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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 SDRVGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, 00002 $ THRSHN, NOUNIT, A, LDA, B, S, T, S2, T2, Q, 00003 $ LDQ, Z, ALPHR1, ALPHI1, BETA1, ALPHR2, ALPHI2, 00004 $ BETA2, VL, VR, WORK, LWORK, RESULT, INFO ) 00005 * 00006 * -- LAPACK test routine (version 3.1) -- 00007 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. 00008 * November 2006 00009 * 00010 * .. Scalar Arguments .. 00011 INTEGER INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES 00012 REAL THRESH, THRSHN 00013 * .. 00014 * .. Array Arguments .. 00015 LOGICAL DOTYPE( * ) 00016 INTEGER ISEED( 4 ), NN( * ) 00017 REAL A( LDA, * ), ALPHI1( * ), ALPHI2( * ), 00018 $ ALPHR1( * ), ALPHR2( * ), B( LDA, * ), 00019 $ BETA1( * ), BETA2( * ), Q( LDQ, * ), 00020 $ RESULT( * ), S( LDA, * ), S2( LDA, * ), 00021 $ T( LDA, * ), T2( LDA, * ), VL( LDQ, * ), 00022 $ VR( LDQ, * ), WORK( * ), Z( LDQ, * ) 00023 * .. 00024 * 00025 * Purpose 00026 * ======= 00027 * 00028 * SDRVGG checks the nonsymmetric generalized eigenvalue driver 00029 * routines. 00030 * T T T 00031 * SGEGS factors A and B as Q S Z and Q T Z , where means 00032 * transpose, T is upper triangular, S is in generalized Schur form 00033 * (block upper triangular, with 1x1 and 2x2 blocks on the diagonal, 00034 * the 2x2 blocks corresponding to complex conjugate pairs of 00035 * generalized eigenvalues), and Q and Z are orthogonal. It also 00036 * computes the generalized eigenvalues (alpha(1),beta(1)), ..., 00037 * (alpha(n),beta(n)), where alpha(j)=S(j,j) and beta(j)=P(j,j) -- 00038 * thus, w(j) = alpha(j)/beta(j) is a root of the generalized 00039 * eigenvalue problem 00040 * 00041 * det( A - w(j) B ) = 0 00042 * 00043 * and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent 00044 * problem 00045 * 00046 * det( m(j) A - B ) = 0 00047 * 00048 * SGEGV computes the generalized eigenvalues (alpha(1),beta(1)), ..., 00049 * (alpha(n),beta(n)), the matrix L whose columns contain the 00050 * generalized left eigenvectors l, and the matrix R whose columns 00051 * contain the generalized right eigenvectors r for the pair (A,B). 00052 * 00053 * When SDRVGG is called, a number of matrix "sizes" ("n's") and a 00054 * number of matrix "types" are specified. For each size ("n") 00055 * and each type of matrix, one matrix will be generated and used 00056 * to test the nonsymmetric eigenroutines. For each matrix, 7 00057 * tests will be performed and compared with the threshhold THRESH: 00058 * 00059 * Results from SGEGS: 00060 * 00061 * T 00062 * (1) | A - Q S Z | / ( |A| n ulp ) 00063 * 00064 * T 00065 * (2) | B - Q T Z | / ( |B| n ulp ) 00066 * 00067 * T 00068 * (3) | I - QQ | / ( n ulp ) 00069 * 00070 * T 00071 * (4) | I - ZZ | / ( n ulp ) 00072 * 00073 * (5) maximum over j of D(j) where: 00074 * 00075 * if alpha(j) is real: 00076 * |alpha(j) - S(j,j)| |beta(j) - T(j,j)| 00077 * D(j) = ------------------------ + ----------------------- 00078 * max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) 00079 * 00080 * if alpha(j) is complex: 00081 * | det( s S - w T ) | 00082 * D(j) = --------------------------------------------------- 00083 * ulp max( s norm(S), |w| norm(T) )*norm( s S - w T ) 00084 * 00085 * and S and T are here the 2 x 2 diagonal blocks of S and T 00086 * corresponding to the j-th eigenvalue. 00087 * 00088 * Results from SGEGV: 00089 * 00090 * (6) max over all left eigenvalue/-vector pairs (beta/alpha,l) of 00091 * 00092 * | l**H * (beta A - alpha B) | / ( ulp max( |beta A|, |alpha B| ) ) 00093 * 00094 * where l**H is the conjugate tranpose of l. 00095 * 00096 * (7) max over all right eigenvalue/-vector pairs (beta/alpha,r) of 00097 * 00098 * | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) ) 00099 * 00100 * Test Matrices 00101 * ---- -------- 00102 * 00103 * The sizes of the test matrices are specified by an array 00104 * NN(1:NSIZES); the value of each element NN(j) specifies one size. 00105 * The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if 00106 * DOTYPE(j) is .TRUE., then matrix type "j" will be generated. 