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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SCHKGG 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE SCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, 00012 * TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1, 00013 * S2, P1, P2, U, LDU, V, Q, Z, ALPHR1, ALPHI1, 00014 * BETA1, ALPHR3, ALPHI3, BETA3, EVECTL, EVECTR, 00015 * WORK, LWORK, LLWORK, RESULT, INFO ) 00016 * 00017 * .. Scalar Arguments .. 00018 * LOGICAL TSTDIF 00019 * INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES 00020 * REAL THRESH, THRSHN 00021 * .. 00022 * .. Array Arguments .. 00023 * LOGICAL DOTYPE( * ), LLWORK( * ) 00024 * INTEGER ISEED( 4 ), NN( * ) 00025 * REAL A( LDA, * ), ALPHI1( * ), ALPHI3( * ), 00026 * $ ALPHR1( * ), ALPHR3( * ), B( LDA, * ), 00027 * $ BETA1( * ), BETA3( * ), EVECTL( LDU, * ), 00028 * $ EVECTR( LDU, * ), H( LDA, * ), P1( LDA, * ), 00029 * $ P2( LDA, * ), Q( LDU, * ), RESULT( 15 ), 00030 * $ S1( LDA, * ), S2( LDA, * ), T( LDA, * ), 00031 * $ U( LDU, * ), V( LDU, * ), WORK( * ), 00032 * $ Z( LDU, * ) 00033 * .. 00034 * 00035 * 00036 *> \par Purpose: 00037 * ============= 00038 *> 00039 *> \verbatim 00040 *> 00041 *> SCHKGG checks the nonsymmetric generalized eigenvalue problem 00042 *> routines. 00043 *> T T T 00044 *> SGGHRD factors A and B as U H V and U T V , where means 00045 *> transpose, H is hessenberg, T is triangular and U and V are 00046 *> orthogonal. 00047 *> T T 00048 *> SHGEQZ factors H and T as Q S Z and Q P Z , where P is upper 00049 *> triangular, S is in generalized Schur form (block upper triangular, 00050 *> with 1x1 and 2x2 blocks on the diagonal, the 2x2 blocks 00051 *> corresponding to complex conjugate pairs of generalized 00052 *> eigenvalues), and Q and Z are orthogonal. It also computes the 00053 *> generalized eigenvalues (alpha(1),beta(1)),...,(alpha(n),beta(n)), 00054 *> where alpha(j)=S(j,j) and beta(j)=P(j,j) -- thus, 00055 *> w(j) = alpha(j)/beta(j) is a root of the generalized eigenvalue 00056 *> problem 00057 *> 00058 *> det( A - w(j) B ) = 0 00059 *> 00060 *> and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent 00061 *> problem 00062 *> 00063 *> det( m(j) A - B ) = 0 00064 *> 00065 *> STGEVC computes the matrix L of left eigenvectors and the matrix R 00066 *> of right eigenvectors for the matrix pair ( S, P ). In the 00067 *> description below, l and r are left and right eigenvectors 00068 *> corresponding to the generalized eigenvalues (alpha,beta). 00069 *> 00070 *> When SCHKGG is called, a number of matrix "sizes" ("n's") and a 00071 *> number of matrix "types" are specified. For each size ("n") 00072 *> and each type of matrix, one matrix will be generated and used 00073 *> to test the nonsymmetric eigenroutines. For each matrix, 15 00074 *> tests will be performed. The first twelve "test ratios" should be 00075 *> small -- O(1). They will be compared with the threshhold THRESH: 00076 *> 00077 *> T 00078 *> (1) | A - U H V | / ( |A| n ulp ) 00079 *> 00080 *> T 00081 *> (2) | B - U T V | / ( |B| n ulp ) 00082 *> 00083 *> T 00084 *> (3) | I - UU | / ( n ulp ) 00085 *> 00086 *> T 00087 *> (4) | I - VV | / ( n ulp ) 00088 *> 00089 *> T 00090 *> (5) | H - Q S Z | / ( |H| n ulp ) 00091 *> 00092 *> T 00093 *> (6) | T - Q P Z | / ( |T| n ulp ) 00094 *> 00095 *> T 00096 *> (7) | I - QQ | / ( n ulp ) 00097 *> 00098 *> T 00099 *> (8) | I - ZZ | / ( n ulp ) 00100 *> 00101 *> (9) max over all left eigenvalue/-vector pairs (beta/alpha,l) of 00102 *> 00103 *> | l**H * (beta S - alpha P) | / ( ulp max( |beta S|, |alpha P| ) ) 00104 *> 00105 *> (10) max over all left eigenvalue/-vector pairs (beta/alpha,l') of 00106 *> T 00107 *> | l'**H * (beta H - alpha T) | / ( ulp max( |beta H|, |alpha T| ) ) 00108 *> 00109 *> where the eigenvectors l' are the result of passing Q to 00110 *> STGEVC and back transforming (HOWMNY='B'). 00111 *> 00112 *> (11) max over all right eigenvalue/-vector pairs (beta/alpha,r) of 00113 *> 00114 *> | (beta S - alpha T) r | / ( ulp max( |beta S|, |alpha T| ) ) 00115 *> 00116 *> (12) max over all right eigenvalue/-vector pairs (beta/alpha,r') of 00117 *> 00118 *> | (beta H - alpha T) r' | / ( ulp max( |beta H|, |alpha T| ) ) 00119 *> 00120 *> where the eigenvectors r' are the result of passing Z to 00121 *> STGEVC and back transforming (HOWMNY='B'). 00122 *> 00123 *> The last three test ratios will usually be small, but there is no 00124 *> mathematical requirement that they be so. They are therefore 00125 *> compared with THRESH only if TSTDIF is .TRUE. 00126 *> 00127 *> (13) | S(Q,Z computed) - S(Q,Z not computed) | / ( |S| ulp ) 00128 *> 00129 *> (14) | P(Q,Z computed) - P(Q,Z not computed) | / ( |P| ulp ) 00130 *> 00131 *> (15) max( |alpha(Q,Z computed) - alpha(Q,Z not computed)|/|S| , 00132 *> |beta(Q,Z computed) - beta(Q,Z not computed)|/|P| ) / ulp 00133 *> 00134 *> In addition, the normalization of L and R are checked, and compared 00135 *> with the threshhold THRSHN. 00136 *> 00137 *> Test Matrices 00138 *> ---- -------- 00139 *> 00140 *> The sizes of the test matrices are specified by an array 00141 *> NN(1:NSIZES); the value of each element NN(j) specifies one size. 00142 *> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if 00143 *> DOTYPE(j) is .TRUE., then matrix type "j" will be generated. 