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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 CDRGSX( NSIZE, NCMAX, THRESH, NIN, NOUT, A, LDA, B, 00002 $ AI, BI, Z, Q, ALPHA, BETA, C, LDC, S, WORK, 00003 $ LWORK, RWORK, IWORK, LIWORK, BWORK, INFO ) 00004 * 00005 * -- LAPACK test routine (version 3.3.1) -- 00006 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00007 * -- April 2011 -- 00008 * 00009 * .. Scalar Arguments .. 00010 INTEGER INFO, LDA, LDC, LIWORK, LWORK, NCMAX, NIN, 00011 $ NOUT, NSIZE 00012 REAL THRESH 00013 * .. 00014 * .. Array Arguments .. 00015 LOGICAL BWORK( * ) 00016 INTEGER IWORK( * ) 00017 REAL RWORK( * ), S( * ) 00018 COMPLEX A( LDA, * ), AI( LDA, * ), ALPHA( * ), 00019 $ B( LDA, * ), BETA( * ), BI( LDA, * ), 00020 $ C( LDC, * ), Q( LDA, * ), WORK( * ), 00021 $ Z( LDA, * ) 00022 * .. 00023 * 00024 * Purpose 00025 * ======= 00026 * 00027 * CDRGSX checks the nonsymmetric generalized eigenvalue (Schur form) 00028 * problem expert driver CGGESX. 00029 * 00030 * CGGES factors A and B as Q*S*Z' and Q*T*Z' , where ' means conjugate 00031 * transpose, S and T are upper triangular (i.e., in generalized Schur 00032 * form), and Q and Z are unitary. It also computes the generalized 00033 * eigenvalues (alpha(j),beta(j)), j=1,...,n. Thus, 00034 * w(j) = alpha(j)/beta(j) is a root of the characteristic equation 00035 * 00036 * det( A - w(j) B ) = 0 00037 * 00038 * Optionally it also reorders the eigenvalues so that a selected 00039 * cluster of eigenvalues appears in the leading diagonal block of the 00040 * Schur forms; computes a reciprocal condition number for the average 00041 * of the selected eigenvalues; and computes a reciprocal condition 00042 * number for the right and left deflating subspaces corresponding to 00043 * the selected eigenvalues. 00044 * 00045 * When CDRGSX is called with NSIZE > 0, five (5) types of built-in 00046 * matrix pairs are used to test the routine CGGESX. 00047 * 00048 * When CDRGSX is called with NSIZE = 0, it reads in test matrix data 00049 * to test CGGESX. 00050 * (need more details on what kind of read-in data are needed). 00051 * 00052 * For each matrix pair, the following tests will be performed and 00053 * compared with the threshhold THRESH except for the tests (7) and (9): 00054 * 00055 * (1) | A - Q S Z' | / ( |A| n ulp ) 00056 * 00057 * (2) | B - Q T Z' | / ( |B| n ulp ) 00058 * 00059 * (3) | I - QQ' | / ( n ulp ) 00060 * 00061 * (4) | I - ZZ' | / ( n ulp ) 00062 * 00063 * (5) if A is in Schur form (i.e. triangular form) 00064 * 00065 * (6) maximum over j of D(j) where: 00066 * 00067 * |alpha(j) - S(j,j)| |beta(j) - T(j,j)| 00068 * D(j) = ------------------------ + ----------------------- 00069 * max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) 00070 * 00071 * (7) if sorting worked and SDIM is the number of eigenvalues 00072 * which were selected. 00073 * 00074 * (8) the estimated value DIF does not differ from the true values of 00075 * Difu and Difl more than a factor 10*THRESH. If the estimate DIF 00076 * equals zero the corresponding true values of Difu and Difl 00077 * should be less than EPS*norm(A, B). If the true value of Difu 00078 * and Difl equal zero, the estimate DIF should be less than 00079 * EPS*norm(A, B). 