84 EXTERNAL lsame, lsamen
90 sord = lsame( path,
'S' ) .OR. lsame( path,
'D' )
91 corz = lsame( path,
'C' ) .OR. lsame( path,
'Z' )
92 IF( .NOT.sord .AND. .NOT.corz )
THEN
93 WRITE( iounit, fmt = 9999 )path
97 IF( lsamen( 2, c2,
'HS' ) )
THEN
102 WRITE( iounit, fmt = 9998 )path
106 WRITE( iounit, fmt = 9988 )
107 WRITE( iounit, fmt = 9987 )
108 WRITE( iounit, fmt = 9986 )
'pairs ',
'pairs ',
'prs.',
110 WRITE( iounit, fmt = 9985 )
114 WRITE( iounit, fmt = 9984 )
'orthogonal',
'''=transpose',
121 WRITE( iounit, fmt = 9997 )path
125 WRITE( iounit, fmt = 9988 )
126 WRITE( iounit, fmt = 9987 )
127 WRITE( iounit, fmt = 9986 )
'e.vals',
'e.vals',
'e.vs',
129 WRITE( iounit, fmt = 9985 )
133 WRITE( iounit, fmt = 9984 )
'unitary',
'*=conj.transp.',
137 ELSE IF( lsamen( 2, c2,
'ST' ) )
THEN
143 WRITE( iounit, fmt = 9996 )path
147 WRITE( iounit, fmt = 9983 )
148 WRITE( iounit, fmt = 9982 )
149 WRITE( iounit, fmt = 9981 )
'Symmetric'
153 WRITE( iounit, fmt = 9968 )
159 WRITE( iounit, fmt = 9995 )path
163 WRITE( iounit, fmt = 9983 )
164 WRITE( iounit, fmt = 9982 )
165 WRITE( iounit, fmt = 9981 )
'Hermitian'
169 WRITE( iounit, fmt = 9967 )
172 ELSE IF( lsamen( 2, c2,
'SG' ) )
THEN
178 WRITE( iounit, fmt = 9992 )path
182 WRITE( iounit, fmt = 9980 )
183 WRITE( iounit, fmt = 9979 )
184 WRITE( iounit, fmt = 9978 )
'Symmetric'
188 WRITE( iounit, fmt = 9977 )
189 WRITE( iounit, fmt = 9976 )
195 WRITE( iounit, fmt = 9991 )path
199 WRITE( iounit, fmt = 9980 )
200 WRITE( iounit, fmt = 9979 )
201 WRITE( iounit, fmt = 9978 )
'Hermitian'
205 WRITE( iounit, fmt = 9975 )
206 WRITE( iounit, fmt = 9974 )
210 ELSE IF( lsamen( 2, c2,
'BD' ) )
THEN
216 WRITE( iounit, fmt = 9994 )path
220 WRITE( iounit, fmt = 9973 )
224 WRITE( iounit, fmt = 9972 )
'orthogonal'
225 WRITE( iounit, fmt = 9971 )
230 WRITE( iounit, fmt = 9993 )path
234 WRITE( iounit, fmt = 9973 )
238 WRITE( iounit, fmt = 9972 )
'unitary '
239 WRITE( iounit, fmt = 9971 )
242 ELSE IF( lsamen( 2, c2,
'BB' ) )
THEN
248 WRITE( iounit, fmt = 9990 )path
252 WRITE( iounit, fmt = 9970 )
256 WRITE( iounit, fmt = 9969 )
'orthogonal'
261 WRITE( iounit, fmt = 9989 )path
265 WRITE( iounit, fmt = 9970 )
269 WRITE( iounit, fmt = 9969 )
'unitary '
274 WRITE( iounit, fmt = 9999 )path
280 9999
FORMAT( 1x, a3,
': no header available' )
281 9998
FORMAT( / 1x, a3,
' -- Real Non-symmetric eigenvalue problem' )
282 9997
FORMAT( / 1x, a3,
' -- Complex Non-symmetric eigenvalue problem' )
283 9996
FORMAT( / 1x, a3,
' -- Real Symmetric eigenvalue problem' )
284 9995
FORMAT( / 1x, a3,
' -- Complex Hermitian eigenvalue problem' )
285 9994
FORMAT( / 1x, a3,
' -- Real Singular Value Decomposition' )
286 9993
FORMAT( / 1x, a3,
' -- Complex Singular Value Decomposition' )
287 9992
FORMAT( / 1x, a3,
' -- Real Symmetric Generalized eigenvalue ',
289 9991
FORMAT( / 1x, a3,
' -- Complex Hermitian Generalized eigenvalue ',
291 9990
FORMAT( / 1x, a3,
' -- Real Band reduc. to bidiagonal form' )
292 9989
FORMAT( / 1x, a3,