00144 *> Currently, the list of possible types is: 00145 *> 00146 *> (1) ( 0, 0 ) (a pair of zero matrices) 00147 *> 00148 *> (2) ( I, 0 ) (an identity and a zero matrix) 00149 *> 00150 *> (3) ( 0, I ) (an identity and a zero matrix) 00151 *> 00152 *> (4) ( I, I ) (a pair of identity matrices) 00153 *> 00154 *> t t 00155 *> (5) ( J , J ) (a pair of transposed Jordan blocks) 00156 *> 00157 *> t ( I 0 ) 00158 *> (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) 00159 *> ( 0 I ) ( 0 J ) 00160 *> and I is a k x k identity and J a (k+1)x(k+1) 00161 *> Jordan block; k=(N-1)/2 00162 *> 00163 *> (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal 00164 *> matrix with those diagonal entries.) 00165 *> (8) ( I, D ) 00166 *> 00167 *> (9) ( big*D, small*I ) where "big" is near overflow and small=1/big 00168 *> 00169 *> (10) ( small*D, big*I ) 00170 *> 00171 *> (11) ( big*I, small*D ) 00172 *> 00173 *> (12) ( small*I, big*D ) 00174 *> 00175 *> (13) ( big*D, big*I ) 00176 *> 00177 *> (14) ( small*D, small*I ) 00178 *> 00179 *> (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and 00180 *> D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) 00181 *> t t 00182 *> (16) U ( J , J ) V where U and V are random orthogonal matrices. 00183 *> 00184 *> (17) U ( T1, T2 ) V where T1 and T2 are upper triangular matrices 00185 *> with random O(1) entries above the diagonal 00186 *> and diagonal entries diag(T1) = 00187 *> ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = 00188 *> ( 0, N-3, N-4,..., 1, 0, 0 ) 00189 *> 00190 *> (18) U ( T1, T2 ) V diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) 00191 *> diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) 00192 *> s = machine precision. 00193 *> 00194 *> (19) U ( T1, T2 ) V diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) 00195 *> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) 00196 *> 00197 *> N-5 00198 *> (20) U ( T1, T2 ) V diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) 00199 *> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) 00200 *> 00201 *> (21) U ( T1, T2 ) V diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) 00202 *> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) 00203 *> where r1,..., r(N-4) are random. 00204 *> 00205 *> (22) U ( big*T1, small*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) 00206 *> diag(T2) = ( 0, 1, ..., 1, 0, 0 ) 00207 *> 00208 *> (23) U ( small*T1, big*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) 00209 *> diag(T2) = ( 0, 1, ..., 1, 0, 0 ) 00210 *> 00211 *> (24) U ( small*T1, small*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) 00212 *> diag(T2) = ( 0, 1, ..., 1, 0, 0 ) 00213 *> 00214 *> (25) U ( big*T1, big*T2 ) V diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) 00215 *> diag(T2) = ( 0, 1, ..., 1, 0, 0 ) 00216 *> 00217 *> (26) U ( T1, T2 ) V where T1 and T2 are random upper-triangular 00218 *> matrices. 00219 *> \endverbatim 00220 * 00221 * Arguments: 00222 * ========== 00223 * 00224 *> \param[in] NSIZES 00225 *> \verbatim 00226 *> NSIZES is INTEGER 00227 *> The number of sizes of matrices to use. If it is zero, 00228 *> SCHKGG does nothing. It must be at least zero. 00229 *> \endverbatim 00230 *> 00231 *> \param[in] NN 00232 *> \verbatim 00233 *> NN is INTEGER array, dimension (NSIZES) 00234 *> An array containing the sizes to be used for the matrices. 00235 *> Zero values will be skipped. The values must be at least 00236 *> zero. 00237 *> \endverbatim 00238 *> 00239 *> \param[in] NTYPES 00240 *> \verbatim 00241 *> NTYPES is INTEGER 00242 *> The number of elements in DOTYPE. If it is zero, SCHKGG 00243 *> does nothing. It must be at least zero. If it is MAXTYP+1 00244 *> and NSIZES is 1, then an additional type, MAXTYP+1 is 00245 *> defined, which is to use whatever matrix is in A. This 00246 *> is only useful if DOTYPE(1:MAXTYP) is .FALSE. and 00247 *> DOTYPE(MAXTYP+1) is .TRUE. . 00248 *> \endverbatim 00249 *> 00250 *> \param[in] DOTYPE 00251 *> \verbatim 00252 *> DOTYPE is LOGICAL array, dimension (NTYPES) 00253 *> If DOTYPE(j) is .TRUE., then for each size in NN a 00254 *> matrix of that size and of type j will be generated. 00255 *> If NTYPES is smaller than the maximum number of types 00256 *> defined (PARAMETER MAXTYP), then types NTYPES+1 through 00257 *> MAXTYP will not be generated. If NTYPES is larger 00258 *> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) 00259 *> will be ignored. 00260 *> \endverbatim 00261 *> 00262 *> \param[in,out] ISEED 00263 *> \verbatim 00264 *> ISEED is INTEGER array, dimension (4) 00265 *> On entry ISEED specifies the seed of the random number 00266 *> generator. The array elements should be between 0 and 4095; 00267 *> if not they will be reduced mod 4096. Also, ISEED(4) must 00268 *> be odd. The random number generator uses a linear 00269 *> congruential sequence limited to small integers, and so 00270 *> should produce machine independent random numbers. The 00271 *> values of ISEED are changed on exit, and can be used in the 00272 *> next call to SCHKGG to continue the same random number 00273 *> sequence. 