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LAPACK 3.3.0
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LAPACK 3.3.0
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00001 SUBROUTINE DDRGSX( NSIZE, NCMAX, THRESH, NIN, NOUT, A, LDA, B, AI, 00002 $ BI, Z, Q, ALPHAR, ALPHAI, BETA, C, LDC, S, 00003 $ WORK, LWORK, IWORK, LIWORK, BWORK, 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, LDC, LIWORK, LWORK, NCMAX, NIN, 00011 $ NOUT, NSIZE 00012 DOUBLE PRECISION THRESH 00013 * .. 00014 * .. Array Arguments .. 00015 LOGICAL BWORK( * ) 00016 INTEGER IWORK( * ) 00017 DOUBLE PRECISION A( LDA, * ), AI( LDA, * ), ALPHAI( * ), 00018 $ ALPHAR( * ), B( LDA, * ), BETA( * ), 00019 $ BI( LDA, * ), C( LDC, * ), Q( LDA, * ), S( * ), 00020 $ WORK( * ), Z( LDA, * ) 00021 * .. 00022 * 00023 * Purpose 00024 * ======= 00025 * 00026 * DDRGSX checks the nonsymmetric generalized eigenvalue (Schur form) 00027 * problem expert driver DGGESX. 00028 * 00029 * DGGESX factors A and B as Q S Z' and Q T Z', where ' means 00030 * transpose, T is upper triangular, S is in generalized Schur form 00031 * (block upper triangular, with 1x1 and 2x2 blocks on the diagonal, 00032 * the 2x2 blocks corresponding to complex conjugate pairs of 00033 * generalized eigenvalues), and Q and Z are orthogonal. It also 00034 * computes the generalized eigenvalues (alpha(1),beta(1)), ..., 00035 * (alpha(n),beta(n)). Thus, w(j) = alpha(j)/beta(j) is a root of the 00036 * characteristic equation 00037 * 00038 * det( A - w(j) B ) = 0 00039 * 00040 * Optionally it also reorders the eigenvalues so that a selected 00041 * cluster of eigenvalues appears in the leading diagonal block of the 00042 * Schur forms; computes a reciprocal condition number for the average 00043 * of the selected eigenvalues; and computes a reciprocal condition 00044 * number for the right and left deflating subspaces corresponding to 00045 * the selected eigenvalues. 00046 * 00047 * When DDRGSX is called with NSIZE > 0, five (5) types of built-in 00048 * matrix pairs are used to test the routine DGGESX. 00049 * 00050 * When DDRGSX is called with NSIZE = 0, it reads in test matrix data 00051 * to test DGGESX. 00052 * 00053 * For each matrix pair, the following tests will be performed and 00054 * compared with the threshhold THRESH except for the tests (7) and (9): 00055 * 00056 * (1) | A - Q S Z' | / ( |A| n ulp ) 00057 * 00058 * (2) | B - Q T Z' | / ( |B| n ulp ) 00059 * 00060 * (3) | I - QQ' | / ( n ulp ) 00061 * 00062 * (4) | I - ZZ' | / ( n ulp ) 00063 * 00064 * (5) if A is in Schur form (i.e. quasi-triangular form) 00065 * 00066 * (6) maximum over j of D(j) where: 00067 * 00068 * if alpha(j) is real: 00069 * |alpha(j) - S(j,j)| |beta(j) - T(j,j)| 00070 * D(j) = ------------------------ + ----------------------- 00071 * max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) 00072 * 00073 * if alpha(j) is complex: 00074 * | det( s S - w T ) | 00075 * D(j) = --------------------------------------------------- 00076 * ulp max( s norm(S), |w| norm(T) )*norm( s S - w T ) 00077 * 00078 * and S and T are here the 2 x 2 diagonal blocks of S and T 00079 * corresponding to the j-th and j+1-th eigenvalues. 00080 * 00081 * (7) if sorting worked and SDIM is the number of eigenvalues 00082 * which were selected. 00083 * 00084 * (8) the estimated value DIF does not differ from the true values of 00085 * Difu and Difl more than a factor 10*THRESH. If the estimate DIF 00086 * equals zero the corresponding true values of Difu and Difl 00087 * should be less than EPS*norm(A, B). If the true value of Difu 00088 * and Difl equal zero, the estimate DIF should be less than 00089 * EPS*norm(A, B). 