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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 SCHKHS( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, 00002 $ NOUNIT, A, LDA, H, T1, T2, U, LDU, Z, UZ, WR1, 00003 $ WI1, WR3, WI3, EVECTL, EVECTR, EVECTY, EVECTX, 00004 $ UU, TAU, WORK, NWORK, IWORK, SELECT, RESULT, 00005 $ INFO ) 00006 * 00007 * -- LAPACK test routine (version 3.1.1) -- 00008 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00009 * February 2007 00010 * 00011 * .. Scalar Arguments .. 00012 INTEGER INFO, LDA, LDU, NOUNIT, NSIZES, NTYPES, NWORK 00013 REAL THRESH 00014 * .. 00015 * .. Array Arguments .. 00016 LOGICAL DOTYPE( * ), SELECT( * ) 00017 INTEGER ISEED( 4 ), IWORK( * ), NN( * ) 00018 REAL A( LDA, * ), EVECTL( LDU, * ), 00019 $ EVECTR( LDU, * ), EVECTX( LDU, * ), 00020 $ EVECTY( LDU, * ), H( LDA, * ), RESULT( 14 ), 00021 $ T1( LDA, * ), T2( LDA, * ), TAU( * ), 00022 $ U( LDU, * ), UU( LDU, * ), UZ( LDU, * ), 00023 $ WI1( * ), WI3( * ), WORK( * ), WR1( * ), 00024 $ WR3( * ), Z( LDU, * ) 00025 * .. 00026 * 00027 * Purpose 00028 * ======= 00029 * 00030 * SCHKHS checks the nonsymmetric eigenvalue problem routines. 00031 * 00032 * SGEHRD factors A as U H U' , where ' means transpose, 00033 * H is hessenberg, and U is an orthogonal matrix. 00034 * 00035 * SORGHR generates the orthogonal matrix U. 00036 * 00037 * SORMHR multiplies a matrix by the orthogonal matrix U. 00038 * 00039 * SHSEQR factors H as Z T Z' , where Z is orthogonal and 00040 * T is "quasi-triangular", and the eigenvalue vector W. 00041 * 00042 * STREVC computes the left and right eigenvector matrices 00043 * L and R for T. 00044 * 00045 * SHSEIN computes the left and right eigenvector matrices 00046 * Y and X for H, using inverse iteration. 00047 * 00048 * When SCHKHS is called, a number of matrix "sizes" ("n's") and a 00049 * number of matrix "types" are specified. For each size ("n") 00050 * and each type of matrix, one matrix will be generated and used 00051 * to test the nonsymmetric eigenroutines. For each matrix, 14 00052 * tests will be performed: 00053 * 00054 * (1) | A - U H U**T | / ( |A| n ulp ) 00055 * 00056 * (2) | I - UU**T | / ( n ulp ) 00057 * 00058 * (3) | H - Z T Z**T | / ( |H| n ulp ) 00059 * 00060 * (4) | I - ZZ**T | / ( n ulp ) 00061 * 00062 * (5) | A - UZ H (UZ)**T | / ( |A| n ulp ) 00063 * 00064 * (6) | I - UZ (UZ)**T | / ( n ulp ) 00065 * 00066 * (7) | T(Z computed) - T(Z not computed) | / ( |T| ulp ) 00067 * 00068 * (8) | W(Z computed) - W(Z not computed) | / ( |W| ulp ) 00069 * 00070 * (9) | TR - RW | / ( |T| |R| ulp ) 00071 * 00072 * (10) | L**H T - W**H L | / ( |T| |L| ulp ) 00073 * 00074 * (11) | HX - XW | / ( |H| |X| ulp ) 00075 * 00076 * (12) | Y**H H - W**H Y | / ( |H| |Y| ulp ) 00077 * 00078 * (13) | AX - XW | / ( |A| |X| ulp ) 00079 * 00080 * (14) | Y**H A - W**H Y | / ( |A| |Y| ulp ) 00081 * 00082 * The "sizes" are specified by an array NN(1:NSIZES); the value of 00083 * each element NN(j) specifies one size. 00084 * The "types" are specified by a logical array DOTYPE( 1:NTYPES ); 00085 * if DOTYPE(j) is .TRUE., then matrix type "j" will be generated. 00086 * Currently, the list of possible types is: 00087 * 00088 * (1) The zero matrix. 00089 * (2) The identity matrix. 00090 * (3) A (transposed) Jordan block, with 1's on the diagonal. 00091 * 00092 * (4) A diagonal matrix with evenly spaced entries 00093 * 1, ..., ULP and random signs. 00094 * (ULP = (first number larger than 1) - 1 ) 00095 * (5) A diagonal matrix with geometrically spaced entries 00096 * 1, ..., ULP and random signs. 00097 * (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP 00098 * and random signs. 00099 * 00100 * (7) Same as (4), but multiplied by SQRT( overflow threshold ) 00101 * (8) Same as (4), but multiplied by SQRT( underflow threshold ) 00102 * 00103 * (9) A matrix of the form U' T U, where U is orthogonal and 00104 * T has evenly spaced entries 1, ..., ULP with random signs 00105 * on the diagonal and random O(1) entries in the upper 00106 * triangle. 00107 * 00108 * (10) A matrix of the form U' T U, where U is orthogonal and 00109 * T has geometrically spaced entries 1, ..., ULP with random 00110 * signs on the diagonal and random O(1) entries in the upper 00111 * triangle. 