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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE SCHKSB( NSIZES, NN, NWDTHS, KK, NTYPES, DOTYPE, ISEED, 00002 $ THRESH, NOUNIT, A, LDA, SD, SE, U, LDU, WORK, 00003 $ LWORK, RESULT, INFO ) 00004 * 00005 * -- LAPACK test routine (version 3.1) -- 00006 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00007 * November 2006 00008 * 00009 * .. Scalar Arguments .. 00010 INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES, 00011 $ NWDTHS 00012 REAL THRESH 00013 * .. 00014 * .. Array Arguments .. 00015 LOGICAL DOTYPE( * ) 00016 INTEGER ISEED( 4 ), KK( * ), NN( * ) 00017 REAL A( LDA, * ), RESULT( * ), SD( * ), SE( * ), 00018 $ U( LDU, * ), WORK( * ) 00019 * .. 00020 * 00021 * Purpose 00022 * ======= 00023 * 00024 * SCHKSB tests the reduction of a symmetric band matrix to tridiagonal 00025 * form, used with the symmetric eigenvalue problem. 00026 * 00027 * SSBTRD factors a symmetric band matrix A as U S U' , where ' means 00028 * transpose, S is symmetric tridiagonal, and U is orthogonal. 00029 * SSBTRD can use either just the lower or just the upper triangle 00030 * of A; SCHKSB checks both cases. 00031 * 00032 * When SCHKSB is called, a number of matrix "sizes" ("n's"), a number 00033 * of bandwidths ("k's"), and a number of matrix "types" are 00034 * specified. For each size ("n"), each bandwidth ("k") less than or 00035 * equal to "n", and each type of matrix, one matrix will be generated 00036 * and used to test the symmetric banded reduction routine. For each 00037 * matrix, a number of tests will be performed: 00038 * 00039 * (1) | A - V S V' | / ( |A| n ulp ) computed by SSBTRD with 00040 * UPLO='U' 00041 * 00042 * (2) | I - UU' | / ( n ulp ) 00043 * 00044 * (3) | A - V S V' | / ( |A| n ulp ) computed by SSBTRD with 00045 * UPLO='L' 00046 * 00047 * (4) | I - UU' | / ( n ulp ) 00048 * 00049 * The "sizes" are specified by an array NN(1:NSIZES); the value of 00050 * each element NN(j) specifies one size. 00051 * The "types" are specified by a logical array DOTYPE( 1:NTYPES ); 00052 * if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. 00053 * Currently, the list of possible types is: 00054 * 00055 * (1) The zero matrix. 00056 * (2) The identity matrix. 00057 * 00058 * (3) A diagonal matrix with evenly spaced entries 00059 * 1, ..., ULP and random signs. 00060 * (ULP = (first number larger than 1) - 1 ) 00061 * (4) A diagonal matrix with geometrically spaced entries 00062 * 1, ..., ULP and random signs. 00063 * (5) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP 00064 * and random signs. 00065 * 00066 * (6) Same as (4), but multiplied by SQRT( overflow threshold ) 00067 * (7) Same as (4), but multiplied by SQRT( underflow threshold ) 00068 * 00069 * (8) A matrix of the form U' D U, where U is orthogonal and 00070 * D has evenly spaced entries 1, ..., ULP with random signs 00071 * on the diagonal. 