00090 * 00091 * (9) If INFO = N+3 is returned by DGGESX, the reordering "failed" 00092 * and we check that DIF = PL = PR = 0 and that the true value of 00093 * Difu and Difl is < EPS*norm(A, B). We count the events when 00094 * INFO=N+3. 00095 * 00096 * For read-in test matrices, the above tests are run except that the 00097 * exact value for DIF (and PL) is input data. Additionally, there is 00098 * one more test run for read-in test matrices: 00099 * 00100 * (10) the estimated value PL does not differ from the true value of 00101 * PLTRU more than a factor THRESH. If the estimate PL equals 00102 * zero the corresponding true value of PLTRU should be less than 00103 * EPS*norm(A, B). If the true value of PLTRU equal zero, the 00104 * estimate PL should be less than EPS*norm(A, B). 00105 * 00106 * Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1) 00107 * matrix pairs are generated and tested. NSIZE should be kept small. 00108 * 00109 * SVD (routine DGESVD) is used for computing the true value of DIF_u 00110 * and DIF_l when testing the built-in test problems. 00111 * 00112 * Built-in Test Matrices 00113 * ====================== 00114 * 00115 * All built-in test matrices are the 2 by 2 block of triangular 00116 * matrices 00117 * 00118 * A = [ A11 A12 ] and B = [ B11 B12 ] 00119 * [ A22 ] [ B22 ] 00120 * 00121 * where for different type of A11 and A22 are given as the following. 00122 * A12 and B12 are chosen so that the generalized Sylvester equation 00123 * 00124 * A11*R - L*A22 = -A12 00125 * B11*R - L*B22 = -B12 00126 * 00127 * have prescribed solution R and L. 00128 * 00129 * Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1). 00130 * B11 = I_m, B22 = I_k 00131 * where J_k(a,b) is the k-by-k Jordan block with ``a'' on 00132 * diagonal and ``b'' on superdiagonal. 00133 * 00134 * Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and 00135 * B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m 00136 * A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and 00137 * B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k 00138 * 00139 * Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each 00140 * second diagonal block in A_11 and each third diagonal block 00141 * in A_22 are made as 2 by 2 blocks. 00142 * 00143 * Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) ) 00144 * for i=1,...,m, j=1,...,m and 00145 * A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) ) 00146 * for i=m+1,...,k, j=m+1,...,k 00147 * 00148 * Type 5: (A,B) and have potentially close or common eigenvalues and 00149 * very large departure from block diagonality A_11 is chosen 00150 * as the m x m leading submatrix of A_1: 00151 * | 1 b | 00152 * | -b 1 | 00153 * | 1+d b | 00154 * | -b 1+d | 00155 * A_1 = | d 1 | 00156 * | -1 d | 00157 * | -d 1 | 00158 * | -1 -d | 00159 * | 1 | 00160 * and A_22 is chosen as the k x k leading submatrix of A_2: 00161 * | -1 b | 00162 * | -b -1 | 00163 * | 1-d b | 00164 * | -b 1-d | 00165 * A_2 = | d 1+b | 00166 * | -1-b d | 00167 * | -d 1+b | 00168 * | -1+b -d | 00169 * | 1-d | 00170 * and matrix B are chosen as identity matrices (see DLATM5). 00171 * 00172 * 00173 * Arguments 00174 * ========= 00175 * 00176 * NSIZE (input) INTEGER 00177 * The maximum size of the matrices to use. NSIZE >= 0. 00178 * If NSIZE = 0, no built-in tests matrices are used, but 00179 * read-in test matrices are used to test DGGESX. 00180 * 00181 * NCMAX (input) INTEGER 00182 * Maximum allowable NMAX for generating Kroneker matrix 00183 * in call to DLAKF2 00184 * 00185 * THRESH (input) DOUBLE PRECISION 00186 * A test will count as "failed" if the "error", computed as 00187 * described above, exceeds THRESH. Note that the error 00188 * is scaled to be O(1), so THRESH should be a reasonably 00189 * small multiple of 1, e.g., 10 or 100. In particular, 00190 * it should not depend on the precision (single vs. double) 00191 * or the size of the matrix. THRESH >= 0. 