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  1954. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  1955. IF( N.GT.0 ) THEN
  1956. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  1957. ELSE
  1958. TEMP3 = ZERO
  1959. END IF
  1960. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  1961. $ MAX( UNFL, TEMP3*ULP )
  1962. *
  1963. 990 CONTINUE
  1964. IF( IUPLO.EQ.1 ) THEN
  1965. INDX = 1
  1966. DO 1010 J = 1, N
  1967. DO 1000 I = 1, J
  1968. WORK( INDX ) = A( I, J )
  1969. INDX = INDX + 1
  1970. 1000 CONTINUE
  1971. 1010 CONTINUE
  1972. ELSE
  1973. INDX = 1
  1974. DO 1030 J = 1, N
  1975. DO 1020 I = J, N
  1976. WORK( INDX ) = A( I, J )
  1977. INDX = INDX + 1
  1978. 1020 CONTINUE
  1979. 1030 CONTINUE
  1980. END IF
  1981. *
  1982. NTEST = NTEST + 1
  1983. *
  1984. SRNAMT = 'DSPEVX'
  1985. CALL DSPEVX( 'V', 'V', UPLO, N, WORK, VL, VU, IL, IU,
  1986. $ ABSTOL, M2, WA2, Z, LDU, V, IWORK,
  1987. $ IWORK( 5*N+1 ), IINFO )
  1988. IF( IINFO.NE.0 ) THEN
  1989. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(V,V,' // UPLO //
  1990. $ ')', IINFO, N, JTYPE, IOLDSD
  1991. INFO = ABS( IINFO )
  1992. IF( IINFO.LT.0 ) THEN
  1993. RETURN
  1994. ELSE
  1995. RESULT( NTEST ) = ULPINV
  1996. RESULT( NTEST+1 ) = ULPINV
  1997. RESULT( NTEST+2 ) = ULPINV
  1998. GO TO 1080
  1999. END IF
  2000. END IF
  2001. *
  2002. * Do tests 46 and 47 (or +54)
  2003. *
  2004. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2005. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2006. *
  2007. NTEST = NTEST + 2
  2008. *
  2009. IF( IUPLO.EQ.1 ) THEN
  2010. INDX = 1
  2011. DO 1050 J = 1, N
  2012. DO 1040 I = 1, J
  2013. WORK( INDX ) = A( I, J )
  2014. INDX = INDX + 1
  2015. 1040 CONTINUE
  2016. 1050 CONTINUE
  2017. ELSE
  2018. INDX = 1
  2019. DO 1070 J = 1, N
  2020. DO 1060 I = J, N
  2021. WORK( INDX ) = A( I, J )
  2022. INDX = INDX + 1
  2023. 1060 CONTINUE
  2024. 1070 CONTINUE
  2025. END IF
  2026. *
  2027. SRNAMT = 'DSPEVX'
  2028. CALL DSPEVX( 'N', 'V', UPLO, N, WORK, VL, VU, IL, IU,
  2029. $ ABSTOL, M3, WA3, Z, LDU, V, IWORK,
  2030. $ IWORK( 5*N+1 ), IINFO )
  2031. IF( IINFO.NE.0 ) THEN
  2032. WRITE( NOUNIT, FMT = 9999 )'DSPEVX(N,V,' // UPLO //
  2033. $ ')', IINFO, N, JTYPE, IOLDSD
  2034. INFO = ABS( IINFO )
  2035. IF( IINFO.LT.0 ) THEN
  2036. RETURN
  2037. ELSE
  2038. RESULT( NTEST ) = ULPINV
  2039. GO TO 1080
  2040. END IF
  2041. END IF
  2042. *
  2043. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2044. RESULT( NTEST ) = ULPINV
  2045. GO TO 1080
  2046. END IF
  2047. *
  2048. * Do test 48 (or +54)
  2049. *
  2050. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2051. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2052. IF( N.GT.0 ) THEN
  2053. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2054. ELSE
  2055. TEMP3 = ZERO
  2056. END IF
  2057. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2058. $ MAX( UNFL, TEMP3*ULP )
  2059. *
  2060. 1080 CONTINUE
  2061. *
  2062. * 6) Call DSBEV and DSBEVX.
  2063. *
  2064. IF( JTYPE.LE.7 ) THEN
  2065. KD = 1
  2066. ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
  2067. KD = MAX( N-1, 0 )
  2068. ELSE
  2069. KD = IHBW
  2070. END IF
  2071. *
  2072. * Load array V with the upper or lower triangular part
  2073. * of the matrix in band form.