00072 * 00073 * (9) A matrix of the form U' D U, where U is orthogonal and 00074 * D has geometrically spaced entries 1, ..., ULP with random 00075 * signs on the diagonal. 00076 * 00077 * (10) A matrix of the form U' D U, where U is orthogonal and 00078 * D has "clustered" entries 1, ULP,..., ULP with random 00079 * signs on the diagonal. 00080 * 00081 * (11) Same as (8), but multiplied by SQRT( overflow threshold ) 00082 * (12) Same as (8), but multiplied by SQRT( underflow threshold ) 00083 * 00084 * (13) Symmetric matrix with random entries chosen from (-1,1). 00085 * (14) Same as (13), but multiplied by SQRT( overflow threshold ) 00086 * (15) Same as (13), but multiplied by SQRT( underflow threshold ) 00087 * 00088 * Arguments 00089 * ========= 00090 * 00091 * NSIZES (input) INTEGER 00092 * The number of sizes of matrices to use. If it is zero, 00093 * SCHKSB does nothing. It must be at least zero. 00094 * 00095 * NN (input) INTEGER array, dimension (NSIZES) 00096 * An array containing the sizes to be used for the matrices. 00097 * Zero values will be skipped. The values must be at least 00098 * zero. 00099 * 00100 * NWDTHS (input) INTEGER 00101 * The number of bandwidths to use. If it is zero, 00102 * SCHKSB does nothing. It must be at least zero. 00103 * 00104 * KK (input) INTEGER array, dimension (NWDTHS) 00105 * An array containing the bandwidths to be used for the band 00106 * matrices. The values must be at least zero. 00107 * 00108 * NTYPES (input) INTEGER 00109 * The number of elements in DOTYPE. If it is zero, SCHKSB 00110 * does nothing. It must be at least zero. If it is MAXTYP+1 00111 * and NSIZES is 1, then an additional type, MAXTYP+1 is 00112 * defined, which is to use whatever matrix is in A. This 00113 * is only useful if DOTYPE(1:MAXTYP) is .FALSE. and 00114 * DOTYPE(MAXTYP+1) is .TRUE. . 00115 * 00116 * DOTYPE (input) LOGICAL array, dimension (NTYPES) 00117 * If DOTYPE(j) is .TRUE., then for each size in NN a 00118 * matrix of that size and of type j will be generated. 00119 * If NTYPES is smaller than the maximum number of types 00120 * defined (PARAMETER MAXTYP), then types NTYPES+1 through 00121 * MAXTYP will not be generated. If NTYPES is larger 00122 * than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) 00123 * will be ignored. 00124 * 00125 * ISEED (input/output) INTEGER array, dimension (4) 00126 * On entry ISEED specifies the seed of the random number 00127 * generator. The array elements should be between 0 and 4095; 00128 * if not they will be reduced mod 4096. Also, ISEED(4) must 00129 * be odd. The random number generator uses a linear 00130 * congruential sequence limited to small integers, and so 00131 * should produce machine independent random numbers. The 00132 * values of ISEED are changed on exit, and can be used in the 00133 * next call to SCHKSB to continue the same random number 00134 * sequence. 