00192 * 00193 * NIN (input) INTEGER 00194 * The FORTRAN unit number for reading in the data file of 00195 * problems to solve. 00196 * 00197 * NOUT (input) INTEGER 00198 * The FORTRAN unit number for printing out error messages 00199 * (e.g., if a routine returns IINFO not equal to 0.) 00200 * 00201 * A (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) 00202 * Used to store the matrix whose eigenvalues are to be 00203 * computed. On exit, A contains the last matrix actually used. 00204 * 00205 * LDA (input) INTEGER 00206 * The leading dimension of A, B, AI, BI, Z and Q, 00207 * LDA >= max( 1, NSIZE ). For the read-in test, 00208 * LDA >= max( 1, N ), N is the size of the test matrices. 00209 * 00210 * B (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) 00211 * Used to store the matrix whose eigenvalues are to be 00212 * computed. On exit, B contains the last matrix actually used. 00213 * 00214 * AI (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) 00215 * Copy of A, modified by DGGESX. 00216 * 00217 * BI (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) 00218 * Copy of B, modified by DGGESX. 00219 * 00220 * Z (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) 00221 * Z holds the left Schur vectors computed by DGGESX. 00222 * 00223 * Q (workspace) DOUBLE PRECISION array, dimension (LDA, NSIZE) 00224 * Q holds the right Schur vectors computed by DGGESX. 00225 * 00226 * ALPHAR (workspace) DOUBLE PRECISION array, dimension (NSIZE) 00227 * ALPHAI (workspace) DOUBLE PRECISION array, dimension (NSIZE) 00228 * BETA (workspace) DOUBLE PRECISION array, dimension (NSIZE) 00229 * On exit, (ALPHAR + ALPHAI*i)/BETA are the eigenvalues. 00230 * 00231 * C (workspace) DOUBLE PRECISION array, dimension (LDC, LDC) 00232 * Store the matrix generated by subroutine DLAKF2, this is the 00233 * matrix formed by Kronecker products used for estimating 00234 * DIF. 00235 * 00236 * LDC (input) INTEGER 00237 * The leading dimension of C. LDC >= max(1, LDA*LDA/2 ). 00238 * 00239 * S (workspace) DOUBLE PRECISION array, dimension (LDC) 00240 * Singular values of C 00241 * 00242 * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) 00243 * 00244 * LWORK (input) INTEGER 00245 * The dimension of the array WORK. 00246 * LWORK >= MAX( 5*NSIZE*NSIZE/2 - 2, 10*(NSIZE+1) ) 00247 * 00248 * IWORK (workspace) INTEGER array, dimension (LIWORK) 00249 * 00250 * LIWORK (input) INTEGER 00251 * The dimension of the array IWORK. LIWORK >= NSIZE + 6. 00252 * 00253 * BWORK (workspace) LOGICAL array, dimension (LDA) 00254 * 00255 * INFO (output) INTEGER 00256 * = 0: successful exit 00257 * < 0: if INFO = -i, the i-th argument had an illegal value. 00258 * > 0: A routine returned an error code. 00259 * 00260 * ===================================================================== 00261 * 00262 * .. Parameters .. 00263 DOUBLE PRECISION ZERO, ONE, TEN 00264 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0, TEN = 1.0D+1 ) 00265 * .. 00266 * .. Local Scalars .. 00267 LOGICAL ILABAD 00268 CHARACTER SENSE 00269 INTEGER BDSPAC, I, I1, IFUNC, IINFO, J, LINFO, MAXWRK, 00270 $ MINWRK, MM, MN2, NERRS, NPTKNT, NTEST, NTESTT, 00271 $ PRTYPE, QBA, QBB 00272 DOUBLE PRECISION ABNRM, BIGNUM, DIFTRU, PLTRU, SMLNUM, TEMP1, 00273 $ TEMP2, THRSH2, ULP, ULPINV, WEIGHT 00274 * .. 00275 * .. Local Arrays .. 00276 DOUBLE PRECISION DIFEST( 2 ), PL( 2 ), RESULT( 10 ) 00277 * .. 00278 * .. External Functions .. 00279 LOGICAL DLCTSX 00280 INTEGER ILAENV 00281 DOUBLE PRECISION DLAMCH, DLANGE 00282 EXTERNAL DLCTSX, ILAENV, DLAMCH, DLANGE 00283 * .. 00284 * .. External Subroutines .. 