  2074. *
  2075. IF( IUPLO.EQ.1 ) THEN
  2076. DO 1100 J = 1, N
  2077. DO 1090 I = MAX( 1, J-KD ), J
  2078. V( KD+1+I-J, J ) = A( I, J )
  2079. 1090 CONTINUE
  2080. 1100 CONTINUE
  2081. ELSE
  2082. DO 1120 J = 1, N
  2083. DO 1110 I = J, MIN( N, J+KD )
  2084. V( 1+I-J, J ) = A( I, J )
  2085. 1110 CONTINUE
  2086. 1120 CONTINUE
  2087. END IF
  2088. *
  2089. NTEST = NTEST + 1
  2090. SRNAMT = 'DSBEV'
  2091. CALL DSBEV( 'V', UPLO, N, KD, V, LDU, D1, Z, LDU, WORK,
  2092. $ IINFO )
  2093. IF( IINFO.NE.0 ) THEN
  2094. WRITE( NOUNIT, FMT = 9999 )'DSBEV(V,' // UPLO // ')',
  2095. $ IINFO, N, JTYPE, IOLDSD
  2096. INFO = ABS( IINFO )
  2097. IF( IINFO.LT.0 ) THEN
  2098. RETURN
  2099. ELSE
  2100. RESULT( NTEST ) = ULPINV
  2101. RESULT( NTEST+1 ) = ULPINV
  2102. RESULT( NTEST+2 ) = ULPINV
  2103. GO TO 1180
  2104. END IF
  2105. END IF
  2106. *
  2107. * Do tests 49 and 50 (or ... )
  2108. *
  2109. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2110. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2111. *
  2112. IF( IUPLO.EQ.1 ) THEN
  2113. DO 1140 J = 1, N
  2114. DO 1130 I = MAX( 1, J-KD ), J
  2115. V( KD+1+I-J, J ) = A( I, J )
  2116. 1130 CONTINUE
  2117. 1140 CONTINUE
  2118. ELSE
  2119. DO 1160 J = 1, N
  2120. DO 1150 I = J, MIN( N, J+KD )
  2121. V( 1+I-J, J ) = A( I, J )
  2122. 1150 CONTINUE
  2123. 1160 CONTINUE
  2124. END IF
  2125. *
  2126. NTEST = NTEST + 2
  2127. SRNAMT = 'DSBEV_2STAGE'
  2128. CALL DSBEV_2STAGE( 'N', UPLO, N, KD, V, LDU, D3, Z, LDU,
  2129. $ WORK, LWORK, IINFO )
  2130. IF( IINFO.NE.0 ) THEN
  2131. WRITE( NOUNIT, FMT = 9999 )
  2132. $ 'DSBEV_2STAGE(N,' // UPLO // ')',
  2133. $ IINFO, N, JTYPE, IOLDSD
  2134. INFO = ABS( IINFO )
  2135. IF( IINFO.LT.0 ) THEN
  2136. RETURN
  2137. ELSE
  2138. RESULT( NTEST ) = ULPINV
  2139. GO TO 1180
  2140. END IF
  2141. END IF
  2142. *
  2143. * Do test 51 (or +54)
  2144. *
  2145. TEMP1 = ZERO
  2146. TEMP2 = ZERO
  2147. DO 1170 J = 1, N
  2148. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2149. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2150. 1170 CONTINUE
  2151. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2152. $ ULP*MAX( TEMP1, TEMP2 ) )
  2153. *
  2154. * Load array V with the upper or lower triangular part
  2155. * of the matrix in band form.
  2156. *
  2157. 1180 CONTINUE
  2158. IF( IUPLO.EQ.1 ) THEN
  2159. DO 1200 J = 1, N
  2160. DO 1190 I = MAX( 1, J-KD ), J
  2161. V( KD+1+I-J, J ) = A( I, J )
  2162. 1190 CONTINUE
  2163. 1200 CONTINUE
  2164. ELSE
  2165. DO 1220 J = 1, N
  2166. DO 1210 I = J, MIN( N, J+KD )
  2167. V( 1+I-J, J ) = A( I, J )
  2168. 1210 CONTINUE
  2169. 1220 CONTINUE
  2170. END IF
  2171. *
  2172. NTEST = NTEST + 1
  2173. SRNAMT = 'DSBEVX'
  2174. CALL DSBEVX( 'V', 'A', UPLO, N, KD, V, LDU, U, LDU, VL,
  2175. $ VU, IL, IU, ABSTOL, M, WA2, Z, LDU, WORK,
  2176. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2177. IF( IINFO.NE.0 ) THEN
  2178. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,A,' // UPLO //
  2179. $ ')', IINFO, N, JTYPE, IOLDSD
  2180. INFO = ABS( IINFO )
  2181. IF( IINFO.LT.0 ) THEN
  2182. RETURN
  2183. ELSE
  2184. RESULT( NTEST ) = ULPINV
  2185. RESULT( NTEST+1 ) = ULPINV
  2186. RESULT( NTEST+2 ) = ULPINV
  2187. GO TO 1280
  2188. END IF
  2189. END IF
  2190. *
  2191. * Do tests 52 and 53 (or +54)
  2192. *
  2193. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA2, D2, Z, LDU, V,
  2194. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2195. *
  2196. NTEST = NTEST + 2
  2197. *
  2198. IF( IUPLO.EQ.1 ) THEN