' -- Complex Band reduc. to bidiagonal form' )
294 9988
FORMAT(
' Matrix types (see xCHKHS for details): ' )
296 9987
FORMAT( /
' Special Matrices:', /
' 1=Zero matrix. ',
297 $
' ',
' 5=Diagonal: geometr. spaced entries.',
298 $ /
' 2=Identity matrix. ',
' 6=Diagona',
299 $
'l: clustered entries.', /
' 3=Transposed Jordan block. ',
300 $
' ',
' 7=Diagonal: large, evenly spaced.', /
' ',
301 $
'4=Diagonal: evenly spaced entries. ',
' 8=Diagonal: s',
302 $
'mall, evenly spaced.' )
303 9986
FORMAT(
' Dense, Non-Symmetric Matrices:', /
' 9=Well-cond., ev',
304 $
'enly spaced eigenvals.',
' 14=Ill-cond., geomet. spaced e',
305 $
'igenals.', /
' 10=Well-cond., geom. spaced eigenvals. ',
306 $
' 15=Ill-conditioned, clustered e.vals.', /
' 11=Well-cond',
307 $
'itioned, clustered e.vals. ',
' 16=Ill-cond., random comp',
308 $
'lex ', a6, /
' 12=Well-cond., random complex ', a6,
' ',
309 $
' 17=Ill-cond., large rand. complx ', a4, /
' 13=Ill-condi',
310 $
'tioned, evenly spaced. ',
' 18=Ill-cond., small rand.',
312 9985
FORMAT(
' 19=Matrix with random O(1) entries. ',
' 21=Matrix ',
313 $
'with small random entries.', /
' 20=Matrix with large ran',
315 9984
FORMAT( /
' Tests performed: ',
'(H is Hessenberg, T is Schur,',
316 $
' U and Z are ', a,
',', / 20x, a,
', W is a diagonal matr',
317 $
'ix of eigenvalues,', / 20x,
'L and R are the left and rig',
318 $
'ht eigenvector matrices)', /
' 1 = | A - U H U', a1,
' |',
319 $
' / ( |A| n ulp ) ',
' 2 = | I - U U', a1,
' | / ',
320 $
'( n ulp )', /
' 3 = | H - Z T Z', a1,
' | / ( |H| n ulp ',
321 $
') ',
' 4 = | I - Z Z', a1,
' | / ( n ulp )',
322 $ /
' 5 = | A - UZ T (UZ)', a1,
' | / ( |A| n ulp ) ',
323 $
' 6 = | I - UZ (UZ)', a1,
' | / ( n ulp )', /
' 7 = | T(',
324 $
'e.vects.) - T(no e.vects.) | / ( |T| ulp )', /
' 8 = | W',
325 $
'(e.vects.) - W(no e.vects.) | / ( |W| ulp )', /
' 9 = | ',
326 $
'TR - RW | / ( |T| |R| ulp ) ',
' 10 = | LT - WL | / (',
327 $
' |T| |L| ulp )', /
' 11= |HX - XW| / (|H| |X| ulp) (inv.',
328 $
'it)',
' 12= |YH - WY| / (|H| |Y| ulp) (inv.it)' )
332 9983
FORMAT(
' Matrix types (see xDRVST for details): ' )
334 9982
FORMAT( /
' Special Matrices:', /
' 1=Zero matrix. ',
335 $
' ',
' 5=Diagonal: clustered entries.', /
' 2=',
336 $
'Identity matrix. ',
' 6=Diagonal: lar',
337 $
'ge, evenly spaced.', /
' 3=Diagonal: evenly spaced entri',
338 $
'es. ',
' 7=Diagonal: small, evenly spaced.', /
' 4=D',
339 $
'iagonal: geometr. spaced entries.' )
340 9981
FORMAT(
' Dense ', a,
' Matrices:', /
' 8=Evenly spaced eigen',
341 $
'vals. ',
' 12=Small, evenly spaced eigenvals.',
342 $ /
' 9=Geometrically spaced eigenvals. ',
' 13=Matrix ',
343 $
'with random O(1) entries.', /
' 10=Clustered eigenvalues.',
344 $
' ',
' 14=Matrix with large random entries.',
345 $ /
' 11=Large, evenly spaced eigenvals. ',
' 15=Matrix ',
346 $
'with small random entries.' )
350 9980
FORMAT(
' Matrix types (see xDRVSG for details): ' )
352 9979
FORMAT( /
' Special Matrices:', /