00107 * Currently, the list of possible types is: 00108 * 00109 * (1) ( 0, 0 ) (a pair of zero matrices) 00110 * 00111 * (2) ( I, 0 ) (an identity and a zero matrix) 00112 * 00113 * (3) ( 0, I ) (an identity and a zero matrix) 00114 * 00115 * (4) ( I, I ) (a pair of identity matrices) 00116 * 00117 * t t 00118 * (5) ( J , J ) (a pair of transposed Jordan blocks) 00119 * 00120 * t ( I 0 ) 00121 * (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) 00122 * ( 0 I ) ( 0 J ) 00123 * and I is a k x k identity and J a (k+1)x(k+1) 00124 * Jordan block; k=(N-1)/2 00125 * 00126 * (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal 00127 * matrix with those diagonal entries.) 00128 * (8) ( I, D ) 00129 * 00130 * (9) ( big*D, small*I ) where "big" is near overflow and small=1/big 00131 * 00132 * (10) ( small*D, big*I ) 00133 * 00134 * (11) ( big*I, small*D ) 00135 * 00136 * (12) ( small*I, big*D ) 00137 * 00138 * (13) ( big*D, big*I ) 00139 * 00140 * (14) ( small*D, small*I ) 00141 * 00142 * (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and 00143 * D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) 00144 * t t 00145 * (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices. 00146 * 00147 * (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices 00148 * with random O(1) entries above the diagonal 00149 * and diagonal entries diag(T1) = 00150 * ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = 00151 * ( 0, N-3, N-4,..., 1, 0, 0 ) 00152 * 00153 * (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) 00154 * diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) 00155 * s = machine precision. 00156 * 00157 * (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) 00158 * diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) 00159 * 00160 * N-5 00161 * (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) 00162 * diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) 00163 * 00164 * (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) 00165 * diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) 00166 * where r1,..., r(N-4) are random. 00167 * 00168 * (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) 00169 * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) 00170 * 00171 * (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) 00172 * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) 00173 * 00174 * (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) 00175 * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) 00176 * 00177 * (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) 00178 * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) 00179 * 00180 * (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular 00181 * matrices. 00182 * 00183 * Arguments 00184 * ========= 00185 * 00186 * NSIZES (input) INTEGER 00187 * The number of sizes of matrices to use. If it is zero, 00188 * SDRVGG does nothing. It must be at least zero. 00189 * 00190 * NN (input) INTEGER array, dimension (NSIZES) 00191 * An array containing the sizes to be used for the matrices. 00192 * Zero values will be skipped. The values must be at least 00193 * zero. 00194 * 00195 * NTYPES (input) INTEGER 00196 * The number of elements in DOTYPE. If it is zero, SDRVGG 00197 * does nothing. It must be at least zero. If it is MAXTYP+1 00198 * and NSIZES is 1, then an additional type, MAXTYP+1 is 00199 * defined, which is to use whatever matrix is in A. This 00200 * is only useful if DOTYPE(1:MAXTYP) is .FALSE. and 00201 * DOTYPE(MAXTYP+1) is .TRUE. . 00202 * 00203 * DOTYPE (input) LOGICAL array, dimension (NTYPES) 00204 * If DOTYPE(j) is .TRUE., then for each size in NN a 00205 * matrix of that size and of type j will be generated. 