  2199. DO 1240 J = 1, N
  2200. DO 1230 I = MAX( 1, J-KD ), J
  2201. V( KD+1+I-J, J ) = A( I, J )
  2202. 1230 CONTINUE
  2203. 1240 CONTINUE
  2204. ELSE
  2205. DO 1260 J = 1, N
  2206. DO 1250 I = J, MIN( N, J+KD )
  2207. V( 1+I-J, J ) = A( I, J )
  2208. 1250 CONTINUE
  2209. 1260 CONTINUE
  2210. END IF
  2211. *
  2212. SRNAMT = 'DSBEVX_2STAGE'
  2213. CALL DSBEVX_2STAGE( 'N', 'A', UPLO, N, KD, V, LDU,
  2214. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2215. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2216. $ IINFO )
  2217. IF( IINFO.NE.0 ) THEN
  2218. WRITE( NOUNIT, FMT = 9999 )
  2219. $ 'DSBEVX_2STAGE(N,A,' // UPLO //
  2220. $ ')', IINFO, N, JTYPE, IOLDSD
  2221. INFO = ABS( IINFO )
  2222. IF( IINFO.LT.0 ) THEN
  2223. RETURN
  2224. ELSE
  2225. RESULT( NTEST ) = ULPINV
  2226. GO TO 1280
  2227. END IF
  2228. END IF
  2229. *
  2230. * Do test 54 (or +54)
  2231. *
  2232. TEMP1 = ZERO
  2233. TEMP2 = ZERO
  2234. DO 1270 J = 1, N
  2235. TEMP1 = MAX( TEMP1, ABS( WA2( J ) ), ABS( WA3( J ) ) )
  2236. TEMP2 = MAX( TEMP2, ABS( WA2( J )-WA3( J ) ) )
  2237. 1270 CONTINUE
  2238. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2239. $ ULP*MAX( TEMP1, TEMP2 ) )
  2240. *
  2241. 1280 CONTINUE
  2242. NTEST = NTEST + 1
  2243. IF( IUPLO.EQ.1 ) THEN
  2244. DO 1300 J = 1, N
  2245. DO 1290 I = MAX( 1, J-KD ), J
  2246. V( KD+1+I-J, J ) = A( I, J )
  2247. 1290 CONTINUE
  2248. 1300 CONTINUE
  2249. ELSE
  2250. DO 1320 J = 1, N
  2251. DO 1310 I = J, MIN( N, J+KD )
  2252. V( 1+I-J, J ) = A( I, J )
  2253. 1310 CONTINUE
  2254. 1320 CONTINUE
  2255. END IF
  2256. *
  2257. SRNAMT = 'DSBEVX'
  2258. CALL DSBEVX( 'V', 'I', UPLO, N, KD, V, LDU, U, LDU, VL,
  2259. $ VU, IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  2260. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2261. IF( IINFO.NE.0 ) THEN
  2262. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,I,' // UPLO //
  2263. $ ')', IINFO, N, JTYPE, IOLDSD
  2264. INFO = ABS( IINFO )
  2265. IF( IINFO.LT.0 ) THEN
  2266. RETURN
  2267. ELSE
  2268. RESULT( NTEST ) = ULPINV
  2269. RESULT( NTEST+1 ) = ULPINV
  2270. RESULT( NTEST+2 ) = ULPINV
  2271. GO TO 1370
  2272. END IF
  2273. END IF
  2274. *
  2275. * Do tests 55 and 56 (or +54)
  2276. *
  2277. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2278. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2279. *
  2280. NTEST = NTEST + 2
  2281. *
  2282. IF( IUPLO.EQ.1 ) THEN
  2283. DO 1340 J = 1, N
  2284. DO 1330 I = MAX( 1, J-KD ), J
  2285. V( KD+1+I-J, J ) = A( I, J )
  2286. 1330 CONTINUE
  2287. 1340 CONTINUE
  2288. ELSE
  2289. DO 1360 J = 1, N
  2290. DO 1350 I = J, MIN( N, J+KD )
  2291. V( 1+I-J, J ) = A( I, J )
  2292. 1350 CONTINUE
  2293. 1360 CONTINUE
  2294. END IF
  2295. *
  2296. SRNAMT = 'DSBEVX_2STAGE'
  2297. CALL DSBEVX_2STAGE( 'N', 'I', UPLO, N, KD, V, LDU,
  2298. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2299. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2300. $ IINFO )
  2301. IF( IINFO.NE.0 ) THEN
  2302. WRITE( NOUNIT, FMT = 9999 )
  2303. $ 'DSBEVX_2STAGE(N,I,' // UPLO //
  2304. $ ')', IINFO, N, JTYPE, IOLDSD
  2305. INFO = ABS( IINFO )
  2306. IF( IINFO.LT.0 ) THEN
  2307. RETURN
  2308. ELSE
  2309. RESULT( NTEST ) = ULPINV
  2310. GO TO 1370
  2311. END IF
  2312. END IF
  2313. *
  2314. * Do test 57 (or +54)
  2315. *
  2316. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2317. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2318. IF( N.GT.0 ) THEN
  2319. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2320. ELSE
