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diff --git a/TESTING/EIG/ddrges3.f b/TESTING/EIG/ddrges3.f new file mode 100644 index 00000000..77363019 --- /dev/null +++ b/TESTING/EIG/ddrges3.f @@ -0,0 +1,997 @@ +*> \brief \b DDRGES3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* SUBROUTINE DDRGES3( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, +* NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHAR, +* ALPHAI, BETA, WORK, LWORK, RESULT, BWORK, +* INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES +* DOUBLE PRECISION THRESH +* .. +* .. Array Arguments .. +* LOGICAL BWORK( * ), DOTYPE( * ) +* INTEGER ISEED( 4 ), NN( * ) +* DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), +* $ B( LDA, * ), BETA( * ), Q( LDQ, * ), +* $ RESULT( 13 ), S( LDA, * ), T( LDA, * ), +* $ WORK( * ), Z( LDQ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DDRGES3 checks the nonsymmetric generalized eigenvalue (Schur form) +*> problem driver DGGES3. +*> +*> DGGES3 factors A and B as Q S Z' and Q T Z' , where ' means +*> transpose, T is upper triangular, S is in generalized Schur form +*> (block upper triangular, with 1x1 and 2x2 blocks on the diagonal, +*> the 2x2 blocks corresponding to complex conjugate pairs of +*> generalized eigenvalues), and Q and Z are orthogonal. It also +*> computes the generalized eigenvalues (alpha(j),beta(j)), j=1,...,n, +*> Thus, w(j) = alpha(j)/beta(j) is a root of the characteristic +*> equation +*> det( A - w(j) B ) = 0 +*> Optionally it also reorder the eigenvalues so that a selected +*> cluster of eigenvalues appears in the leading diagonal block of the +*> Schur forms. +*> +*> When DDRGES3 is called, a number of matrix "sizes" ("N's") and a +*> number of matrix "TYPES" are specified. For each size ("N") +*> and each TYPE of matrix, a pair of matrices (A, B) will be generated +*> and used for testing. For each matrix pair, the following 13 tests +*> will be performed and compared with the threshhold THRESH except +*> the tests (5), (11) and (13). +*> +*> +*> (1) | A - Q S Z' | / ( |A| n ulp ) (no sorting of eigenvalues) +*> +*> +*> (2) | B - Q T Z' | / ( |B| n ulp ) (no sorting of eigenvalues) +*> +*> +*> (3) | I - QQ' | / ( n ulp ) (no sorting of eigenvalues) +*> +*> +*> (4) | I - ZZ' | / ( n ulp ) (no sorting of eigenvalues) +*> +*> (5) if A is in Schur form (i.e. quasi-triangular form) +*> (no sorting of eigenvalues) +*> +*> (6) if eigenvalues = diagonal blocks of the Schur form (S, T), +*> i.e., test the maximum over j of D(j) where: +*> +*> if alpha(j) is real: +*> |alpha(j) - S(j,j)| |beta(j) - T(j,j)| +*> D(j) = ------------------------ + ----------------------- +*> max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) +*> +*> if alpha(j) is complex: +*> | det( s S - w T ) | +*> D(j) = --------------------------------------------------- +*> ulp max( s norm(S), |w| norm(T) )*norm( s S - w T ) +*> +*> and S and T are here the 2 x 2 diagonal blocks of S and T +*> corresponding to the j-th and j+1-th eigenvalues. +*> (no sorting of eigenvalues) +*> +*> (7) | (A,B) - Q (S,T) Z' | / ( | (A,B) | n ulp ) +*> (with sorting of eigenvalues). +*> +*> (8) | I - QQ' | / ( n ulp ) (with sorting of eigenvalues). +*> +*> (9) | I - ZZ' | / ( n ulp ) (with sorting of eigenvalues). +*> +*> (10) if A is in Schur form (i.e. quasi-triangular form) +*> (with sorting of eigenvalues). +*> +*> (11) if eigenvalues = diagonal blocks of the Schur form (S, T), +*> i.e. test the maximum over j of D(j) where: +*> +*> if alpha(j) is real: +*> |alpha(j) - S(j,j)| |beta(j) - T(j,j)| +*> D(j) = ------------------------ + ----------------------- +*> max(|alpha(j)|,|S(j,j)|) max(|beta(j)|,|T(j,j)|) +*> +*> if alpha(j) is complex: +*> | det( s S - w T ) | +*> D(j) = --------------------------------------------------- +*> ulp max( s norm(S), |w| norm(T) )*norm( s S - w T ) +*> +*> and S and T are here the 2 x 2 diagonal blocks of S and T +*> corresponding to the j-th and j+1-th eigenvalues. +*> (with sorting of eigenvalues). +*> +*> (12) if sorting worked and SDIM is the number of eigenvalues +*> which were SELECTed. +*> +*> Test Matrices +*> ============= +*> +*> The sizes of the test matrices are specified by an array +*> NN(1:NSIZES); the value of each element NN(j) specifies one size. +*> The "types" are specified by a logical array DOTYPE( 1:NTYPES ); if +*> DOTYPE(j) is .TRUE., then matrix type "j" will be generated. +*> Currently, the list of possible types is: +*> +*> (1) ( 0, 0 ) (a pair of zero matrices) +*> +*> (2) ( I, 0 ) (an identity and a zero matrix) +*> +*> (3) ( 0, I ) (an identity and a zero matrix) +*> +*> (4) ( I, I ) (a pair of identity matrices) +*> +*> t t +*> (5) ( J , J ) (a pair of transposed Jordan blocks) +*> +*> t ( I 0 ) +*> (6) ( X, Y ) where X = ( J 0 ) and Y = ( t ) +*> ( 0 I ) ( 0 J ) +*> and I is a k x k identity and J a (k+1)x(k+1) +*> Jordan block; k=(N-1)/2 +*> +*> (7) ( D, I ) where D is diag( 0, 1,..., N-1 ) (a diagonal +*> matrix with those diagonal entries.) +*> (8) ( I, D ) +*> +*> (9) ( big*D, small*I ) where "big" is near overflow and small=1/big +*> +*> (10) ( small*D, big*I ) +*> +*> (11) ( big*I, small*D ) +*> +*> (12) ( small*I, big*D ) +*> +*> (13) ( big*D, big*I ) +*> +*> (14) ( small*D, small*I ) +*> +*> (15) ( D1, D2 ) where D1 is diag( 0, 0, 1, ..., N-3, 0 ) and +*> D2 is diag( 0, N-3, N-4,..., 1, 0, 0 ) +*> t t +*> (16) Q ( J , J ) Z where Q and Z are random orthogonal matrices. +*> +*> (17) Q ( T1, T2 ) Z where T1 and T2 are upper triangular matrices +*> with random O(1) entries above the diagonal +*> and diagonal entries diag(T1) = +*> ( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = +*> ( 0, N-3, N-4,..., 1, 0, 0 ) +*> +*> (18) Q ( T1, T2 ) Z diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) +*> diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) +*> s = machine precision. +*> +*> (19) Q ( T1, T2 ) Z diag(T1)=( 0,0,1,1, 1-d, ..., 1-(N-5)*d=s, 0 ) +*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0 ) +*> +*> N-5 +*> (20) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) +*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) +*> +*> (21) Q ( T1, T2 ) Z diag(T1)=( 0, 0, 1, r1, r2, ..., r(N-4), 0 ) +*> diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) +*> where r1,..., r(N-4) are random. +*> +*> (22) Q ( big*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) +*> diag(T2) = ( 0, 1, ..., 1, 0, 0 ) +*> +*> (23) Q ( small*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) +*> diag(T2) = ( 0, 1, ..., 1, 0, 0 ) +*> +*> (24) Q ( small*T1, small*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) +*> diag(T2) = ( 0, 1, ..., 1, 0, 0 ) +*> +*> (25) Q ( big*T1, big*T2 ) Z diag(T1) = ( 0, 0, 1, ..., N-3, 0 ) +*> diag(T2) = ( 0, 1, ..., 1, 0, 0 ) +*> +*> (26) Q ( T1, T2 ) Z where T1 and T2 are random upper-triangular +*> matrices. +*> +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] NSIZES +*> \verbatim +*> NSIZES is INTEGER +*> The number of sizes of matrices to use. If it is zero, +*> DDRGES3 does nothing. NSIZES >= 0. +*> \endverbatim +*> +*> \param[in] NN +*> \verbatim +*> NN is INTEGER array, dimension (NSIZES) +*> An array containing the sizes to be used for the matrices. +*> Zero values will be skipped. NN >= 0. +*> \endverbatim +*> +*> \param[in] NTYPES +*> \verbatim +*> NTYPES is INTEGER +*> The number of elements in DOTYPE. If it is zero, DDRGES3 +*> does nothing. It must be at least zero. If it is MAXTYP+1 +*> and NSIZES is 1, then an additional type, MAXTYP+1 is +*> defined, which is to use whatever matrix is in A on input. +*> This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and +*> DOTYPE(MAXTYP+1) is .TRUE. . +*> \endverbatim +*> +*> \param[in] DOTYPE +*> \verbatim +*> DOTYPE is LOGICAL array, dimension (NTYPES) +*> If DOTYPE(j) is .TRUE., then for each size in NN a +*> matrix of that size and of type j will be generated. +*> If NTYPES is smaller than the maximum number of types +*> defined (PARAMETER MAXTYP), then types NTYPES+1 through +*> MAXTYP will not be generated. If NTYPES is larger +*> than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES) +*> will be ignored. +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry ISEED specifies the seed of the random number +*> generator. The array elements should be between 0 and 4095; +*> if not they will be reduced mod 4096. Also, ISEED(4) must +*> be odd. The random number generator uses a linear +*> congruential sequence limited to small integers, and so +*> should produce machine independent random numbers. The +*> values of ISEED are changed on exit, and can be used in the +*> next call to DDRGES3 to continue the same random number +*> sequence. +*> \endverbatim +*> +*> \param[in] THRESH +*> \verbatim +*> THRESH is DOUBLE PRECISION +*> A test will count as "failed" if the "error", computed as +*> described above, exceeds THRESH. Note that the error is +*> scaled to be O(1), so THRESH should be a reasonably small +*> multiple of 1, e.g., 10 or 100. In particular, it should +*> not depend on the precision (single vs. double) or the size +*> of the matrix. THRESH >= 0. +*> \endverbatim +*> +*> \param[in] NOUNIT +*> \verbatim +*> NOUNIT is INTEGER +*> The FORTRAN unit number for printing out error messages +*> (e.g., if a routine returns IINFO not equal to 0.) +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, +*> dimension(LDA, max(NN)) +*> Used to hold the original A matrix. Used as input only +*> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and +*> DOTYPE(MAXTYP+1)=.TRUE. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of A, B, S, and T. +*> It must be at least 1 and at least max( NN ). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is DOUBLE PRECISION array, +*> dimension(LDA, max(NN)) +*> Used to hold the original B matrix. Used as input only +*> if NTYPES=MAXTYP+1, DOTYPE(1:MAXTYP)=.FALSE., and +*> DOTYPE(MAXTYP+1)=.TRUE. +*> \endverbatim +*> +*> \param[out] S +*> \verbatim +*> S is DOUBLE PRECISION array, dimension (LDA, max(NN)) +*> The Schur form matrix computed from A by DGGES3. On exit, S +*> contains the Schur form matrix corresponding to the matrix +*> in A. +*> \endverbatim +*> +*> \param[out] T +*> \verbatim +*> T is DOUBLE PRECISION array, dimension (LDA, max(NN)) +*> The upper triangular matrix computed from B by DGGES3. +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is DOUBLE PRECISION array, dimension (LDQ, max(NN)) +*> The (left) orthogonal matrix computed by DGGES3. +*> \endverbatim +*> +*> \param[in] LDQ +*> \verbatim +*> LDQ is INTEGER +*> The leading dimension of Q and Z. It must +*> be at least 