numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/TESTING/EIG/sdrvev.f | 34073B | -rw-r--r-- |
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*> \brief \b SDRVEV * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, * NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, * VR, LDVR, LRE, LDLRE, RESULT, WORK, NWORK, * IWORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NOUNIT, NSIZES, * $ NTYPES, NWORK * REAL THRESH * .. * .. Array Arguments .. * LOGICAL DOTYPE( * ) * INTEGER ISEED( 4 ), IWORK( * ), NN( * ) * REAL A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ), * $ RESULT( 7 ), VL( LDVL, * ), VR( LDVR, * ), * $ WI( * ), WI1( * ), WORK( * ), WR( * ), WR1( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SDRVEV checks the nonsymmetric eigenvalue problem driver SGEEV. *> *> When SDRVEV 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, one matrix will be generated and used *> to test the nonsymmetric eigenroutines. For each matrix, 7 *> tests will be performed: *> *> (1) | A * VR - VR * W | / ( n |A| ulp ) *> *> Here VR is the matrix of unit right eigenvectors. *> W is a block diagonal matrix, with a 1x1 block for each *> real eigenvalue and a 2x2 block for each complex conjugate *> pair. If eigenvalues j and j+1 are a complex conjugate pair, *> so WR(j) = WR(j+1) = wr and WI(j) = - WI(j+1) = wi, then the *> 2 x 2 block corresponding to the pair will be: *> *> ( wr wi ) *> ( -wi wr ) *> *> Such a block multiplying an n x 2 matrix ( ur ui ) on the *> right will be the same as multiplying ur + i*ui by wr + i*wi. *> *> (2) | A**H * VL - VL * W**H | / ( n |A| ulp ) *> *> Here VL is the matrix of unit left eigenvectors, A**H is the *> conjugate transpose of A, and W is as above. *> *> (3) | |VR(i)| - 1 | / ulp and whether largest component real *> *> VR(i) denotes the i-th column of VR. *> *> (4) | |VL(i)| - 1 | / ulp and whether largest component real *> *> VL(i) denotes the i-th column of VL. *> *> (5) W(full) = W(partial) *> *> W(full) denotes the eigenvalues computed when both VR and VL *> are also computed, and W(partial) denotes the eigenvalues *> computed when only W, only W and VR, or only W and VL are *> computed. *> *> (6) VR(full) = VR(partial) *> *> VR(full) denotes the right eigenvectors computed when both VR *> and VL are computed, and VR(partial) denotes the result *> when only VR is computed. *> *> (7) VL(full) = VL(partial) *> *> VL(full) denotes the left eigenvectors computed when both VR *> and VL are also computed, and VL(partial) denotes the result *> when only VL is computed. *> *> The "sizes" 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) The zero matrix. *> (2) The identity matrix. *> (3) A (transposed) Jordan block, with 1's on the diagonal. *> *> (4) A diagonal matrix with evenly spaced entries *> 1, ..., ULP and random signs. *> (ULP = (first number larger than 1) - 1 ) *> (5) A diagonal matrix with geometrically spaced entries *> 1, ..., ULP and random signs. *> (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP *> and random signs. *> *> (7) Same as (4), but multiplied by a constant near *> the overflow threshold *> (8) Same as (4), but multiplied by a constant near *> the underflow threshold *> *> (9) A matrix of the form U' T U, where U is orthogonal and *> T has evenly spaced entries 1, ..., ULP with random signs *> on the diagonal and random O(1) entries in the upper *> triangle. *> *> (10) A matrix of the form U' T U, where U is orthogonal and *> T has geometrically spaced entries 1, ..., ULP with random *> signs on the diagonal and random O(1) entries in the upper *> triangle. *> *> (11) A matrix of the form U' T U, where U is orthogonal and *> T has "clustered" entries 1, ULP,..., ULP with random *> signs on the diagonal and random O(1) entries in the upper *> triangle. *> *> (12) A matrix of the form U' T U, where U is orthogonal and *> T has real or complex conjugate paired eigenvalues randomly *> chosen from ( ULP, 1 ) and random O(1) entries in the