00112 * 00113 * (11) A matrix of the form U' T U, where U is orthogonal and 00114 * T has "clustered" entries 1, ULP,..., ULP with random 00115 * signs on the diagonal and random O(1) entries in the upper 00116 * triangle. 00117 * 00118 * (12) A matrix of the form U' T U, where U is orthogonal and 00119 * T has real or complex conjugate paired eigenvalues randomly 00120 * chosen from ( ULP, 1 ) and random O(1) entries in the upper 00121 * triangle. 00122 * 00123 * (13) A matrix of the form X' T X, where X has condition 00124 * SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP 00125 * with random signs on the diagonal and random O(1) entries 00126 * in the upper triangle. 00127 * 00128 * (14) A matrix of the form X' T X, where X has condition 00129 * SQRT( ULP ) and T has geometrically spaced entries 00130 * 1, ..., ULP with random signs on the diagonal and random 00131 * O(1) entries in the upper triangle. 00132 * 00133 * (15) A matrix of the form X' T X, where X has condition 00134 * SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP 00135 * with random signs on the diagonal and random O(1) entries 00136 * in the upper triangle. 00137 * 00138 * (16) A matrix of the form X' T X, where X has condition 00139 * SQRT( ULP ) and T has real or complex conjugate paired 00140 * eigenvalues randomly chosen from ( ULP, 1 ) and random 00141 * O(1) entries in the upper triangle. 00142 * 00143 * (17) Same as (16), but multiplied by SQRT( overflow threshold ) 00144 * (18) Same as (16), but multiplied by SQRT( underflow threshold ) 00145 * 00146 * (19) Nonsymmetric matrix with random entries chosen from (-1,1). 00147 * (20) Same as (19), but multiplied by SQRT( overflow threshold ) 00148 * (21) Same as (19), but multiplied by SQRT( underflow threshold ) 00149 * 00150 * Arguments 00151 * ========== 00152 * 00153 * NSIZES - INTEGER 00154 * The number of sizes of matrices to use. If it is zero, 00155 * SCHKHS does nothing. It must be at least zero. 00156 * Not modified. 00157 * 00158 * NN - INTEGER array, dimension (NSIZES) 00159 * An array containing the sizes to be used for the matrices. 00160 * Zero values will be skipped. The values must be at least 00161 * zero. 00162 * Not modified. 00163 * 00164 * NTYPES - INTEGER 00165 * The number of elements in DOTYPE. If it is zero, SCHKHS 00166 * does nothing. It must be at least zero. If it is MAXTYP+1 00167 * and NSIZES is 1, then an additional type, MAXTYP+1 is 00168 * defined, which is to use whatever matrix is in A. This 00169 * is only useful if DOTYPE(1:MAXTYP) is .FALSE. and 00170 * DOTYPE(MAXTYP+1) is .TRUE. . 00171 * Not modified. 00172 * 00173 * DOTYPE - LOGICAL array, dimension (NTYPES) 00174 * If DOTYPE(j) is .TRUE., then for each size in NN a 00175 * matrix of that size and of type j will be generated. 00176 * If NTYPES is smaller than the maximum number of types 00177 * defined (PARAMETER MAXTYP), then types NTYPES+1 through 00178 * MAXTYP will not be generated. If NTYPES is larger 00179 * than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) 00180 * will be ignored. 00181 * Not modified. 00182 * 00183 * ISEED - INTEGER array, dimension (4) 00184 * On entry ISEED specifies the seed of the random number 00185 * generator. The array elements should be between 0 and 4095; 00186 * if not they will be reduced mod 4096. Also, ISEED(4) must 00187 * be odd. The random number generator uses a linear 00188 * congruential sequence limited to small integers, and so 00189 * should produce machine independent random numbers. The 00190 * values of ISEED are changed on exit, and can be used in the 00191 * next call to SCHKHS to continue the same random number 00192 * sequence. 00193 * Modified. 00194 * 00195 * THRESH - REAL 00196 * A test will count as "failed" if the "error", computed as 00197 * described above, exceeds THRESH. Note that the error 00198 * is scaled to be O(1), so THRESH should be a reasonably 00199 * small multiple of 1, e.g., 10 or 100. In particular, 00200 * it should not depend on the precision (single vs. double) 00201 * or the size of the matrix. It must be at least zero. 00202 * Not modified. 00203 * 00204 * NOUNIT - INTEGER 00205 * The FORTRAN unit number for printing out error messages 00206 * (e.g., if a routine returns IINFO not equal to 0.) 00207 * Not modified. 