00274 *> \endverbatim 00275 *> 00276 *> \param[in] THRESH 00277 *> \verbatim 00278 *> THRESH is REAL 00279 *> A test will count as "failed" if the "error", computed as 00280 *> described above, exceeds THRESH. Note that the error is 00281 *> scaled to be O(1), so THRESH should be a reasonably small 00282 *> multiple of 1, e.g., 10 or 100. In particular, it should 00283 *> not depend on the precision (single vs. double) or the size 00284 *> of the matrix. It must be at least zero. 00285 *> \endverbatim 00286 *> 00287 *> \param[in] TSTDIF 00288 *> \verbatim 00289 *> TSTDIF is LOGICAL 00290 *> Specifies whether test ratios 13-15 will be computed and 00291 *> compared with THRESH. 00292 *> = .FALSE.: Only test ratios 1-12 will be computed and tested. 00293 *> Ratios 13-15 will be set to zero. 00294 *> = .TRUE.: All the test ratios 1-15 will be computed and 00295 *> tested. 00296 *> \endverbatim 00297 *> 00298 *> \param[in] THRSHN 00299 *> \verbatim 00300 *> THRSHN is REAL 00301 *> Threshhold for reporting eigenvector normalization error. 00302 *> If the normalization of any eigenvector differs from 1 by 00303 *> more than THRSHN*ulp, then a special error message will be 00304 *> printed. (This is handled separately from the other tests, 00305 *> since only a compiler or programming error should cause an 00306 *> error message, at least if THRSHN is at least 5--10.) 00307 *> \endverbatim 00308 *> 00309 *> \param[in] NOUNIT 00310 *> \verbatim 00311 *> NOUNIT is INTEGER 00312 *> The FORTRAN unit number for printing out error messages 00313 *> (e.g., if a routine returns IINFO not equal to 0.) 00314 *> \endverbatim 00315 *> 00316 *> \param[in,out] A 00317 *> \verbatim 00318 *> A is REAL array, dimension 00319 *> (LDA, max(NN)) 00320 *> Used to hold the original A matrix. Used as input only 00321 *> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and 00322 *> DOTYPE(MAXTYP+1)=.TRUE. 00323 *> \endverbatim 00324 *> 00325 *> \param[in] LDA 00326 *> \verbatim 00327 *> LDA is INTEGER 00328 *> The leading dimension of A, B, H, T, S1, P1, S2, and P2. 00329 *> It must be at least 1 and at least max( NN ). 00330 *> \endverbatim 00331 *> 00332 *> \param[in,out] B 00333 *> \verbatim 00334 *> B is REAL array, dimension 00335 *> (LDA, max(NN)) 00336 *> Used to hold the original B matrix. Used as input only 00337 *> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and 00338 *> DOTYPE(MAXTYP+1)=.TRUE. 00339 *> \endverbatim 00340 *> 00341 *> \param[out] H 00342 *> \verbatim 00343 *> H is REAL array, dimension (LDA, max(NN)) 00344 *> The upper Hessenberg matrix computed from A by SGGHRD. 00345 *> \endverbatim 00346 *> 00347 *> \param[out] T 00348 *> \verbatim 00349 *> T is REAL array, dimension (LDA, max(NN)) 00350 *> The upper triangular matrix computed from B by SGGHRD. 00351 *> \endverbatim 00352 *> 00353 *> \param[out] S1 00354 *> \verbatim 00355 *> S1 is REAL array, dimension (LDA, max(NN)) 00356 *> The Schur (block upper triangular) matrix computed from H by 00357 *> SHGEQZ when Q and Z are also computed. 00358 *> \endverbatim 00359 *> 00360 *> \param[out] S2 00361 *> \verbatim 00362 *> S2 is REAL array, dimension (LDA, max(NN)) 00363 *> The Schur (block upper triangular) matrix computed from H by 00364 *> SHGEQZ when Q and Z are not computed. 00365 *> \endverbatim 00366 *> 00367 *> \param[out] P1 00368 *> \verbatim 00369 *> P1 is REAL array, dimension (LDA, max(NN)) 00370 *> The upper triangular matrix computed from T by SHGEQZ 00371 *> when Q and Z are also computed. 00372 *> \endverbatim 00373 *> 00374 *> \param[out] P2 00375 *> \verbatim 00376 *> P2 is REAL array, dimension (LDA, max(NN)) 00377 *> The upper triangular matrix computed from T by SHGEQZ 00378 *> when Q and Z are not computed. 00379 *> \endverbatim 00380 *> 00381 *> \param[out] U 00382 *> \verbatim 00383 *> U is REAL array, dimension (LDU, max(NN)) 00384 *> The (left) orthogonal matrix computed by SGGHRD. 00385 *> \endverbatim 00386 *> 00387 *> \param[in] LDU 00388 *> \verbatim 00389 *> LDU is INTEGER 00390 *> The leading dimension of U, V, Q, Z, EVECTL, and EVECTR. It 00391 *> must be at least 1 and at least max( NN ). 00392 *> \endverbatim 00393 *> 00394 *> \param[out] V 00395 *> \verbatim 00396 *> V is REAL array, dimension (LDU, max(NN)) 00397 *> The (right) orthogonal matrix computed by SGGHRD. 00398 *> \endverbatim 00399 *> 00400 *> \param[out] Q 00401 *> \verbatim 00402 *> Q is REAL array, dimension (LDU, max(NN)) 00403 *> The (left) orthogonal matrix computed by SHGEQZ. 00404 *> \endverbatim 00405 *> 00406 *> \param[out] Z 00407 *> \verbatim 00408 *> Z is REAL array, dimension (LDU, max(NN)) 00409 *> The (left) orthogonal matrix computed by SHGEQZ. 00410 *> \endverbatim 00411 *> 00412 *> \param[out] ALPHR1 00413 *> \verbatim 00414 *> ALPHR1 is REAL array, dimension (max(NN)) 00415 *> \endverbatim 00416 *> 00417 *> \param[out] ALPHI1 00418 *> \verbatim 00419 *> ALPHI1 is REAL array, dimension (max(NN)) 00420 *> \endverbatim 00421 *> 00422 *> \param[out] BETA1 00423 *> \verbatim 00424 *> BETA1 is REAL array, dimension (max(NN)) 00425 *> 00426 *> The generalized eigenvalues of (A,B) computed by SHGEQZ 00427 *> when Q, Z, and the full Schur matrices are computed. 