00080 * 00081 * (9) If INFO = N+3 is returned by CGGESX, the reordering "failed" 00082 * and we check that DIF = PL = PR = 0 and that the true value of 00083 * Difu and Difl is < EPS*norm(A, B). We count the events when 00084 * INFO=N+3. 00085 * 00086 * For read-in test matrices, the same tests are run except that the 00087 * exact value for DIF (and PL) is input data. Additionally, there is 00088 * one more test run for read-in test matrices: 00089 * 00090 * (10) the estimated value PL does not differ from the true value of 00091 * PLTRU more than a factor THRESH. If the estimate PL equals 00092 * zero the corresponding true value of PLTRU should be less than 00093 * EPS*norm(A, B). If the true value of PLTRU equal zero, the 00094 * estimate PL should be less than EPS*norm(A, B). 00095 * 00096 * Note that for the built-in tests, a total of 10*NSIZE*(NSIZE-1) 00097 * matrix pairs are generated and tested. NSIZE should be kept small. 00098 * 00099 * SVD (routine CGESVD) is used for computing the true value of DIF_u 00100 * and DIF_l when testing the built-in test problems. 00101 * 00102 * Built-in Test Matrices 00103 * ====================== 00104 * 00105 * All built-in test matrices are the 2 by 2 block of triangular 00106 * matrices 00107 * 00108 * A = [ A11 A12 ] and B = [ B11 B12 ] 00109 * [ A22 ] [ B22 ] 00110 * 00111 * where for different type of A11 and A22 are given as the following. 00112 * A12 and B12 are chosen so that the generalized Sylvester equation 00113 * 00114 * A11*R - L*A22 = -A12 00115 * B11*R - L*B22 = -B12 00116 * 00117 * have prescribed solution R and L. 00118 * 00119 * Type 1: A11 = J_m(1,-1) and A_22 = J_k(1-a,1). 00120 * B11 = I_m, B22 = I_k 00121 * where J_k(a,b) is the k-by-k Jordan block with ``a'' on 00122 * diagonal and ``b'' on superdiagonal. 00123 * 00124 * Type 2: A11 = (a_ij) = ( 2(.5-sin(i)) ) and 00125 * B11 = (b_ij) = ( 2(.5-sin(ij)) ) for i=1,...,m, j=i,...,m 00126 * A22 = (a_ij) = ( 2(.5-sin(i+j)) ) and 00127 * B22 = (b_ij) = ( 2(.5-sin(ij)) ) for i=m+1,...,k, j=i,...,k 00128 * 00129 * Type 3: A11, A22 and B11, B22 are chosen as for Type 2, but each 00130 * second diagonal block in A_11 and each third diagonal block 00131 * in A_22 are made as 2 by 2 blocks. 00132 * 00133 * Type 4: A11 = ( 20(.5 - sin(ij)) ) and B22 = ( 2(.5 - sin(i+j)) ) 00134 * for i=1,...,m, j=1,...,m and 00135 * A22 = ( 20(.5 - sin(i+j)) ) and B22 = ( 2(.5 - sin(ij)) ) 00136 * for i=m+1,...,k, j=m+1,...,k 00137 * 00138 * Type 5: (A,B) and have potentially close or common eigenvalues and 00139 * very large departure from block diagonality A_11 is chosen 00140 * as the m x m leading submatrix of A_1: 00141 * | 1 b | 00142 * | -b 1 | 00143 * | 1+d b | 00144 * | -b 1+d | 00145 * A_1 = | d 1 | 00146 * | -1 d | 00147 * | -d 1 | 00148 * | -1 -d | 00149 * | 1 | 00150 * and A_22 is chosen as the k x k leading submatrix of A_2: 00151 * | -1 b | 00152 * | -b -1 | 00153 * | 1-d b | 00154 * | -b 1-d | 00155 * A_2 = | d 1+b | 00156 * | -1-b d | 00157 * | -d 1+b | 00158 * | -1+b -d | 00159 * | 1-d | 00160 * and matrix B are chosen as identity matrices (see SLATM5). 