1 and at least max( NN ). +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension( LDQ, max(NN) ) +*> The (right) orthogonal matrix computed by DGGES3. +*> \endverbatim +*> +*> \param[out] ALPHAR +*> \verbatim +*> ALPHAR is DOUBLE PRECISION array, dimension (max(NN)) +*> \endverbatim +*> +*> \param[out] ALPHAI +*> \verbatim +*> ALPHAI is DOUBLE PRECISION array, dimension (max(NN)) +*> \endverbatim +*> +*> \param[out] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION array, dimension (max(NN)) +*> +*> The generalized eigenvalues of (A,B) computed by DGGES3. +*> ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th +*> generalized eigenvalue of A and B. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (LWORK) +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. +*> LWORK >= MAX( 10*(N+1), 3*N*N ), where N is the largest +*> matrix dimension. +*> \endverbatim +*> +*> \param[out] RESULT +*> \verbatim +*> RESULT is DOUBLE PRECISION array, dimension (15) +*> The values computed by the tests described above. +*> The values are currently limited to 1/ulp, to avoid overflow. +*> \endverbatim +*> +*> \param[out] BWORK +*> \verbatim +*> BWORK is LOGICAL array, dimension (N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value. +*> > 0: A routine returned an error code. INFO is the +*> absolute value of the INFO value returned. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date February 2015 +* +*> \ingroup double_eig +* +* ===================================================================== + SUBROUTINE DDRGES3( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, + $ NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, ALPHAR, + $ ALPHAI, BETA, WORK, LWORK, RESULT, BWORK, + $ INFO ) +* +* -- LAPACK test routine (version 3.6.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* February 2015 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, LDQ, LWORK, NOUNIT, NSIZES, NTYPES + DOUBLE PRECISION THRESH +* .. +* .. Array Arguments .. + LOGICAL BWORK( * ), DOTYPE( * ) + INTEGER ISEED( 4 ), NN( * ) + DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), + $ B( LDA, * ), BETA( * ), Q( LDQ, * ), + $ RESULT( 13 ), S( LDA, * ), T( LDA, * ), + $ WORK( * ), Z( LDQ, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) + INTEGER MAXTYP + PARAMETER ( MAXTYP = 26 ) +* .. +* .. Local Scalars .. + LOGICAL BADNN, ILABAD + CHARACTER SORT + INTEGER I, I1, IADD, IERR, IINFO, IN, ISORT, J, JC, JR, + $ JSIZE, JTYPE, KNTEIG, MAXWRK, MINWRK, MTYPES, + $ N, N1, NB, NERRS, NMATS, NMAX, NTEST, NTESTT, + $ RSUB, SDIM + DOUBLE PRECISION SAFMAX, SAFMIN, TEMP1, TEMP2, ULP, ULPINV +* .. +* .. Local Arrays .. + INTEGER IASIGN( MAXTYP ), IBSIGN( MAXTYP ), + $ IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ), + $ KATYPE( MAXTYP ), KAZERO( MAXTYP ), + $ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ), + $ KBZERO( MAXTYP ), KCLASS( MAXTYP ), + $ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 ) + DOUBLE PRECISION RMAGN( 0: 3 ) +* .. +* .. External Functions .. + LOGICAL DLCTES + INTEGER ILAENV + DOUBLE PRECISION DLAMCH, DLARND + EXTERNAL DLCTES, ILAENV, DLAMCH, DLARND +* .. +* .. External Subroutines .. + EXTERNAL ALASVM, DGET51, DGET53, DGET54, DGGES3, DLABAD, + $ DLACPY, DLARFG, DLASET, DLATM4, DORM2R, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, MAX, MIN, SIGN +* .. +* .. Data statements .. + DATA KCLASS / 15*1, 10*2, 1*3 / + DATA KZ1 / 0, 1, 2, 1, 3, 3 / + DATA KZ2 / 0, 0, 1, 2, 1, 1 / + DATA KADD / 0, 0, 0, 0, 3, 2 / + DATA KATYPE / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4, + $ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 / + DATA KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4, + $ 1, 1, -4, 2, -4, 8*8, 0 / + DATA KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3, + $ 4*5, 4*3, 1 / + DATA KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4, + $ 4*6, 4*4, 1 / + DATA KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3, + $ 2, 1 / + DATA KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3, + $ 2, 1 / + DATA KTRIAN / 16*0, 10*1 / + DATA IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0, + $ 5*2, 0 / + DATA IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 9*0 / +* .. +* .. Executable Statements .. +* +* Check for errors +* + INFO = 0 +* + BADNN = .FALSE. + NMAX = 1 + DO 10 J = 1, NSIZES + NMAX = MAX( NMAX, NN( J ) ) + IF( NN( J ).LT.0 ) + $ BADNN = .TRUE. + 10 CONTINUE +* + IF( NSIZES.LT.0 ) THEN + INFO = -1 + ELSE IF( BADNN ) THEN + INFO = -2 + ELSE IF( NTYPES.LT.0 ) THEN + INFO = -3 + ELSE IF( THRESH.LT.ZERO ) THEN + INFO = -6 + ELSE IF( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN + INFO = -9 + ELSE IF( LDQ.LE.1 .OR. LDQ.LT.NMAX ) THEN + INFO = -14 + END IF +* +* Compute workspace +* (Note: Comments in the code beginning "Workspace:" describe the +* minimal amount of workspace needed at that point in the code, +* as well as the preferred amount for good performance. +* NB refers to the optimal block size for the immediately +* following subroutine, as returned by ILAENV. +* + MINWRK = 1 + IF( INFO.EQ.0 .AND. LWORK.GE.1 ) THEN + MINWRK = MAX( 10*( NMAX+1 ), 3*NMAX*NMAX ) + NB = MAX( 1, ILAENV( 1, 'DGEQRF', ' ', NMAX, NMAX, -1, -1 ), + $ ILAENV( 1, 'DORMQR', 'LT', NMAX, NMAX, NMAX, -1 ), + $ ILAENV( 1, 'DORGQR', ' ', NMAX, NMAX, NMAX, -1 ) ) + MAXWRK = MAX( 10*( NMAX+1 ), 2*NMAX+NMAX*NB, 3*NMAX*NMAX ) + WORK( 1 ) = MAXWRK + END IF +* + IF( LWORK.LT.MINWRK ) + $ INFO = -20 +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DDRGES3', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) + $ RETURN +* + SAFMIN = DLAMCH( 'Safe minimum' ) + ULP = DLAMCH( 'Epsilon' )*DLAMCH( 'Base' ) + SAFMIN = SAFMIN / ULP + SAFMAX = ONE / SAFMIN + CALL DLABAD( SAFMIN, SAFMAX ) + ULPINV = ONE / ULP +* +* The values RMAGN(2:3) depend on N, see below. +* + RMAGN( 0 ) = ZERO + RMAGN( 1 ) = ONE +* +* Loop over matrix sizes +* + NTESTT = 0 + NERRS = 0 + NMATS = 0 +* + DO 190 JSIZE = 1, NSIZES + N = NN( JSIZE ) + N1 = MAX( 1, N ) + RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 ) + RMAGN( 3 ) = SAFMIN*ULPINV*DBLE( N1 ) +* + IF( NSIZES.NE.1 ) THEN + MTYPES = MIN( MAXTYP, NTYPES ) + ELSE + MTYPES = MIN( MAXTYP+1, NTYPES ) + END IF +* +* Loop over matrix types +* + DO 180 JTYPE = 1, MTYPES + IF( .NOT.DOTYPE( JTYPE ) ) + $ GO TO 180 + NMATS = NMATS + 1 + NTEST = 0 +* +* Save ISEED in case of an error. +* + DO 20 J = 1, 4 + IOLDSD( J ) = ISEED( J ) + 20 CONTINUE +* +* Initialize RESULT +* + DO 30 J = 1, 13 + RESULT( J ) = ZERO + 30 CONTINUE +* +* Generate test matrices A and B +* +* Description of control parameters: +* +* KZLASS: =1 means w/o rotation, =2 means w/ rotation, +* =3 means random. +* KATYPE: the "type" to be passed to DLATM4 for computing A. +* KAZERO: the pattern of zeros on the diagonal for A: +* =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ), +* =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ), +* =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of +* non-zero entries.) +* KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1), +* =2: large, =3: small. +* IASIGN: 1 if the diagonal elements of A are to be +* multiplied by a random magnitude 1 number, =2 if +* randomly chosen diagonal blocks are to be rotated +* to form 2x2 blocks. +* KBTYPE, KBZERO, KBMAGN, IBSIGN: the same, but for B. +* KTRIAN: =0: don't fill in the upper triangle, =1: do. +* KZ1, KZ2, KADD: used to implement KAZERO and KBZERO. +* RMAGN: used to implement KAMAGN and KBMAGN. +* + IF( MTYPES.GT.MAXTYP ) + $ GO TO 110 + IINFO = 0 + IF( KCLASS( JTYPE ).LT.3 ) THEN +* +* Generate A (w/o rotation) +* + IF( ABS( KATYPE( JTYPE ) ).EQ.3 ) THEN + IN = 2*( ( N-1 ) / 2 ) + 1 + IF( IN.NE.N ) + $ CALL DLASET( 'Full', N, N, ZERO, ZERO, A, LDA ) + ELSE + IN = N + END IF + CALL DLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ), + $ KZ2( KAZERO( JTYPE ) ), IASIGN( JTYPE ), + $ RMAGN( KAMAGN( JTYPE ) ), ULP, + $ RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 2, + $ ISEED, A, LDA ) + IADD = KADD( KAZERO( JTYPE ) ) + IF( IADD.GT.0 .AND. IADD.LE.N ) + $ A( IADD, IADD ) = ONE +* +* Generate B (w/o rotation) +* + IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN + IN = 2*( ( N-1 ) / 2 ) + 1 + IF( IN.NE.N ) + $ CALL DLASET( 'Full', N, N, ZERO, ZERO, B, LDA ) + ELSE + IN = N + END IF + CALL DLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ), + $ KZ2( KBZERO( JTYPE ) ), IBSIGN( JTYPE ), + $ RMAGN( KBMAGN( JTYPE ) ), ONE, + $ RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 2, + $ ISEED, B, LDA ) + IADD = KADD( KBZERO( JTYPE ) ) + IF( IADD.NE.0 .AND. IADD.LE.N ) + $ B( IADD, IADD ) = ONE +* + IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN +* +* Include rotations +* +* Generate Q, Z as Householder transformations times +* a diagonal matrix. +* + DO 50 JC = 1, N - 1 + DO 40 JR = JC, N + Q( JR, JC ) = DLARND( 3, ISEED ) + Z( JR, JC ) = DLARND( 3, ISEED ) + 40 CONTINUE + CALL DLARFG( N+1-JC, Q( JC, JC ), Q( JC+1, JC ), 1, + $ WORK( JC ) ) + WORK( 2*N+JC ) = SIGN( ONE, Q( JC, JC ) ) + Q( JC, JC ) = ONE + CALL DLARFG( N+1-JC, Z( JC, JC ), Z( JC+1, JC ), 1, + $ WORK( N+JC ) ) + WORK( 3*N+JC ) = SIGN( ONE, Z( JC, JC ) ) + Z( JC, JC ) = ONE + 50 CONTINUE + Q( N, N ) = ONE + WORK( N ) = ZERO + WORK( 3*N ) = SIGN( ONE, DLARND( 2, ISEED ) ) + Z( N, N ) = ONE + WORK( 2*N ) = ZERO + WORK( 4*N ) = SIGN( ONE, DLARND( 2, ISEED ) ) +* +* Apply the diagonal matrices +* + DO 70 JC = 1, N + DO 60 JR = 1, N + A( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )* + $ A( JR, JC ) + B( JR, JC ) = WORK( 2*N+JR )*WORK( 3*N+JC )* + $ B( JR, JC ) + 60 CONTINUE + 70 CONTINUE + CALL DORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A, + $ LDA, WORK( 2*N+1 ), IINFO ) + IF( IINFO.NE.0 ) + $ GO TO 100 + CALL DORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ), + $ A, LDA, WORK( 2*N+1 ), IINFO ) + IF( IINFO.NE.0 ) + $ GO TO 100 + CALL DORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B, + $ LDA, WORK( 2*N+1 ), IINFO ) + IF( IINFO.NE.0 ) + $ GO TO 100 + CALL DORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ), + $ B, LDA, WORK( 2*N+1 ), IINFO ) + IF( IINFO.NE.0 ) + $ GO TO 100 + END IF + ELSE +* +* Random matrices +* + DO 90 JC = 1, N + DO 80 JR = 1, N + A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )* + $ DLARND( 2, ISEED ) + B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )* + $ DLARND( 2, ISEED ) + 80 CONTINUE + 90 CONTINUE + END IF +* + 100 CONTINUE +* + IF( IINFO.NE.0 ) THEN + WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE, + $ IOLDSD + INFO = ABS( IINFO ) + RETURN + END IF +* + 110 CONTINUE +* + DO 120 I = 1, 13 + RESULT( I ) = -ONE + 120 CONTINUE +* +* Test with and without sorting of eigenvalues +* + DO 150 ISORT = 0, 1 + IF( ISORT.EQ.0 ) THEN + SORT = 'N' + RSUB = 0 + ELSE + SORT = 'S' + RSUB = 5 + END IF +* +* Call DGGES3 to compute H, T, Q, Z, alpha, and beta. +* + CALL DLACPY( 'Full', N, N, A, LDA, S, LDA ) + CALL DLACPY( 'Full', N, N, B, LDA, T, LDA ) + NTEST = 1 + RSUB + ISORT + RESULT( 1+RSUB+ISORT ) = ULPINV + CALL DGGES3( 'V', 'V', SORT, DLCTES, N, S, LDA, T, LDA, + $ SDIM, ALPHAR, ALPHAI, BETA, Q, LDQ, Z, LDQ, + $ WORK, LWORK, BWORK, IINFO ) + IF( IINFO.NE.0 .AND. IINFO.NE.N+2 ) THEN + RESULT( 1+RSUB+ISORT ) = ULPINV + WRITE( NOUNIT, FMT = 9999 )'DGGES3', IINFO, N, JTYPE, + $ IOLDSD + INFO = ABS( IINFO ) + GO TO 160 + END IF +* + NTEST = 4 + RSUB +* +* Do tests 1--4 (or tests 7--9 when reordering ) +* + IF( ISORT.EQ.0 ) THEN + CALL DGET51( 1, N, A, LDA, S, LDA, Q, LDQ, Z, LDQ, + $ WORK, RESULT( 1 ) ) + CALL DGET51( 1, N, B, LDA, T, LDA, Q, LDQ, Z, LDQ, + $ WORK, RESULT( 2 ) ) + ELSE + CALL DGET54( N, A, LDA, B, LDA, S, LDA, T, LDA, Q, + $ LDQ, Z, LDQ, WORK, RESULT( 7 ) ) + END IF + CALL DGET51( 3, N, A, LDA, T, LDA, Q, LDQ, Q, LDQ, WORK, + $ RESULT( 3+RSUB ) ) + CALL DGET51( 3, N, B, LDA, T, LDA, Z, LDQ, Z, LDQ, WORK, + $ RESULT( 4+RSUB ) ) +* +* Do test 5 and 6 (or Tests 10 and 11 when reordering): +* check Schur form of A and compare eigenvalues with +* diagonals. +* + NTEST = 6 + RSUB + TEMP1 = ZERO +* + DO 130 J = 1, N + ILABAD = .FALSE. + IF( ALPHAI( J ).EQ.ZERO ) THEN + TEMP2 = ( ABS( ALPHAR( J )-S( J, J ) ) / + $ MAX( SAFMIN, ABS( ALPHAR( J ) ), ABS( S( J, + $ J ) ) )+ABS( BETA( J )-T( J, J ) ) / + $ MAX( SAFMIN, ABS( BETA( J ) ), ABS( T( J, + $ J ) ) ) ) / ULP +* + IF( J.LT.N ) THEN + IF( S( J+1, J ).NE.ZERO ) THEN + ILABAD = .TRUE. + RESULT( 5+RSUB ) = ULPINV + END IF + END IF + IF( J.GT.1 ) THEN + IF( S( J, J-1 ).NE.ZERO ) THEN + ILABAD = .TRUE. + RESULT( 5+RSUB ) = ULPINV + END IF + END IF +* + ELSE + IF( ALPHAI( J ).GT.ZERO ) THEN + I1 = J + ELSE + I1 = J - 1 + END IF + IF( I1.LE.0 .OR. I1.GE.N ) THEN + ILABAD = .TRUE. + ELSE IF( I1.LT.N-1 ) THEN + IF( S( I1+2, I1+1 ).NE.ZERO ) THEN + ILABAD = .TRUE. + RESULT( 5+RSUB ) = ULPINV + END IF + ELSE IF( I1.GT.1 ) THEN + IF( S( I1, I1-1 ).NE.ZERO ) THEN + ILABAD = .TRUE. + RESULT( 5+RSUB ) = ULPINV + END IF + END IF + IF( .NOT.ILABAD ) THEN + CALL DGET53( S( I1, I1 ), LDA, T( I1, I1 ), LDA, + $ BETA( J ), ALPHAR( J ), + $ ALPHAI( J ), TEMP2, IERR ) + IF( IERR.GE.3 ) THEN + WRITE( NOUNIT, FMT = 9998 )IERR, J, N, + $ JTYPE, IOLDSD + INFO = ABS( IERR ) + END IF + ELSE + TEMP2 = ULPINV + END IF +* + END IF + TEMP1 = MAX( TEMP1, TEMP2 ) + IF( ILABAD ) THEN + WRITE( NOUNIT, FMT = 9997 )J, N, JTYPE, IOLDSD + END IF + 130 CONTINUE + RESULT( 6+RSUB ) = TEMP1 +* + IF( ISORT.GE.1 ) THEN +* +* Do test 12 +* + NTEST = 12 + RESULT( 12 ) = ZERO + KNTEIG = 0 + DO 140 I = 1, N + IF( DLCTES( ALPHAR( I ), ALPHAI( I ), + $ BETA( I ) ) .OR. DLCTES( ALPHAR( I ), + $ -ALPHAI( I ), BETA( I ) ) ) THEN + KNTEIG = KNTEIG + 1 + END IF + IF( I.LT.N ) THEN + IF( ( DLCTES( ALPHAR( I+1 ), ALPHAI( I+1 ), + $ BETA( I+1 ) ) .OR. DLCTES( ALPHAR( I+1 ), + $ -ALPHAI( I+1 ), BETA( I+1 ) ) ) .AND. + $ ( .NOT.