00135 * 00136 * THRESH (input) REAL 00137 * A test will count as "failed" if the "error", computed as 00138 * described above, exceeds THRESH. Note that the error 00139 * is scaled to be O(1), so THRESH should be a reasonably 00140 * small multiple of 1, e.g., 10 or 100. In particular, 00141 * it should not depend on the precision (single vs. double) 00142 * or the size of the matrix. It must be at least zero. 00143 * 00144 * NOUNIT (input) INTEGER 00145 * The FORTRAN unit number for printing out error messages 00146 * (e.g., if a routine returns IINFO not equal to 0.) 00147 * 00148 * A (input/workspace) REAL array, dimension 00149 * (LDA, max(NN)) 00150 * Used to hold the matrix whose eigenvalues are to be 00151 * computed. 00152 * 00153 * LDA (input) INTEGER 00154 * The leading dimension of A. It must be at least 2 (not 1!) 00155 * and at least max( KK )+1. 00156 * 00157 * SD (workspace) REAL array, dimension (max(NN)) 00158 * Used to hold the diagonal of the tridiagonal matrix computed 00159 * by SSBTRD. 00160 * 00161 * SE (workspace) REAL array, dimension (max(NN)) 00162 * Used to hold the off-diagonal of the tridiagonal matrix 00163 * computed by SSBTRD. 00164 * 00165 * U (workspace) REAL array, dimension (LDU, max(NN)) 00166 * Used to hold the orthogonal matrix computed by SSBTRD. 00167 * 00168 * LDU (input) INTEGER 00169 * The leading dimension of U. It must be at least 1 00170 * and at least max( NN ). 00171 * 00172 * WORK (workspace) REAL array, dimension (LWORK) 00173 * 00174 * LWORK (input) INTEGER 00175 * The number of entries in WORK. This must be at least 00176 * max( LDA+1, max(NN)+1 )*max(NN). 00177 * 00178 * RESULT (output) REAL array, dimension (4) 00179 * The values computed by the tests described above. 00180 * The values are currently limited to 1/ulp, to avoid 00181 * overflow. 00182 * 00183 * INFO (output) INTEGER 00184 * If 0, then everything ran OK. 00185 * 00186 *----------------------------------------------------------------------- 00187 * 00188 * Some Local Variables and Parameters: 00189 * ---- ----- --------- --- ---------- 00190 * ZERO, ONE Real 0 and 1. 00191 * MAXTYP The number of types defined. 00192 * NTEST The number of tests performed, or which can 00193 * be performed so far, for the current matrix. 00194 * NTESTT The total number of tests performed so far. 00195 * NMAX Largest value in NN. 00196 * NMATS The number of matrices generated so far. 00197 * NERRS The number of tests which have exceeded THRESH 00198 * so far. 00199 * COND, IMODE Values to be passed to the matrix generators. 00200 * ANORM Norm of A; passed to matrix generators. 00201 * 00202 * OVFL, UNFL Overflow and underflow thresholds. 00203 * ULP, ULPINV Finest relative precision and its inverse. 00204 * RTOVFL, RTUNFL Square roots of the previous 2 values. 