' 1=Zero matrix. ',
353 $
' ',
' 5=Diagonal: clustered entries.', /
' 2=',
354 $
'Identity matrix. ',
' 6=Diagonal: lar',
355 $
'ge, evenly spaced.', /
' 3=Diagonal: evenly spaced entri',
356 $
'es. ',
' 7=Diagonal: small, evenly spaced.', /
' 4=D',
357 $
'iagonal: geometr. spaced entries.' )
358 9978
FORMAT(
' Dense or Banded ', a,
' Matrices: ',
359 $ /
' 8=Evenly spaced eigenvals. ',
360 $
' 15=Matrix with small random entries.',
361 $ /
' 9=Geometrically spaced eigenvals. ',
362 $
' 16=Evenly spaced eigenvals, KA=1, KB=1.',
363 $ /
' 10=Clustered eigenvalues. ',
364 $
' 17=Evenly spaced eigenvals, KA=2, KB=1.',
365 $ /
' 11=Large, evenly spaced eigenvals. ',
366 $
' 18=Evenly spaced eigenvals, KA=2, KB=2.',
367 $ /
' 12=Small, evenly spaced eigenvals. ',
368 $
' 19=Evenly spaced eigenvals, KA=3, KB=1.',
369 $ /
' 13=Matrix with random O(1) entries. ',
370 $
' 20=Evenly spaced eigenvals, KA=3, KB=2.',
371 $ /
' 14=Matrix with large random entries.',
372 $
' 21=Evenly spaced eigenvals, KA=3, KB=3.' )
373 9977
FORMAT( /
' Tests performed: ',
374 $ /
'( For each pair (A,B), where A is of the given type ',
375 $ /
' and B is a random well-conditioned matrix. D is ',
376 $ /
' diagonal, and Z is orthogonal. )',
377 $ /
' 1 = SSYGV, with ITYPE=1 and UPLO=''U'':',
378 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
379 $ /
' 2 = SSPGV, with ITYPE=1 and UPLO=''U'':',
380 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
381 $ /
' 3 = SSBGV, with ITYPE=1 and UPLO=''U'':',
382 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
383 $ /
' 4 = SSYGV, with ITYPE=1 and UPLO=''L'':',
384 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
385 $ /
' 5 = SSPGV, with ITYPE=1 and UPLO=''L'':',
386 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
387 $ /
' 6 = SSBGV, with ITYPE=1 and UPLO=''L'':',
388 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ' )
389 9976
FORMAT(
' 7 = SSYGV, with ITYPE=2 and UPLO=''U'':',
390 $
' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
391 $ /
' 8 = SSPGV, with ITYPE=2 and UPLO=''U'':',
392 $
' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
393 $ /
' 9 = SSPGV, with ITYPE=2 and UPLO=''L'':',
394 $
' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
395 $ /
'10 = SSPGV, with ITYPE=2 and UPLO=''L'':',
396 $
' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
397 $ /
'11 = SSYGV, with ITYPE=3 and UPLO=''U'':',
398 $
' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
399 $ /
'12 = SSPGV, with ITYPE=3 and UPLO=''U'':',
400 $
' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
401 $ /
'13 = SSYGV, with ITYPE=3 and UPLO=''L'':',
402 $
' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
403 $ /
'14 = SSPGV, with ITYPE=3 and UPLO=''L'':',
404 $
' | B A Z - Z D | / ( |A| |Z| n ulp ) ' )
405 9975
FORMAT( /
' Tests performed: ',
406 $ /
'( For each pair (A,B), where A is of the given type ',
407 $ /
' and B is a random well-conditioned matrix. D is ',
408 $ /