00161 * 00162 * 00163 * Arguments 00164 * ========= 00165 * 00166 * NSIZE (input) INTEGER 00167 * The maximum size of the matrices to use. NSIZE >= 0. 00168 * If NSIZE = 0, no built-in tests matrices are used, but 00169 * read-in test matrices are used to test SGGESX. 00170 * 00171 * NCMAX (input) INTEGER 00172 * Maximum allowable NMAX for generating Kroneker matrix 00173 * in call to CLAKF2 00174 * 00175 * THRESH (input) REAL 00176 * A test will count as "failed" if the "error", computed as 00177 * described above, exceeds THRESH. Note that the error 00178 * is scaled to be O(1), so THRESH should be a reasonably 00179 * small multiple of 1, e.g., 10 or 100. In particular, 00180 * it should not depend on the precision (single vs. double) 00181 * or the size of the matrix. THRESH >= 0. 00182 * 00183 * NIN (input) INTEGER 00184 * The FORTRAN unit number for reading in the data file of 00185 * problems to solve. 00186 * 00187 * NOUT (input) INTEGER 00188 * The FORTRAN unit number for printing out error messages 00189 * (e.g., if a routine returns INFO not equal to 0.) 00190 * 00191 * A (workspace) COMPLEX array, dimension (LDA, NSIZE) 00192 * Used to store the matrix whose eigenvalues are to be 00193 * computed. On exit, A contains the last matrix actually used. 00194 * 00195 * LDA (input) INTEGER 00196 * The leading dimension of A, B, AI, BI, Z and Q, 00197 * LDA >= max( 1, NSIZE ). For the read-in test, 00198 * LDA >= max( 1, N ), N is the size of the test matrices. 00199 * 00200 * B (workspace) COMPLEX array, dimension (LDA, NSIZE) 00201 * Used to store the matrix whose eigenvalues are to be 00202 * computed. On exit, B contains the last matrix actually used. 00203 * 00204 * AI (workspace) COMPLEX array, dimension (LDA, NSIZE) 00205 * Copy of A, modified by CGGESX. 00206 * 00207 * BI (workspace) COMPLEX array, dimension (LDA, NSIZE) 00208 * Copy of B, modified by CGGESX. 00209 * 00210 * Z (workspace) COMPLEX array, dimension (LDA, NSIZE) 00211 * Z holds the left Schur vectors computed by CGGESX. 00212 * 00213 * Q (workspace) COMPLEX array, dimension (LDA, NSIZE) 00214 * Q holds the right Schur vectors computed by CGGESX. 00215 * 00216 * ALPHA (workspace) COMPLEX array, dimension (NSIZE) 00217 * BETA (workspace) COMPLEX array, dimension (NSIZE) 00218 * On exit, ALPHA/BETA are the eigenvalues. 00219 * 00220 * C (workspace) COMPLEX array, dimension (LDC, LDC) 00221 * Store the matrix generated by subroutine CLAKF2, this is the 00222 * matrix formed by Kronecker products used for estimating 00223 * DIF. 00224 * 00225 * LDC (input) INTEGER 00226 * The leading dimension of C. LDC >= max(1, LDA*LDA/2 ). 00227 * 00228 * S (workspace) REAL array, dimension (LDC) 00229 * Singular values of C 00230 * 00231 * WORK (workspace) COMPLEX array, dimension (LWORK) 00232 * 00233 * LWORK (input) INTEGER 00234 * The dimension of the array WORK. LWORK >= 3*NSIZE*NSIZE/2 00235 * 00236 * RWORK (workspace) REAL array, 00237 * dimension (5*NSIZE*NSIZE/2 - 4) 00238 * 00239 * IWORK (workspace) INTEGER array, dimension (LIWORK) 00240 * 00241 * LIWORK (input) INTEGER 00242 * The dimension of the array IWORK. LIWORK >= NSIZE + 2. 