00285 EXTERNAL ALASVM, DGESVD, DGET51, DGET53, DGGESX, DLABAD, 00286 $ DLACPY, DLAKF2, DLASET, DLATM5, XERBLA 00287 * .. 00288 * .. Intrinsic Functions .. 00289 INTRINSIC ABS, MAX, SQRT 00290 * .. 00291 * .. Scalars in Common .. 00292 LOGICAL FS 00293 INTEGER K, M, MPLUSN, N 00294 * .. 00295 * .. Common blocks .. 00296 COMMON / MN / M, N, MPLUSN, K, FS 00297 * .. 00298 * .. Executable Statements .. 00299 * 00300 * Check for errors 00301 * 00302 IF( NSIZE.LT.0 ) THEN 00303 INFO = -1 00304 ELSE IF( THRESH.LT.ZERO ) THEN 00305 INFO = -2 00306 ELSE IF( NIN.LE.0 ) THEN 00307 INFO = -3 00308 ELSE IF( NOUT.LE.0 ) THEN 00309 INFO = -4 00310 ELSE IF( LDA.LT.1 .OR. LDA.LT.NSIZE ) THEN 00311 INFO = -6 00312 ELSE IF( LDC.LT.1 .OR. LDC.LT.NSIZE*NSIZE / 2 ) THEN 00313 INFO = -17 00314 ELSE IF( LIWORK.LT.NSIZE+6 ) THEN 00315 INFO = -21 00316 END IF 00317 * 00318 * Compute workspace 00319 * (Note: Comments in the code beginning "Workspace:" describe the 00320 * minimal amount of workspace needed at that point in the code, 00321 * as well as the preferred amount for good performance. 00322 * NB refers to the optimal block size for the immediately 00323 * following subroutine, as returned by ILAENV.) 00324 * 00325 MINWRK = 1 00326 IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN 00327 MINWRK = MAX( 10*( NSIZE+1 ), 5*NSIZE*NSIZE / 2 ) 00328 * 00329 * workspace for sggesx 00330 * 00331 MAXWRK = 9*( NSIZE+1 ) + NSIZE* 00332 $ ILAENV( 1, 'DGEQRF', ' ', NSIZE, 1, NSIZE, 0 ) 00333 MAXWRK = MAX( MAXWRK, 9*( NSIZE+1 )+NSIZE* 00334 $ ILAENV( 1, 'DORGQR', ' ', NSIZE, 1, NSIZE, -1 ) ) 00335 * 00336 * workspace for dgesvd 00337 * 00338 BDSPAC = 5*NSIZE*NSIZE / 2 00339 MAXWRK = MAX( MAXWRK, 3*NSIZE*NSIZE / 2+NSIZE*NSIZE* 00340 $ ILAENV( 1, 'DGEBRD', ' ', NSIZE*NSIZE / 2, 00341 $ NSIZE*NSIZE / 2, -1, -1 ) ) 00342 MAXWRK = MAX( MAXWRK, BDSPAC ) 00343 * 00344 MAXWRK = MAX( MAXWRK, MINWRK ) 00345 * 00346 WORK( 1 ) = MAXWRK 00347 END IF 00348 * 00349 IF( LWORK.LT.MINWRK ) 00350 $ INFO = -19 00351 * 00352 IF( INFO.NE.0 ) THEN 00353 CALL XERBLA( 'DDRGSX', -INFO ) 00354 RETURN 00355 END IF 00356 * 00357 * Important constants 00358 * 00359 ULP = DLAMCH( 'P' ) 00360 ULPINV = ONE / ULP 00361 SMLNUM = DLAMCH( 'S' ) / ULP 00362 BIGNUM = ONE / SMLNUM 00363 CALL DLABAD( SMLNUM, BIGNUM ) 00364 THRSH2 = TEN*THRESH 00365 NTESTT = 0 00366 NERRS = 0 00367 * 00368 * Go to the tests for read-in matrix pairs 00369 * 00370 IFUNC = 0 00371 IF( NSIZE.EQ.0 ) 00372 $ GO TO 70 00373 * 00374 * Test the built-in matrix pairs. 00375 * Loop over different functions (IFUNC) of DGGESX, types (PRTYPE) 00376 * of test matrices, different size (M+N) 00377 * 00378 PRTYPE = 0 00379 QBA = 3 00380 QBB = 4 00381 WEIGHT = SQRT( ULP ) 00382 * 00383 DO 60 IFUNC = 0, 3 00384 DO 50 PRTYPE = 1, 5 00385 DO 40 M = 1, NSIZE - 1 00386 DO 30 N = 1, NSIZE - M 00387 * 00388 WEIGHT = ONE / WEIGHT 00389 MPLUSN = M + N 00390 * 00391 * Generate test matrices 00392 * 00393 FS = .TRUE. 00394 K = 0 00395 * 00396 CALL DLASET( 'Full', MPLUSN, MPLUSN, ZERO, ZERO, AI, 00397 $ LDA ) 00398 CALL DLASET( 'Full', MPLUSN, MPLUSN, ZERO, ZERO, BI, 00399 $ LDA ) 00400 * 00401 CALL DLATM5( PRTYPE, M, N, AI, LDA, AI( M+1, M+1 ), 00402 $ LDA, AI( 1, M+1 ), LDA, BI, LDA, 00403 $ BI( M+1, M+1 ), LDA, BI( 1, M+1 ), LDA, 00404 $ Q, LDA, Z, LDA, WEIGHT, QBA, QBB ) 00405 * 00406 * Compute the Schur factorization and swapping the 00407 * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. 00408 * Swapping is accomplished via the function DLCTSX 00409 * which is supplied below. 