00428 *> On exit, ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th 00429 *> generalized eigenvalue of the matrices in A and B. 00430 *> \endverbatim 00431 *> 00432 *> \param[out] ALPHR3 00433 *> \verbatim 00434 *> ALPHR3 is REAL array, dimension (max(NN)) 00435 *> \endverbatim 00436 *> 00437 *> \param[out] ALPHI3 00438 *> \verbatim 00439 *> ALPHI3 is REAL array, dimension (max(NN)) 00440 *> \endverbatim 00441 *> 00442 *> \param[out] BETA3 00443 *> \verbatim 00444 *> BETA3 is REAL array, dimension (max(NN)) 00445 *> \endverbatim 00446 *> 00447 *> \param[out] EVECTL 00448 *> \verbatim 00449 *> EVECTL is REAL array, dimension (LDU, max(NN)) 00450 *> The (block lower triangular) left eigenvector matrix for 00451 *> the matrices in S1 and P1. (See STGEVC for the format.) 00452 *> \endverbatim 00453 *> 00454 *> \param[out] EVECTR 00455 *> \verbatim 00456 *> EVECTR is REAL array, dimension (LDU, max(NN)) 00457 *> The (block upper triangular) right eigenvector matrix for 00458 *> the matrices in S1 and P1. (See STGEVC for the format.) 00459 *> \endverbatim 00460 *> 00461 *> \param[out] WORK 00462 *> \verbatim 00463 *> WORK is REAL array, dimension (LWORK) 00464 *> \endverbatim 00465 *> 00466 *> \param[in] LWORK 00467 *> \verbatim 00468 *> LWORK is INTEGER 00469 *> The number of entries in WORK. This must be at least 00470 *> max( 2 * N**2, 6*N, 1 ), for all N=NN(j). 00471 *> \endverbatim 00472 *> 00473 *> \param[out] LLWORK 00474 *> \verbatim 00475 *> LLWORK is LOGICAL array, dimension (max(NN)) 00476 *> \endverbatim 00477 *> 00478 *> \param[out] RESULT 00479 *> \verbatim 00480 *> RESULT is REAL array, dimension (15) 00481 *> The values computed by the tests described above. 00482 *> The values are currently limited to 1/ulp, to avoid 00483 *> overflow. 00484 *> \endverbatim 00485 *> 00486 *> \param[out] INFO 00487 *> \verbatim 00488 *> INFO is INTEGER 00489 *> = 0: successful exit 00490 *> < 0: if INFO = -i, the i-th argument had an illegal value 00491 *> > 0: A routine returned an error code. INFO is the 00492 *> absolute value of the INFO value returned. 00493 *> \endverbatim 00494 * 00495 * Authors: 00496 * ======== 00497 * 00498 *> \author Univ. of Tennessee 00499 *> \author Univ. of California Berkeley 00500 *> \author Univ. of Colorado Denver 00501 *> \author NAG Ltd. 00502 * 00503 *> \date November 2011 00504 * 00505 *> \ingroup single_eig 00506 * 00507 * ===================================================================== 00508 SUBROUTINE SCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, 00509 $ TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1, 00510 $ S2, P1, P2, U, LDU, V, Q, Z, ALPHR1, ALPHI1, 00511 $ BETA1, ALPHR3, ALPHI3, BETA3, EVECTL, EVECTR, 00512 $ WORK, LWORK, LLWORK, RESULT, INFO ) 00513 * 00514 * -- LAPACK test routine (version 3.4.0) -- 00515 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00516 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00517 * November 2011 00518 * 00519 * .. Scalar Arguments .. 00520 LOGICAL TSTDIF 00521 INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES 00522 REAL THRESH, THRSHN 00523 * .. 00524 * .. Array Arguments .. 00525 LOGICAL DOTYPE( * ), LLWORK( * ) 00526 INTEGER ISEED( 4 ), NN( * ) 00527 REAL A( LDA, * ), ALPHI1( * ), ALPHI3( * ), 00528 $ ALPHR1( * ), ALPHR3( * ), B( LDA, * ), 00529 $ BETA1( * ), BETA3( * ), EVECTL( LDU, * ), 00530 $ EVECTR( LDU, * ), H( LDA, * ), P1( LDA, * ), 00531 $ P2( LDA, * ), Q( LDU, * ), RESULT( 15 ), 00532 $ S1( LDA, * ), S2( LDA, * ), T( LDA, * ), 00533 $ U( LDU, * ), V( LDU, * ), WORK( * ), 00534 $ Z( LDU, * ) 00535 * .. 00536 * 00537 * ===================================================================== 00538 * 00539 * .. Parameters .. 00540 REAL ZERO, ONE 00541 PARAMETER ( ZERO = 0.0, ONE = 1.0 ) 00542 INTEGER MAXTYP 00543 PARAMETER ( MAXTYP = 26 ) 00544 * .. 00545 * .. Local Scalars .. 00546 LOGICAL BADNN 00547 INTEGER I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE, 00548 $ LWKOPT, MTYPES, N, N1, NERRS, NMATS, NMAX, 00549 $ NTEST, NTESTT 00550 REAL ANORM, BNORM, SAFMAX, SAFMIN, TEMP1, TEMP2, 00551 $ ULP, ULPINV 00552 * .. 00553 * .. Local Arrays .. 00554 INTEGER IASIGN( MAXTYP ), IBSIGN( MAXTYP ), 00555 $ IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ), 00556 $ KATYPE( MAXTYP ), KAZERO( MAXTYP ), 00557 $ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ), 00558 $ KBZERO( MAXTYP ), KCLASS( MAXTYP ), 00559 $ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 ) 00560 REAL DUMMA( 4 ), RMAGN( 0: 3 ) 00561 * .. 00562 * .. External Functions .. 00563 REAL SLAMCH, SLANGE, SLARND 00564 EXTERNAL SLAMCH, SLANGE, SLARND 00565 * .. 00566 * .. External Subroutines .. 00567 EXTERNAL SGEQR2, SGET51, SGET52, SGGHRD, SHGEQZ, SLABAD, 00568 $ SLACPY, SLARFG, SLASET, SLASUM, SLATM4, SORM2R, 00569 $ STGEVC, XERBLA 00570 * .. 00571 * .. Intrinsic Functions .. 00572 INTRINSIC ABS, MAX, MIN, REAL, SIGN 00573 * .. 00574 * .. Data statements .. 