00208 * 00209 * A - REAL array, dimension (LDA,max(NN)) 00210 * Used to hold the matrix whose eigenvalues are to be 00211 * computed. On exit, A contains the last matrix actually 00212 * used. 00213 * Modified. 00214 * 00215 * LDA - INTEGER 00216 * The leading dimension of A, H, T1 and T2. It must be at 00217 * least 1 and at least max( NN ). 00218 * Not modified. 00219 * 00220 * H - REAL array, dimension (LDA,max(NN)) 00221 * The upper hessenberg matrix computed by SGEHRD. On exit, 00222 * H contains the Hessenberg form of the matrix in A. 00223 * Modified. 00224 * 00225 * T1 - REAL array, dimension (LDA,max(NN)) 00226 * The Schur (="quasi-triangular") matrix computed by SHSEQR 00227 * if Z is computed. On exit, T1 contains the Schur form of 00228 * the matrix in A. 00229 * Modified. 00230 * 00231 * T2 - REAL array, dimension (LDA,max(NN)) 00232 * The Schur matrix computed by SHSEQR when Z is not computed. 00233 * This should be identical to T1. 00234 * Modified. 00235 * 00236 * LDU - INTEGER 00237 * The leading dimension of U, Z, UZ and UU. It must be at 00238 * least 1 and at least max( NN ). 00239 * Not modified. 00240 * 00241 * U - REAL array, dimension (LDU,max(NN)) 00242 * The orthogonal matrix computed by SGEHRD. 00243 * Modified. 00244 * 00245 * Z - REAL array, dimension (LDU,max(NN)) 00246 * The orthogonal matrix computed by SHSEQR. 00247 * Modified. 00248 * 00249 * UZ - REAL array, dimension (LDU,max(NN)) 00250 * The product of U times Z. 00251 * Modified. 00252 * 00253 * WR1 - REAL array, dimension (max(NN)) 00254 * WI1 - REAL array, dimension (max(NN)) 00255 * The real and imaginary parts of the eigenvalues of A, 00256 * as computed when Z is computed. 00257 * On exit, WR1 + WI1*i are the eigenvalues of the matrix in A. 00258 * Modified. 00259 * 00260 * WR3 - REAL array, dimension (max(NN)) 00261 * WI3 - REAL array, dimension (max(NN)) 00262 * Like WR1, WI1, these arrays contain the eigenvalues of A, 00263 * but those computed when SHSEQR only computes the 00264 * eigenvalues, i.e., not the Schur vectors and no more of the 00265 * Schur form than is necessary for computing the 00266 * eigenvalues. 00267 * Modified. 00268 * 00269 * EVECTL - REAL array, dimension (LDU,max(NN)) 00270 * The (upper triangular) left eigenvector matrix for the 00271 * matrix in T1. For complex conjugate pairs, the real part 00272 * is stored in one row and the imaginary part in the next. 00273 * Modified. 00274 * 00275 * EVECTR - REAL array, dimension (LDU,max(NN)) 00276 * The (upper triangular) right eigenvector matrix for the 00277 * matrix in T1. For complex conjugate pairs, the real part 00278 * is stored in one column and the imaginary part in the next. 00279 * Modified. 00280 * 00281 * EVECTY - REAL array, dimension (LDU,max(NN)) 00282 * The left eigenvector matrix for the 00283 * matrix in H. For complex conjugate pairs, the real part 00284 * is stored in one row and the imaginary part in the next. 00285 * Modified. 00286 * 00287 * EVECTX - REAL array, dimension (LDU,max(NN)) 00288 * The right eigenvector matrix for the 00289 * matrix in H. For complex conjugate pairs, the real part 00290 * is stored in one column and the imaginary part in the next. 00291 * Modified. 00292 * 00293 * UU - REAL array, dimension (LDU,max(NN)) 00294 * Details of the orthogonal matrix computed by SGEHRD. 00295 * Modified. 00296 * 00297 * TAU - REAL array, dimension(max(NN)) 00298 * Further details of the orthogonal matrix computed by SGEHRD. 00299 * Modified. 00300 * 00301 * WORK - REAL array, dimension (NWORK) 00302 * Workspace. 00303 * Modified. 00304 * 00305 * NWORK - INTEGER 00306 * The number of entries in WORK. NWORK >= 4*NN(j)*NN(j) + 2. 00307 * 00308 * IWORK - INTEGER array, dimension (max(NN)) 00309 * Workspace. 00310 * Modified. 00311 * 00312 * SELECT - LOGICAL array, dimension (max(NN)) 00313 * Workspace. 00314 * Modified. 00315 * 00316 * RESULT - REAL array, dimension (14) 00317 * The values computed by the fourteen tests described above. 00318 * The values are currently limited to 1/ulp, to avoid 00319 * overflow. 00320 * Modified. 00321 * 00322 * INFO - INTEGER 00323 * If 0, then everything ran OK. 00324 * -1: NSIZES < 0 00325 * -2: Some NN(j) < 0 00326 * -3: NTYPES < 0 00327 * -6: THRESH < 0 00328 * -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). 00329 * -14: LDU < 1 or LDU < NMAX. 00330 * -28: NWORK too small. 