00243 * 00244 * BWORK (workspace) LOGICAL array, dimension (NSIZE) 00245 * 00246 * INFO (output) INTEGER 00247 * = 0: successful exit 00248 * < 0: if INFO = -i, the i-th argument had an illegal value. 00249 * > 0: A routine returned an error code. 00250 * 00251 * ===================================================================== 00252 * 00253 * .. Parameters .. 00254 REAL ZERO, ONE, TEN 00255 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TEN = 1.0E+1 ) 00256 COMPLEX CZERO 00257 PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ) ) 00258 * .. 00259 * .. Local Scalars .. 00260 LOGICAL ILABAD 00261 CHARACTER SENSE 00262 INTEGER BDSPAC, I, IFUNC, J, LINFO, MAXWRK, MINWRK, MM, 00263 $ MN2, NERRS, NPTKNT, NTEST, NTESTT, PRTYPE, QBA, 00264 $ QBB 00265 REAL ABNRM, BIGNUM, DIFTRU, PLTRU, SMLNUM, TEMP1, 00266 $ TEMP2, THRSH2, ULP, ULPINV, WEIGHT 00267 COMPLEX X 00268 * .. 00269 * .. Local Arrays .. 00270 REAL DIFEST( 2 ), PL( 2 ), RESULT( 10 ) 00271 * .. 00272 * .. External Functions .. 00273 LOGICAL CLCTSX 00274 INTEGER ILAENV 00275 REAL CLANGE, SLAMCH 00276 EXTERNAL CLCTSX, ILAENV, CLANGE, SLAMCH 00277 * .. 00278 * .. External Subroutines .. 00279 EXTERNAL ALASVM, CGESVD, CGET51, CGGESX, CLACPY, CLAKF2, 00280 $ CLASET, CLATM5, SLABAD, XERBLA 00281 * .. 00282 * .. Scalars in Common .. 00283 LOGICAL FS 00284 INTEGER K, M, MPLUSN, N 00285 * .. 00286 * .. Common blocks .. 00287 COMMON / MN / M, N, MPLUSN, K, FS 00288 * .. 00289 * .. Intrinsic Functions .. 00290 INTRINSIC ABS, AIMAG, MAX, REAL, SQRT 00291 * .. 00292 * .. Statement Functions .. 00293 REAL ABS1 00294 * .. 00295 * .. Statement Function definitions .. 00296 ABS1( X ) = ABS( REAL( X ) ) + ABS( AIMAG( X ) ) 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 = -15 00314 ELSE IF( LIWORK.LT.NSIZE+2 ) 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 = 3*NSIZE*NSIZE / 2 00328 * 00329 * workspace for cggesx 00330 * 00331 MAXWRK = NSIZE*( 1+ILAENV( 1, 'CGEQRF', ' ', NSIZE, 1, NSIZE, 00332 $ 0 ) ) 00333 MAXWRK = MAX( MAXWRK, NSIZE*( 1+ILAENV( 1, 'CUNGQR', ' ', 00334 $ NSIZE, 1, NSIZE, -1 ) ) ) 00335 * 00336 * workspace for cgesvd 00337 * 00338 BDSPAC = 3*NSIZE*NSIZE / 2 00339 MAXWRK = MAX( MAXWRK, NSIZE*NSIZE* 00340 $ ( 1+ILAENV( 1, 'CGEBRD', ' ', 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 = -18 00351 * 00352 IF( INFO.NE.0 ) THEN 00353 CALL XERBLA( 'CDRGSX', -INFO ) 00354 RETURN 00355 END IF 00356 * 00357 * Important constants 00358 * 00359 ULP = SLAMCH( 'P' ) 00360 ULPINV = ONE / ULP 00361 SMLNUM = SLAMCH( 'S' ) / ULP 00362 BIGNUM = ONE / SMLNUM 00363 CALL SLABAD( 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 CGGESX, 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 CLASET( 'Full', MPLUSN, MPLUSN, CZERO, CZERO, AI, 00397 $ LDA ) 00398 CALL CLASET( 'Full', MPLUSN, MPLUSN, CZERO, CZERO, BI, 00399 $ LDA ) 00400 * 00401 CALL CLATM5( 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 CLCTSX 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 CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA ) 00422 