00206 * If NTYPES is smaller than the maximum number of types 00207 * defined (PARAMETER MAXTYP), then types NTYPES+1 through 00208 * MAXTYP will not be generated. If NTYPES is larger 00209 * than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) 00210 * will be ignored. 00211 * 00212 * ISEED (input/output) INTEGER array, dimension (4) 00213 * On entry ISEED specifies the seed of the random number 00214 * generator. The array elements should be between 0 and 4095; 00215 * if not they will be reduced mod 4096. Also, ISEED(4) must 00216 * be odd. The random number generator uses a linear 00217 * congruential sequence limited to small integers, and so 00218 * should produce machine independent random numbers. The 00219 * values of ISEED are changed on exit, and can be used in the 00220 * next call to SDRVGG to continue the same random number 00221 * sequence. 00222 * 00223 * THRESH (input) REAL 00224 * A test will count as "failed" if the "error", computed as 00225 * described above, exceeds THRESH. Note that the error is 00226 * scaled to be O(1), so THRESH should be a reasonably small 00227 * multiple of 1, e.g., 10 or 100. In particular, it should 00228 * not depend on the precision (single vs. double) or the size 00229 * of the matrix. It must be at least zero. 00230 * 00231 * THRSHN (input) REAL 00232 * Threshhold for reporting eigenvector normalization error. 00233 * If the normalization of any eigenvector differs from 1 by 00234 * more than THRSHN*ulp, then a special error message will be 00235 * printed. (This is handled separately from the other tests, 00236 * since only a compiler or programming error should cause an 00237 * error message, at least if THRSHN is at least 5--10.) 00238 * 00239 * NOUNIT (input) INTEGER 00240 * The FORTRAN unit number for printing out error messages 00241 * (e.g., if a routine returns IINFO not equal to 0.) 00242 * 00243 * A (input/workspace) REAL array, dimension 00244 * (LDA, max(NN)) 00245 * Used to hold the original A matrix. Used as input only 00246 * if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and 00247 * DOTYPE(MAXTYP+1)=.TRUE. 00248 * 00249 * LDA (input) INTEGER 00250 * The leading dimension of A, B, S, T, S2, and T2. 00251 * It must be at least 1 and at least max( NN ). 00252 * 00253 * B (input/workspace) REAL array, dimension 00254 * (LDA, max(NN)) 00255 * Used to hold the original B matrix. Used as input only 00256 * if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and 00257 * DOTYPE(MAXTYP+1)=.TRUE. 00258 * 00259 * S (workspace) REAL array, dimension (LDA, max(NN)) 00260 * The Schur form matrix computed from A by SGEGS. On exit, S 00261 * contains the Schur form matrix corresponding to the matrix 00262 * in A. 00263 * 00264 * T (workspace) REAL array, dimension (LDA, max(NN)) 00265 * The upper triangular matrix computed from B by SGEGS. 00266 * 00267 * S2 (workspace) REAL array, dimension (LDA, max(NN)) 00268 * The matrix computed from A by SGEGV. This will be the 00269 * Schur form of some matrix related to A, but will not, in 00270 * general, be the same as S. 00271 * 00272 * T2 (workspace) REAL array, dimension (LDA, max(NN)) 00273 * The matrix computed from B by SGEGV. This will be the 00274 * Schur form of some matrix related to B, but will not, in 00275 * general, be the same as T. 00276 * 00277 * Q (workspace) REAL array, dimension (LDQ, max(NN)) 00278 * The (left) orthogonal matrix computed by SGEGS. 00279 * 00280 * LDQ (input) INTEGER 00281 * The leading dimension of Q, Z, VL, and VR. It must 00282 * be at least 1 and at least max( NN ). 00283 * 00284 * Z (workspace) REAL array of 00285 * dimension( LDQ, max(NN) ) 00286 * The (right) orthogonal matrix computed by SGEGS. 00287 * 00288 * ALPHR1 (workspace) REAL array, dimension (max(NN)) 00289 * ALPHI1 (workspace) REAL array, dimension (max(NN)) 00290 * BETA1 (workspace) REAL array, dimension (max(NN)) 00291 * 00292 * The generalized eigenvalues of (A,B) computed by SGEGS. 