upper *> triangle. *> *> (13) A matrix of the form X' T X, where X has condition *> SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP *> with random signs on the diagonal and random O(1) entries *> in the upper triangle. *> *> (14) A matrix of the form X' T X, where X has condition *> SQRT( ULP ) and T has geometrically spaced entries *> 1, ..., ULP with random signs on the diagonal and random *> O(1) entries in the upper triangle. *> *> (15) A matrix of the form X' T X, where X has condition *> SQRT( ULP ) and T has "clustered" entries 1, ULP,..., ULP *> with random signs on the diagonal and random O(1) entries *> in the upper triangle. *> *> (16) A matrix of the form X' T X, where X has condition *> SQRT( ULP ) and T has real or complex conjugate paired *> eigenvalues randomly chosen from ( ULP, 1 ) and random *> O(1) entries in the upper triangle. *> *> (17) Same as (16), but multiplied by a constant *> near the overflow threshold *> (18) Same as (16), but multiplied by a constant *> near the underflow threshold *> *> (19) Nonsymmetric matrix with random entries chosen from (-1,1). *> If N is at least 4, all entries in first two rows and last *> row, and first column and last two columns are zero. *> (20) Same as (19), but multiplied by a constant *> near the overflow threshold *> (21) Same as (19), but multiplied by a constant *> near the underflow threshold *> \endverbatim * * Arguments: * ========== * *> \param[in] NSIZES *> \verbatim *> NSIZES is INTEGER *> The number of sizes of matrices to use. If it is zero, *> SDRVEV does nothing. It must be at least zero. *> \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. The values must be at least *> zero. *> \endverbatim *> *> \param[in] NTYPES *> \verbatim *> NTYPES is INTEGER *> The number of elements in DOTYPE. If it is zero, SDRVEV *> 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 SDRVEV to continue the same random number *> sequence. *> \endverbatim *> *> \param[in] THRESH *> \verbatim *> THRESH is REAL *> 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 INFO not equal to 0.) *> \endverbatim *> *> \param[out] A *> \verbatim *> A is REAL array, dimension (LDA, max(NN)) *> Used to hold the matrix whose eigenvalues are to be *> computed. On exit, A contains the last matrix actually used. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of A, and H. LDA must be at *> least 1 and at least max(NN). *> \endverbatim *> *> \param[out] H *> \verbatim *> H is REAL array, dimension (LDA, max(NN)) *> Another copy of the test matrix A, modified by SGEEV. *> \endverbatim *> *> \param[out] WR *> \verbatim *> WR is REAL array, dimension (max(NN)) *> \endverbatim *> *> \param[out] WI *> \verbatim *> WI is REAL array, dimension (max(NN)) *> *> The real and imaginary parts of the eigenvalues of A. *> On exit, WR + WI*i are the eigenvalues of the matrix in A. *> \endverbatim *> *> \param[out] WR1 *> \verbatim *> WR1 is REAL array, dimension (max(NN)) *> \endverbatim *> *> \param[out] WI1 *> \verbatim *> WI1 is REAL array, dimension (max(NN)) *> *> Like WR, WI, these arrays contain the eigenvalues of A, *> but those computed when SGEEV only computes a partial *> eigendecomposition, i.e. not the eigenvalues and left *> and right eigenvectors. *> \endverbatim *> *> \param[out] VL *> \verbatim *> VL is REAL array, dimension (LDVL, max(NN)) *> VL holds the computed left eigenvectors. *> \endverbatim *> *> \param[in] LDVL *> \verbatim *> LDVL is INTEGER *> Leading dimension of VL. Must be at least max(1,max(NN)). *> \endverbatim *> *> \param[out] VR *> \verbatim *> VR is REAL array, dimension (LDVR, max(NN)) *> VR holds the computed right eigenvectors. *> \endverbatim *> *> \param[in] LDVR *> \verbatim *> LDVR is INTEGER *> Leading dimension of VR. Must be at least max(1,max(NN)). *> \endverbatim *> *> \param[out] LRE *> \verbatim *> LRE is REAL array, dimension (LDLRE,max(NN)) *> LRE holds the computed right or left eigenvectors. *> \endverbatim *> *> \param[in] LDLRE *> \verbatim *> LDLRE is INTEGER *> Leading dimension of LRE. Must be at least max(1,max(NN)). *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is REAL array, dimension (7) *> The values computed by the seven tests described above. *> The values are currently limited to 1/ulp, to avoid overflow. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (NWORK) *> \endverbatim *> *> \param[in] NWORK *> \verbatim *> NWORK is INTEGER *> The number of entries in WORK. This must be at least *> 5*NN(j)+2*NN(j)**2 for all j. *> \endverbatim *> *> \param[out] IWORK *> \verbatim *> IWORK is INTEGER array, dimension (max(NN)) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> If 0, then everything ran OK. *> -1: NSIZES < 0 *> -2: Some NN(j) < 0 *> -3: NTYPES < 0 *> -6: THRESH < 0 *> -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). *> -16: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ). *> -18: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ). *> -20: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ). *> -23: NWORK too small. *> If SLATMR, SLATMS, SLATME or SGEEV returns an error code, *> the absolute value of it is returned. *> *>----------------------------------------------------------------------- *> *> Some Local Variables and Parameters: *> ---- ----- --------- --- ---------- *> *> ZERO, ONE Real 0 and 1. *> MAXTYP The number of types defined. *> NMAX Largest value in NN. *> NERRS The number of tests which have exceeded THRESH *> COND, CONDS, *> IMODE Values to be passed to the matrix generators. *> ANORM Norm of A; passed to matrix generators. *> *> OVFL, UNFL Overflow and underflow thresholds. *> ULP, ULPINV Finest relative precision and its inverse. *> RTULP, RTULPI Square roots of the previous 4 values. *> *> The following four arrays decode JTYPE: *> KTYPE(j) The general type (1-10) for type "j". *> KMODE(j) The MODE value to be passed to the matrix *> generator for type "j". *> KMAGN(j) The order of magnitude ( O(1), *> O(overflow^(1/2) ), O(underflow^(1/2) ) *> KCONDS(j) Selectw whether CONDS is to be 1 or *> 1/sqrt(ulp). (0 means irrelevant.) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_eig * * ===================================================================== SUBROUTINE SDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, $ NOUNIT, A, LDA, H, WR, WI, WR1, WI1, VL, LDVL, $ VR, LDVR, LRE, LDLRE, RESULT, WORK, NWORK, $ IWORK, 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, LDLRE, LDVL, LDVR, NOUNIT, NSIZES, $ NTYPES, NWORK REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), NN( * ) REAL A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ), $ RESULT( 7 ), VL( LDVL, * ), VR( LDVR, * ), $ WI( * ), WI1( * ), WORK( * ), WR( * ), WR1( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) REAL TWO PARAMETER ( TWO = 2.0E0 ) INTEGER MAXTYP PARAMETER ( MAXTYP = 21 ) * .. * .. Local Scalars .. LOGICAL BADNN CHARACTER*3 PATH INTEGER IINFO, IMODE, ITYPE, IWK, J, JCOL, JJ, JSIZE, $ JTYPE, MTYPES, N, NERRS, NFAIL, NMAX, $ NNWORK, NTEST, NTESTF, NTESTT REAL ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TNRM, $ ULP, ULPINV, UNFL, VMX, VRMX, VTST * .. * .. Local Arrays .. CHARACTER ADUMMA( 1 ) INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ), $ KMAGN( MAXTYP ), KMODE( MAXTYP ), $ KTYPE( MAXTYP ) REAL DUM( 1 ), RES( 2 ) * .. * .. External Functions .. REAL SLAMCH, SLAPY2, SNRM2 EXTERNAL SLAMCH, SLAPY2, SNRM2 * .. * .. External Subroutines .. EXTERNAL SGEEV, SGET22, SLACPY, SLASUM, SLATME, $ SLATMR, SLATMS, SLASET, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN, SQRT * .. * .. Data statements .. DATA KTYPE / 1, 2, 3, 5*4, 4*6, 6*6, 3*9 / DATA KMAGN / 3*1, 1, 1, 1, 2, 3, 4*1, 1, 1, 1, 1, 2, $ 3, 1, 2, 3 / DATA KMODE / 3*0, 4, 3, 1, 4, 4, 4, 3, 1, 5, 4, 3, $ 1, 5, 5, 5, 4, 3, 1 / DATA KCONDS / 3*0, 5*0, 4*1, 6*2, 3*0 / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'EV' * * Check for errors * NTESTT = 0 NTESTF = 0 INFO = 0 * * Important constants * BADNN = .FALSE. NMAX = 