00575 DATA KCLASS / 15*1, 10*2, 1*3 / 00576 DATA KZ1 / 0, 1, 2, 1, 3, 3 / 00577 DATA KZ2 / 0, 0, 1, 2, 1, 1 / 00578 DATA KADD / 0, 0, 0, 0, 3, 2 / 00579 DATA KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4, 00580 $ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 / 00581 DATA KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4, 00582 $ 1, 1, -4, 2, -4, 8*8, 0 / 00583 DATA KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3, 00584 $ 4*5, 4*3, 1 / 00585 DATA KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4, 00586 $ 4*6, 4*4, 1 / 00587 DATA KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3, 00588 $ 2, 1 / 00589 DATA KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3, 00590 $ 2, 1 / 00591 DATA KTRIAN / 16*0, 10*1 / 00592 DATA IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0, 00593 $ 5*2, 0 / 00594 DATA IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 / 00595 * .. 00596 * .. Executable Statements .. 00597 * 00598 * Check for errors 00599 * 00600 INFO = 0 00601 * 00602 BADNN = .FALSE. 00603 NMAX = 1 00604 DO 10 J = 1, NSIZES 00605 NMAX = MAX( NMAX, NN( J ) ) 00606 IF( NN( J ).LT.0 ) 00607 $ BADNN = .TRUE. 00608 10 CONTINUE 00609 * 00610 * Maximum blocksize and shift -- we assume that blocksize and number 00611 * of shifts are monotone increasing functions of N. 00612 * 00613 LWKOPT = MAX( 6*NMAX, 2*NMAX*NMAX, 1 ) 00614 * 00615 * Check for errors 00616 * 00617 IF( NSIZES.LT.0 ) THEN 00618 INFO = -1 00619 ELSE IF( BADNN ) THEN 00620 INFO = -2 00621 ELSE IF( NTYPES.LT.0 ) THEN 00622 INFO = -3 00623 ELSE IF( THRESH.LT.ZERO ) THEN 00624 INFO = -6 00625 ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN 00626 INFO = -10 00627 ELSE IF( LDU.LE.1 .OR. LDU.LT.NMAX ) THEN 00628 INFO = -19 00629 ELSE IF( LWKOPT.GT.LWORK ) THEN 00630 INFO = -30 00631 END IF 00632 * 00633 IF( INFO.NE.0 ) THEN 00634 CALL XERBLA( 'SCHKGG', -INFO ) 00635 RETURN 00636 END IF 00637 * 00638 * Quick return if possible 00639 * 00640 IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) 00641 $ RETURN 00642 * 00643 SAFMIN = SLAMCH( 'Safe minimum' ) 00644 ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' ) 00645 SAFMIN = SAFMIN / ULP 00646 SAFMAX = ONE / SAFMIN 00647 CALL SLABAD( SAFMIN, SAFMAX ) 00648 ULPINV = ONE / ULP 00649 * 00650 * The values RMAGN(2:3) depend on N, see below. 00651 * 00652 RMAGN( 0 ) = ZERO 00653 RMAGN( 1 ) = ONE 00654 * 00655 * Loop over sizes, types 00656 * 00657 NTESTT = 0 00658 NERRS = 0 00659 NMATS = 0 00660 * 00661 DO 240 JSIZE = 1, NSIZES 00662 N = NN( JSIZE ) 00663 N1 = MAX( 1, N ) 00664 RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 ) 00665 RMAGN( 3 ) = SAFMIN*ULPINV*N1 00666 * 00667 IF( NSIZES.NE.1 ) THEN 00668 MTYPES = MIN( MAXTYP, NTYPES ) 00669 ELSE 00670 MTYPES = MIN( MAXTYP+1, NTYPES ) 00671 END IF 00672 * 00673 DO 230 JTYPE = 1, MTYPES 00674 IF( .NOT.DOTYPE( JTYPE ) ) 00675 $ GO TO 230 00676 NMATS = NMATS + 1 00677 NTEST = 0 00678 * 00679 * Save ISEED in case of an error. 00680 * 00681 DO 20 J = 1, 4 00682 IOLDSD( J ) = ISEED( J ) 00683 20 CONTINUE 00684 * 00685 * Initialize RESULT 00686 * 00687 DO 30 J = 1, 15 00688 RESULT( J ) = ZERO 00689 30 CONTINUE 00690 * 00691 * Compute A and B 00692 * 00693 * Description of control parameters: 00694 * 00695 * KCLASS: =1 means w/o rotation, =2 means w/ rotation, 00696 * =3 means random. 00697 * KATYPE: the "type" to be passed to SLATM4 for computing A. 00698 * KAZERO: the pattern of zeros on the diagonal for A: 00699 * =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), 00700 * =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), 00701 * =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of 00702 * non-zero entries.) 00703 * KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), 00704 * =2: large, =3: small. 00705 * IASIGN: 1 if the diagonal elements of A are to be 00706 * multiplied by a random magnitude 1 number, =2 if 00707 * randomly chosen diagonal blocks are to be rotated 00708 * to form 2x2 blocks. 00709 * KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B. 00710 * KTRIAN: =0: don't fill in the upper triangle, =1: do. 00711 * KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. 00712 * RMAGN: used to implement KAMAGN and KBMAGN. 00713 * 00714 IF( MTYPES.GT.MAXTYP ) 00715 $ GO TO 110 00716 IINFO = 0 00717 IF( KCLASS( JTYPE ).LT.3 ) THEN 00718 * 00719 * Generate A (w/o rotation) 00720 * 00721 IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN 00722 IN = 2*( ( N-1 ) / 2 ) + 1 00723 IF( IN.NE.N ) 00724 $ CALL SLASET( 'Full', N, N, ZERO, ZERO, A, LDA ) 00725 ELSE 00726 IN = N 00727 END IF 00728 CALL SLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ), 00729 $ KZ2( KAZERO( JTYPE ) ), IASIGN( JTYPE ), 00730 $ RMAGN( KAMAGN( JTYPE ) ), ULP, 00731 $ RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2, 00732 $ ISEED, A, LDA ) 00733 IADD = KADD( KAZERO( JTYPE ) ) 00734 IF( IADD.GT.0 .AND. IADD.LE.N ) 00735 $ A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) ) 00736 * 00737 * Generate B (w/o rotation) 00738 * 00739 IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN 00740 IN = 2*( ( N-1 ) / 2 ) + 1 00741 IF( IN.NE.N ) 00742 $ CALL SLASET( 'Full', N, N, ZERO, ZERO, B, LDA ) 00743 ELSE 00744 IN = N 00745 END IF 00746 CALL SLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ), 00747 $ KZ2( KBZERO( JTYPE ) ), IBSIGN( JTYPE ), 00748 $ RMAGN( KBMAGN( JTYPE ) ), ONE, 00749 $ RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2, 00750 $ ISEED, B, LDA ) 00751 IADD = KADD( KBZERO( JTYPE ) ) 00752 IF( IADD.NE.0 .AND. IADD.LE.N ) 00753 $ B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) ) 00754 * 00755 IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN 00756 * 00757 * Include rotations 00758 * 00759 * Generate U, V as Householder transformations times 00760 * a diagonal matrix. 