00410 * 00411 IF( IFUNC.EQ.0 ) THEN 00412 SENSE = 'N' 00413 ELSE IF( IFUNC.EQ.1 ) THEN 00414 SENSE = 'E' 00415 ELSE IF( IFUNC.EQ.2 ) THEN 00416 SENSE = 'V' 00417 ELSE IF( IFUNC.EQ.3 ) THEN 00418 SENSE = 'B' 00419 END IF 00420 * 00421 CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA ) 00422 CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA ) 00423 * 00424 CALL DGGESX( 'V', 'V', 'S', DLCTSX, SENSE, MPLUSN, AI, 00425 $ LDA, BI, LDA, MM, ALPHAR, ALPHAI, BETA, 00426 $ Q, LDA, Z, LDA, PL, DIFEST, WORK, LWORK, 00427 $ IWORK, LIWORK, BWORK, LINFO ) 00428 * 00429 IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN 00430 RESULT( 1 ) = ULPINV 00431 WRITE( NOUT, FMT = 9999 )'DGGESX', LINFO, MPLUSN, 00432 $ PRTYPE 00433 INFO = LINFO 00434 GO TO 30 00435 END IF 00436 * 00437 * Compute the norm(A, B) 00438 * 00439 CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK, 00440 $ MPLUSN ) 00441 CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, 00442 $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN ) 00443 ABNRM = DLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN, 00444 $ WORK ) 00445 * 00446 * Do tests (1) to (4) 00447 * 00448 CALL DGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z, 00449 $ LDA, WORK, RESULT( 1 ) ) 00450 CALL DGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z, 00451 $ LDA, WORK, RESULT( 2 ) ) 00452 CALL DGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q, 00453 $ LDA, WORK, RESULT( 3 ) ) 00454 CALL DGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z, 00455 $ LDA, WORK, RESULT( 4 ) ) 00456 NTEST = 4 00457 * 00458 * Do tests (5) and (6): check Schur form of A and 00459 * compare eigenvalues with diagonals. 00460 * 00461 TEMP1 = ZERO 00462 RESULT( 5 ) = ZERO 00463 RESULT( 6 ) = ZERO 00464 * 00465 DO 10 J = 1, MPLUSN 00466 ILABAD = .FALSE. 00467 IF( ALPHAI( J ).EQ.ZERO ) THEN 00468 TEMP2 = ( ABS( ALPHAR( J )-AI( J, J ) ) / 00469 $ MAX( SMLNUM, ABS( ALPHAR( J ) ), 00470 $ ABS( AI( J, J ) ) )+ 00471 $ ABS( BETA( J )-BI( J, J ) ) / 00472 $ MAX( SMLNUM, ABS( BETA( J ) ), 00473 $ ABS( BI( J, J ) ) ) ) / ULP 00474 IF( J.LT.MPLUSN ) THEN 00475 IF( AI( J+1, J ).NE.ZERO ) THEN 00476 ILABAD = .TRUE. 00477 RESULT( 5 ) = ULPINV 00478 END IF 00479 END IF 00480 IF( J.GT.1 ) THEN 00481 IF( AI( J, J-1 ).NE.ZERO ) THEN 00482 ILABAD = .TRUE. 00483 RESULT( 5 ) = ULPINV 00484 END IF 00485 END IF 00486 ELSE 00487 IF( ALPHAI( J ).GT.ZERO ) THEN 00488 I1 = J 00489 ELSE 00490 I1 = J - 1 00491 END IF 00492 IF( I1.LE.0 .OR. I1.GE.MPLUSN ) THEN 00493 ILABAD = .TRUE. 00494 ELSE IF( I1.LT.MPLUSN-1 ) THEN 00495 IF( AI( I1+2, I1+1 ).NE.ZERO ) THEN 00496 ILABAD = .TRUE. 00497 RESULT( 5 ) = ULPINV 00498 END IF 00499 ELSE IF( I1.GT.1 ) THEN 00500 IF( AI( I1, I1-1 ).NE.ZERO ) THEN 00501 ILABAD = .TRUE. 00502 RESULT( 5 ) = ULPINV 00503 END IF 00504 END IF 00505 IF( .NOT.ILABAD ) THEN 00506 CALL DGET53( AI( I1, I1 ), LDA, BI( I1, I1 ), 00507 $ LDA, BETA( J ), ALPHAR( J ), 00508 $ ALPHAI( J ), TEMP2, IINFO ) 00509 IF( IINFO.GE.3 ) THEN 00510 WRITE( NOUT, FMT = 9997 )IINFO, J, 00511 $ MPLUSN, PRTYPE 00512 INFO = ABS( IINFO ) 00513 END IF 00514 ELSE 00515 TEMP2 = ULPINV 00516 END IF 00517 END IF 00518 TEMP1 = MAX( TEMP1, TEMP2 ) 00519 IF( ILABAD ) THEN 00520 WRITE( NOUT, FMT = 9996 )J, MPLUSN, PRTYPE 00521 END IF 00522 10 CONTINUE 00523 RESULT( 6 ) = TEMP1 00524 NTEST = NTEST + 2 00525 * 00526 * Test (7) (if sorting worked) 00527 * 00528 RESULT( 7 ) = ZERO 00529 IF( LINFO.EQ.MPLUSN+3 ) THEN 00530 RESULT( 7 ) = ULPINV 00531 ELSE IF( MM.NE.N ) THEN 00532 RESULT( 7 ) = ULPINV 00533 END IF 00534 NTEST = NTEST + 1 00535 * 00536 * Test (8): compare the estimated value DIF and its 00537 * value. first, compute the exact DIF. 00538 * 00539 RESULT( 8 ) = ZERO 00540 MN2 = MM*( MPLUSN-MM )*2 00541 IF( IFUNC.GE.2 .AND. MN2.LE.NCMAX*NCMAX ) THEN 00542 * 00543 * Note: for either following two causes, there are 00544 * almost same number of test cases fail the test. 00545 * 00546 CALL