  2321. TEMP3 = ZERO
  2322. END IF
  2323. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2324. $ MAX( UNFL, TEMP3*ULP )
  2325. *
  2326. 1370 CONTINUE
  2327. NTEST = NTEST + 1
  2328. IF( IUPLO.EQ.1 ) THEN
  2329. DO 1390 J = 1, N
  2330. DO 1380 I = MAX( 1, J-KD ), J
  2331. V( KD+1+I-J, J ) = A( I, J )
  2332. 1380 CONTINUE
  2333. 1390 CONTINUE
  2334. ELSE
  2335. DO 1410 J = 1, N
  2336. DO 1400 I = J, MIN( N, J+KD )
  2337. V( 1+I-J, J ) = A( I, J )
  2338. 1400 CONTINUE
  2339. 1410 CONTINUE
  2340. END IF
  2341. *
  2342. SRNAMT = 'DSBEVX'
  2343. CALL DSBEVX( 'V', 'V', UPLO, N, KD, V, LDU, U, LDU, VL,
  2344. $ VU, IL, IU, ABSTOL, M2, WA2, Z, LDU, WORK,
  2345. $ IWORK, IWORK( 5*N+1 ), IINFO )
  2346. IF( IINFO.NE.0 ) THEN
  2347. WRITE( NOUNIT, FMT = 9999 )'DSBEVX(V,V,' // UPLO //
  2348. $ ')', IINFO, N, JTYPE, IOLDSD
  2349. INFO = ABS( IINFO )
  2350. IF( IINFO.LT.0 ) THEN
  2351. RETURN
  2352. ELSE
  2353. RESULT( NTEST ) = ULPINV
  2354. RESULT( NTEST+1 ) = ULPINV
  2355. RESULT( NTEST+2 ) = ULPINV
  2356. GO TO 1460
  2357. END IF
  2358. END IF
  2359. *
  2360. * Do tests 58 and 59 (or +54)
  2361. *
  2362. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2363. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2364. *
  2365. NTEST = NTEST + 2
  2366. *
  2367. IF( IUPLO.EQ.1 ) THEN
  2368. DO 1430 J = 1, N
  2369. DO 1420 I = MAX( 1, J-KD ), J
  2370. V( KD+1+I-J, J ) = A( I, J )
  2371. 1420 CONTINUE
  2372. 1430 CONTINUE
  2373. ELSE
  2374. DO 1450 J = 1, N
  2375. DO 1440 I = J, MIN( N, J+KD )
  2376. V( 1+I-J, J ) = A( I, J )
  2377. 1440 CONTINUE
  2378. 1450 CONTINUE
  2379. END IF
  2380. *
  2381. SRNAMT = 'DSBEVX_2STAGE'
  2382. CALL DSBEVX_2STAGE( 'N', 'V', UPLO, N, KD, V, LDU,
  2383. $ U, LDU, VL, VU, IL, IU, ABSTOL, M3, WA3,
  2384. $ Z, LDU, WORK, LWORK, IWORK, IWORK( 5*N+1 ),
  2385. $ IINFO )
  2386. IF( IINFO.NE.0 ) THEN
  2387. WRITE( NOUNIT, FMT = 9999 )
  2388. $ 'DSBEVX_2STAGE(N,V,' // UPLO //
  2389. $ ')', IINFO, N, JTYPE, IOLDSD
  2390. INFO = ABS( IINFO )
  2391. IF( IINFO.LT.0 ) THEN
  2392. RETURN
  2393. ELSE
  2394. RESULT( NTEST ) = ULPINV
  2395. GO TO 1460
  2396. END IF
  2397. END IF
  2398. *
  2399. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2400. RESULT( NTEST ) = ULPINV
  2401. GO TO 1460
  2402. END IF
  2403. *
  2404. * Do test 60 (or +54)
  2405. *
  2406. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2407. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2408. IF( N.GT.0 ) THEN
  2409. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2410. ELSE
  2411. TEMP3 = ZERO
  2412. END IF
  2413. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2414. $ MAX( UNFL, TEMP3*ULP )
  2415. *
  2416. 1460 CONTINUE
  2417. *
  2418. * 7) Call DSYEVD
  2419. *
  2420. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  2421. *
  2422. NTEST = NTEST + 1
  2423. SRNAMT = 'DSYEVD'
  2424. CALL DSYEVD( 'V', UPLO, N, A, LDU, D1, WORK, LWEDC,
  2425. $ IWORK, LIWEDC, IINFO )
  2426. IF( IINFO.NE.0 ) THEN
  2427. WRITE( NOUNIT, FMT = 9999 )'DSYEVD(V,' // UPLO //
  2428. $ ')', IINFO, N, JTYPE, IOLDSD
  2429. INFO = ABS( IINFO )
  2430. IF( IINFO.LT.0 ) THEN
  2431. RETURN
  2432. ELSE
  2433. RESULT( NTEST ) = ULPINV
  2434. RESULT( NTEST+1 ) = ULPINV
  2435. RESULT( NTEST+2 ) = ULPINV
  2436. GO TO 1480
  2437. END IF
  2438. END IF
  2439. *
  2440. * Do tests 61 and 62 (or +54)
  2441. *
  2442. CALL DSYT21( 1, UPLO, N, 0, V, LDU, D1, D2, A, LDU, Z,
  2443. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2444. *