00331 * If SLATMR, SLATMS, or SLATME returns an error code, the 00332 * absolute value of it is returned. 00333 * If 1, then SHSEQR could not find all the shifts. 00334 * If 2, then the EISPACK code (for small blocks) failed. 00335 * If >2, then 30*N iterations were not enough to find an 00336 * eigenvalue or to decompose the problem. 00337 * Modified. 00338 * 00339 *----------------------------------------------------------------------- 00340 * 00341 * Some Local Variables and Parameters: 00342 * ---- ----- --------- --- ---------- 00343 * 00344 * ZERO, ONE Real 0 and 1. 00345 * MAXTYP The number of types defined. 00346 * MTEST The number of tests defined: care must be taken 00347 * that (1) the size of RESULT, (2) the number of 00348 * tests actually performed, and (3) MTEST agree. 00349 * NTEST The number of tests performed on this matrix 00350 * so far. This should be less than MTEST, and 00351 * equal to it by the last test. It will be less 00352 * if any of the routines being tested indicates 00353 * that it could not compute the matrices that 00354 * would be tested. 00355 * NMAX Largest value in NN. 00356 * NMATS The number of matrices generated so far. 00357 * NERRS The number of tests which have exceeded THRESH 00358 * so far (computed by SLAFTS). 00359 * COND, CONDS, 00360 * IMODE Values to be passed to the matrix generators. 00361 * ANORM Norm of A; passed to matrix generators. 00362 * 00363 * OVFL, UNFL Overflow and underflow thresholds. 00364 * ULP, ULPINV Finest relative precision and its inverse. 00365 * RTOVFL, RTUNFL, 00366 * RTULP, RTULPI Square roots of the previous 4 values. 00367 * 00368 * The following four arrays decode JTYPE: 00369 * KTYPE(j) The general type (1-10) for type "j". 00370 * KMODE(j) The MODE value to be passed to the matrix 00371 * generator for type "j". 00372 * KMAGN(j) The order of magnitude ( O(1), 00373 * O(overflow^(1/2) ), O(underflow^(1/2) ) 00374 * KCONDS(j) Selects whether CONDS is to be 1 or 00375 * 1/sqrt(ulp). (0 means irrelevant.) 00376 * 00377 * ===================================================================== 00378 * 00379 * .. Parameters .. 00380 REAL ZERO, ONE 00381 PARAMETER ( ZERO = 0.0, ONE = 1.0 ) 00382 INTEGER MAXTYP 00383 PARAMETER ( MAXTYP = 21 ) 00384 * .. 00385 * .. Local Scalars .. 00386 LOGICAL BADNN, MATCH 00387 INTEGER I, IHI, IINFO, ILO, IMODE, IN, ITYPE, J, JCOL, 00388 $ JJ, JSIZE, JTYPE, K, MTYPES, N, N1, NERRS, 00389 $ NMATS, NMAX, NSELC, NSELR, NTEST, NTESTT 00390 REAL ANINV, ANORM, COND, CONDS, OVFL, RTOVFL, RTULP, 00391 $ RTULPI, RTUNFL, TEMP1, TEMP2, ULP, ULPINV, UNFL 00392 * .. 00393 * .. Local Arrays .. 00394 CHARACTER ADUMMA( 1 ) 00395 INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ), 00396 $ KMAGN( MAXTYP ), KMODE( MAXTYP ), 00397 $ KTYPE( MAXTYP ) 00398 REAL DUMMA( 6 ) 00399 * .. 00400 * .. External Functions .. 00401 REAL SLAMCH 00402 EXTERNAL SLAMCH 00403 * .. 00404 * .. External Subroutines .. 00405 EXTERNAL SCOPY, SGEHRD, SGEMM, SGET10, SGET22, SHSEIN, 00406 $ SHSEQR, SHST01, SLABAD, SLACPY, SLAFTS, SLASET, 00407 $ SLASUM, SLATME, SLATMR, SLATMS, SORGHR, SORMHR, 00408 $ STREVC, XERBLA 00409 * .. 00410 * .. Intrinsic Functions .. 00411 INTRINSIC ABS, MAX, MIN, REAL, SQRT 00412 * .. 00413 * .. Data statements .. 00414 DATA KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 / 00415 DATA KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2, 00416 $ 3, 1, 2, 3 / 00417 DATA KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3, 00418 $ 1, 5, 5, 5, 4, 3, 1 / 00419 DATA KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 / 00420 * .. 00421 * .. Executable Statements .. 00422 * 00423 * Check for errors 00424 * 00425 NTESTT = 0 00426 INFO = 0 00427 * 00428 BADNN = .FALSE. 