00761 * 00762 DO 50 JC = 1, N - 1 00763 DO 40 JR = JC, N 00764 U( JR, JC ) = SLARND( 3, ISEED ) 00765 V( JR, JC ) = SLARND( 3, ISEED ) 00766 40 CONTINUE 00767 CALL SLARFG( N+1-JC, U( JC, JC ), U( JC+1, JC ), 1, 00768 $ WORK( JC ) ) 00769 WORK( 2*N+JC ) = SIGN( ONE, U( JC, JC ) ) 00770 U( JC, JC ) = ONE 00771 CALL SLARFG( N+1-JC, V( JC, JC ), V( JC+1, JC ), 1, 00772 $ WORK( N+JC ) ) 00773 WORK( 3*N+JC ) = SIGN( ONE, V( JC, JC ) ) 00774 V( JC, JC ) = ONE 00775 50 CONTINUE 00776 U( N, N ) = ONE 00777 WORK( N ) = ZERO 00778 WORK( 3*N ) = SIGN( ONE, SLARND( 2, ISEED ) ) 00779 V( N, N ) = ONE 00780 WORK( 2*N ) = ZERO 00781 WORK( 4*N ) = SIGN( ONE, SLARND( 2, ISEED ) ) 00782 * 00783 * Apply the diagonal matrices 00784 * 00785 DO 70 JC = 1, N 00786 DO 60 JR = 1, N 00787 A( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )* 00788 $ A( JR, JC ) 00789 B( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )* 00790 $ B( JR, JC ) 00791 60 CONTINUE 00792 70 CONTINUE 00793 CALL SORM2R( 'L', 'N', N, N, N-1, U, LDU, WORK, A, 00794 $ LDA, WORK( 2*N+1 ), IINFO ) 00795 IF( IINFO.NE.0 ) 00796 $ GO TO 100 00797 CALL SORM2R( 'R', 'T', N, N, N-1, V, LDU, WORK( N+1 ), 00798 $ A, LDA, WORK( 2*N+1 ), IINFO ) 00799 IF( IINFO.NE.0 ) 00800 $ GO TO 100 00801 CALL SORM2R( 'L', 'N', N, N, N-1, U, LDU, WORK, B, 00802 $ LDA, WORK( 2*N+1 ), IINFO ) 00803 IF( IINFO.NE.0 ) 00804 $ GO TO 100 00805 CALL SORM2R( 'R', 'T', N, N, N-1, V, LDU, WORK( N+1 ), 00806 $ B, LDA, WORK( 2*N+1 ), IINFO ) 00807 IF( IINFO.NE.0 ) 00808 $ GO TO 100 00809 END IF 00810 ELSE 00811 * 00812 * Random matrices 00813 * 00814 DO 90 JC = 1, N 00815 DO 80 JR = 1, N 00816 A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )* 00817 $ SLARND( 2, ISEED ) 00818 B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )* 00819 $ SLARND( 2, ISEED ) 00820 80 CONTINUE 00821 90 CONTINUE 00822 END IF 00823 * 00824 ANORM = SLANGE( '1', N, N, A, LDA, WORK ) 00825 BNORM = SLANGE( '1', N, N, B, LDA, WORK ) 00826 * 00827 100 CONTINUE 00828 * 00829 IF( IINFO.NE.0 ) THEN 00830 WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE, 00831 $ IOLDSD 00832 INFO = ABS( IINFO ) 00833 RETURN 00834 END IF 00835 * 00836 110 CONTINUE 00837 * 00838 * Call SGEQR2, SORM2R, and SGGHRD to compute H, T, U, and V 00839 * 00840 CALL SLACPY( ' ', N, N, A, LDA, H, LDA ) 00841 CALL SLACPY( ' ', N, N, B, LDA, T, LDA ) 00842 NTEST = 1 00843 RESULT( 1 ) = ULPINV 00844 * 00845 CALL SGEQR2( N, N, T, LDA, WORK, WORK( N+1 ), IINFO ) 00846 IF( IINFO.NE.0 ) THEN 00847 WRITE( NOUNIT, FMT = 9999 )'SGEQR2', IINFO, N, JTYPE, 00848 $ IOLDSD 00849 INFO = ABS( IINFO ) 00850 GO TO 210 00851 END IF 00852 * 00853 CALL SORM2R( 'L', 'T', N, N, N, T, LDA, WORK, H, LDA, 00854 $ WORK( N+1 ), IINFO ) 00855 IF( IINFO.NE.0 ) THEN 00856 WRITE( NOUNIT, FMT = 9999 )'SORM2R', IINFO, N, JTYPE, 00857 $ IOLDSD 00858 INFO = ABS( IINFO ) 00859 GO TO 210 00860 END IF 00861 * 00862 CALL SLASET( 'Full', N, N, ZERO, ONE, U, LDU ) 00863 CALL SORM2R( 'R', 'N', N, N, N, T, LDA, WORK, U, LDU, 00864 $ WORK( N+1 ), IINFO ) 00865 IF( IINFO.NE.0 ) THEN 00866 WRITE( NOUNIT, FMT = 9999 )'SORM2R', IINFO, N, JTYPE, 00867 $ IOLDSD 00868 INFO = ABS( IINFO ) 00869 GO TO 210 00870 END IF 00871 * 00872 CALL SGGHRD( 'V', 'I', N, 1, N, H, LDA, T, LDA, U, LDU, V, 00873 $ LDU, IINFO ) 00874 IF( IINFO.NE.0 ) THEN 00875 WRITE( NOUNIT, FMT = 9999 )'SGGHRD', IINFO, N, JTYPE, 00876 $ IOLDSD 00877 INFO = ABS( IINFO ) 00878 GO TO 210 00879 END IF 00880 NTEST = 4 00881 * 00882 * Do tests 1--4 00883 * 00884 CALL SGET51( 1, N, A, LDA, H, LDA, U, LDU, V, LDU, WORK, 00885 $ RESULT( 1 ) ) 00886 CALL SGET51( 1, N, B, LDA, T, LDA, U, LDU, V, LDU, WORK, 00887 $ RESULT( 2 ) ) 00888 CALL SGET51( 3, N, B, LDA, T, LDA, U, LDU, U, LDU, WORK, 00889 $ RESULT( 3 ) ) 00890 CALL SGET51( 3, N, B, LDA, T, LDA, V, LDU, V, LDU, WORK, 00891 $ RESULT( 4 ) ) 00892 * 00893 * Call SHGEQZ to compute S1, P1, S2, P2, Q, and Z, do tests. 00894 * 00895 * Compute T1 and UZ 00896 * 00897 * Eigenvalues only 00898 * 00899 CALL SLACPY( ' ', N, N, H, LDA, S2, LDA ) 00900 CALL SLACPY( ' ', N, N, T, LDA, P2, LDA ) 00901 NTEST = 5 00902 RESULT( 5 ) = ULPINV 00903 * 00904 CALL SHGEQZ( 'E', 'N', 'N', N, 1, N, S2, LDA, P2, LDA, 00905 $ ALPHR3, ALPHI3, BETA3, Q, LDU, Z, LDU, WORK, 00906 $ LWORK, IINFO ) 00907 IF( IINFO.NE.0 ) THEN 00908 WRITE( NOUNIT, FMT = 9999 )'SHGEQZ(E)', IINFO, N, JTYPE, 00909 $ IOLDSD 00910 INFO = ABS( IINFO ) 00911 GO TO 210 00912 END IF 00913 * 00914 * Eigenvalues and Full Schur Form 00915 * 00916 CALL SLACPY( ' ', N, N, H, LDA, S2, LDA ) 00917 CALL SLACPY( ' ', N, N, T, LDA, P2, LDA ) 00918 * 00919 CALL SHGEQZ( 'S', 'N', 'N', N, 1, N, S2, LDA, P2, LDA, 00920 $ ALPHR1, ALPHI1, BETA1, Q, LDU, Z, LDU, WORK, 