  2445. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2446. *
  2447. NTEST = NTEST + 2
  2448. SRNAMT = 'DSYEVD_2STAGE'
  2449. CALL DSYEVD_2STAGE( 'N', UPLO, N, A, LDU, D3, WORK,
  2450. $ LWORK, IWORK, LIWEDC, IINFO )
  2451. IF( IINFO.NE.0 ) THEN
  2452. WRITE( NOUNIT, FMT = 9999 )
  2453. $ 'DSYEVD_2STAGE(N,' // UPLO //
  2454. $ ')', IINFO, N, JTYPE, IOLDSD
  2455. INFO = ABS( IINFO )
  2456. IF( IINFO.LT.0 ) THEN
  2457. RETURN
  2458. ELSE
  2459. RESULT( NTEST ) = ULPINV
  2460. GO TO 1480
  2461. END IF
  2462. END IF
  2463. *
  2464. * Do test 63 (or +54)
  2465. *
  2466. TEMP1 = ZERO
  2467. TEMP2 = ZERO
  2468. DO 1470 J = 1, N
  2469. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2470. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2471. 1470 CONTINUE
  2472. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2473. $ ULP*MAX( TEMP1, TEMP2 ) )
  2474. *
  2475. 1480 CONTINUE
  2476. *
  2477. * 8) Call DSPEVD.
  2478. *
  2479. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2480. *
  2481. * Load array WORK with the upper or lower triangular
  2482. * part of the matrix in packed form.
  2483. *
  2484. IF( IUPLO.EQ.1 ) THEN
  2485. INDX = 1
  2486. DO 1500 J = 1, N
  2487. DO 1490 I = 1, J
  2488. WORK( INDX ) = A( I, J )
  2489. INDX = INDX + 1
  2490. 1490 CONTINUE
  2491. 1500 CONTINUE
  2492. ELSE
  2493. INDX = 1
  2494. DO 1520 J = 1, N
  2495. DO 1510 I = J, N
  2496. WORK( INDX ) = A( I, J )
  2497. INDX = INDX + 1
  2498. 1510 CONTINUE
  2499. 1520 CONTINUE
  2500. END IF
  2501. *
  2502. NTEST = NTEST + 1
  2503. SRNAMT = 'DSPEVD'
  2504. CALL DSPEVD( 'V', UPLO, N, WORK, D1, Z, LDU,
  2505. $ WORK( INDX ), LWEDC-INDX+1, IWORK, LIWEDC,
  2506. $ IINFO )
  2507. IF( IINFO.NE.0 ) THEN
  2508. WRITE( NOUNIT, FMT = 9999 )'DSPEVD(V,' // UPLO //
  2509. $ ')', IINFO, N, JTYPE, IOLDSD
  2510. INFO = ABS( IINFO )
  2511. IF( IINFO.LT.0 ) THEN
  2512. RETURN
  2513. ELSE
  2514. RESULT( NTEST ) = ULPINV
  2515. RESULT( NTEST+1 ) = ULPINV
  2516. RESULT( NTEST+2 ) = ULPINV
  2517. GO TO 1580
  2518. END IF
  2519. END IF
  2520. *
  2521. * Do tests 64 and 65 (or +54)
  2522. *
  2523. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2524. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2525. *
  2526. IF( IUPLO.EQ.1 ) THEN
  2527. INDX = 1
  2528. DO 1540 J = 1, N
  2529. DO 1530 I = 1, J
  2530. *
  2531. WORK( INDX ) = A( I, J )
  2532. INDX = INDX + 1
  2533. 1530 CONTINUE
  2534. 1540 CONTINUE
  2535. ELSE
  2536. INDX = 1
  2537. DO 1560 J = 1, N
  2538. DO 1550 I = J, N
  2539. WORK( INDX ) = A( I, J )
  2540. INDX = INDX + 1
  2541. 1550 CONTINUE
  2542. 1560 CONTINUE
  2543. END IF
  2544. *
  2545. NTEST = NTEST + 2
  2546. SRNAMT = 'DSPEVD'
  2547. CALL DSPEVD( 'N', UPLO, N, WORK, D3, Z, LDU,
  2548. $ WORK( INDX ), LWEDC-INDX+1, IWORK, LIWEDC,
  2549. $ IINFO )
  2550. IF( IINFO.NE.0 ) THEN
  2551. WRITE( NOUNIT, FMT = 9999 )'DSPEVD(N,' // UPLO //
  2552. $ ')', IINFO, N, JTYPE, IOLDSD
  2553. INFO = ABS( IINFO )
  2554. IF( IINFO.LT.0 ) THEN
  2555. RETURN
  2556. ELSE
  2557. RESULT( NTEST ) = ULPINV
  2558. GO TO 1580
  2559. END IF
  2560. END IF
  2561. *
  2562. * Do test 66 (or +54)
  2563. *
  2564. TEMP1 = ZERO
  2565. TEMP2 = ZERO
  2566. DO 1570 J = 1, N
  2567. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2568. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2569. 1570 CONTINUE
  2570. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2571. $ ULP*MAX( TEMP1, TEMP2 ) )
  2572. 1580 CONTINUE
  2573. *
  2574. * 9) Call DSBEVD.