00429 NMAX = 0 00430 DO 10 J = 1, NSIZES 00431 NMAX = MAX( NMAX, NN( J ) ) 00432 IF( NN( J ).LT.0 ) 00433 $ BADNN = .TRUE. 00434 10 CONTINUE 00435 * 00436 * Check for errors 00437 * 00438 IF( NSIZES.LT.0 ) THEN 00439 INFO = -1 00440 ELSE IF( BADNN ) THEN 00441 INFO = -2 00442 ELSE IF( NTYPES.LT.0 ) THEN 00443 INFO = -3 00444 ELSE IF( THRESH.LT.ZERO ) THEN 00445 INFO = -6 00446 ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN 00447 INFO = -9 00448 ELSE IF( LDU.LE.1 .OR. LDU.LT.NMAX ) THEN 00449 INFO = -14 00450 ELSE IF( 4*NMAX*NMAX+2.GT.NWORK ) THEN 00451 INFO = -28 00452 END IF 00453 * 00454 IF( INFO.NE.0 ) THEN 00455 CALL XERBLA( 'SCHKHS', -INFO ) 00456 RETURN 00457 END IF 00458 * 00459 * Quick return if possible 00460 * 00461 IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) 00462 $ RETURN 00463 * 00464 * More important constants 00465 * 00466 UNFL = SLAMCH( 'Safe minimum' ) 00467 OVFL = SLAMCH( 'Overflow' ) 00468 CALL SLABAD( UNFL, OVFL ) 00469 ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' ) 00470 ULPINV = ONE / ULP 00471 RTUNFL = SQRT( UNFL ) 00472 RTOVFL = SQRT( OVFL ) 00473 RTULP = SQRT( ULP ) 00474 RTULPI = ONE / RTULP 00475 * 00476 * Loop over sizes, types 00477 * 00478 NERRS = 0 00479 NMATS = 0 00480 * 00481 DO 270 JSIZE = 1, NSIZES 00482 N = NN( JSIZE ) 00483 IF( N.EQ.0 ) 00484 $ GO TO 270 00485 N1 = MAX( 1, N ) 00486 ANINV = ONE / REAL( N1 ) 00487 * 00488 IF( NSIZES.NE.1 ) THEN 00489 MTYPES = MIN( MAXTYP, NTYPES ) 00490 ELSE 00491 MTYPES = MIN( MAXTYP+1, NTYPES ) 00492 END IF 00493 * 00494 DO 260 JTYPE = 1, MTYPES 00495 IF( .NOT.DOTYPE( JTYPE ) ) 00496 $ GO TO 260 00497 NMATS = NMATS + 1 00498 NTEST = 0 00499 * 00500 * Save ISEED in case of an error. 00501 * 00502 DO 20 J = 1, 4 00503 IOLDSD( J ) = ISEED( J ) 00504 20 CONTINUE 00505 * 00506 * Initialize RESULT 00507 * 00508 DO 30 J = 1, 14 00509 RESULT( J ) = ZERO 00510 30 CONTINUE 00511 * 00512 * Compute "A" 00513 * 00514 * Control parameters: 00515 * 00516 * KMAGN KCONDS KMODE KTYPE 00517 * =1 O(1) 1 clustered 1 zero 00518 * =2 large large clustered 2 identity 00519 * =3 small exponential Jordan 00520 * =4 arithmetic diagonal, (w/ eigenvalues) 00521 * =5 random log symmetric, w/ eigenvalues 00522 * =6 random general, w/ eigenvalues 00523 * =7 random diagonal 00524 * =8 random symmetric 00525 * =9 random general 00526 * =10 random triangular 00527 * 00528 IF( MTYPES.GT.MAXTYP ) 00529 $ GO TO 100 00530 * 00531 ITYPE = KTYPE( JTYPE ) 00532 IMODE = KMODE( JTYPE ) 00533 * 00534 * Compute norm 00535 * 00536 GO TO ( 40, 50, 60 )KMAGN( JTYPE ) 00537 * 00538 40 CONTINUE 00539 ANORM = ONE 00540 GO TO 70 00541 * 00542 50 CONTINUE 00543 ANORM = ( RTOVFL*ULP )*ANINV 00544 GO TO 70 00545 * 00546 60 CONTINUE 00547 ANORM = RTUNFL*N*ULPINV 00548 GO TO 70 00549 * 00550 70 CONTINUE 00551 * 00552 CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) 00553 IINFO = 0 00554 COND = ULPINV 00555 * 00556 * Special Matrices 00557 * 00558 IF( ITYPE.EQ.1 ) THEN 00559 * 00560 * Zero 00561 * 00562 IINFO = 0 00563 * 00564 ELSE IF( ITYPE.EQ.2 ) THEN 00565 * 00566 * Identity 00567 * 00568 DO 80 JCOL = 1, N 00569 A( JCOL, JCOL ) = ANORM 00570 80 CONTINUE 00571 * 00572 ELSE IF( ITYPE.EQ.3 ) THEN 00573 * 00574 * Jordan Block 00575 * 00576 DO 90 JCOL = 1, N 00577 A( JCOL, JCOL ) = ANORM 00578 IF( JCOL.GT.1 ) 00579 $ A( JCOL, JCOL-1 ) = ONE 00580 90 CONTINUE 00581 * 00582 ELSE IF( ITYPE.EQ.4 ) THEN 00583 * 00584 * Diagonal Matrix, [Eigen]values Specified 00585 * 00586 CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND, 00587 $ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ), 00588 $ IINFO ) 00589 * 00590 ELSE IF( ITYPE.EQ.5 ) THEN 00591 * 00592 * Symmetric, eigenvalues specified 00593 * 00594 CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND, 00595 $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ), 00596 $ IINFO ) 00597 * 00598 ELSE IF( ITYPE.EQ.6 ) THEN 00599 * 00600 * General, eigenvalues specified 00601 * 00602 IF( KCONDS( JTYPE ).EQ.1 ) THEN 00603 CONDS = ONE 00604 ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN 00605 CONDS = RTULPI 00606 ELSE 00607 CONDS = ZERO 00608 END IF 00609 * 00610 ADUMMA( 1 ) = ' ' 00611 CALL SLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE, 00612 $ ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4, 00613 $ CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ), 00614 $ IINFO ) 00615 * 00616 ELSE IF( ITYPE.EQ.7 ) THEN 00617 * 00618 * Diagonal, random eigenvalues 00619 * 00620 CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE, 00621 $ 'T', 'N', WORK( N+1 ), 1, ONE, 00622 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0, 00623 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) 00624 * 00625 ELSE IF( ITYPE.EQ.8 ) THEN 00626 * 00627 * Symmetric, random eigenvalues 00628 * 00629 CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE, 00630 $ 'T', 'N', WORK( N+1 ), 1, ONE, 00631 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N, 00632 