' diagonal, and Z is unitary. )',
409 $ /
' 1 = CHEGV, with ITYPE=1 and UPLO=''U'':',
410 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
411 $ /
' 2 = CHPGV, with ITYPE=1 and UPLO=''U'':',
412 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
413 $ /
' 3 = CHBGV, with ITYPE=1 and UPLO=''U'':',
414 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
415 $ /
' 4 = CHEGV, with ITYPE=1 and UPLO=''L'':',
416 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
417 $ /
' 5 = CHPGV, with ITYPE=1 and UPLO=''L'':',
418 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ',
419 $ /
' 6 = CHBGV, with ITYPE=1 and UPLO=''L'':',
420 $
' | A Z - B Z D | / ( |A| |Z| n ulp ) ' )
421 9974
FORMAT(
' 7 = CHEGV, with ITYPE=2 and UPLO=''U'':',
422 $
' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
423 $ /
' 8 = CHPGV, with ITYPE=2 and UPLO=''U'':',
424 $
' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
425 $ /
' 9 = CHPGV, with ITYPE=2 and UPLO=''L'':',
426 $
' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
427 $ /
'10 = CHPGV, with ITYPE=2 and UPLO=''L'':',
428 $
' | A B Z - Z D | / ( |A| |Z| n ulp ) ',
429 $ /
'11 = CHEGV, with ITYPE=3 and UPLO=''U'':',
430 $
' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
431 $ /
'12 = CHPGV, with ITYPE=3 and UPLO=''U'':',
432 $
' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
433 $ /
'13 = CHEGV, with ITYPE=3 and UPLO=''L'':',
434 $
' | B A Z - Z D | / ( |A| |Z| n ulp ) ',
435 $ /
'14 = CHPGV, with ITYPE=3 and UPLO=''L'':',
436 $
' | B A Z - Z D | / ( |A| |Z| n ulp ) ' )
440 9973
FORMAT(
' Matrix types (see xCHKBD for details):',
441 $ /
' Diagonal matrices:', /
' 1: Zero', 28x,
442 $
' 5: Clustered entries', /
' 2: Identity', 24x,
443 $
' 6: Large, evenly spaced entries',
444 $ /
' 3: Evenly spaced entries', 11x,
445 $
' 7: Small, evenly spaced entries',
446 $ /
' 4: Geometrically spaced entries',
447 $ /
' General matrices:', /
' 8: Evenly spaced sing. vals.',
448 $ 7x,
'12: Small, evenly spaced sing vals',
449 $ /
' 9: Geometrically spaced sing vals ',
450 $
'13: Random, O(1) entries', /
' 10: Clustered sing. vals.',
451 $ 11x,
'14: Random, scaled near overflow',
452 $ /
' 11: Large, evenly spaced sing vals ',
453 $
'15: Random, scaled near underflow' )
455 9972
FORMAT( /
' Test ratios: ',
456 $
'(B: bidiagonal, S: diagonal, Q, P, U, and V: ', a10, / 16x,
457 $
'X: m x nrhs, Y = Q'' X, and Z = U'' Y)' )
458 9971
FORMAT(
' 1: norm( A - Q B P'' ) / ( norm(A) max(m,n) ulp )',
459 $ /
' 2: norm( I - Q'' Q ) / ( m ulp )',
460 $ /
' 3: norm( I - P'' P ) / ( n ulp )',
461 $ /
' 4: norm( B - U S V'' ) / ( norm(B) min(m,n) ulp )',
462 $ /
' 5: norm( Y - U Z ) / ',
463 $
'( norm(Z) max(min(m,n),k) ulp )',
464 $ /
' 6: norm( I - U'' U ) / ( min(m,n) ulp )',
465 $ /
' 7: norm( I - V'' V ) / ( min(m,n) ulp )',
466 $ /
' 8: Test ordering of S (0 if nondecreasing, 1/ulp ',
468 $ /
' 9: norm( S - S1 ) / ( norm(S) ulp ),',
469 $
' where S1 is computed', / 43x,
470 $