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA ) 00423 * 00424 CALL CGGESX( 'V', 'V', 'S', CLCTSX, SENSE, MPLUSN, AI, 00425 $ LDA, BI, LDA, MM, ALPHA, BETA, Q, LDA, Z, 00426 $ LDA, PL, DIFEST, WORK, LWORK, RWORK, 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 )'CGGESX', LINFO, MPLUSN, 00432 $ PRTYPE 00433 INFO = LINFO 00434 GO TO 30 00435 END IF 00436 * 00437 * Compute the norm(A, B) 00438 * 00439 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK, 00440 $ MPLUSN ) 00441 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, 00442 $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN ) 00443 ABNRM = CLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN, 00444 $ RWORK ) 00445 * 00446 * Do tests (1) to (4) 00447 * 00448 RESULT( 2 ) = ZERO 00449 CALL CGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z, 00450 $ LDA, WORK, RWORK, RESULT( 1 ) ) 00451 CALL CGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z, 00452 $ LDA, WORK, RWORK, RESULT( 2 ) ) 00453 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q, 00454 $ LDA, WORK, RWORK, RESULT( 3 ) ) 00455 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z, 00456 $ LDA, WORK, RWORK, RESULT( 4 ) ) 00457 NTEST = 4 00458 * 00459 * Do tests (5) and (6): check Schur form of A and 00460 * compare eigenvalues with diagonals. 00461 * 00462 TEMP1 = ZERO 00463 RESULT( 5 ) = ZERO 00464 RESULT( 6 ) = ZERO 00465 * 00466 DO 10 J = 1, MPLUSN 00467 ILABAD = .FALSE. 00468 TEMP2 = ( ABS1( ALPHA( J )-AI( J, J ) ) / 00469 $ MAX( SMLNUM, ABS1( ALPHA( J ) ), 00470 $ ABS1( AI( J, J ) ) )+ 00471 $ ABS1( BETA( J )-BI( J, J ) ) / 00472 $ MAX( SMLNUM, ABS1( BETA( J ) ), 00473 $ ABS1( 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 TEMP1 = MAX( TEMP1, TEMP2 ) 00487 IF( ILABAD ) THEN 00488 WRITE( NOUT, FMT = 9997 )J, MPLUSN, PRTYPE 00489 END IF 00490 10 CONTINUE 00491 RESULT( 6 ) = TEMP1 00492 NTEST = NTEST + 2 00493 * 00494 * Test (7) (if sorting worked) 00495 * 00496 RESULT( 7 ) = ZERO 00497 IF( LINFO.EQ.MPLUSN+3 ) THEN 00498 RESULT( 7 ) = ULPINV 00499 ELSE IF( MM.NE.N ) THEN 00500 RESULT( 7 ) = ULPINV 00501 END IF 00502 NTEST = NTEST + 1 00503 * 00504 * Test (8): compare the estimated value DIF and its 00505 * value. first, compute the exact DIF. 00506 * 00507 RESULT( 8 ) = ZERO 00508 MN2 = MM*( MPLUSN-MM )*2 00509 IF( IFUNC.GE.2 .AND. MN2.LE.NCMAX*NCMAX ) THEN 00510 * 00511 * Note: for either following two cases, there are 00512 * almost same number of test cases fail the test. 00513 * 00514 CALL CLAKF2( MM, MPLUSN-MM, AI, LDA, 00515 $ AI( MM+1, MM+1 ), BI, 00516 $ BI( MM+1, MM+1 ), C, LDC ) 00517 * 00518 CALL CGESVD( 'N', 'N', MN2, MN2, C, LDC, S, WORK, 00519 $ 1, WORK( 2 ), 1, WORK( 3 ), LWORK-2, 00520 $ RWORK, INFO ) 00521 DIFTRU = S( MN2 ) 00522 * 00523 IF( DIFEST( 2 ).EQ.ZERO ) THEN 00524 IF( DIFTRU.GT.ABNRM*ULP ) 00525 $ RESULT( 8 ) = ULPINV 00526 ELSE IF( DIFTRU.EQ.ZERO ) THEN 00527 IF( DIFEST( 2 ).GT.ABNRM*ULP ) 00528 $ RESULT( 8 ) = ULPINV 00529 ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR. 00530 $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN 00531 RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ), 00532 $ DIFEST( 2 ) / DIFTRU ) 00533 END IF 00534 NTEST = NTEST + 1 00535 END IF 00536 * 00537 * Test (9) 00538 * 00539 RESULT( 9 ) = ZERO 00540 IF( LINFO.EQ.