  2575. *
  2576. IF( JTYPE.LE.7 ) THEN
  2577. KD = 1
  2578. ELSE IF( JTYPE.GE.8 .AND. JTYPE.LE.15 ) THEN
  2579. KD = MAX( N-1, 0 )
  2580. ELSE
  2581. KD = IHBW
  2582. END IF
  2583. *
  2584. * Load array V with the upper or lower triangular part
  2585. * of the matrix in band form.
  2586. *
  2587. IF( IUPLO.EQ.1 ) THEN
  2588. DO 1600 J = 1, N
  2589. DO 1590 I = MAX( 1, J-KD ), J
  2590. V( KD+1+I-J, J ) = A( I, J )
  2591. 1590 CONTINUE
  2592. 1600 CONTINUE
  2593. ELSE
  2594. DO 1620 J = 1, N
  2595. DO 1610 I = J, MIN( N, J+KD )
  2596. V( 1+I-J, J ) = A( I, J )
  2597. 1610 CONTINUE
  2598. 1620 CONTINUE
  2599. END IF
  2600. *
  2601. NTEST = NTEST + 1
  2602. SRNAMT = 'DSBEVD'
  2603. CALL DSBEVD( 'V', UPLO, N, KD, V, LDU, D1, Z, LDU, WORK,
  2604. $ LWEDC, IWORK, LIWEDC, IINFO )
  2605. IF( IINFO.NE.0 ) THEN
  2606. WRITE( NOUNIT, FMT = 9999 )'DSBEVD(V,' // UPLO //
  2607. $ ')', IINFO, N, JTYPE, IOLDSD
  2608. INFO = ABS( IINFO )
  2609. IF( IINFO.LT.0 ) THEN
  2610. RETURN
  2611. ELSE
  2612. RESULT( NTEST ) = ULPINV
  2613. RESULT( NTEST+1 ) = ULPINV
  2614. RESULT( NTEST+2 ) = ULPINV
  2615. GO TO 1680
  2616. END IF
  2617. END IF
  2618. *
  2619. * Do tests 67 and 68 (or +54)
  2620. *
  2621. CALL DSYT21( 1, UPLO, N, 0, A, LDA, D1, D2, Z, LDU, V,
  2622. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2623. *
  2624. IF( IUPLO.EQ.1 ) THEN
  2625. DO 1640 J = 1, N
  2626. DO 1630 I = MAX( 1, J-KD ), J
  2627. V( KD+1+I-J, J ) = A( I, J )
  2628. 1630 CONTINUE
  2629. 1640 CONTINUE
  2630. ELSE
  2631. DO 1660 J = 1, N
  2632. DO 1650 I = J, MIN( N, J+KD )
  2633. V( 1+I-J, J ) = A( I, J )
  2634. 1650 CONTINUE
  2635. 1660 CONTINUE
  2636. END IF
  2637. *
  2638. NTEST = NTEST + 2
  2639. SRNAMT = 'DSBEVD_2STAGE'
  2640. CALL DSBEVD_2STAGE( 'N', UPLO, N, KD, V, LDU, D3, Z, LDU,
  2641. $ WORK, LWORK, IWORK, LIWEDC, IINFO )
  2642. IF( IINFO.NE.0 ) THEN
  2643. WRITE( NOUNIT, FMT = 9999 )
  2644. $ 'DSBEVD_2STAGE(N,' // UPLO //
  2645. $ ')', IINFO, N, JTYPE, IOLDSD
  2646. INFO = ABS( IINFO )
  2647. IF( IINFO.LT.0 ) THEN
  2648. RETURN
  2649. ELSE
  2650. RESULT( NTEST ) = ULPINV
  2651. GO TO 1680
  2652. END IF
  2653. END IF
  2654. *
  2655. * Do test 69 (or +54)
  2656. *
  2657. TEMP1 = ZERO
  2658. TEMP2 = ZERO
  2659. DO 1670 J = 1, N
  2660. TEMP1 = MAX( TEMP1, ABS( D1( J ) ), ABS( D3( J ) ) )
  2661. TEMP2 = MAX( TEMP2, ABS( D1( J )-D3( J ) ) )
  2662. 1670 CONTINUE
  2663. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2664. $ ULP*MAX( TEMP1, TEMP2 ) )
  2665. *
  2666. 1680 CONTINUE
  2667. *
  2668. *
  2669. CALL DLACPY( ' ', N, N, A, LDA, V, LDU )
  2670. NTEST = NTEST + 1
  2671. SRNAMT = 'DSYEVR'
  2672. CALL DSYEVR( 'V', 'A', UPLO, N, A, LDU, VL, VU, IL, IU,
  2673. $ ABSTOL, M, WA1, Z, LDU, IWORK, WORK, LWORK,
  2674. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2675. IF( IINFO.NE.0 ) THEN
  2676. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,A,' // UPLO //