DLAKF2( MM, MPLUSN-MM, AI, LDA, 00547 $ AI( MM+1, MM+1 ), BI, 00548 $ BI( MM+1, MM+1 ), C, LDC ) 00549 * 00550 CALL DGESVD( 'N', 'N', MN2, MN2, C, LDC, S, WORK, 00551 $ 1, WORK( 2 ), 1, WORK( 3 ), LWORK-2, 00552 $ INFO ) 00553 DIFTRU = S( MN2 ) 00554 * 00555 IF( DIFEST( 2 ).EQ.ZERO ) THEN 00556 IF( DIFTRU.GT.ABNRM*ULP ) 00557 $ RESULT( 8 ) = ULPINV 00558 ELSE IF( DIFTRU.EQ.ZERO ) THEN 00559 IF( DIFEST( 2 ).GT.ABNRM*ULP ) 00560 $ RESULT( 8 ) = ULPINV 00561 ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR. 00562 $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN 00563 RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ), 00564 $ DIFEST( 2 ) / DIFTRU ) 00565 END IF 00566 NTEST = NTEST + 1 00567 END IF 00568 * 00569 * Test (9) 00570 * 00571 RESULT( 9 ) = ZERO 00572 IF( LINFO.EQ.( MPLUSN+2 ) ) THEN 00573 IF( DIFTRU.GT.ABNRM*ULP ) 00574 $ RESULT( 9 ) = ULPINV 00575 IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) ) 00576 $ RESULT( 9 ) = ULPINV 00577 IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) ) 00578 $ RESULT( 9 ) = ULPINV 00579 NTEST = NTEST + 1 00580 END IF 00581 * 00582 NTESTT = NTESTT + NTEST 00583 * 00584 * Print out tests which fail. 00585 * 00586 DO 20 J = 1, 9 00587 IF( RESULT( J ).GE.THRESH ) THEN 00588 * 00589 * If this is the first test to fail, 00590 * print a header to the data file. 00591 * 00592 IF( NERRS.EQ.0 ) THEN 00593 WRITE( NOUT, FMT = 9995 )'SGX' 00594 * 00595 * Matrix types 00596 * 00597 WRITE( NOUT, FMT = 9993 ) 00598 * 00599 * Tests performed 00600 * 00601 WRITE( NOUT, FMT = 9992 )'orthogonal', '''', 00602 $ 'transpose', ( '''', I = 1, 4 ) 00603 * 00604 END IF 00605 NERRS = NERRS + 1 00606 IF( RESULT( J ).LT.10000.0D0 ) THEN 00607 WRITE( NOUT, FMT = 9991 )MPLUSN, PRTYPE, 00608 $ WEIGHT, M, J, RESULT( J ) 00609 ELSE 00610 WRITE( NOUT, FMT = 9990 )MPLUSN, PRTYPE, 00611 $ WEIGHT, M, J, RESULT( J ) 00612 END IF 00613 END IF 00614 20 CONTINUE 00615 * 00616 30 CONTINUE 00617 40 CONTINUE 00618 50 CONTINUE 00619 60 CONTINUE 00620 * 00621 GO TO 150 00622 * 00623 70 CONTINUE 00624 * 00625 * Read in data from file to check accuracy of condition estimation 00626 * Read input data until N=0 00627 * 00628 NPTKNT = 0 00629 * 00630 80 CONTINUE 00631 READ( NIN, FMT = *, END = 140 )MPLUSN 00632 IF( MPLUSN.EQ.0 ) 00633 $ GO TO 140 00634 READ( NIN, FMT = *, END = 140 )N 00635 DO 90 I = 1, MPLUSN 00636 READ( NIN, FMT = * )( AI( I, J ), J = 1, MPLUSN ) 00637 90 CONTINUE 00638 DO 100 I = 1, MPLUSN 00639 READ( NIN, FMT = * )( BI( I, J ), J = 1, MPLUSN ) 00640 100 CONTINUE 00641 READ( NIN, FMT = * )PLTRU, DIFTRU 00642 * 00643 NPTKNT = NPTKNT + 1 00644 FS = .TRUE. 00645 K = 0 00646 M = MPLUSN - N 00647 * 00648 CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA ) 00649 CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA ) 00650 * 00651 * Compute the Schur factorization while swaping the 00652 * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. 00653 * 00654 CALL DGGESX( 'V', 'V', 'S', DLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA, 00655 $ MM, ALPHAR, ALPHAI, BETA, Q, LDA, Z, LDA, PL, DIFEST, 00656 $ WORK, LWORK, IWORK, LIWORK, BWORK, LINFO ) 00657 * 00658 IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN 00659 RESULT( 1 ) = ULPINV 00660 WRITE( NOUT, FMT = 9998 )'DGGESX', LINFO, MPLUSN, NPTKNT 00661 GO TO 130 00662 END IF 00663 * 00664 * Compute the norm(A, B) 00665 * (should this be norm of (A,B) or (AI,BI)?) 