( MPLUSN+2 ) ) THEN 00541 IF( DIFTRU.GT.ABNRM*ULP ) 00542 $ RESULT( 9 ) = ULPINV 00543 IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) ) 00544 $ RESULT( 9 ) = ULPINV 00545 IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) ) 00546 $ RESULT( 9 ) = ULPINV 00547 NTEST = NTEST + 1 00548 END IF 00549 * 00550 NTESTT = NTESTT + NTEST 00551 * 00552 * Print out tests which fail. 00553 * 00554 DO 20 J = 1, 9 00555 IF( RESULT( J ).GE.THRESH ) THEN 00556 * 00557 * If this is the first test to fail, 00558 * print a header to the data file. 00559 * 00560 IF( NERRS.EQ.0 ) THEN 00561 WRITE( NOUT, FMT = 9996 )'CGX' 00562 * 00563 * Matrix types 00564 * 00565 WRITE( NOUT, FMT = 9994 ) 00566 * 00567 * Tests performed 00568 * 00569 WRITE( NOUT, FMT = 9993 )'unitary', '''', 00570 $ 'transpose', ( '''', I = 1, 4 ) 00571 * 00572 END IF 00573 NERRS = NERRS + 1 00574 IF( RESULT( J ).LT.10000.0 ) THEN 00575 WRITE( NOUT, FMT = 9992 )MPLUSN, PRTYPE, 00576 $ WEIGHT, M, J, RESULT( J ) 00577 ELSE 00578 WRITE( NOUT, FMT = 9991 )MPLUSN, PRTYPE, 00579 $ WEIGHT, M, J, RESULT( J ) 00580 END IF 00581 END IF 00582 20 CONTINUE 00583 * 00584 30 CONTINUE 00585 40 CONTINUE 00586 50 CONTINUE 00587 60 CONTINUE 00588 * 00589 GO TO 150 00590 * 00591 70 CONTINUE 00592 * 00593 * Read in data from file to check accuracy of condition estimation 00594 * Read input data until N=0 00595 * 00596 NPTKNT = 0 00597 * 00598 80 CONTINUE 00599 READ( NIN, FMT = *, END = 140 )MPLUSN 00600 IF( MPLUSN.EQ.0 ) 00601 $ GO TO 140 00602 READ( NIN, FMT = *, END = 140 )N 00603 DO 90 I = 1, MPLUSN 00604 READ( NIN, FMT = * )( AI( I, J ), J = 1, MPLUSN ) 00605 90 CONTINUE 00606 DO 100 I = 1, MPLUSN 00607 READ( NIN, FMT = * )( BI( I, J ), J = 1, MPLUSN ) 00608 100 CONTINUE 00609 READ( NIN, FMT = * )PLTRU, DIFTRU 00610 * 00611 NPTKNT = NPTKNT + 1 00612 FS = .TRUE. 00613 K = 0 00614 M = MPLUSN - N 00615 * 00616 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, A, LDA ) 00617 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, B, LDA ) 00618 * 00619 * Compute the Schur factorization while swaping the 00620 * m-by-m (1,1)-blocks with n-by-n (2,2)-blocks. 00621 * 00622 CALL CGGESX( 'V', 'V', 'S', CLCTSX, 'B', MPLUSN, AI, LDA, BI, LDA, 00623 $ MM, ALPHA, BETA, Q, LDA, Z, LDA, PL, DIFEST, WORK, 00624 $ LWORK, RWORK, IWORK, LIWORK, BWORK, LINFO ) 00625 * 00626 IF( LINFO.NE.0 .AND. LINFO.NE.MPLUSN+2 ) THEN 00627 RESULT( 1 ) = ULPINV 00628 WRITE( NOUT, FMT = 9998 )'CGGESX', LINFO, MPLUSN, NPTKNT 00629 GO TO 130 00630 END IF 00631 * 00632 * Compute the norm(A, B) 00633 * (should this be norm of (A,B) or (AI,BI)?) 00634 * 00635 CALL CLACPY( 'Full', MPLUSN, MPLUSN, AI, LDA, WORK, MPLUSN ) 00636 CALL CLACPY( 'Full', MPLUSN, MPLUSN, BI, LDA, 00637 $ WORK( MPLUSN*MPLUSN+1 ), MPLUSN ) 00638 ABNRM = CLANGE( 'Fro', MPLUSN, 2*MPLUSN, WORK, MPLUSN, RWORK ) 00639 * 00640 * Do tests (1) to (4) 00641 * 00642 CALL CGET51( 1, MPLUSN, A, LDA, AI, LDA, Q, LDA, Z, LDA, WORK, 00643 $ RWORK, RESULT( 1 ) ) 00644 CALL CGET51( 1, MPLUSN, B, LDA, BI, LDA, Q, LDA, Z, LDA, WORK, 00645 $ RWORK, RESULT( 2 ) ) 00646 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Q, LDA, Q, LDA, WORK, 00647 $ RWORK, RESULT( 3 ) ) 00648 CALL CGET51( 3, MPLUSN, B, LDA, BI, LDA, Z, LDA, Z, LDA, WORK, 00649 $ RWORK, RESULT( 4 ) ) 00650 * 00651 * Do tests (5) and (6): check Schur form of A and compare 00652 * eigenvalues with diagonals. 