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) 00633 * 00634 ELSE IF( ITYPE.EQ.9 ) THEN 00635 * 00636 * General, random eigenvalues 00637 * 00638 CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE, 00639 $ 'T', 'N', WORK( N+1 ), 1, ONE, 00640 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N, 00641 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) 00642 * 00643 ELSE IF( ITYPE.EQ.10 ) THEN 00644 * 00645 * Triangular, random eigenvalues 00646 * 00647 CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE, 00648 $ 'T', 'N', WORK( N+1 ), 1, ONE, 00649 $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0, 00650 $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) 00651 * 00652 ELSE 00653 * 00654 IINFO = 1 00655 END IF 00656 * 00657 IF( IINFO.NE.0 ) THEN 00658 WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE, 00659 $ IOLDSD 00660 INFO = ABS( IINFO ) 00661 RETURN 00662 END IF 00663 * 00664 100 CONTINUE 00665 * 00666 * Call SGEHRD to compute H and U, do tests. 00667 * 00668 CALL SLACPY( ' ', N, N, A, LDA, H, LDA ) 00669 * 00670 NTEST = 1 00671 * 00672 ILO = 1 00673 IHI = N 00674 * 00675 CALL SGEHRD( N, ILO, IHI, H, LDA, WORK, WORK( N+1 ), 00676 $ NWORK-N, IINFO ) 00677 * 00678 IF( IINFO.NE.0 ) THEN 00679 RESULT( 1 ) = ULPINV 00680 WRITE( NOUNIT, FMT = 9999 )'SGEHRD', IINFO, N, JTYPE, 00681 $ IOLDSD 00682 INFO = ABS( IINFO ) 00683 GO TO 250 00684 END IF 00685 * 00686 DO 120 J = 1, N - 1 00687 UU( J+1, J ) = ZERO 00688 DO 110 I = J + 2, N 00689 U( I, J ) = H( I, J ) 00690 UU( I, J ) = H( I, J ) 00691 H( I, J ) = ZERO 00692 110 CONTINUE 00693 120 CONTINUE 00694 CALL SCOPY( N-1, WORK, 1, TAU, 1 ) 00695 CALL SORGHR( N, ILO, IHI, U, LDU, WORK, WORK( N+1 ), 00696 $ NWORK-N, IINFO ) 00697 NTEST = 2 00698 * 00699 CALL SHST01( N, ILO, IHI, A, LDA, H, LDA, U, LDU, WORK, 00700 $ NWORK, RESULT( 1 ) ) 00701 * 00702 * Call SHSEQR to compute T1, T2 and Z, do tests. 00703 * 00704 * Eigenvalues only (WR3,WI3) 00705 * 00706 CALL SLACPY( ' ', N, N, H, LDA, T2, LDA ) 00707 NTEST = 3 00708 RESULT( 3 ) = ULPINV 00709 * 00710 CALL SHSEQR( 'E', 'N', N, ILO, IHI, T2, LDA, WR3, WI3, UZ, 00711 $ LDU, WORK, NWORK, IINFO ) 00712 IF( IINFO.NE.0 ) THEN 00713 WRITE( NOUNIT, FMT = 9999 )'SHSEQR(E)', IINFO, N, JTYPE, 00714 $ IOLDSD 00715 IF( IINFO.LE.N+2 ) THEN 00716 INFO = ABS( IINFO ) 00717 GO TO 250 00718 END IF 00719 END IF 00720 * 00721 * Eigenvalues (WR1,WI1) and Full Schur Form (T2) 00722 * 00723 CALL SLACPY( ' ', N, N, H, LDA, T2, LDA ) 00724 * 00725 CALL SHSEQR( 'S', 'N', N, ILO, IHI, T2, LDA, WR1, WI1, UZ, 00726 $ LDU, WORK, NWORK, IINFO ) 00727 IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN 00728 WRITE( NOUNIT, FMT = 9999 )'SHSEQR(S)', IINFO, N, JTYPE, 00729 $ IOLDSD 00730 INFO = ABS( IINFO ) 00731 GO TO 250 00732 END IF 00733 * 00734 * Eigenvalues (WR1,WI1), Schur Form (T1), and Schur vectors 00735 * (UZ) 00736 * 00737 CALL SLACPY( ' ', N, N, H, LDA, T1, LDA ) 00738 CALL SLACPY( ' ', N, N, U, LDU, UZ, LDA ) 00739 * 00740 CALL SHSEQR( 'S', 'V', N, ILO, IHI, T1, LDA, WR1, WI1, UZ, 00741 $ LDU, WORK, NWORK, IINFO ) 00742 IF( IINFO.NE.0 .AND. IINFO.LE.N+2 ) THEN 00743 WRITE( NOUNIT, FMT = 9999 )'SHSEQR(V)', IINFO, N, JTYPE, 00744 $ IOLDSD 00745 INFO = ABS( IINFO ) 00746 GO TO 250 00747 END IF 00748 * 00749 * Compute Z = U' UZ 00750 * 00751 CALL SGEMM( 'T', 'N', N, N, N, ONE, U, LDU, UZ, LDU, ZERO, 00752 $ Z, LDU ) 00753 NTEST = 8 00754 * 00755 * Do Tests 3: | H - Z T Z' | / ( |H| n ulp ) 00756 * and 4: | I - Z Z' | / ( n ulp ) 00757 * 00758 CALL SHST01( N, ILO, IHI, H, LDA, T1, LDA, Z, LDU, WORK, 00759 $ NWORK, RESULT( 3 ) ) 00760 * 00761 * Do Tests 5: | A - UZ T (UZ)' | / ( |A| n ulp ) 00762 * and 6: | I - UZ (UZ)' | / ( n ulp ) 00763 * 00764 CALL SHST01( N, ILO, IHI, A, LDA, T1, LDA, UZ, LDU, WORK, 00765 $ NWORK, RESULT( 5 ) ) 00766 * 00767 * Do Test 7: | T2 - T1 | / ( |T| n ulp ) 00768 * 00769 CALL SGET10( N, N, T2, LDA, T1, LDA, WORK, RESULT( 7 ) ) 00770 * 00771 * Do Test 8: | W3 - W1 | / ( max(|W1|,|W3|) ulp ) 00772 * 00773 TEMP1 = ZERO 00774 TEMP2 = ZERO 00775 DO 130 J = 1, N 00776 TEMP1 = MAX( TEMP1, ABS( WR1( J ) )+ABS( WI1( J ) ), 00777 $ ABS( WR3( J ) )+ABS( WI3( J ) ) ) 00778 TEMP2 = MAX( TEMP2, ABS( WR1( J )-WR3( J ) )+ 00779 $ ABS( WR1( J )-WR3( J ) ) ) 00780 130 CONTINUE 00781 * 00782 RESULT( 8 ) = TEMP2 / MAX( UNFL, ULP*MAX( TEMP1, TEMP2 ) ) 00783 * 00784 * Compute the Left and Right Eigenvectors of T 00785 * 00786 * Compute the Right eigenvector Matrix: 00787 * 00788 NTEST = 9 00789 RESULT( 9 ) = ULPINV 00790 * 00791 * Select last max(N/4,1) real, max(N/4,1) complex eigenvectors 00792 * 00793 NSELC = 0 00794 NSELR = 0 00795 J = N 00796 140 CONTINUE 00797 IF( WI1( J ).EQ.ZERO ) THEN 00798 IF( NSELR.LT.MAX( N / 4, 1 ) ) THEN 00799 NSELR = NSELR + 1 00800 SELECT( J ) = .TRUE. 00801 ELSE 00802 SELECT( J ) = .FALSE. 