( DLCTES( ALPHAR( I ), ALPHAI( I ), + $ BETA( I ) ) .OR. DLCTES( ALPHAR( I ), + $ -ALPHAI( I ), BETA( I ) ) ) ) .AND. + $ IINFO.NE.N+2 ) THEN + RESULT( 12 ) = ULPINV + END IF + END IF + 140 CONTINUE + IF( SDIM.NE.KNTEIG ) THEN + RESULT( 12 ) = ULPINV + END IF + END IF +* + 150 CONTINUE +* +* End of Loop -- Check for RESULT(j) > THRESH +* + 160 CONTINUE +* + NTESTT = NTESTT + NTEST +* +* Print out tests which fail. +* + DO 170 JR = 1, NTEST + IF( RESULT( JR ).GE.THRESH ) THEN +* +* If this is the first test to fail, +* print a header to the data file. +* + IF( NERRS.EQ.0 ) THEN + WRITE( NOUNIT, FMT = 9996 )'DGS' +* +* Matrix types +* + WRITE( NOUNIT, FMT = 9995 ) + WRITE( NOUNIT, FMT = 9994 ) + WRITE( NOUNIT, FMT = 9993 )'Orthogonal' +* +* Tests performed +* + WRITE( NOUNIT, FMT = 9992 )'orthogonal', '''', + $ 'transpose', ( '''', J = 1, 8 ) +* + END IF + NERRS = NERRS + 1 + IF( RESULT( JR ).LT.10000.0D0 ) THEN + WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR, + $ RESULT( JR ) + ELSE + WRITE( NOUNIT, FMT = 9990 )N, JTYPE, IOLDSD, JR, + $ RESULT( JR ) + END IF + END IF + 170 CONTINUE +* + 180 CONTINUE + 190 CONTINUE +* +* Summary +* + CALL ALASVM( 'DGS', NOUNIT, NERRS, NTESTT, 0 ) +* + WORK( 1 ) = MAXWRK +* + RETURN +* + 9999 FORMAT( ' DDRGES3: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', + $ I6, ', JTYPE=', I6, ', ISEED=(', 4( I4, ',' ), I5, ')' ) +* + 9998 FORMAT( ' DDRGES3: DGET53 returned INFO=', I1, ' for eigenvalue ', + $ I6, '.', / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', + $ 4( I4, ',' ), I5, ')' ) +* + 9997 FORMAT( ' DDRGES3: S not in Schur form at eigenvalue ', I6, '.', + $ / 9X, 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), + $ I5, ')' ) +* + 9996 FORMAT( / 1X, A3, ' -- Real Generalized Schur form driver' ) +* + 9995 FORMAT( ' Matrix types (see DDRGES3 for details): ' ) +* + 9994 FORMAT( ' Special Matrices:', 23X, + $ '(J''=transposed Jordan block)', + $ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ', + $ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ', + $ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I', + $ ') 11=(large*I, small*D) 13=(large*D, large*I)', / + $ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ', + $ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' ) + 9993 FORMAT( ' Matrices Rotated by Random ', A, ' Matrices U, V:', + $ / ' 16=Transposed Jordan Blocks 19=geometric ', + $ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ', + $ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ', + $ 'alpha, beta=0,1 21=random alpha, beta=0,1', + $ / ' Large & Small Matrices:', / ' 22=(large, small) ', + $ '23=(small,large) 24=(small,small) 25=(large,large)', + $ / ' 26=random O(1) matrices.' ) +* + 9992 FORMAT( / ' Tests performed: (S is Schur, T is triangular, ', + $ 'Q and Z are ', A, ',', / 19X, + $ 'l and r are the appropriate left and right', / 19X, + $ 'eigenvectors, resp., a is alpha, b is beta, and', / 19X, A, + $ ' means ', A, '.)', / ' Without ordering: ', + $ / ' 1 = | A - Q S Z', A, + $ ' | / ( |A| n ulp ) 2 = | B - Q T Z', A, + $ ' | / ( |B| n ulp )', / ' 3 = | I - QQ', A, + $ ' | / ( n ulp ) 4 = | I - ZZ', A, + $ ' | / ( n ulp )', / ' 5 = A is in Schur form S', + $ / ' 6 = difference between (alpha,beta)', + $ ' and diagonals of (S,T)', / ' With ordering: ', + $ / ' 7 = | (A,B) - Q (S,T) Z', A, + $ ' | / ( |(A,B)| n ulp ) ', / ' 8 = | I - QQ', A, + $ ' | / ( n ulp ) 9 = | I - ZZ', A, + $ ' | / ( n ulp )', / ' 10 = A is in Schur form S', + $ / ' 11 = difference between (alpha,beta) and diagonals', + $ ' of (S,T)', / ' 12 = SDIM is the correct number of ', + $ 'selected eigenvalues', / ) + 9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', + $ 4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 ) + 9990 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', + $ 4( I4, ',' ), ' result ', I2, ' is', 1P, D10.3 ) +* +* End of DDRGES3 +* + END |