00293 * ( ALPHR1(k)+ALPHI1(k)*i ) / BETA1(k) is the k-th 00294 * generalized eigenvalue of the matrices in A and B. 00295 * 00296 * ALPHR2 (workspace) REAL array, dimension (max(NN)) 00297 * ALPHI2 (workspace) REAL array, dimension (max(NN)) 00298 * BETA2 (workspace) REAL array, dimension (max(NN)) 00299 * 00300 * The generalized eigenvalues of (A,B) computed by SGEGV. 00301 * ( ALPHR2(k)+ALPHI2(k)*i ) / BETA2(k) is the k-th 00302 * generalized eigenvalue of the matrices in A and B. 00303 * 00304 * VL (workspace) REAL array, dimension (LDQ, max(NN)) 00305 * The (block lower triangular) left eigenvector matrix for 00306 * the matrices in A and B. (See STGEVC for the format.) 00307 * 00308 * VR (workspace) REAL array, dimension (LDQ, max(NN)) 00309 * The (block upper triangular) right eigenvector matrix for 00310 * the matrices in A and B. (See STGEVC for the format.) 00311 * 00312 * WORK (workspace) REAL array, dimension (LWORK) 00313 * 00314 * LWORK (input) INTEGER 00315 * The number of entries in WORK. This must be at least 00316 * 2*N + MAX( 6*N, N*(NB+1), (k+1)*(2*k+N+1) ), where 00317 * "k" is the sum of the blocksize and number-of-shifts for 00318 * SHGEQZ, and NB is the greatest of the blocksizes for 00319 * SGEQRF, SORMQR, and SORGQR. (The blocksizes and the 00320 * number-of-shifts are retrieved through calls to ILAENV.) 00321 * 00322 * RESULT (output) REAL array, dimension (15) 00323 * The values computed by the tests described above. 00324 * The values are currently limited to 1/ulp, to avoid 00325 * overflow. 00326 * 00327 * INFO (output) INTEGER 00328 * = 0: successful exit 00329 * < 0: if INFO = -i, the i-th argument had an illegal value. 00330 * > 0: A routine returned an error code. INFO is the 00331 * absolute value of the INFO value returned. 00332 * 00333 * ===================================================================== 00334 * 00335 * .. Parameters .. 00336 REAL ZERO, ONE 00337 PARAMETER ( ZERO = 0.0, ONE = 1.0 ) 00338 INTEGER MAXTYP 00339 PARAMETER ( MAXTYP = 26 ) 00340 * .. 00341 * .. Local Scalars .. 00342 LOGICAL BADNN, ILABAD 00343 INTEGER I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE, 00344 $ LWKOPT, MTYPES, N, N1, NB, NBZ, NERRS, NMATS, 00345 $ NMAX, NS, NTEST, NTESTT 00346 REAL SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV 00347 * .. 00348 * .. Local Arrays .. 00349 INTEGER IASIGN( MAXTYP ), IBSIGN( MAXTYP ), 00350 $ IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ), 00351 $ KATYPE( MAXTYP ), KAZERO( MAXTYP ), 00352 $ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ), 00353 $ KBZERO( MAXTYP ), KCLASS( MAXTYP ), 00354 $ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 ) 00355 REAL DUMMA( 4 ), RMAGN( 0: 3 ) 00356 * .. 00357 * .. External Functions .. 00358 INTEGER ILAENV 00359 REAL SLAMCH, SLARND 00360 EXTERNAL ILAENV, SLAMCH, SLARND 00361 * .. 00362 * .. External Subroutines .. 00363 EXTERNAL ALASVM, SGEGS, SGEGV, SGET51, SGET52, SGET53, 00364 $ SLABAD, SLACPY, SLARFG, SLASET, SLATM4, SORM2R, 00365 $ XERBLA 00366 * .. 00367 * .. Intrinsic Functions .. 00368 INTRINSIC ABS, MAX, MIN, REAL, SIGN 00369 * .. 00370 * .. Data statements .. 00371 DATA KCLASS / 15*1, 10*2, 1*3 / 00372 DATA KZ1 / 0, 1, 2, 1, 3, 3 / 00373 DATA KZ2 / 0, 0, 1, 2, 1, 1 / 00374 DATA KADD / 0, 0, 0, 0, 3, 2 / 00375 DATA KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4, 00376 $ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 / 00377 DATA KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4, 00378 $ 1, 1, -4, 2, -4, 8*8, 0 / 00379 DATA KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3, 00380 $ 4*5, 4*3, 1 / 00381 DATA KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4, 00382 $ 4*6, 4*4, 1 / 00383 DATA KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3, 00384 $ 2, 1 / 00385 DATA KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3, 00386 $ 2, 1 / 00387 DATA KTRIAN / 16*0, 10*1 / 00388 DATA IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0, 00389 $ 5*2, 0 / 00390 DATA IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 / 00391 * .. 