numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
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| lapack/TESTING/EIG/ddrgev3.f | 35220B | -rw-r--r-- |
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*> \brief \b DDRGEV3 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DDRGEV3( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, * NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE, * ALPHAR, ALPHAI, BETA, ALPHR1, ALPHI1, BETA1, * WORK, LWORK, RESULT, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDQ, LDQE, LWORK, NOUNIT, NSIZES, * $ NTYPES * DOUBLE PRECISION THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER ISEED( 4 ), NN( * ) * DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), * $ ALPHI1( * ), ALPHR1( * ), B( LDA, * ), * $ BETA( * ), BETA1( * ), Q( LDQ, * ), * $ QE( LDQE, * ), RESULT( * ), S( LDA, * ), * $ T( LDA, * ), WORK( * ), Z( LDQ, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DDRGEV3 checks the nonsymmetric generalized eigenvalue problem driver *> routine DGGEV3. *> *> DGGEV3 computes for a pair of n-by-n nonsymmetric matrices (A,B) the *> generalized eigenvalues and, optionally, the left and right *> eigenvectors. *> *> A generalized eigenvalue for a pair of matrices (A,B) is a scalar w *> or a ratio alpha/beta = w, such that A - w*B is singular. It is *> usually represented as the pair (alpha,beta), as there is reasonable *> interpretation for beta=0, and even for both being zero. *> *> A right generalized eigenvector corresponding to a generalized *> eigenvalue w for a pair of matrices (A,B) is a vector r such that *> (A - wB) * r = 0. A left generalized eigenvector is a vector l such *> that l**H * (A - wB) = 0, where l**H is the conjugate-transpose of l. *> *> When DDRGEV3 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 tests *> will be performed and compared with the threshold THRESH. *> *> Results from DGGEV3: *> *> (1) max over all left eigenvalue/-vector pairs (alpha/beta,l) of *> *> | VL**H * (beta A - alpha B) |/( ulp max(|beta A|, |alpha B|) ) *> *> where VL**H is the conjugate-transpose of VL. *> *> (2) | |VL(i)| - 1 | / ulp and whether largest component real *> *> VL(i) denotes the i-th column of VL. *> *> (3) max over all left eigenvalue/-vector pairs (alpha/beta,r) of *> *> | (beta A - alpha B) * VR | / ( ulp max(|beta A|, |alpha B|) ) *> *> (4) | |VR(i)| - 1 | / ulp and whether largest component real *> *> VR(i) denotes the i-th column of VR. *> *> (5) W(full) = W(partial) *> W(full) denotes the eigenvalues computed when both l and r *> are also computed, and W(partial) denotes the eigenvalues *> computed when only W, only W and r, or only W and l are *> computed. *> *> (6) VL(full) = VL(partial) *> VL(full) denotes the left eigenvectors computed when both l *> and r are computed, and VL(partial) denotes the result *> when only l is computed. *> *> (7) VR(full) = VR(partial) *> VR(full) denotes the right eigenvectors computed when both l *> and r are also computed, and VR(partial) denotes the result *> when only l is computed. *> *> *> 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, *> DDRGEV3 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, DDRGEV3 *> 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. 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 DDRGEV3 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. It must be at least zero. *> \endverbatim *> *> \param[in] NOUNIT *> \verbatim *> NOUNIT is INTEGER *> The FORTRAN unit number for printing out error messages *> (e.g., if a routine returns IERR 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 DGGEV3. 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 DGGEV3. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is DOUBLE PRECISION array, *> dimension (LDQ, max(NN)) *> The (left) eigenvectors matrix computed by DGGEV3. *> \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 DGGEV3. *> \endverbatim *> *> \param[out] QE *> \verbatim *> QE is DOUBLE PRECISION array, dimension( LDQ, max(NN) ) *> QE holds the computed right or left eigenvectors. *> \endverbatim *> *> \param[in] LDQE *> \verbatim *> LDQE is INTEGER *> The leading dimension of QE. LDQE >= max(1,max(NN)). *> \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 DGGEV3. *> ( ALPHAR(k)+ALPHAI(k)*i ) / BETA(k) is the k-th *> generalized eigenvalue of A and B. *> \endverbatim *> *> \param[out] ALPHR1 *> \verbatim *> ALPHR1 is DOUBLE PRECISION array, dimension (max(NN)) *> \endverbatim *> *> \param[out] ALPHI1 *> \verbatim *> ALPHI1 is DOUBLE PRECISION array, dimension (max(NN)) *> \endverbatim *> *> \param[out] BETA1 *> \verbatim *> BETA1 is DOUBLE PRECISION array, dimension (max(NN)) *> *> Like ALPHAR, ALPHAI, BETA, these arrays contain the *> eigenvalues of A and B, but those computed when DGGEV3 only *> computes a partial eigendecomposition, i.e. not the *> eigenvalues and left and right eigenvectors. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The number of entries in WORK. LWORK >= MAX( 8*N, N*(N+1) ). *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (2) *> The values computed by the tests described above. *> The values are currently limited to 1/ulp, to avoid overflow. *> \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. * *> \ingroup double_eig * * ===================================================================== SUBROUTINE DDRGEV3( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, $ NOUNIT, A, LDA, B, S, T, Q, LDQ, Z, QE, LDQE, $ ALPHAR, ALPHAI, BETA, ALPHR1, ALPHI1, BETA1, $ WORK, LWORK, RESULT, INFO ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER INFO, LDA, LDQ, LDQE, LWORK, NOUNIT, NSIZES, $ NTYPES DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), NN( * ) DOUBLE PRECISION A( LDA, * ), ALPHAI( * ), ALPHAR( * ), $ ALPHI1( * ), ALPHR1( * ), B( LDA, * ), $ BETA( * ), BETA1( * ), Q( LDQ, * ), $ QE( LDQE, * ), RESULT( * ), 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 = 27 ) * .. * .. Local Scalars .. LOGICAL BADNN INTEGER I, IADD, IERR, IN, J, JC, JR, JSIZE, JTYPE, $ MAXWRK, MINWRK, MTYPES, N, N1, NERRS, NMATS, $ NMAX, NTESTT DOUBLE PRECISION SAFMAX, SAFMIN, 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 .. INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLARND EXTERNAL ILAENV, DLAMCH, DLARND * .. * .. External Subroutines .. EXTERNAL ALASVM, DGET52, DGGEV3, DLACPY, DLARFG, DLASET, $ DLATM4, DORM2R, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, SIGN * .. * .. Data statements .. DATA KCLASS / 15*1, 10*2, 1*3, 1*4 / 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, 0 / DATA KBTYPE / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4, $ 1, 1, -4, 2, -4, 8*8, 0, 0 / DATA KAZERO / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3, $ 4*5, 4*3, 1, 1 / DATA KBZERO / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4, $ 4*6, 4*4, 1, 1 / DATA KAMAGN / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3, $ 2, 1, 3 / DATA KBMAGN / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3, $ 2, 1, 3 / DATA KTRIAN / 16*0, 11*1 / DATA IASIGN / 6*0, 2, 0, 2*2, 2*0, 3*2, 0, 2, 3*0, $ 5*2, 2*0 / DATA IBSIGN / 7*0, 2, 2*0, 2*2, 2*0, 2, 0, 2, 10*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 ELSE IF( LDQE.LE.1 .OR. LDQE.LT.NMAX ) THEN INFO = -17 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( 1, 8*NMAX, NMAX*( NMAX+1 ) ) MAXWRK = 7*NMAX + NMAX*ILAENV( 1, 'DGEQRF', ' ', NMAX, 1, NMAX, $ 0 ) MAXWRK = MAX( MAXWRK, NMAX*( NMAX+1 ) ) WORK( 1 ) = MAXWRK END IF * IF( LWORK.LT.MINWRK ) $ INFO = -25 * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DDRGEV3', -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 ULPINV = ONE / ULP * * The values RMAGN(2:3) depend on N, see below. * RMAGN( 0 ) = ZERO RMAGN( 1 ) = ONE * * Loop over sizes, types * NTESTT = 0 NERRS = 0 NMATS = 0 * DO 220 JSIZE = 1, NSIZES N = NN( JSIZE ) N1 = MAX( 1, N ) RMAGN( 2 ) = SAFMAX*ULP / DBLE( N1 ) RMAGN( 3 ) = SAFMIN*ULPINV*N1 * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 210 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 210 NMATS = NMATS + 1 * * Save ISEED in case of an error. * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * * Generate test matrices A and B * * Description of control parameters: * * KZLASS: =1 means w/o rotation, =2 means w/ rotation, * =3 means random, =4 means random generalized * upper Hessenberg. * 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 100 IERR = 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 40 JC = 1, N - 1 DO 30 JR = JC, N Q( JR, JC ) = DLARND( 3, ISEED ) Z( JR, JC ) = DLARND( 3, ISEED ) 30 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 40 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 60 JC = 1, N DO 50 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 ) 50 CONTINUE 60 CONTINUE CALL DORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, A, $ LDA, WORK( 2*N+1 ), IERR ) IF( IERR.NE.0 ) $ GO TO 90 CALL DORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ), $ A, LDA, WORK( 2*N+1 ), IERR ) IF( IERR.NE.0 ) $ GO TO 90 CALL DORM2R( 'L', 'N', N, N, N-1, Q, LDQ, WORK, B, $ LDA, WORK( 2*N+1 ), IERR ) IF( IERR.NE.0 ) $ GO TO 90 CALL DORM2R( 'R', 'T', N, N, N-1, Z, LDQ, WORK( N+1 ), $ B, LDA, WORK( 2*N+1 ), IERR ) IF( IERR.NE.0 ) $ GO TO 90 END IF ELSE IF (KCLASS( JTYPE ).EQ.3) THEN * * Random matrices * DO 80 JC = 1, N DO 70 JR = 1, N A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )* $ DLARND( 2, ISEED ) B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )* $ DLARND( 2, ISEED ) 70 CONTINUE 80 CONTINUE ELSE * * Random upper Hessenberg pencil with singular B * DO 81 JC = 1, N DO 71 JR = 1, min( JC + 1, N) A( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )* $ DLARND( 2, ISEED ) 71 CONTINUE DO 72 JR = JC + 2, N A( JR, JC ) = ZERO 72 CONTINUE 81 CONTINUE DO 82 JC = 1, N DO 73 JR = 1, JC B( JR, JC ) = RMAGN( KAMAGN( JTYPE ) )* $ DLARND( 2, ISEED ) 73 CONTINUE DO 74 JR = JC + 1, N B( JR, JC ) = ZERO 74 CONTINUE 82 CONTINUE DO 83 JC = 1, N, 4 B( JC, JC ) = ZERO 83 CONTINUE END IF * 90 CONTINUE * IF( IERR.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'Generator', IERR, N, JTYPE, $ IOLDSD INFO = ABS( IERR ) RETURN END IF * 100 CONTINUE * DO 110 I = 1, 7 RESULT( I ) = -ONE 110 CONTINUE * * Call XLAENV to set the parameters used in DLAQZ0 * CALL XLAENV( 12, 10 ) CALL XLAENV( 13, 12 ) CALL XLAENV( 14, 13 ) CALL XLAENV( 15, 2 ) CALL XLAENV( 17, 10 ) * * Call DGGEV3 to compute eigenvalues and eigenvectors. * CALL DLACPY( ' ', N, N, A, LDA, S, LDA ) CALL DLACPY( ' ', N, N, B, LDA, T, LDA ) CALL DGGEV3( 'V', 'V', N, S, LDA, T, LDA, ALPHAR, ALPHAI, $ BETA, Q, LDQ, Z, LDQ, WORK, LWORK, IERR ) IF( IERR.NE.0 .AND. IERR.NE.N+1 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'DGGEV31', IERR, N, JTYPE, $ IOLDSD INFO = ABS( IERR ) GO TO 190 END IF * * Do the tests (1) and (2) * CALL DGET52( .TRUE., N, A, LDA, B, LDA, Q, LDQ, ALPHAR, $ ALPHAI, BETA, WORK, RESULT( 1 ) ) IF( RESULT( 2 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Left', 'DGGEV31', $ RESULT( 2 ), N, JTYPE, IOLDSD END IF * * Do the tests (3) and (4) * CALL DGET52( .FALSE., N, A, LDA, B, LDA, Z, LDQ, ALPHAR, $ ALPHAI, BETA, WORK, RESULT( 3 ) ) IF( RESULT( 4 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Right', 'DGGEV31', $ RESULT( 4 ), N, JTYPE, IOLDSD END IF * * Do the test (5) * CALL