00921 $ LWORK, IINFO ) 00922 IF( IINFO.NE.0 ) THEN 00923 WRITE( NOUNIT, FMT = 9999 )'SHGEQZ(S)', IINFO, N, JTYPE, 00924 $ IOLDSD 00925 INFO = ABS( IINFO ) 00926 GO TO 210 00927 END IF 00928 * 00929 * Eigenvalues, Schur Form, and Schur Vectors 00930 * 00931 CALL SLACPY( ' ', N, N, H, LDA, S1, LDA ) 00932 CALL SLACPY( ' ', N, N, T, LDA, P1, LDA ) 00933 * 00934 CALL SHGEQZ( 'S', 'I', 'I', N, 1, N, S1, LDA, P1, LDA, 00935 $ ALPHR1, ALPHI1, BETA1, Q, LDU, Z, LDU, WORK, 00936 $ LWORK, IINFO ) 00937 IF( IINFO.NE.0 ) THEN 00938 WRITE( NOUNIT, FMT = 9999 )'SHGEQZ(V)', IINFO, N, JTYPE, 00939 $ IOLDSD 00940 INFO = ABS( IINFO ) 00941 GO TO 210 00942 END IF 00943 * 00944 NTEST = 8 00945 * 00946 * Do Tests 5--8 00947 * 00948 CALL SGET51( 1, N, H, LDA, S1, LDA, Q, LDU, Z, LDU, WORK, 00949 $ RESULT( 5 ) ) 00950 CALL SGET51( 1, N, T, LDA, P1, LDA, Q, LDU, Z, LDU, WORK, 00951 $ RESULT( 6 ) ) 00952 CALL SGET51( 3, N, T, LDA, P1, LDA, Q, LDU, Q, LDU, WORK, 00953 $ RESULT( 7 ) ) 00954 CALL SGET51( 3, N, T, LDA, P1, LDA, Z, LDU, Z, LDU, WORK, 00955 $ RESULT( 8 ) ) 00956 * 00957 * Compute the Left and Right Eigenvectors of (S1,P1) 00958 * 00959 * 9: Compute the left eigenvector Matrix without 00960 * back transforming: 00961 * 00962 NTEST = 9 00963 RESULT( 9 ) = ULPINV 00964 * 00965 * To test "SELECT" option, compute half of the eigenvectors 00966 * in one call, and half in another 00967 * 00968 I1 = N / 2 00969 DO 120 J = 1, I1 00970 LLWORK( J ) = .TRUE. 00971 120 CONTINUE 00972 DO 130 J = I1 + 1, N 00973 LLWORK( J ) = .FALSE. 00974 130 CONTINUE 00975 * 00976 CALL STGEVC( 'L', 'S', LLWORK, N, S1, LDA, P1, LDA, EVECTL, 00977 $ LDU, DUMMA, LDU, N, IN, WORK, IINFO ) 00978 IF( IINFO.NE.0 ) THEN 00979 WRITE( NOUNIT, FMT = 9999 )'STGEVC(L,S1)', IINFO, N, 00980 $ JTYPE, IOLDSD 00981 INFO = ABS( IINFO ) 00982 GO TO 210 00983 END IF 00984 * 00985 I1 = IN 00986 DO 140 J = 1, I1 00987 LLWORK( J ) = .FALSE. 00988 140 CONTINUE 00989 DO 150 J = I1 + 1, N 00990 LLWORK( J ) = .TRUE. 00991 150 CONTINUE 00992 * 00993 CALL STGEVC( 'L', 'S', LLWORK, N, S1, LDA, P1, LDA, 00994 $ EVECTL( 1, I1+1 ), LDU, DUMMA, LDU, N, IN, 00995 $ WORK, IINFO ) 00996 IF( IINFO.NE.0 ) THEN 00997 WRITE( NOUNIT, FMT = 9999 )'STGEVC(L,S2)', IINFO, N, 00998 $ JTYPE, IOLDSD 00999 INFO = ABS( IINFO ) 01000 GO TO 210 01001 END IF 01002 * 01003 CALL SGET52( .TRUE., N, S1, LDA, P1, LDA, EVECTL, LDU, 01004 $ ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) ) 01005 RESULT( 9 ) = DUMMA( 1 ) 01006 IF( DUMMA( 2 ).GT.THRSHN ) THEN 01007 WRITE( NOUNIT, FMT = 9998 )'Left', 'STGEVC(HOWMNY=S)', 01008 $ DUMMA( 2 ), N, JTYPE, IOLDSD 01009 END IF 01010 * 01011 * 10: Compute the left eigenvector Matrix with 01012 * back transforming: 01013 * 01014 NTEST = 10 01015 RESULT( 10 ) = ULPINV 01016 CALL SLACPY( 'F', N, N, Q, LDU, EVECTL, LDU ) 01017 CALL STGEVC( 'L', 'B', LLWORK, N, S1, LDA, P1, LDA, EVECTL, 01018 $ LDU, DUMMA, LDU, N, IN, WORK, IINFO ) 01019 IF( IINFO.NE.0 ) THEN 01020 WRITE( NOUNIT, FMT = 9999 )'STGEVC(L,B)', IINFO, N, 01021 $ JTYPE, IOLDSD 01022 INFO = ABS( IINFO ) 01023 GO TO 210 01024 END IF 01025 * 01026 CALL SGET52( .TRUE., N, H, LDA, T, LDA, EVECTL, LDU, ALPHR1, 01027 $ ALPHI1, BETA1, WORK, DUMMA( 1 ) ) 01028 RESULT( 10 ) = DUMMA( 1 ) 01029 IF( DUMMA( 2 ).GT.THRSHN ) THEN 01030 WRITE( NOUNIT, FMT = 9998 )'Left', 'STGEVC(HOWMNY=B)', 01031 $ DUMMA( 2 ), N, JTYPE, IOLDSD 01032 END IF 01033 * 01034 * 11: Compute the right eigenvector Matrix without 01035 * back transforming: 01036 * 01037 NTEST = 11 01038 RESULT( 11 ) = ULPINV 01039 * 01040 * To test "SELECT" option, compute half of the eigenvectors 01041 * in one call, and half in another 01042 * 01043 I1 = N / 2 01044 DO 160 J = 1, I1 01045 LLWORK( J ) = .TRUE. 01046 160 CONTINUE 01047 DO 170 J = I1 + 1, N 01048 LLWORK( J ) = .FALSE. 01049 170 CONTINUE 01050 * 01051 CALL STGEVC( 'R', 'S', LLWORK, N, S1, LDA, P1, LDA, DUMMA, 01052 $ LDU, EVECTR, LDU, N, IN, WORK, IINFO ) 01053 IF( IINFO.NE.0 ) THEN 01054 WRITE( NOUNIT, FMT = 9999 )'STGEVC(R,S1)', IINFO, N, 01055 $ JTYPE, IOLDSD 01056 INFO = ABS( IINFO ) 01057 GO TO 210 01058 END IF 01059 * 01060 I1 = IN 01061 DO 180 J = 1, I1 01062 LLWORK( J ) = .FALSE. 01063 180 CONTINUE 01064 DO 190 J = I1 + 1, N 01065 LLWORK( J ) = .TRUE. 01066 190 CONTINUE 01067 * 01068 CALL STGEVC( 'R', 'S', LLWORK, N, S1, LDA, P1, LDA, DUMMA, 01069 $ LDU, EVECTR( 1, I1+1 ), LDU, N, IN, WORK, 01070 $ IINFO ) 01071 IF( IINFO.NE.0 ) THEN 01072 WRITE( NOUNIT, FMT = 9999 )'STGEVC(R,S2)', IINFO, N, 01073 $ JTYPE, IOLDSD 01074 INFO = ABS( IINFO ) 01075 GO TO 210 01076 END IF 01077 * 01078 CALL SGET52( .FALSE., N, S1, LDA, P1, LDA, EVECTR, LDU, 01079 $ ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) ) 01080 RESULT( 11 ) = DUMMA( 1 ) 01081 IF( DUMMA( 2 ).GT.THRESH ) THEN 01082 WRITE( NOUNIT, FMT = 9998 )'Right', 'STGEVC(HOWMNY=S)', 01083 $ DUMMA( 2 ), N, JTYPE, IOLDSD 01084 END IF 01085 * 01086 * 12: Compute the right eigenvector Matrix with 01087 * back transforming: 01088 * 01089 NTEST = 12 01090 RESULT( 12 ) = ULPINV 01091 CALL SLACPY( 'F', N, N, Z, LDU, EVECTR, LDU ) 01092 CALL STGEVC( 'R', 'B', LLWORK, N, S1, LDA, P1, LDA, DUMMA, 01093 $ LDU, EVECTR, LDU, N, IN, WORK, IINFO ) 01094 