' without computing U and V''',
471 $ /
' 10: Sturm sequence test ',
472 $
'(0 if sing. vals of B within THRESH of S)',
473 $ /
' 11: norm( A - (QU) S (V'' P'') ) / ',
474 $
'( norm(A) max(m,n) ulp )',
475 $ /
' 12: norm( X - (QU) Z ) / ( |X| max(M,k) ulp )',
476 $ /
' 13: norm( I - (QU)''(QU) ) / ( M ulp )',
477 $ /
' 14: norm( I - (V'' P'') (P V) ) / ( N ulp )',
478 $ /
' 15: norm( B - U S V'' ) / ( norm(B) min(m,n) ulp )',
479 $ /
' 16: norm( I - U'' U ) / ( min(m,n) ulp )',
480 $ /
' 17: norm( I - V'' V ) / ( min(m,n) ulp )',
481 $ /
' 18: Test ordering of S (0 if nondecreasing, 1/ulp ',
483 $ /
' 19: norm( S - S1 ) / ( norm(S) ulp ),',
484 $
' where S1 is computed', / 43x,
485 $
' without computing U and V''',
486 $ /
' 20: norm( B - U S V'' ) / ( norm(B) min(m,n) ulp )',
488 $ /
' 21: norm( I - U'' U ) / ( min(m,n) ulp )',
489 $ /
' 22: norm( I - V'' V ) / ( min(m,n) ulp )',
490 $ /
' 23: Test ordering of S (0 if nondecreasing, 1/ulp ',
492 $ /
' 24: norm( S - S1 ) / ( norm(S) ulp ),',
493 $
' where S1 is computed', / 44x,
494 $
' without computing U and V''',
495 $ /
' 25: norm( S - U'' B V ) / ( norm(B) n ulp )',
497 $ /
' 26: norm( I - U'' U ) / ( min(m,n) ulp )',
498 $ /
' 27: norm( I - V'' V ) / ( min(m,n) ulp )',
499 $ /
' 28: Test ordering of S (0 if nondecreasing, 1/ulp ',
501 $ /
' 29: norm( S - S1 ) / ( norm(S) ulp ),',
502 $
' where S1 is computed', / 44x,
503 $
' without computing U and V''',
504 $ /
' 30: norm( S - U'' B V ) / ( norm(B) n ulp )',
506 $ /
' 31: norm( I - U'' U ) / ( min(m,n) ulp )',
507 $ /
' 32: norm( I - V'' V ) / ( min(m,n) ulp )',
508 $ /
' 33: Test ordering of S (0 if nondecreasing, 1/ulp ',
510 $ /
' 34: norm( S - S1 ) / ( norm(S) ulp ),',
511 $
' where S1 is computed', / 44x,
512 $
' without computing U and V''' )
516 9970
FORMAT(
' Matrix types (see xCHKBB for details):',
517 $ /
' Diagonal matrices:', /
' 1: Zero', 28x,
518 $
' 5: Clustered entries', /
' 2: Identity', 24x,
519 $
' 6: Large, evenly spaced entries',
520 $ /
' 3: Evenly spaced entries', 11x,
521 $
' 7: Small, evenly spaced entries',
522 $ /
' 4: Geometrically spaced entries',
523 $ /
' General matrices:', /
' 8: Evenly spaced sing. vals.',
524 $ 7x,
'12: Small, evenly spaced sing vals',
525 $ /
' 9: Geometrically spaced sing vals ',
526 $
'13: Random, O(1) entries', /
' 10: Clustered sing. vals.',
527 $ 11x,
'14: Random, scaled near overflow',
528 $ /
' 11: Large, evenly spaced sing vals ',
529 $
'15: Random, scaled near underflow' )
531 9969
FORMAT( /
' Test ratios: ',
'(B: upper bidiagonal, Q and P: ',
532 $ a10, / 16x,
'C: m x nrhs, PT = P'', Y = Q'' C)',
533 $ /
' 1: norm( A - Q B PT ) / ( norm(A) max(m,n) ulp )',
534 $ /
' 2: norm( I - Q'' Q ) / ( m ulp )',
535 $ /
' 3: norm( I - PT PT'' ) / ( n ulp )',
536 $ /
' 4: norm( Y - Q'' C ) / ( norm(Y) max(m,nrhs) ulp )' )
537 9968
FORMAT( /
' Tests performed: See sdrvst.f' )
538 9967
FORMAT( /
' Tests performed: See cdrvst.f' )
subroutine slahd2(iounit, path)
SLAHD2