00392 * .. Executable Statements .. 00393 * 00394 * Check for errors 00395 * 00396 INFO = 0 00397 * 00398 BADNN = .FALSE. 00399 NMAX = 1 00400 DO 10 J = 1, NSIZES 00401 NMAX = MAX( NMAX, NN( J ) ) 00402 IF( NN( J ).LT.0 ) 00403 $ BADNN = .TRUE. 00404 10 CONTINUE 00405 * 00406 * Maximum blocksize and shift -- we assume that blocksize and number 00407 * of shifts are monotone increasing functions of N. 00408 * 00409 NB = MAX( 1, ILAENV( 1, 'SGEQRF', ' ', NMAX, NMAX, -1, -1 ), 00410 $ ILAENV( 1, 'SORMQR', 'LT', NMAX, NMAX, NMAX, -1 ), 00411 $ ILAENV( 1, 'SORGQR', ' ', NMAX, NMAX, NMAX, -1 ) ) 00412 NBZ = ILAENV( 1, 'SHGEQZ', 'SII', NMAX, 1, NMAX, 0 ) 00413 NS = ILAENV( 4, 'SHGEQZ', 'SII', NMAX, 1, NMAX, 0 ) 00414 I1 = NBZ + NS 00415 LWKOPT = 2*NMAX + MAX( 6*NMAX, NMAX*( NB+1 ), 00416 $ ( 2*I1+NMAX+1 )*( I1+1 ) ) 00417 * 00418 * Check for errors 00419 * 00420 IF( NSIZES.LT.0 ) THEN 00421 INFO = -1 00422 ELSE IF( BADNN ) THEN 00423 INFO = -2 00424 ELSE IF( NTYPES.LT.0 ) THEN 00425 INFO = -3 00426 ELSE IF( THRESH.LT.ZERO ) THEN 00427 INFO = -6 00428 ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN 00429 INFO = -10 00430 ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN 00431 INFO = -19 00432 ELSE IF( LWKOPT.GT.LWORK ) THEN 00433 INFO = -30 00434 END IF 00435 * 00436 IF( INFO.NE.0 ) THEN 00437 CALL XERBLA( 'SDRVGG', -INFO ) 00438 RETURN 00439 END IF 00440 * 00441 * Quick return if possible 00442 * 00443 IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) 00444 $ RETURN 00445 * 00446 SAFMIN = SLAMCH( 'Safe minimum' ) 00447 ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' ) 00448 SAFMIN = SAFMIN / ULP 00449 SAFMAX = ONE / SAFMIN 00450 CALL SLABAD( SAFMIN, SAFMAX ) 00451 ULPINV = ONE / ULP 00452 * 00453 * The values RMAGN(2:3) depend on N, see below. 00454 * 00455 RMAGN( 0 ) = ZERO 00456 RMAGN( 1 ) = ONE 00457 * 00458 * Loop over sizes, types 00459 * 00460 NTESTT = 0 00461 NERRS = 0 00462 NMATS = 0 00463 * 00464 DO 170 JSIZE = 1, NSIZES 00465 N = NN( JSIZE ) 00466 N1 = MAX( 1, N ) 00467 RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 ) 00468 RMAGN( 3 ) = SAFMIN*ULPINV*N1 00469 * 00470 IF( NSIZES.NE.1 ) THEN 00471 MTYPES = MIN( MAXTYP, NTYPES ) 00472 ELSE 00473 MTYPES = MIN( MAXTYP+1, NTYPES ) 00474 END IF 00475 * 00476 DO 160 JTYPE = 1, MTYPES 00477 IF( .NOT.DOTYPE( JTYPE ) ) 00478 $ GO TO 160 00479 NMATS = NMATS + 1 00480 NTEST = 0 00481 * 00482 * Save ISEED in case of an error. 00483 * 00484 DO 20 J = 1, 4 00485 IOLDSD( J ) = ISEED( J ) 00486 20 CONTINUE 00487 * 00488 * Initialize RESULT 00489 * 00490 DO 30 J = 1, 15 00491 RESULT( J ) = ZERO 00492 30 CONTINUE 00493 * 00494 * Compute A and B 00495 * 00496 * Description of control parameters: 00497 * 00498 * KCLASS: =1 means w/o rotation, =2 means w/ rotation, 00499 * =3 means random. 00500 * KATYPE: the "type" to be passed to SLATM4 for computing A. 00501 * KAZERO: the pattern of zeros on the diagonal for A: 00502 * =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), 00503 * =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), 00504 * =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of 00505 * non-zero entries.) 00506 * KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), 00507 * =2: large, =3: small. 00508 * IASIGN: 1 if the diagonal elements of A are to be 00509 * multiplied by a random magnitude 1 number, =2 if 00510 * randomly chosen diagonal blocks are to be rotated 00511 * to form 2x2 blocks. 00512 * KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B. 00513 * KTRIAN: =0: don't fill in the upper triangle, =1: do. 00514 * KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. 00515 * RMAGN: used to implement KAMAGN and KBMAGN. 