  2677. $ ')', IINFO, N, JTYPE, IOLDSD
  2678. INFO = ABS( IINFO )
  2679. IF( IINFO.LT.0 ) THEN
  2680. RETURN
  2681. ELSE
  2682. RESULT( NTEST ) = ULPINV
  2683. RESULT( NTEST+1 ) = ULPINV
  2684. RESULT( NTEST+2 ) = ULPINV
  2685. GO TO 1700
  2686. END IF
  2687. END IF
  2688. *
  2689. * Do tests 70 and 71 (or ... )
  2690. *
  2691. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2692. *
  2693. CALL DSYT21( 1, UPLO, N, 0, A, LDU, WA1, D2, Z, LDU, V,
  2694. $ LDU, TAU, WORK, RESULT( NTEST ) )
  2695. *
  2696. NTEST = NTEST + 2
  2697. SRNAMT = 'DSYEVR_2STAGE'
  2698. CALL DSYEVR_2STAGE( 'N', 'A', UPLO, N, A, LDU, VL, VU,
  2699. $ IL, IU, ABSTOL, M2, WA2, Z, LDU, IWORK,
  2700. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2701. $ IINFO )
  2702. IF( IINFO.NE.0 ) THEN
  2703. WRITE( NOUNIT, FMT = 9999 )
  2704. $ 'DSYEVR_2STAGE(N,A,' // UPLO //
  2705. $ ')', IINFO, N, JTYPE, IOLDSD
  2706. INFO = ABS( IINFO )
  2707. IF( IINFO.LT.0 ) THEN
  2708. RETURN
  2709. ELSE
  2710. RESULT( NTEST ) = ULPINV
  2711. GO TO 1700
  2712. END IF
  2713. END IF
  2714. *
  2715. * Do test 72 (or ... )
  2716. *
  2717. TEMP1 = ZERO
  2718. TEMP2 = ZERO
  2719. DO 1690 J = 1, N
  2720. TEMP1 = MAX( TEMP1, ABS( WA1( J ) ), ABS( WA2( J ) ) )
  2721. TEMP2 = MAX( TEMP2, ABS( WA1( J )-WA2( J ) ) )
  2722. 1690 CONTINUE
  2723. RESULT( NTEST ) = TEMP2 / MAX( UNFL,
  2724. $ ULP*MAX( TEMP1, TEMP2 ) )
  2725. *
  2726. 1700 CONTINUE
  2727. *
  2728. NTEST = NTEST + 1
  2729. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2730. SRNAMT = 'DSYEVR'
  2731. CALL DSYEVR( 'V', 'I', UPLO, N, A, LDU, VL, VU, IL, IU,
  2732. $ ABSTOL, M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  2733. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2734. IF( IINFO.NE.0 ) THEN
  2735. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,I,' // UPLO //
  2736. $ ')', IINFO, N, JTYPE, IOLDSD
  2737. INFO = ABS( IINFO )
  2738. IF( IINFO.LT.0 ) THEN
  2739. RETURN
  2740. ELSE
  2741. RESULT( NTEST ) = ULPINV
  2742. RESULT( NTEST+1 ) = ULPINV
  2743. RESULT( NTEST+2 ) = ULPINV
  2744. GO TO 1710
  2745. END IF
  2746. END IF
  2747. *
  2748. * Do tests 73 and 74 (or +54)
  2749. *
  2750. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2751. *
  2752. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2753. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2754. *
  2755. NTEST = NTEST + 2
  2756. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2757. SRNAMT = 'DSYEVR_2STAGE'
  2758. CALL DSYEVR_2STAGE( 'N', 'I', UPLO, N, A, LDU, VL, VU,
  2759. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, IWORK,
  2760. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2761. $ IINFO )
  2762. IF( IINFO.NE.0 ) THEN
  2763. WRITE( NOUNIT, FMT = 9999 )
  2764. $ 'DSYEVR_2STAGE(N,I,' // UPLO //
  2765. $ ')', IINFO, N, JTYPE, IOLDSD
  2766. INFO = ABS( IINFO )
  2767. IF( IINFO.LT.0 ) THEN
  2768. RETURN
  2769. ELSE
  2770. RESULT( NTEST ) = ULPINV
  2771. GO TO 1710