00666 * 00667 CALL DLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK, MPLUSN ) 00668 CALL DLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, 00669 $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN ) 00670 ABNRM = DLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN, WORK ) 00671 * 00672 * Do tests (1) to (4) 00673 * 00674 CALL DGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z, LDA, WORK, 00675 $ RESULT( 1 ) ) 00676 CALL DGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z, LDA, WORK, 00677 $ RESULT( 2 ) ) 00678 CALL DGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q, LDA, WORK, 00679 $ RESULT( 3 ) ) 00680 CALL DGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z, LDA, WORK, 00681 $ RESULT( 4 ) ) 00682 * 00683 * Do tests (5) and (6): check Schur form of A and compare 00684 * eigenvalues with diagonals. 00685 * 00686 NTEST = 6 00687 TEMP1 = ZERO 00688 RESULT( 5 ) = ZERO 00689 RESULT( 6 ) = ZERO 00690 * 00691 DO 110 J = 1, MPLUSN 00692 ILABAD = .FALSE. 00693 IF( ALPHAI( J ).EQ.ZERO ) THEN 00694 TEMP2 = ( ABS( ALPHAR( J )-AI( J, J ) ) / 00695 $ MAX( SMLNUM, ABS( ALPHAR( J ) ), ABS( AI( J, 00696 $ J ) ) )+ABS( BETA( J )-BI( J, J ) ) / 00697 $ MAX( SMLNUM, ABS( BETA( J ) ), ABS( BI( J, J ) ) ) ) 00698 $ / ULP 00699 IF( J.LT.MPLUSN ) THEN 00700 IF( AI( J+1, J ).NE.ZERO ) THEN 00701 ILABAD = .TRUE. 00702 RESULT( 5 ) = ULPINV 00703 END IF 00704 END IF 00705 IF( J.GT.1 ) THEN 00706 IF( AI( J, J-1 ).NE.ZERO ) THEN 00707 ILABAD = .TRUE. 00708 RESULT( 5 ) = ULPINV 00709 END IF 00710 END IF 00711 ELSE 00712 IF( ALPHAI( J ).GT.ZERO ) THEN 00713 I1 = J 00714 ELSE 00715 I1 = J - 1 00716 END IF 00717 IF( I1.LE.0 .OR. I1.GE.MPLUSN ) THEN 00718 ILABAD = .TRUE. 00719 ELSE IF( I1.LT.MPLUSN-1 ) THEN 00720 IF( AI( I1+2, I1+1 ).NE.ZERO ) THEN 00721 ILABAD = .TRUE. 00722 RESULT( 5 ) = ULPINV 00723 END IF 00724 ELSE IF( I1.GT.1 ) THEN 00725 IF( AI( I1, I1-1 ).NE.ZERO ) THEN 00726 ILABAD = .TRUE. 00727 RESULT( 5 ) = ULPINV 00728 END IF 00729 END IF 00730 IF( .NOT.ILABAD ) THEN 00731 CALL DGET53( AI( I1, I1 ), LDA, BI( I1, I1 ), LDA, 00732 $ BETA( J ), ALPHAR( J ), ALPHAI( J ), TEMP2, 00733 $ IINFO ) 00734 IF( IINFO.GE.3 ) THEN 00735 WRITE( NOUT, FMT = 9997 )IINFO, J, MPLUSN, NPTKNT 00736 INFO = ABS( IINFO ) 00737 END IF 00738 ELSE 00739 TEMP2 = ULPINV 00740 END IF 00741 END IF 00742 TEMP1 = MAX( TEMP1, TEMP2 ) 00743 IF( ILABAD ) THEN 00744 WRITE( NOUT, FMT = 9996 )J, MPLUSN, NPTKNT 00745 END IF 00746 110 CONTINUE 00747 RESULT( 6 ) = TEMP1 00748 * 00749 * Test (7) (if sorting worked) <--------- need to be checked. 00750 * 00751 NTEST = 7 00752 RESULT( 7 ) = ZERO 00753 IF( LINFO.EQ.MPLUSN+3 ) 00754 $ RESULT( 7 ) = ULPINV 00755 * 00756 * Test (8): compare the estimated value of DIF and its true value. 00757 * 00758 NTEST = 8 00759 RESULT( 8 ) = ZERO 00760 IF( DIFEST( 2 ).EQ.ZERO ) THEN 00761 IF( DIFTRU.GT.ABNRM*ULP ) 00762 $ RESULT( 8 ) = ULPINV 00763 ELSE IF( DIFTRU.EQ.ZERO ) THEN 00764 IF( DIFEST( 2 ).GT.ABNRM*ULP ) 00765 $ RESULT( 8 ) = ULPINV 00766 ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR. 00767 $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN 00768 RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ), DIFEST( 2 ) / DIFTRU ) 00769 END IF 00770 * 00771 * Test (9) 00772 * 00773 NTEST = 9 00774 RESULT( 9 ) = ZERO 00775 IF( LINFO.EQ.( MPLUSN+2 ) ) THEN 00776 IF( DIFTRU.GT.ABNRM*ULP ) 00777 $ RESULT( 9 ) = ULPINV 00778 IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) ) 00779 $ RESULT( 9 ) = ULPINV 00780 IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) ) 00781 $ RESULT( 9 ) = ULPINV 00782 END IF 00783 * 00784 * Test (10): compare the estimated value of PL and it true value. 