00205 * The following four arrays decode JTYPE: 00206 * KTYPE(j) The general type (1-10) for type "j". 00207 * KMODE(j) The MODE value to be passed to the matrix 00208 * generator for type "j". 00209 * KMAGN(j) The order of magnitude ( O(1), 00210 * O(overflow^(1/2) ), O(underflow^(1/2) ) 00211 * 00212 * ===================================================================== 00213 * 00214 * .. Parameters .. 00215 REAL ZERO, ONE, TWO, TEN 00216 PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0, 00217 $ TEN = 10.0E0 ) 00218 REAL HALF 00219 PARAMETER ( HALF = ONE / TWO ) 00220 INTEGER MAXTYP 00221 PARAMETER ( MAXTYP = 15 ) 00222 * .. 00223 * .. Local Scalars .. 00224 LOGICAL BADNN, BADNNB 00225 INTEGER I, IINFO, IMODE, ITYPE, J, JC, JCOL, JR, JSIZE, 00226 $ JTYPE, JWIDTH, K, KMAX, MTYPES, N, NERRS, 00227 $ NMATS, NMAX, NTEST, NTESTT 00228 REAL ANINV, ANORM, COND, OVFL, RTOVFL, RTUNFL, 00229 $ TEMP1, ULP, ULPINV, UNFL 00230 * .. 00231 * .. Local Arrays .. 00232 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ), 00233 $ KMODE( MAXTYP ), KTYPE( MAXTYP ) 00234 * .. 00235 * .. External Functions .. 00236 REAL SLAMCH 00237 EXTERNAL SLAMCH 00238 * .. 00239 * .. External Subroutines .. 00240 EXTERNAL SLACPY, SLASUM, SLATMR, SLATMS, SLASET, SSBT21, 00241 $ SSBTRD, XERBLA 00242 * .. 00243 * .. Intrinsic Functions .. 00244 INTRINSIC ABS, MAX, MIN, REAL, SQRT 00245 * .. 00246 * .. Data statements .. 00247 DATA KTYPE / 1, 2, 5*4, 5*5, 3*8 / 00248 DATA KMAGN / 2*1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1, 00249 $ 2, 3 / 00250 DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0, 00251 $ 0, 0 / 00252 * .. 00253 * .. Executable Statements .. 00254 * 00255 * Check for errors 00256 * 00257 NTESTT = 0 00258 INFO = 0 00259 * 00260 * Important constants 00261 * 00262 BADNN = .FALSE. 00263 NMAX = 1 00264 DO 10 J = 1, NSIZES 00265 NMAX = MAX( NMAX, NN( J ) ) 00266 IF( NN( J ).LT.0 ) 00267 $ BADNN = .TRUE. 00268 10 CONTINUE 00269 * 00270 BADNNB = .FALSE. 00271 KMAX = 0 00272 DO 20 J = 1, NSIZES 00273 KMAX = MAX( KMAX, KK( J ) ) 00274 IF( KK( J ).LT.0 ) 00275 $ BADNNB = .TRUE. 00276 20 CONTINUE 00277 KMAX = MIN( NMAX-1, KMAX ) 00278 * 00279 * Check for errors 00280 * 00281 IF( NSIZES.LT.0 ) THEN 00282 INFO = -1 00283 ELSE IF( BADNN ) THEN 00284 INFO = -2 00285 ELSE IF( NWDTHS.LT.0 ) THEN 00286 INFO = -3 00287 ELSE IF( BADNNB ) THEN 00288 INFO = -4 00289 ELSE IF( NTYPES.LT.0 ) THEN 00290 INFO = -5 00291 ELSE IF( LDA.LT.KMAX+1 ) THEN 00292 INFO = -11 00293 ELSE IF( LDU.LT.NMAX ) THEN 00294 INFO = -15 00295 ELSE IF( ( MAX( LDA, NMAX )+1 )*NMAX.GT.LWORK ) THEN 00296 INFO = -17 00297 END IF 00298 * 00299 IF( INFO.NE.0 ) THEN 00300 CALL XERBLA( 'SCHKSB', -INFO ) 00301 RETURN 00302 END IF 00303 * 00304 * Quick return if possible 00305 * 00306 IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 .OR. NWDTHS.EQ.0 ) 00307 $ RETURN 00308 * 00309 * More Important