  2772. END IF
  2773. END IF
  2774. *
  2775. * Do test 75 (or +54)
  2776. *
  2777. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2778. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2779. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2780. $ MAX( UNFL, ULP*TEMP3 )
  2781. 1710 CONTINUE
  2782. *
  2783. NTEST = NTEST + 1
  2784. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2785. SRNAMT = 'DSYEVR'
  2786. CALL DSYEVR( 'V', 'V', UPLO, N, A, LDU, VL, VU, IL, IU,
  2787. $ ABSTOL, M2, WA2, Z, LDU, IWORK, WORK, LWORK,
  2788. $ IWORK(2*N+1), LIWORK-2*N, IINFO )
  2789. IF( IINFO.NE.0 ) THEN
  2790. WRITE( NOUNIT, FMT = 9999 )'DSYEVR(V,V,' // UPLO //
  2791. $ ')', IINFO, N, JTYPE, IOLDSD
  2792. INFO = ABS( IINFO )
  2793. IF( IINFO.LT.0 ) THEN
  2794. RETURN
  2795. ELSE
  2796. RESULT( NTEST ) = ULPINV
  2797. RESULT( NTEST+1 ) = ULPINV
  2798. RESULT( NTEST+2 ) = ULPINV
  2799. GO TO 700
  2800. END IF
  2801. END IF
  2802. *
  2803. * Do tests 76 and 77 (or +54)
  2804. *
  2805. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2806. *
  2807. CALL DSYT22( 1, UPLO, N, M2, 0, A, LDU, WA2, D2, Z, LDU,
  2808. $ V, LDU, TAU, WORK, RESULT( NTEST ) )
  2809. *
  2810. NTEST = NTEST + 2
  2811. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2812. SRNAMT = 'DSYEVR_2STAGE'
  2813. CALL DSYEVR_2STAGE( 'N', 'V', UPLO, N, A, LDU, VL, VU,
  2814. $ IL, IU, ABSTOL, M3, WA3, Z, LDU, IWORK,
  2815. $ WORK, LWORK, IWORK(2*N+1), LIWORK-2*N,
  2816. $ IINFO )
  2817. IF( IINFO.NE.0 ) THEN
  2818. WRITE( NOUNIT, FMT = 9999 )
  2819. $ 'DSYEVR_2STAGE(N,V,' // UPLO //
  2820. $ ')', IINFO, N, JTYPE, IOLDSD
  2821. INFO = ABS( IINFO )
  2822. IF( IINFO.LT.0 ) THEN
  2823. RETURN
  2824. ELSE
  2825. RESULT( NTEST ) = ULPINV
  2826. GO TO 700
  2827. END IF
  2828. END IF
  2829. *
  2830. IF( M3.EQ.0 .AND. N.GT.0 ) THEN
  2831. RESULT( NTEST ) = ULPINV
  2832. GO TO 700
  2833. END IF
  2834. *
  2835. * Do test 78 (or +54)
  2836. *
  2837. TEMP1 = DSXT1( 1, WA2, M2, WA3, M3, ABSTOL, ULP, UNFL )
  2838. TEMP2 = DSXT1( 1, WA3, M3, WA2, M2, ABSTOL, ULP, UNFL )
  2839. IF( N.GT.0 ) THEN
  2840. TEMP3 = MAX( ABS( WA1( 1 ) ), ABS( WA1( N ) ) )
  2841. ELSE
  2842. TEMP3 = ZERO
  2843. END IF
  2844. RESULT( NTEST ) = ( TEMP1+TEMP2 ) /
  2845. $ MAX( UNFL, TEMP3*ULP )
  2846. *
  2847. CALL DLACPY( ' ', N, N, V, LDU, A, LDA )
  2848. *
  2849. 1720 CONTINUE
  2850. *
  2851. * End of Loop -- Check for RESULT(j) > THRESH
  2852. *
  2853. NTESTT = NTESTT + NTEST
  2854. *
  2855. CALL DLAFTS( 'DST', N, N, JTYPE, NTEST, RESULT, IOLDSD,
  2856. $ THRESH, NOUNIT, NERRS )
  2857. *
  2858. 1730 CONTINUE
  2859. 1740 CONTINUE
  2860. *
  2861. * Summary
  2862. *
  2863. CALL ALASVM( 'DST', NOUNIT, NERRS, NTESTT, 0 )
  2864. *
  2865. 9999 FORMAT( ' DDRVST2STG: ', A, ' returned INFO=', I6, '.', / 9X,
  2866. $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' )
  2867. *
  2868. RETURN
  2869. *
  2870. * End of DDRVST2STG
  2871. *
  2872. END