00785 * 00786 NTEST = 10 00787 RESULT( 10 ) = ZERO 00788 IF( PL( 1 ).EQ.ZERO ) THEN 00789 IF( PLTRU.GT.ABNRM*ULP ) 00790 $ RESULT( 10 ) = ULPINV 00791 ELSE IF( PLTRU.EQ.ZERO ) THEN 00792 IF( PL( 1 ).GT.ABNRM*ULP ) 00793 $ RESULT( 10 ) = ULPINV 00794 ELSE IF( ( PLTRU.GT.THRESH*PL( 1 ) ) .OR. 00795 $ ( PLTRU*THRESH.LT.PL( 1 ) ) ) THEN 00796 RESULT( 10 ) = ULPINV 00797 END IF 00798 * 00799 NTESTT = NTESTT + NTEST 00800 * 00801 * Print out tests which fail. 00802 * 00803 DO 120 J = 1, NTEST 00804 IF( RESULT( J ).GE.THRESH ) THEN 00805 * 00806 * If this is the first test to fail, 00807 * print a header to the data file. 00808 * 00809 IF( NERRS.EQ.0 ) THEN 00810 WRITE( NOUT, FMT = 9995 )'SGX' 00811 * 00812 * Matrix types 00813 * 00814 WRITE( NOUT, FMT = 9994 ) 00815 * 00816 * Tests performed 00817 * 00818 WRITE( NOUT, FMT = 9992 )'orthogonal', '''', 00819 $ 'transpose', ( '''', I = 1, 4 ) 00820 * 00821 END IF 00822 NERRS = NERRS + 1 00823 IF( RESULT( J ).LT.10000.0D0 ) THEN 00824 WRITE( NOUT, FMT = 9989 )NPTKNT, MPLUSN, J, RESULT( J ) 00825 ELSE 00826 WRITE( NOUT, FMT = 9988 )NPTKNT, MPLUSN, J, RESULT( J ) 00827 END IF 00828 END IF 00829 * 00830 120 CONTINUE 00831 * 00832 130 CONTINUE 00833 GO TO 80 00834 140 CONTINUE 00835 * 00836 150 CONTINUE 00837 * 00838 * Summary 00839 * 00840 CALL ALASVM( 'SGX', NOUT, NERRS, NTESTT, 0 ) 00841 * 00842 WORK( 1 ) = MAXWRK 00843 * 00844 RETURN 00845 * 00846 9999 FORMAT( ' DDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', 00847 $ I6, ', JTYPE=', I6, ')' ) 00848 * 00849 9998 FORMAT( ' DDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', 00850 $ I6, ', Input Example #', I2, ')' ) 00851 * 00852 9997 FORMAT( ' DDRGSX: DGET53 returned INFO=', I1, ' for eigenvalue ', 00853 $ I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ')' ) 00854 * 00855 9996 FORMAT( ' DDRGSX: S not in Schur form at eigenvalue ', I6, '.', 00856 $ / 9X, 'N=', I6, ', JTYPE=', I6, ')' ) 00857 * 00858 9995 FORMAT( / 1X, A3, ' -- Real Expert Generalized Schur form', 00859 $ ' problem driver' ) 00860 * 00861 9994 FORMAT( 'Input Example' ) 00862 * 00863 9993 FORMAT( ' Matrix types: ', / 00864 $ ' 1: A is a block diagonal matrix of Jordan blocks ', 00865 $ 'and B is the identity ', / ' matrix, ', 00866 $ / ' 2: A and B are upper triangular matrices, ', 00867 $ / ' 3: A and B are as type 2, but each second diagonal ', 00868 $ 'block in A_11 and ', / 00869 $ ' each third diaongal block in A_22 are 2x2 blocks,', 00870 $ / ' 4: A and B are block diagonal matrices, ', 00871 $ / ' 5: (A,B) has potentially close or common ', 00872 $ 'eigenvalues.', / ) 00873 * 00874 9992 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ', 00875 $ 'Q and Z are ', A, ',', / 19X, 00876 $ ' a is alpha, b is beta, and ', A, ' means ', A, '.)', 00877 $ / ' 1 = | A - Q S Z', A, 00878 $ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A, 00879 $ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A, 00880 $ ' | / ( n ulp ) 4 = | I - ZZ', A, 00881 $ ' | / ( n ulp )', / ' 5 = 1/ULP if A is not in ', 00882 $ 'Schur form S', / ' 6 = difference between (alpha,beta)', 00883 $ ' and diagonals of (S,T)', / 00884 $ ' 7 = 1/ULP if SDIM is not the correct number of ', 00885 $ 'selected eigenvalues', / 00886 $ ' 8 = 1/ULP if DIFEST/DIFTRU > 10*THRESH or ', 00887 $ 'DIFTRU/DIFEST > 10*THRESH', 00888 $ / ' 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) ', 00889 $ 'when reordering fails', / 00890 $ ' 10 = 1/ULP if PLEST/PLTRU > THRESH or ', 00891 $ 'PLTRU/PLEST > THRESH', / 00892 $ ' ( Test 10 is only for input examples )', / ) 00893 9991 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', D10.4, 00894 $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, F8.2 ) 00895 9990 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', D10.4, 00896 $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, D10.4 ) 00897 9989 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',', 00898 $ ' result ', I2, ' is', 0P, F8.2 ) 00899 9988 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',', 00900 $ ' result ', I2, ' is', 1P, D10.3 ) 00901 * 00902 * End of DDRGSX 00903 * 00904 END
1.7.3 