00516 * 00517 IF( MTYPES.GT.MAXTYP ) 00518 $ GO TO 110 00519 IINFO = 0 00520 IF( KCLASS( JTYPE ).LT.3 ) THEN 00521 * 00522 * Generate A (w/o rotation) 00523 * 00524 IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN 00525 IN = 2*( ( N-1 ) / 2 ) + 1 00526 IF( IN.NE.N ) 00527 $ CALL SLASET( 'Full', N, N, ZERO, ZERO, A, LDA ) 00528 ELSE 00529 IN = N 00530 END IF 00531 CALL SLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ), 00532 $ KZ2( KAZERO( JTYPE ) ), IASIGN( JTYPE ), 00533 $ RMAGN( KAMAGN( JTYPE ) ), ULP, 00534 $ RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2, 00535 $ ISEED, A, LDA ) 00536 IADD = KADD( KAZERO( JTYPE ) ) 00537 IF( IADD.GT.0 .AND. IADD.LE.N ) 00538 $ A( IADD, IADD ) = ONE 00539 * 00540 * Generate B (w/o rotation) 00541 * 00542 IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN 00543 IN = 2*( ( N-1 ) / 2 ) + 1 00544 IF( IN.NE.N ) 00545 $ CALL SLASET( 'Full', N, N, ZERO, ZERO, B, LDA ) 00546 ELSE 00547 IN = N 00548 END IF 00549 CALL SLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ), 00550 $ KZ2( KBZERO( JTYPE ) ), IBSIGN( JTYPE ), 00551 $ RMAGN( KBMAGN( JTYPE ) ), ONE, 00552 $ RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2, 00553 $ ISEED, B, LDA ) 00554 IADD = KADD( KBZERO( JTYPE ) ) 00555 IF( IADD.NE.0 .AND. IADD.LE.N ) 00556 $ B( IADD, IADD ) = ONE 00557 * 00558 IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN 00559 * 00560 * Include rotations 00561 * 00562 * Generate Q, Z as Householder transformations times 00563 * a diagonal matrix. 00564 * 00565 DO 50 JC = 1, N - 1 00566 DO 40 JR = JC, N 00567 Q( JR, JC ) = SLARND( 3, ISEED ) 00568 Z( JR, JC ) = SLARND( 3, ISEED ) 00569 40 CONTINUE 00570 CALL SLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1, 00571 $ WORK( JC ) ) 00572 WORK( 2*N+JC ) = SIGN( ONE, Q( JC, JC ) ) 00573 Q( JC, JC ) = ONE 00574 CALL SLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1, 00575 $ WORK( N+JC ) ) 00576 WORK( 3*N+JC ) = SIGN( ONE, Z( JC, JC ) ) 00577 Z( JC, JC ) = ONE 00578 50 CONTINUE 00579 Q( N, N ) = ONE 00580 WORK( N ) = ZERO 00581 WORK( 3*N ) = SIGN( ONE, SLARND( 2, ISEED ) ) 00582 Z( N, N ) = ONE 00583 WORK( 2*N ) = ZERO 00584 WORK( 4*N ) = SIGN( ONE, SLARND( 2, ISEED ) ) 00585 * 00586 * Apply the diagonal matrices 00587 * 00588 DO 70 JC = 1, N 00589 DO 60 JR = 1, N 00590 A( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )* 00591 $ A( JR, JC ) 00592 B( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )* 00593 $ B( JR, JC ) 00594 60 CONTINUE 00595 70 CONTINUE 00596 CALL SORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A, 00597 $ LDA, WORK( 2*N+1 ), IINFO ) 00598 IF( IINFO.NE.0 ) 00599 $ GO TO 100 00600 CALL SORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ), 00601 $ A, LDA, WORK( 2*N+1 ), IINFO ) 00602 IF( IINFO.NE.0 ) 00603 $ GO TO 100 00604 CALL SORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B, 00605 $ LDA, WORK( 2*N+1 ), IINFO ) 00606 IF( IINFO.NE.0 ) 00607 $ GO TO 100 00608 CALL SORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ), 00609 $ B, LDA, WORK( 2*N+1 ), IINFO ) 00610 IF( IINFO.NE.0 ) 00611 $ GO TO 100 00612 END IF 00613 ELSE 00614 * 00615 * Random matrices 00616 * 00617 DO 90 JC = 1, N 00618 DO 80 JR = 1, N 00619 A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )* 00620 $ SLARND( 2, ISEED ) 00621 B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )* 00622 $ SLARND( 2, ISEED ) 00623 80 CONTINUE 00624 90 CONTINUE 00625 END IF 00626 * 00627 100 CONTINUE 00628 * 00629 IF( IINFO.NE.0 ) THEN 00630 WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE, 00631 $ IOLDSD 00632 INFO = ABS( IINFO ) 00633 RETURN 00634 END IF 00635 * 00636 110 CONTINUE 00637 * 00638 * Call SGEGS to compute H, T, Q, Z, alpha, and beta. 00639 * 00640 CALL SLACPY( ' ', N, N, A, LDA, S, LDA ) 00641 CALL SLACPY( ' ', N, N, B, LDA, T, LDA ) 00642 NTEST = 1 00643 RESULT( 1 ) = ULPINV 00644 * 00645 CALL SGEGS( 'V', 