IF( IINFO.NE.0 ) THEN 01095 WRITE( NOUNIT, FMT = 9999 )'STGEVC(R,B)', IINFO, N, 01096 $ JTYPE, IOLDSD 01097 INFO = ABS( IINFO ) 01098 GO TO 210 01099 END IF 01100 * 01101 CALL SGET52( .FALSE., N, H, LDA, T, LDA, EVECTR, LDU, 01102 $ ALPHR1, ALPHI1, BETA1, WORK, DUMMA( 1 ) ) 01103 RESULT( 12 ) = DUMMA( 1 ) 01104 IF( DUMMA( 2 ).GT.THRESH ) THEN 01105 WRITE( NOUNIT, FMT = 9998 )'Right', 'STGEVC(HOWMNY=B)', 01106 $ DUMMA( 2 ), N, JTYPE, IOLDSD 01107 END IF 01108 * 01109 * Tests 13--15 are done only on request 01110 * 01111 IF( TSTDIF ) THEN 01112 * 01113 * Do Tests 13--14 01114 * 01115 CALL SGET51( 2, N, S1, LDA, S2, LDA, Q, LDU, Z, LDU, 01116 $ WORK, RESULT( 13 ) ) 01117 CALL SGET51( 2, N, P1, LDA, P2, LDA, Q, LDU, Z, LDU, 01118 $ WORK, RESULT( 14 ) ) 01119 * 01120 * Do Test 15 01121 * 01122 TEMP1 = ZERO 01123 TEMP2 = ZERO 01124 DO 200 J = 1, N 01125 TEMP1 = MAX( TEMP1, ABS( ALPHR1( J )-ALPHR3( J ) )+ 01126 $ ABS( ALPHI1( J )-ALPHI3( J ) ) ) 01127 TEMP2 = MAX( TEMP2, ABS( BETA1( J )-BETA3( J ) ) ) 01128 200 CONTINUE 01129 * 01130 TEMP1 = TEMP1 / MAX( SAFMIN, ULP*MAX( TEMP1, ANORM ) ) 01131 TEMP2 = TEMP2 / MAX( SAFMIN, ULP*MAX( TEMP2, BNORM ) ) 01132 RESULT( 15 ) = MAX( TEMP1, TEMP2 ) 01133 NTEST = 15 01134 ELSE 01135 RESULT( 13 ) = ZERO 01136 RESULT( 14 ) = ZERO 01137 RESULT( 15 ) = ZERO 01138 NTEST = 12 01139 END IF 01140 * 01141 * End of Loop -- Check for RESULT(j) > THRESH 01142 * 01143 210 CONTINUE 01144 * 01145 NTESTT = NTESTT + NTEST 01146 * 01147 * Print out tests which fail. 01148 * 01149 DO 220 JR = 1, NTEST 01150 IF( RESULT( JR ).GE.THRESH ) THEN 01151 * 01152 * If this is the first test to fail, 01153 * print a header to the data file. 01154 * 01155 IF( NERRS.EQ.0 ) THEN 01156 WRITE( NOUNIT, FMT = 9997 )'SGG' 01157 * 01158 * Matrix types 01159 * 01160 WRITE( NOUNIT, FMT = 9996 ) 01161 WRITE( NOUNIT, FMT = 9995 ) 01162 WRITE( NOUNIT, FMT = 9994 )'Orthogonal' 01163 * 01164 * Tests performed 01165 * 01166 WRITE( NOUNIT, FMT = 9993 )'orthogonal', '''', 01167 $ 'transpose', ( '''', J = 1, 10 ) 01168 * 01169 END IF 01170 NERRS = NERRS + 1 01171 IF( RESULT( JR ).LT.10000.0 ) THEN 01172 WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR, 01173 $ RESULT( JR ) 01174 ELSE 01175 WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR, 01176 $ RESULT( JR ) 01177 END IF 01178 END IF 01179 220 CONTINUE 01180 * 01181 230 CONTINUE 01182 240 CONTINUE 01183 * 01184 * Summary 01185 * 01186 CALL SLASUM( 'SGG', NOUNIT, NERRS, NTESTT ) 01187 RETURN 01188 * 01189 9999 FORMAT( ' SCHKGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', 01190 $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) 01191 * 01192 9998 FORMAT( ' SCHKGG: ', A, ' Eigenvectors from ', A, ' incorrectly ', 01193 $ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X, 01194 $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, 01195 $ ')' ) 01196 * 01197 9997 FORMAT( / 1X, A3, ' -- Real Generalized eigenvalue problem' ) 01198 * 01199 9996 FORMAT( ' Matrix types (see SCHKGG for details): ' ) 01200 * 01201 9995 FORMAT( ' Special Matrices:', 23X, 01202 $ '(J''=transposed Jordan block)', 01203 $ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ', 01204 $ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ', 01205 $ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I', 01206 $ ') 11=(large*I, small*D) 13=(large*D, large*I)', / 01207 $ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ', 01208 $ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' ) 01209 9994 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:', 01210 $ / ' 16=Transposed Jordan Blocks 19=geometric ', 01211 $ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ', 01212 $ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ', 01213 $ 'alpha, beta=0,1 21=random alpha, beta=0,1', 01214 $ / ' Large & Small Matrices:', / ' 22=(large, small) ', 01215 $ '23=(small,large) 24=(small,small) 25=(large,large)', 01216 $ / ' 26=random O(1) matrices.' ) 01217 * 01218 9993 FORMAT( / ' Tests performed: (H is Hessenberg, S is Schur, B, ', 01219 $ 'T, P are triangular,', / 20X, 'U, V, Q, and Z are ', A, 01220 $ ', l and r are the', / 20X, 01221 $ 'appropriate left and right eigenvectors, resp., a is', 01222 $ / 20X, 'alpha, b is beta, and ', A, ' means ', A, '.)', 01223 $ / ' 1 = | A - U H V', A, 01224 $ ' | / ( |A| n ulp ) 2 = | B - U T V', A, 01225 $ ' | / ( |B| n ulp )', / ' 3 = | I - UU', A, 01226 $ ' | / ( n ulp ) 4 = | I - VV', A, 01227 $ ' | / ( n ulp )', / ' 5 = | H - Q S Z', A, 01228 $ ' | / ( |H| n ulp )', 6X, '6 = | T - Q P Z', A, 01229 $ ' | / ( |T| n ulp )', / ' 7 = | I - QQ', A, 01230 $ ' | / ( n ulp ) 8 = | I - ZZ', A, 01231 $ ' | / ( n ulp )', / ' 9 = max | ( b S - a P )', A, 01232 $ ' l | / const. 10 = max | ( b H - a T )', A, 01233 $ ' l | / const.', / 01234 $ ' 11= max | ( b S - a P ) r | / const. 12 = max | ( b H', 01235 $ ' - a T ) r | / const.', / 1X ) 01236 * 01237 9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', 01238 $ 4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 ) 01239 9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', 01240 $ 4( I4, ',' ), ' result ', I2, ' is', 1P, E10.3 ) 01241 * 01242 * End of SCHKGG 01243 * 01244 END