constants 00310 * 00311 UNFL = SLAMCH( 'Safe minimum' ) 00312 OVFL = ONE / UNFL 00313 ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' ) 00314 ULPINV = ONE / ULP 00315 RTUNFL = SQRT( UNFL ) 00316 RTOVFL = SQRT( OVFL ) 00317 * 00318 * Loop over sizes, types 00319 * 00320 NERRS = 0 00321 NMATS = 0 00322 * 00323 DO 190 JSIZE = 1, NSIZES 00324 N = NN( JSIZE ) 00325 ANINV = ONE / REAL( MAX( 1, N ) ) 00326 * 00327 DO 180 JWIDTH = 1, NWDTHS 00328 K = KK( JWIDTH ) 00329 IF( K.GT.N ) 00330 $ GO TO 180 00331 K = MAX( 0, MIN( N-1, K ) ) 00332 * 00333 IF( NSIZES.NE.1 ) THEN 00334 MTYPES = MIN( MAXTYP, NTYPES ) 00335 ELSE 00336 MTYPES = MIN( MAXTYP+1, NTYPES ) 00337 END IF 00338 * 00339 DO 170 JTYPE = 1, MTYPES 00340 IF( .NOT.DOTYPE( JTYPE ) ) 00341 $ GO TO 170 00342 NMATS = NMATS + 1 00343 NTEST = 0 00344 * 00345 DO 30 J = 1, 4 00346 IOLDSD( J ) = ISEED( J ) 00347 30 CONTINUE 00348 * 00349 * Compute "A". 00350 * Store as "Upper"; later, we will copy to other format. 00351 * 00352 * Control parameters: 00353 * 00354 * KMAGN KMODE KTYPE 00355 * =1 O(1) clustered 1 zero 00356 * =2 large clustered 2 identity 00357 * =3 small exponential (none) 00358 * =4 arithmetic diagonal, (w/ eigenvalues) 00359 * =5 random log symmetric, w/ eigenvalues 00360 * =6 random (none) 00361 * =7 random diagonal 00362 * =8 random symmetric 00363 * =9 positive definite 00364 * =10 diagonally dominant tridiagonal 00365 * 00366 IF( MTYPES.GT.MAXTYP ) 00367 $ GO TO 100 00368 * 00369 ITYPE = KTYPE( JTYPE ) 00370 IMODE = KMODE( JTYPE ) 00371 * 00372 * Compute norm 00373 * 00374 GO TO ( 40, 50, 60 )KMAGN( JTYPE ) 00375 * 00376 40 CONTINUE 00377 ANORM = ONE 00378 GO TO 70 00379 * 00380 50 CONTINUE 00381 ANORM = ( RTOVFL*ULP )*ANINV 00382 GO TO 70 00383 * 00384 60 CONTINUE 00385 ANORM = RTUNFL*N*ULPINV 00386 GO TO 70 00387 * 00388 70 CONTINUE 00389 * 00390 CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) 00391 IINFO = 0 00392 IF( JTYPE.LE.15 ) THEN 00393 COND = ULPINV 00394 ELSE 00395 COND = ULPINV*ANINV / TEN 00396 END IF 00397 * 00398 * Special Matrices -- Identity & Jordan block 00399 * 00400 * Zero 00401 * 00402 IF( ITYPE.EQ.1 ) THEN 00403 IINFO = 0 00404 * 00405 ELSE IF( ITYPE.EQ.2 ) THEN 00406 * 00407 * Identity 00408 * 00409 DO 80 JCOL = 1, N 00410 A( K+1, JCOL ) = ANORM 00411 80 CONTINUE 00412 * 00413 ELSE IF( ITYPE.EQ.4 ) THEN 00414 * 00415 * Diagonal Matrix, [Eigen]values Specified 00416 * 00417 CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND, 00418 $ ANORM, 0, 0, 'Q', A( K+1, 1 ), LDA, 00419 $ WORK( N+1 ), IINFO ) 00420 * 00421 ELSE IF( ITYPE.EQ.5 ) THEN 00422 * 00423 * Symmetric, eigenvalues specified 00424 * 00425 CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND, 00426 $ ANORM, K, K, 'Q', A, LDA, WORK( N+1 ), 00427 $ IINFO ) 00428 * 00429 ELSE IF( ITYPE.EQ.7 ) THEN 00430 * 00431 * Diagonal, random eigenvalues 00432 * 00433 CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE, 00434 $ 'T', 'N', WORK( N+1 ), 1, ONE, 00435 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0, 00436 $ ZERO, ANORM, 'Q', A( K+1, 1 ), LDA, 00437 $ IDUMMA, IINFO ) 00438 * 00439 ELSE IF( ITYPE.EQ.8 ) THEN 00440 * 00441 * Symmetric, random eigenvalues 00442 * 00443 CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE, 00444 $ 'T', 'N', WORK( N+1 ), 1, ONE, 00445 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, K, K, 00446 $ ZERO, ANORM, 'Q', A, LDA, IDUMMA, IINFO ) 00447 * 00448 ELSE IF( ITYPE.EQ.9 ) THEN 00449 * 00450 * Positive definite, eigenvalues specified. 00451 * 00452 CALL SLATMS( N, N, 'S', ISEED, 'P', WORK, IMODE, COND, 00453 $ ANORM, K, K, 'Q', A, LDA, WORK( N+1 ), 00454 $ IINFO ) 00455 * 00456 ELSE IF( ITYPE.EQ.10 ) THEN 00457 * 00458 * Positive definite tridiagonal, eigenvalues specified. 00459 * 00460 IF( N.GT.1 ) 00461 $ K = MAX( 1, K ) 00462 CALL SLATMS( N, N, 'S', ISEED, 'P', WORK, IMODE, COND, 00463 $ ANORM, 1, 1, 'Q', A( K, 1 ), LDA, 00464 $ WORK( N+1 ), IINFO ) 00465 DO 90 I = 2, N 00466 TEMP1 = ABS( A( K, I ) ) / 00467 $ SQRT( ABS( A( K+1, I-1 )*A( K+1, I ) ) ) 00468 IF( TEMP1.GT.HALF ) THEN 00469 A( K, I ) = HALF*SQRT( ABS( A( K+1, 00470 $ I-1 )*A( K+1, I ) ) ) 00471 END IF 00472 90 CONTINUE 00473 * 00474 ELSE 00475 * 00476 IINFO = 1 00477 END IF 00478 * 00479 IF( IINFO.NE.0 ) THEN 00480 WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, 00481 $ JTYPE, IOLDSD 00482 INFO = ABS( IINFO ) 00483 RETURN 00484 END IF 00485 * 00486 100 CONTINUE 00487 * 00488 * Call SSBTRD to compute S and U from upper triangle. 00489 * 00490 CALL SLACPY( ' ', K+1, N, A, LDA, WORK, LDA ) 00491 * 00492 NTEST = 1 00493 CALL SSBTRD( 'V', 'U', N, K, WORK, LDA, SD, SE, U, LDU, 00494 $ WORK( LDA*N+1 ), IINFO ) 00495 * 00496 IF( IINFO.NE.0 ) THEN 00497 WRITE( NOUNIT, FMT = 9999 )'SSBTRD(U)', IINFO, N, 00498 $ JTYPE, IOLDSD 00499 INFO = ABS( IINFO ) 00500 IF( IINFO.LT.0 ) THEN 00501 RETURN 00502 ELSE 00503 RESULT( 1 ) = ULPINV 00504 GO TO 150 00505 END IF 00506 END IF 00507 * 00508 * Do tests 1 and 2 00509 * 00510 CALL SSBT21( 'Upper', N, K, 1, A, LDA, SD, SE, U, LDU, 00511 $ WORK, RESULT( 1 ) ) 00512 * 00513 * Convert A from Upper-Triangle-Only storage to 00514 * Lower-Triangle-Only storage. 00515 * 00516 DO 120 JC = 1, N 00517 DO 110 JR = 0, MIN( K, N-JC ) 00518 A( JR+1, JC ) = A( K+1-JR, JC+JR ) 00519 110 CONTINUE 00520 120 CONTINUE 00521 DO 140 JC = N + 1 - K, N 00522 DO 130 JR = MIN( K, N-JC ) + 1, K 00523 A( JR+1, JC ) = ZERO 00524 130 CONTINUE 00525 140 CONTINUE 00526 * 00527 * Call SSBTRD to compute S and U from lower triangle 00528 * 00529 CALL SLACPY( ' ', K+1, N, A, LDA, WORK, LDA ) 00530 * 00531 NTEST = 3 00532 CALL SSBTRD( 'V', 'L', N, K, WORK, LDA, SD, SE, U, LDU, 00533 $ WORK( LDA*N+1 ), IINFO ) 00534 * 00535 IF( IINFO.NE.0 ) THEN 00536 WRITE( NOUNIT, FMT = 9999 )'SSBTRD(L)', IINFO, N, 00537 $ JTYPE, IOLDSD 00538 INFO = ABS( IINFO ) 00539 IF( IINFO.LT.0 ) THEN 00540 RETURN 00541 ELSE 00542 RESULT( 3 ) = ULPINV 00543 GO TO 150 00544 END IF 00545 END IF 00546 NTEST = 4 00547 * 00548 * Do tests 3 and 4 00549 * 00550 CALL SSBT21( 'Lower', N, K, 1, A, LDA, SD, SE, U, LDU, 00551 $ WORK, RESULT( 3 ) ) 00552 * 00553 * End of Loop -- Check for RESULT(j) > THRESH 00554 * 00555 150 CONTINUE 00556 NTESTT = NTESTT + NTEST 00557 * 00558 * Print out tests which fail. 00559 * 00560 DO 160 JR = 1, NTEST 00561 IF( RESULT( JR ).GE.THRESH ) THEN 00562 * 00563 * If this is the first test to fail, 00564 * print a header to the data file. 00565 * 00566 IF( NERRS.EQ.0 ) THEN 00567 WRITE( NOUNIT, FMT = 9998 )'SSB' 00568 WRITE( NOUNIT, FMT = 9997 ) 00569 WRITE( NOUNIT, FMT = 9996 ) 00570 WRITE( NOUNIT, FMT = 9995 )'Symmetric' 00571 WRITE( NOUNIT, FMT = 9994 )'orthogonal', '''', 00572 $ 'transpose', ( '''', J = 1, 4 ) 00573 END IF 00574 NERRS = NERRS + 1 00575 WRITE( NOUNIT, FMT = 9993 )N, K, IOLDSD, JTYPE, 00576 $ JR, RESULT( JR ) 00577 END IF 00578 160 CONTINUE 00579 * 00580 170 CONTINUE 00581 180 CONTINUE 00582 190 CONTINUE 00583 * 00584 * Summary 00585 * 00586 CALL SLASUM( 'SSB', NOUNIT, NERRS, NTESTT ) 00587 RETURN 00588 * 00589 9999 FORMAT( ' SCHKSB: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', 00590 $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) 00591 * 00592 9998 FORMAT( / 1X, A3, 00593 $ ' -- Real Symmetric Banded Tridiagonal Reduction Routines' ) 00594 9997 FORMAT( ' Matrix types (see SCHKSB for details): ' ) 00595 * 00596 9996 FORMAT( / ' Special Matrices:', 00597 $ / ' 1=Zero matrix. ', 00598 $ ' 5=Diagonal: clustered entries.', 00599 $ / ' 2=Identity matrix. ', 00600 $ ' 6=Diagonal: large, evenly spaced.', 00601 $ / ' 3=Diagonal: evenly spaced entries. ', 00602 $ ' 7=Diagonal: small, evenly spaced.', 00603 $ / ' 4=Diagonal: geometr. spaced entries.' ) 00604 9995 FORMAT( ' Dense ', A, ' Banded Matrices:', 00605 $ / ' 8=Evenly spaced eigenvals. ', 00606 $ ' 12=Small, evenly spaced eigenvals.', 00607 $ / ' 9=Geometrically spaced eigenvals. ', 00608 $ ' 13=Matrix with random O(1) entries.', 00609 $ / ' 10=Clustered eigenvalues. ', 00610 $ ' 14=Matrix with large random entries.', 00611 $ / ' 11=Large, evenly spaced eigenvals. ', 00612 $ ' 15=Matrix with small random entries.' ) 00613 * 00614 9994 FORMAT( / ' Tests performed: (S is Tridiag, U is ', A, ',', 00615 $ / 20X, A, ' means ', A, '.', / ' UPLO=''U'':', 00616 $ / ' 1= | A - U S U', A1, ' | / ( |A| n ulp ) ', 00617 $ ' 2= | I - U U', A1, ' | / ( n ulp )', / ' UPLO=''L'':', 00618 $ / ' 3= | A - U S U', A1, ' | / ( |A| n ulp ) ', 00619 $ ' 4= | I - U U', A1, ' | / ( n ulp )' ) 00620 9993 FORMAT( ' N=', I5, ', K=', I4, ', seed=', 4( I4, ',' ), ' type ', 00621 $ I2, ', test(', I2, ')=', G10.3 ) 00622 * 00623 * End of SCHKSB 00624 * 00625 END
1.7.3 