'V', N, S, LDA, T, LDA, ALPHR1, ALPHI1, 00646 $ BETA1, Q, LDQ, Z, LDQ, WORK, LWORK, IINFO ) 00647 IF( IINFO.NE.0 ) THEN 00648 WRITE( NOUNIT, FMT = 9999 )'SGEGS', IINFO, N, JTYPE, 00649 $ IOLDSD 00650 INFO = ABS( IINFO ) 00651 GO TO 140 00652 END IF 00653 * 00654 NTEST = 4 00655 * 00656 * Do tests 1--4 00657 * 00658 CALL SGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ, WORK, 00659 $ RESULT( 1 ) ) 00660 CALL SGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ, WORK, 00661 $ RESULT( 2 ) ) 00662 CALL SGET51( 3, N, B, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK, 00663 $ RESULT( 3 ) ) 00664 CALL SGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK, 00665 $ RESULT( 4 ) ) 00666 * 00667 * Do test 5: compare eigenvalues with diagonals. 00668 * Also check Schur form of A. 00669 * 00670 TEMP1 = ZERO 00671 * 00672 DO 120 J = 1, N 00673 ILABAD = .FALSE. 00674 IF( ALPHI1( J ).EQ.ZERO ) THEN 00675 TEMP2 = ( ABS( ALPHR1( J )-S( J, J ) ) / 00676 $ MAX( SAFMIN, ABS( ALPHR1( J ) ), ABS( S( J, 00677 $ J ) ) )+ABS( BETA1( J )-T( J, J ) ) / 00678 $ MAX( SAFMIN, ABS( BETA1( J ) ), ABS( T( J, 00679 $ J ) ) ) ) / ULP 00680 IF( J.LT.N ) THEN 00681 IF( S( J+1, J ).NE.ZERO ) 00682 $ ILABAD = .TRUE. 00683 END IF 00684 IF( J.GT.1 ) THEN 00685 IF( S( J, J-1 ).NE.ZERO ) 00686 $ ILABAD = .TRUE. 00687 END IF 00688 ELSE 00689 IF( ALPHI1( J ).GT.ZERO ) THEN 00690 I1 = J 00691 ELSE 00692 I1 = J - 1 00693 END IF 00694 IF( I1.LE.0 .OR. I1.GE.N ) THEN 00695 ILABAD = .TRUE. 00696 ELSE IF( I1.LT.N-1 ) THEN 00697 IF( S( I1+2, I1+1 ).NE.ZERO ) 00698 $ ILABAD = .TRUE. 00699 ELSE IF( I1.GT.1 ) THEN 00700 IF( S( I1, I1-1 ).NE.ZERO ) 00701 $ ILABAD = .TRUE. 00702 END IF 00703 IF( .NOT.ILABAD ) THEN 00704 CALL SGET53( S( I1, I1 ), LDA, T( I1, I1 ), LDA, 00705 $ BETA1( J ), ALPHR1( J ), ALPHI1( J ), 00706 $ TEMP2, IINFO ) 00707 IF( IINFO.GE.3 ) THEN 00708 WRITE( NOUNIT, FMT = 9997 )IINFO, J, N, JTYPE, 00709 $ IOLDSD 00710 INFO = ABS( IINFO ) 00711 END IF 00712 ELSE 00713 TEMP2 = ULPINV 00714 END IF 00715 END IF 00716 TEMP1 = MAX( TEMP1, TEMP2 ) 00717 IF( ILABAD ) THEN 00718 WRITE( NOUNIT, FMT = 9996 )J, N, JTYPE, IOLDSD 00719 END IF 00720 120 CONTINUE 00721 RESULT( 5 ) = TEMP1 00722 * 00723 * Call SGEGV to compute S2, T2, VL, and VR, do tests. 00724 * 00725 * Eigenvalues and Eigenvectors 00726 * 00727 CALL SLACPY( ' ', N, N, A, LDA, S2, LDA ) 00728 CALL SLACPY( ' ', N, N, B, LDA, T2, LDA ) 00729 NTEST = 6 00730 RESULT( 6 ) = ULPINV 00731 * 00732 CALL SGEGV( 'V', 'V', N, S2, LDA, T2, LDA, ALPHR2, ALPHI2, 00733 $ BETA2, VL, LDQ, VR, LDQ, WORK, LWORK, IINFO ) 00734 IF( IINFO.NE.0 ) THEN 00735 WRITE( NOUNIT, FMT = 9999 )'SGEGV', IINFO, N, JTYPE, 00736 $ IOLDSD 00737 INFO = ABS( IINFO ) 00738 GO TO 140 00739 END IF 00740 * 00741 NTEST = 7 00742 * 00743 * Do Tests 6 and 7 00744 * 00745 CALL SGET52( .TRUE., N, A, LDA, B, LDA, VL, LDQ, ALPHR2, 00746 $ ALPHI2, BETA2, WORK, DUMMA( 1 ) ) 00747 RESULT( 6 ) = DUMMA( 1 ) 00748 IF( DUMMA( 2 ).GT.THRSHN ) THEN 00749 WRITE( NOUNIT, FMT = 9998 )'Left', 'SGEGV', DUMMA( 2 ), 00750 $ N, JTYPE, IOLDSD 00751 END IF 00752 * 00753 CALL SGET52( .FALSE., N, A, LDA, B, LDA, VR, LDQ, ALPHR2, 00754 $ ALPHI2, BETA2, WORK, DUMMA( 1 ) ) 00755 RESULT( 7 ) = DUMMA( 1 ) 00756 IF( DUMMA( 2 ).GT.THRESH ) THEN 00757 WRITE( NOUNIT, FMT = 9998 )'Right', 'SGEGV', DUMMA( 2 ), 00758 $ N, JTYPE, IOLDSD 00759 END IF 00760 * 00761 * Check form of Complex eigenvalues. 00762 * 00763 DO 130 J = 1, N 00764 ILABAD = .FALSE. 