00803 END IF 00804 J = J - 1 00805 ELSE 00806 IF( NSELC.LT.MAX( N / 4, 1 ) ) THEN 00807 NSELC = NSELC + 1 00808 SELECT( J ) = .TRUE. 00809 SELECT( J-1 ) = .FALSE. 00810 ELSE 00811 SELECT( J ) = .FALSE. 00812 SELECT( J-1 ) = .FALSE. 00813 END IF 00814 J = J - 2 00815 END IF 00816 IF( J.GT.0 ) 00817 $ GO TO 140 00818 * 00819 CALL STREVC( 'Right', 'All', SELECT, N, T1, LDA, DUMMA, LDU, 00820 $ EVECTR, LDU, N, IN, WORK, IINFO ) 00821 IF( IINFO.NE.0 ) THEN 00822 WRITE( NOUNIT, FMT = 9999 )'STREVC(R,A)', IINFO, N, 00823 $ JTYPE, IOLDSD 00824 INFO = ABS( IINFO ) 00825 GO TO 250 00826 END IF 00827 * 00828 * Test 9: | TR - RW | / ( |T| |R| ulp ) 00829 * 00830 CALL SGET22( 'N', 'N', 'N', N, T1, LDA, EVECTR, LDU, WR1, 00831 $ WI1, WORK, DUMMA( 1 ) ) 00832 RESULT( 9 ) = DUMMA( 1 ) 00833 IF( DUMMA( 2 ).GT.THRESH ) THEN 00834 WRITE( NOUNIT, FMT = 9998 )'Right', 'STREVC', 00835 $ DUMMA( 2 ), N, JTYPE, IOLDSD 00836 END IF 00837 * 00838 * Compute selected right eigenvectors and confirm that 00839 * they agree with previous right eigenvectors 00840 * 00841 CALL STREVC( 'Right', 'Some', SELECT, N, T1, LDA, DUMMA, 00842 $ LDU, EVECTL, LDU, N, IN, WORK, IINFO ) 00843 IF( IINFO.NE.0 ) THEN 00844 WRITE( NOUNIT, FMT = 9999 )'STREVC(R,S)', IINFO, N, 00845 $ JTYPE, IOLDSD 00846 INFO = ABS( IINFO ) 00847 GO TO 250 00848 END IF 00849 * 00850 K = 1 00851 MATCH = .TRUE. 00852 DO 170 J = 1, N 00853 IF( SELECT( J ) .AND. WI1( J ).EQ.ZERO ) THEN 00854 DO 150 JJ = 1, N 00855 IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) ) THEN 00856 MATCH = .FALSE. 00857 GO TO 180 00858 END IF 00859 150 CONTINUE 00860 K = K + 1 00861 ELSE IF( SELECT( J ) .AND. WI1( J ).NE.ZERO ) THEN 00862 DO 160 JJ = 1, N 00863 IF( EVECTR( JJ, J ).NE.EVECTL( JJ, K ) .OR. 00864 $ EVECTR( JJ, J+1 ).NE.EVECTL( JJ, K+1 ) ) THEN 00865 MATCH = .FALSE. 00866 GO TO 180 00867 END IF 00868 160 CONTINUE 00869 K = K + 2 00870 END IF 00871 170 CONTINUE 00872 180 CONTINUE 00873 IF( .NOT.MATCH ) 00874 $ WRITE( NOUNIT, FMT = 9997 )'Right', 'STREVC', N, JTYPE, 00875 $ IOLDSD 00876 * 00877 * Compute the Left eigenvector Matrix: 00878 * 00879 NTEST = 10 00880 RESULT( 10 ) = ULPINV 00881 CALL STREVC( 'Left', 'All', SELECT, N, T1, LDA, EVECTL, LDU, 00882 $ DUMMA, LDU, N, IN, WORK, IINFO ) 00883 IF( IINFO.NE.0 ) THEN 00884 WRITE( NOUNIT, FMT = 9999 )'STREVC(L,A)', IINFO, N, 00885 $ JTYPE, IOLDSD 00886 INFO = ABS( IINFO ) 00887 GO TO 250 00888 END IF 00889 * 00890 * Test 10: | LT - WL | / ( |T| |L| ulp ) 00891 * 00892 CALL SGET22( 'Trans', 'N', 'Conj', N, T1, LDA, EVECTL, LDU, 00893 $ WR1, WI1, WORK, DUMMA( 3 ) ) 00894 RESULT( 10 ) = DUMMA( 3 ) 00895 IF( DUMMA( 4 ).GT.THRESH ) THEN 00896 WRITE( NOUNIT, FMT = 9998 )'Left', 'STREVC', DUMMA( 4 ), 00897 $ N, JTYPE, IOLDSD 00898 END IF 00899 * 00900 * Compute selected left eigenvectors and confirm that 00901 * they agree with previous left eigenvectors 00902 * 00903 CALL STREVC( 'Left', 'Some', SELECT, N, T1, LDA, EVECTR, 00904 $ LDU, DUMMA, LDU, N, IN, WORK, IINFO ) 00905 IF( IINFO.NE.0 ) THEN 00906 WRITE( NOUNIT, FMT = 9999 )'STREVC(L,S)', IINFO, N, 00907 $ JTYPE, IOLDSD 00908 INFO = ABS( IINFO ) 00909 GO TO 250 00910 END IF 00911 * 00912 K = 1 00913 MATCH = .TRUE. 00914 DO 210 J = 1, N 00915 IF( SELECT( J ) .AND. WI1( J ).EQ.ZERO ) THEN 00916 DO 190 JJ = 1, N 00917 IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) ) THEN 00918 MATCH = .FALSE. 00919 GO TO 220 00920 END IF 00921 190 CONTINUE 00922 K = K + 1 00923 ELSE IF( SELECT( J ) .AND. WI1( J ).NE.ZERO ) THEN 00924 DO 200 JJ = 1, N 00925 IF( EVECTL( JJ, J ).NE.EVECTR( JJ, K ) .OR. 00926 $ EVECTL( JJ, J+1 ).NE.EVECTR( JJ, K+1 ) ) THEN 00927 MATCH = .FALSE. 