DLACPY( ' ', N, N, A, LDA, S, LDA ) CALL DLACPY( ' ', N, N, B, LDA, T, LDA ) CALL DGGEV3( 'N', 'N', N, S, LDA, T, LDA, ALPHR1, ALPHI1, $ BETA1, Q, LDQ, Z, LDQ, WORK, LWORK, IERR ) IF( IERR.NE.0 .AND. IERR.NE.N+1 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'DGGEV32', IERR, N, JTYPE, $ IOLDSD INFO = ABS( IERR ) GO TO 190 END IF * DO 120 J = 1, N IF( ALPHAR( J ).NE.ALPHR1( J ) .OR. ALPHAI( J ).NE. $ ALPHI1( J ) .OR. BETA( J ).NE.BETA1( J ) )RESULT( 5 ) $ = ULPINV 120 CONTINUE * * Do the test (6): Compute eigenvalues and left eigenvectors, * and test them * CALL DLACPY( ' ', N, N, A, LDA, S, LDA ) CALL DLACPY( ' ', N, N, B, LDA, T, LDA ) CALL DGGEV3( 'V', 'N', N, S, LDA, T, LDA, ALPHR1, ALPHI1, $ BETA1, QE, LDQE, Z, LDQ, WORK, LWORK, IERR ) IF( IERR.NE.0 .AND. IERR.NE.N+1 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'DGGEV33', IERR, N, JTYPE, $ IOLDSD INFO = ABS( IERR ) GO TO 190 END IF * DO 130 J = 1, N IF( ALPHAR( J ).NE.ALPHR1( J ) .OR. ALPHAI( J ).NE. $ ALPHI1( J ) .OR. BETA( J ).NE.BETA1( J ) )RESULT( 6 ) $ = ULPINV 130 CONTINUE * DO 150 J = 1, N DO 140 JC = 1, N IF( Q( J, JC ).NE.QE( J, JC ) ) $ RESULT( 6 ) = ULPINV 140 CONTINUE 150 CONTINUE * * DO the test (7): Compute eigenvalues and right eigenvectors, * and test them * CALL DLACPY( ' ', N, N, A, LDA, S, LDA ) CALL DLACPY( ' ', N, N, B, LDA, T, LDA ) CALL DGGEV3( 'N', 'V', N, S, LDA, T, LDA, ALPHR1, ALPHI1, $ BETA1, Q, LDQ, QE, LDQE, WORK, LWORK, IERR ) IF( IERR.NE.0 .AND. IERR.NE.N+1 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9999 )'DGGEV34', IERR, N, JTYPE, $ IOLDSD INFO = ABS( IERR ) GO TO 190 END IF * DO 160 J = 1, N IF( ALPHAR( J ).NE.ALPHR1( J ) .OR. ALPHAI( J ).NE. $ ALPHI1( J ) .OR. BETA( J ).NE.BETA1( J ) )RESULT( 7 ) $ = ULPINV 160 CONTINUE * DO 180 J = 1, N DO 170 JC = 1, N IF( Z( J, JC ).NE.QE( J, JC ) ) $ RESULT( 7 ) = ULPINV 170 CONTINUE 180 CONTINUE * * End of Loop -- Check for RESULT(j) > THRESH * 190 CONTINUE * NTESTT = NTESTT + 7 * * Print out tests which fail. * DO 200 JR = 1, 7 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 = 9997 )'DGV' * * Matrix types * WRITE( NOUNIT, FMT = 9996 ) WRITE( NOUNIT, FMT = 9995 ) WRITE( NOUNIT, FMT = 9994 )'Orthogonal' * * Tests performed * WRITE( NOUNIT, FMT = 9993 ) * END IF NERRS = NERRS + 1 IF( RESULT( JR ).LT.10000.0D0 ) THEN WRITE( NOUNIT, FMT = 9992 )N, JTYPE, IOLDSD, JR, $ RESULT( JR ) ELSE WRITE( NOUNIT, FMT = 9991 )N, JTYPE, IOLDSD, JR, $ RESULT( JR ) END IF END IF 200 CONTINUE * 210 CONTINUE 220 CONTINUE * * Summary * CALL ALASVM( 'DGV', NOUNIT, NERRS, NTESTT, 0 ) * WORK( 1 ) = MAXWRK * RETURN * 9999 FORMAT( ' DDRGEV3: ', A, ' returned INFO=', I6, '.', / 3X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 4( I4, ',' ), I5, ')' ) * 9998 FORMAT( ' DDRGEV3: ', A, ' Eigenvectors from ', A, $ ' incorrectly normalized.', / ' Bits of error=', 0P, G10.3, $ ',', 3X, 'N=', I4, ', JTYPE=', I3, ', ISEED=(', $ 4( I4, ',' ), I5, ')' ) * 9997 FORMAT( / 1X, A3, ' -- Real Generalized eigenvalue problem driver' $ ) * 9996 FORMAT( ' Matrix types (see DDRGEV3 for details): ' ) * 9995 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)' ) 9994 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.' ) * 9993 FORMAT( / ' Tests performed: ', $ / ' 1 = max | ( b A - a B )''*l | / const.,', $ / ' 2 = | |VR(i)| - 1 | / ulp,', $ / ' 3 = max | ( b A - a B )*r | / const.', $ / ' 4 = | |VL(i)| - 1 | / ulp,', $ / ' 5 = 0 if W same no matter if r or l computed,', $ / ' 6 = 0 if l same no matter if l computed,', $ / ' 7 = 0 if r same no matter if r computed,', / 1X ) 9992 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', $ 4( I4, ',' ), ' result ', I2, ' is', 0P, F8.2 ) 9991 FORMAT( ' Matrix order=', I5, ', type=', I2, ', seed=', $ 4( I4, ',' ), ' result ', I2, ' is', 1P, D10.3 ) * * End of DDRGEV3 * END