00765 IF( ALPHI2( J ).GT.ZERO ) THEN 00766 IF( J.EQ.N ) THEN 00767 ILABAD = .TRUE. 00768 ELSE IF( ALPHI2( J+1 ).GE.ZERO ) THEN 00769 ILABAD = .TRUE. 00770 END IF 00771 ELSE IF( ALPHI2( J ).LT.ZERO ) THEN 00772 IF( J.EQ.1 ) THEN 00773 ILABAD = .TRUE. 00774 ELSE IF( ALPHI2( J-1 ).LE.ZERO ) THEN 00775 ILABAD = .TRUE. 00776 END IF 00777 END IF 00778 IF( ILABAD ) THEN 00779 WRITE( NOUNIT, FMT = 9996 )J, N, JTYPE, IOLDSD 00780 END IF 00781 130 CONTINUE 00782 * 00783 * End of Loop -- Check for RESULT(j) > THRESH 00784 * 00785 140 CONTINUE 00786 * 00787 NTESTT = NTESTT + NTEST 00788 * 00789 * Print out tests which fail. 00790 * 00791 DO 150 JR = 1, NTEST 00792 IF( RESULT( JR ).GE.THRESH ) THEN 00793 * 00794 * If this is the first test to fail, 00795 * print a header to the data file. 00796 * 00797 IF( NERRS.EQ.0 ) THEN 00798 WRITE( NOUNIT, FMT = 9995 )'SGG' 00799 * 00800 * Matrix types 00801 * 00802 WRITE( NOUNIT, FMT = 9994 ) 00803 WRITE( NOUNIT, FMT = 9993 ) 00804 WRITE( NOUNIT, FMT = 9992 )'Orthogonal' 00805 * 00806 * Tests performed 00807 * 00808 WRITE( NOUNIT, FMT = 9991 )'orthogonal', '''', 00809 $ 'transpose', ( '''', J = 1, 5 ) 00810 * 00811 END IF 00812 NERRS = NERRS + 1 00813 IF( RESULT( JR ).LT.10000.0 ) THEN 00814 WRITE( NOUNIT, FMT = 9990 )N, JTYPE, IOLDSD, JR, 00815 $ RESULT( JR ) 00816 ELSE 00817 WRITE( NOUNIT, FMT = 9989 )N, JTYPE, IOLDSD, JR, 00818 $ RESULT( JR ) 00819 END IF 00820 END IF 00821 150 CONTINUE 00822 * 00823 160 CONTINUE 00824 170 CONTINUE 00825 * 00826 * Summary 00827 * 00828 CALL ALASVM( 'SGG', NOUNIT, NERRS, NTESTT, 0 ) 00829 RETURN 00830 * 00831 9999 FORMAT( ' SDRVGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', 00832 $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) 00833 * 00834 9998 FORMAT( ' SDRVGG: ', A, ' Eigenvectors from ', A, ' incorrectly ', 00835 $ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X, 00836 $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, 00837 $ ')' ) 00838 * 00839 9997 FORMAT( ' SDRVGG: SGET53 returned INFO=', I1, ' for eigenvalue ', 00840 $ I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 00841 $ 3( I5, ',' ), I5, ')' ) 00842 * 00843 9996 FORMAT( ' SDRVGG: S not in Schur form at eigenvalue ', I6, '.', 00844 $ / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), 00845 $ I5, ')' ) 00846 * 00847 9995 FORMAT( / 1X, A3, ' -- Real Generalized eigenvalue problem driver' 00848 $ ) 00849 * 00850 9994 FORMAT( ' Matrix types (see SDRVGG for details): ' ) 00851 * 00852 9993 FORMAT( ' Special Matrices:', 23X, 00853 $ '(J''=transposed Jordan block)', 00854 $ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ', 00855 $ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ', 00856 $ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I', 00857 $ ') 11=(large*I, small*D) 13=(large*D, large*I)', / 00858 $ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ', 00859 $ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' ) 00860 9992 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:', 00861 $ / ' 16=Transposed Jordan Blocks 19=geometric ', 00862 $ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ', 00863 $ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ', 00864 $ 'alpha, beta=0,1 21=random alpha, beta=0,1', 00865 $ / ' Large & Small Matrices:', / ' 22=(large, small) ', 00866 $ '23=(small,large) 24=(small,small) 25=(large,large)', 00867 $ / ' 26=random O(1) matrices.' ) 00868 * 00869 9991 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ', 00870 $ 'Q and Z are ', A, ',', / 20X, 00871 $ 'l and r are the appropriate left and right', / 19X, 00872 $ 'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A, 00873 $ ' means ', A, '.)', / ' 1 = | A - Q S Z', A, 00874 $ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A, 00875 $ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A, 00876 $ ' | / ( n ulp ) 4 = | I - ZZ', A, 00877 $ ' | / ( n ulp )', / 00878 $ ' 5 = difference between (alpha,beta) and diagonals of', 00879 $ ' (S,T)', / ' 6 = max | ( b A - a B )', A, 00880 $ ' l | / const. 7 = max | ( b A - a B ) r | / const.', 00881 $ / 1X ) 00882 9990 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', 00883 $ 4( I4, ',' ), ' result ', I3, ' is', 0P, F8.2 ) 00884 9989 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', 00885 $ 4( I4, ',' ), ' result ', I3, ' is', 1P, E10.3 ) 00886 * 00887 * End of SDRVGG 00888 * 00889 END
1.7.3 