00928 GO TO 220 00929 END IF 00930 200 CONTINUE 00931 K = K + 2 00932 END IF 00933 210 CONTINUE 00934 220 CONTINUE 00935 IF( .NOT.MATCH ) 00936 $ WRITE( NOUNIT, FMT = 9997 )'Left', 'STREVC', N, JTYPE, 00937 $ IOLDSD 00938 * 00939 * Call SHSEIN for Right eigenvectors of H, do test 11 00940 * 00941 NTEST = 11 00942 RESULT( 11 ) = ULPINV 00943 DO 230 J = 1, N 00944 SELECT( J ) = .TRUE. 00945 230 CONTINUE 00946 * 00947 CALL SHSEIN( 'Right', 'Qr', 'Ninitv', SELECT, N, H, LDA, 00948 $ WR3, WI3, DUMMA, LDU, EVECTX, LDU, N1, IN, 00949 $ WORK, IWORK, IWORK, IINFO ) 00950 IF( IINFO.NE.0 ) THEN 00951 WRITE( NOUNIT, FMT = 9999 )'SHSEIN(R)', IINFO, N, JTYPE, 00952 $ IOLDSD 00953 INFO = ABS( IINFO ) 00954 IF( IINFO.LT.0 ) 00955 $ GO TO 250 00956 ELSE 00957 * 00958 * Test 11: | HX - XW | / ( |H| |X| ulp ) 00959 * 00960 * (from inverse iteration) 00961 * 00962 CALL SGET22( 'N', 'N', 'N', N, H, LDA, EVECTX, LDU, WR3, 00963 $ WI3, WORK, DUMMA( 1 ) ) 00964 IF( DUMMA( 1 ).LT.ULPINV ) 00965 $ RESULT( 11 ) = DUMMA( 1 )*ANINV 00966 IF( DUMMA( 2 ).GT.THRESH ) THEN 00967 WRITE( NOUNIT, FMT = 9998 )'Right', 'SHSEIN', 00968 $ DUMMA( 2 ), N, JTYPE, IOLDSD 00969 END IF 00970 END IF 00971 * 00972 * Call SHSEIN for Left eigenvectors of H, do test 12 00973 * 00974 NTEST = 12 00975 RESULT( 12 ) = ULPINV 00976 DO 240 J = 1, N 00977 SELECT( J ) = .TRUE. 00978 240 CONTINUE 00979 * 00980 CALL SHSEIN( 'Left', 'Qr', 'Ninitv', SELECT, N, H, LDA, WR3, 00981 $ WI3, EVECTY, LDU, DUMMA, LDU, N1, IN, WORK, 00982 $ IWORK, IWORK, IINFO ) 00983 IF( IINFO.NE.0 ) THEN 00984 WRITE( NOUNIT, FMT = 9999 )'SHSEIN(L)', IINFO, N, JTYPE, 00985 $ IOLDSD 00986 INFO = ABS( IINFO ) 00987 IF( IINFO.LT.0 ) 00988 $ GO TO 250 00989 ELSE 00990 * 00991 * Test 12: | YH - WY | / ( |H| |Y| ulp ) 00992 * 00993 * (from inverse iteration) 00994 * 00995 CALL SGET22( 'C', 'N', 'C', N, H, LDA, EVECTY, LDU, WR3, 00996 $ WI3, WORK, DUMMA( 3 ) ) 00997 IF( DUMMA( 3 ).LT.ULPINV ) 00998 $ RESULT( 12 ) = DUMMA( 3 )*ANINV 00999 IF( DUMMA( 4 ).GT.THRESH ) THEN 01000 WRITE( NOUNIT, FMT = 9998 )'Left', 'SHSEIN', 01001 $ DUMMA( 4 ), N, JTYPE, IOLDSD 01002 END IF 01003 END IF 01004 * 01005 * Call SORMHR for Right eigenvectors of A, do test 13 01006 * 01007 NTEST = 13 01008 RESULT( 13 ) = ULPINV 01009 * 01010 CALL SORMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU, 01011 $ LDU, TAU, EVECTX, LDU, WORK, NWORK, IINFO ) 01012 IF( IINFO.NE.0 ) THEN 01013 WRITE( NOUNIT, FMT = 9999 )'SORMHR(R)', IINFO, N, JTYPE, 01014 $ IOLDSD 01015 INFO = ABS( IINFO ) 01016 IF( IINFO.LT.0 ) 01017 $ GO TO 250 01018 ELSE 01019 * 01020 * Test 13: | AX - XW | / ( |A| |X| ulp ) 01021 * 01022 * (from inverse iteration) 01023 * 01024 CALL SGET22( 'N', 'N', 'N', N, A, LDA, EVECTX, LDU, WR3, 01025 $ WI3, WORK, DUMMA( 1 ) ) 01026 IF( DUMMA( 1 ).LT.ULPINV ) 01027 $ RESULT( 13 ) = DUMMA( 1 )*ANINV 01028 END IF 01029 * 01030 * Call SORMHR for Left eigenvectors of A, do test 14 01031 * 01032 NTEST = 14 01033 RESULT( 14 ) = ULPINV 01034 * 01035 CALL SORMHR( 'Left', 'No transpose', N, N, ILO, IHI, UU, 01036 $ LDU, TAU, EVECTY, LDU, WORK, NWORK, IINFO ) 01037 IF( IINFO.NE.0 ) THEN 01038 WRITE( NOUNIT, FMT = 9999 )'SORMHR(L)', IINFO, N, JTYPE, 01039 $ IOLDSD 01040 INFO = ABS( IINFO ) 01041 IF( IINFO.LT.0 ) 01042 $ GO TO 250 01043 ELSE 01044 * 01045 * Test 14: | YA - WY | / ( |A| |Y| ulp ) 01046 * 01047 * (from inverse iteration) 01048 * 01049 CALL SGET22( 'C', 'N', 'C', N, A, LDA, EVECTY, LDU, WR3, 01050 $ WI3, WORK, DUMMA( 3 ) ) 01051 IF( DUMMA( 3 ).LT.ULPINV ) 01052 $ RESULT( 14 ) = DUMMA( 3 )*ANINV 01053 END IF 01054 * 01055 * End of Loop -- Check for RESULT(j) > THRESH 01056 * 01057 250 CONTINUE 01058 * 01059 NTESTT = NTESTT + NTEST 01060 CALL SLAFTS( 'SHS', N, N, JTYPE, NTEST, RESULT, IOLDSD, 01061 $ THRESH, NOUNIT, NERRS ) 01062 * 01063 260 CONTINUE 01064 270 CONTINUE 01065 * 01066 * Summary 01067 * 01068 CALL SLASUM( 'SHS', NOUNIT, NERRS, NTESTT ) 01069 * 01070 RETURN 01071 * 01072 9999 FORMAT( ' SCHKHS: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', 01073 $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) 01074 9998 FORMAT( ' SCHKHS: ', A, ' Eigenvectors from ', A, ' incorrectly ', 01075 $ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X, 01076 $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, 01077 $ ')' ) 01078 9997 FORMAT( ' SCHKHS: Selected ', A, ' Eigenvectors from ', A, 01079 $ ' do not match other eigenvectors ', 9X, 'N=', I6, 01080 $ ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) 01081 * 01082 * End of SCHKHS 01083 * 01084 END
1.7.3 