00653 * 00654 NTEST = 6 00655 TEMP1 = ZERO 00656 RESULT( 5 ) = ZERO 00657 RESULT( 6 ) = ZERO 00658 * 00659 DO 110 J = 1, MPLUSN 00660 ILABAD = .FALSE. 00661 TEMP2 = ( ABS1( ALPHA( J )-AI( J, J ) ) / 00662 $ MAX( SMLNUM, ABS1( ALPHA( J ) ), ABS1( AI( J, J ) ) )+ 00663 $ ABS1( BETA( J )-BI( J, J ) ) / 00664 $ MAX( SMLNUM, ABS1( BETA( J ) ), ABS1( BI( J, J ) ) ) ) 00665 $ / ULP 00666 IF( J.LT.MPLUSN ) THEN 00667 IF( AI( J+1, J ).NE.ZERO ) THEN 00668 ILABAD = .TRUE. 00669 RESULT( 5 ) = ULPINV 00670 END IF 00671 END IF 00672 IF( J.GT.1 ) THEN 00673 IF( AI( J, J-1 ).NE.ZERO ) THEN 00674 ILABAD = .TRUE. 00675 RESULT( 5 ) = ULPINV 00676 END IF 00677 END IF 00678 TEMP1 = MAX( TEMP1, TEMP2 ) 00679 IF( ILABAD ) THEN 00680 WRITE( NOUT, FMT = 9997 )J, MPLUSN, NPTKNT 00681 END IF 00682 110 CONTINUE 00683 RESULT( 6 ) = TEMP1 00684 * 00685 * Test (7) (if sorting worked) <--------- need to be checked. 00686 * 00687 NTEST = 7 00688 RESULT( 7 ) = ZERO 00689 IF( LINFO.EQ.MPLUSN+3 ) 00690 $ RESULT( 7 ) = ULPINV 00691 * 00692 * Test (8): compare the estimated value of DIF and its true value. 00693 * 00694 NTEST = 8 00695 RESULT( 8 ) = ZERO 00696 IF( DIFEST( 2 ).EQ.ZERO ) THEN 00697 IF( DIFTRU.GT.ABNRM*ULP ) 00698 $ RESULT( 8 ) = ULPINV 00699 ELSE IF( DIFTRU.EQ.ZERO ) THEN 00700 IF( DIFEST( 2 ).GT.ABNRM*ULP ) 00701 $ RESULT( 8 ) = ULPINV 00702 ELSE IF( ( DIFTRU.GT.THRSH2*DIFEST( 2 ) ) .OR. 00703 $ ( DIFTRU*THRSH2.LT.DIFEST( 2 ) ) ) THEN 00704 RESULT( 8 ) = MAX( DIFTRU / DIFEST( 2 ), DIFEST( 2 ) / DIFTRU ) 00705 END IF 00706 * 00707 * Test (9) 00708 * 00709 NTEST = 9 00710 RESULT( 9 ) = ZERO 00711 IF( LINFO.EQ.( MPLUSN+2 ) ) THEN 00712 IF( DIFTRU.GT.ABNRM*ULP ) 00713 $ RESULT( 9 ) = ULPINV 00714 IF( ( IFUNC.GT.1 ) .AND. ( DIFEST( 2 ).NE.ZERO ) ) 00715 $ RESULT( 9 ) = ULPINV 00716 IF( ( IFUNC.EQ.1 ) .AND. ( PL( 1 ).NE.ZERO ) ) 00717 $ RESULT( 9 ) = ULPINV 00718 END IF 00719 * 00720 * Test (10): compare the estimated value of PL and it true value. 00721 * 00722 NTEST = 10 00723 RESULT( 10 ) = ZERO 00724 IF( PL( 1 ).EQ.ZERO ) THEN 00725 IF( PLTRU.GT.ABNRM*ULP ) 00726 $ RESULT( 10 ) = ULPINV 00727 ELSE IF( PLTRU.EQ.ZERO ) THEN 00728 IF( PL( 1 ).GT.ABNRM*ULP ) 00729 $ RESULT( 10 ) = ULPINV 00730 ELSE IF( ( PLTRU.GT.THRESH*PL( 1 ) ) .OR. 00731 $ ( PLTRU*THRESH.LT.PL( 1 ) ) ) THEN 00732 RESULT( 10 ) = ULPINV 00733 END IF 00734 * 00735 NTESTT = NTESTT + NTEST 00736 * 00737 * Print out tests which fail. 00738 * 00739 DO 120 J = 1, NTEST 00740 IF( RESULT( J ).GE.THRESH ) THEN 00741 * 00742 * If this is the first test to fail, 00743 * print a header to the data file. 00744 * 00745 IF( NERRS.EQ.0 ) THEN 00746 WRITE( NOUT, FMT = 9996 )'CGX' 00747 * 00748 * Matrix types 00749 * 00750 WRITE( NOUT, FMT = 9995 ) 00751 * 00752 * Tests performed 00753 * 00754 WRITE( NOUT, FMT = 9993 )'unitary', '''', 'transpose', 00755 $ ( '''', I = 1, 4 ) 00756 * 00757 END IF 00758 NERRS = NERRS + 1 00759 IF( RESULT( J ).LT.10000.0 ) THEN 00760 WRITE( NOUT, FMT = 9990 )NPTKNT, MPLUSN, J, RESULT( J ) 00761 ELSE 00762 WRITE( NOUT, FMT = 9989 )NPTKNT, MPLUSN, J, RESULT( J ) 00763 END IF 00764 END IF 00765 * 00766 120 CONTINUE 00767 * 00768 130 CONTINUE 00769 GO TO 80 00770 140 CONTINUE 00771 * 00772 150 CONTINUE 00773 * 00774 * Summary 00775 * 00776 CALL ALASVM( 'CGX', NOUT, NERRS, NTESTT, 0 ) 00777 * 00778 WORK( 1 ) = MAXWRK 00779 * 00780 RETURN 00781 * 00782 9999 FORMAT( ' CDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', 00783 $ I6, ', JTYPE=', I6, ')' ) 00784 * 00785 9998 FORMAT( ' CDRGSX: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', 00786 $ I6, ', Input Example #', I2, ')' ) 00787 * 00788 9997 FORMAT( ' CDRGSX: S not in Schur form at eigenvalue ', I6, '.', 00789 $ / 9X, 'N=', I6, ', JTYPE=', I6, ')' ) 00790 * 00791 9996 FORMAT( / 1X, A3, ' -- Complex Expert Generalized Schur form', 00792 $ ' problem driver' ) 00793 * 00794 9995 FORMAT( 'Input Example' ) 00795 * 00796 9994 FORMAT( ' Matrix types: ', / 00797 $ ' 1: A is a block diagonal matrix of Jordan blocks ', 00798 $ 'and B is the identity ', / ' matrix, ', 00799 $ / ' 2: A and B are upper triangular matrices, ', 00800 $ / ' 3: A and B are as type 2, but each second diagonal ', 00801 $ 'block in A_11 and ', / 00802 $ ' each third diaongal block in A_22 are 2x2 blocks,', 00803 $ / ' 4: A and B are block diagonal matrices, ', 00804 $ / ' 5: (A,B) has potentially close or common ', 00805 $ 'eigenvalues.', / ) 00806 * 00807 9993 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ', 00808 $ 'Q and Z are ', A, ',', / 19X, 00809 $ ' a is alpha, b is beta, and ', A, ' means ', A, '.)', 00810 $ / ' 1 = | A - Q S Z', A, 00811 $ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A, 00812 $ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A, 00813 $ ' | / ( n ulp ) 4 = | I - ZZ', A, 00814 $ ' | / ( n ulp )', / ' 5 = 1/ULP if A is not in ', 00815 $ 'Schur form S', / ' 6 = difference between (alpha,beta)', 00816 $ ' and diagonals of (S,T)', / 00817 $ ' 7 = 1/ULP if SDIM is not the correct number of ', 00818 $ 'selected eigenvalues', / 00819 $ ' 8 = 1/ULP if DIFEST/DIFTRU > 10*THRESH or ', 00820 $ 'DIFTRU/DIFEST > 10*THRESH', 00821 $ / ' 9 = 1/ULP if DIFEST <> 0 or DIFTRU > ULP*norm(A,B) ', 00822 $ 'when reordering fails', / 00823 $ ' 10 = 1/ULP if PLEST/PLTRU > THRESH or ', 00824 $ 'PLTRU/PLEST > THRESH', / 00825 $ ' ( Test 10 is only for input examples )', / ) 00826 9992 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', E10.3, 00827 $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, F8.2 ) 00828 9991 FORMAT( ' Matrix order=', I2, ', type=', I2, ', a=', E10.3, 00829 $ ', order(A_11)=', I2, ', result ', I2, ' is ', 0P, E10.3 ) 00830 9990 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',', 00831 $ ' result ', I2, ' is', 0P, F8.2 ) 00832 9989 FORMAT( ' Input example #', I2, ', matrix order=', I4, ',', 00833 $ ' result ', I2, ' is', 1P, E10.3 ) 00834 * 00835 * End of CDRGSX 00836 * 00837 END
1.7.3 