0 DO 10 J = 1, NSIZES NMAX = MAX( NMAX, NN( J ) ) IF( NN( J ).LT.0 ) $ BADNN = .TRUE. 10 CONTINUE * * Check for errors * 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( NOUNIT.LE.0 ) THEN INFO = -7 ELSE IF( LDA.LT.1 .OR. LDA.LT.NMAX ) THEN INFO = -9 ELSE IF( LDVL.LT.1 .OR. LDVL.LT.NMAX ) THEN INFO = -16 ELSE IF( LDVR.LT.1 .OR. LDVR.LT.NMAX ) THEN INFO = -18 ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.NMAX ) THEN INFO = -20 ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN INFO = -23 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'SDRVEV', -INFO ) RETURN END IF * * Quick return if nothing to do * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ RETURN * * More Important constants * UNFL = SLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL ULP = SLAMCH( 'Precision' ) ULPINV = ONE / ULP RTULP = SQRT( ULP ) RTULPI = ONE / RTULP * * Loop over sizes, types * NERRS = 0 * DO 270 JSIZE = 1, NSIZES N = NN( JSIZE ) IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 260 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 260 * * Save ISEED in case of an error. * DO 20 J = 1, 4 IOLDSD( J ) = ISEED( J ) 20 CONTINUE * * Compute "A" * * Control parameters: * * KMAGN KCONDS KMODE KTYPE * =1 O(1) 1 clustered 1 zero * =2 large large clustered 2 identity * =3 small exponential Jordan * =4 arithmetic diagonal, (w/ eigenvalues) * =5 random log symmetric, w/ eigenvalues * =6 random general, w/ eigenvalues * =7 random diagonal * =8 random symmetric * =9 random general * =10 random triangular * IF( MTYPES.GT.MAXTYP ) $ GO TO 90 * ITYPE = KTYPE( JTYPE ) IMODE = KMODE( JTYPE ) * * Compute norm * GO TO ( 30, 40, 50 )KMAGN( JTYPE ) * 30 CONTINUE ANORM = ONE GO TO 60 * 40 CONTINUE ANORM = OVFL*ULP GO TO 60 * 50 CONTINUE ANORM = UNFL*ULPINV GO TO 60 * 60 CONTINUE * CALL SLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA ) IINFO = 0 COND = ULPINV * * Special Matrices -- Identity & Jordan block * * Zero * IF( ITYPE.EQ.1 ) THEN IINFO = 0 * ELSE IF( ITYPE.EQ.2 ) THEN * * Identity * DO 70 JCOL = 1, N A( JCOL, JCOL ) = ANORM 70 CONTINUE * ELSE IF( ITYPE.EQ.3 ) THEN * * Jordan Block * DO 80 JCOL = 1, N A( JCOL, JCOL ) = ANORM IF( JCOL.GT.1 ) $ A( JCOL, JCOL-1 ) = ONE 80 CONTINUE * ELSE IF( ITYPE.EQ.4 ) THEN * * Diagonal Matrix, [Eigen]values Specified * CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND, $ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ), $ IINFO ) * ELSE IF( ITYPE.EQ.5 ) THEN * * Symmetric, eigenvalues specified * CALL SLATMS( N, N, 'S', ISEED, 'S', WORK, IMODE, COND, $ ANORM, N, N, 'N', A, LDA, WORK( N+1 ), $ IINFO ) * ELSE IF( ITYPE.EQ.6 ) THEN * * General, eigenvalues specified * IF( KCONDS( JTYPE ).EQ.1 ) THEN CONDS = ONE ELSE IF( KCONDS( JTYPE ).EQ.2 ) THEN CONDS = RTULPI ELSE CONDS = ZERO END IF * ADUMMA( 1 ) = ' ' CALL SLATME( N, 'S', ISEED, WORK, IMODE, COND, ONE, $ ADUMMA, 'T', 'T', 'T', WORK( N+1 ), 4, $ CONDS, N, N, ANORM, A, LDA, WORK( 2*N+1 ), $ IINFO ) * ELSE IF( ITYPE.EQ.7 ) THEN * * Diagonal, random eigenvalues * CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE, $ 'T', 'N', WORK( N+1 ), 1, ONE, $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, 0, 0, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) * ELSE IF( ITYPE.EQ.8 ) THEN * * Symmetric, random eigenvalues * CALL SLATMR( N, N, 'S', ISEED, 'S', WORK, 6, ONE, ONE, $ 'T', 'N', WORK( N+1 ), 1, ONE, $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) * ELSE IF( ITYPE.EQ.9 ) THEN * * General, random eigenvalues * CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE, $ 'T', 'N', WORK( N+1 ), 1, ONE, $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, N, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) IF( N.GE.4 ) THEN CALL SLASET( 'Full', 2, N, ZERO, ZERO, A, LDA ) CALL SLASET( 'Full', N-3, 1, ZERO, ZERO, A( 3, 1 ), $ LDA ) CALL SLASET( 'Full', N-3, 2, ZERO, ZERO, A( 3, N-1 ), $ LDA ) CALL SLASET( 'Full', 1, N, ZERO, ZERO, A( N, 1 ), $ LDA ) END IF * ELSE IF( ITYPE.EQ.10 ) THEN * * Triangular, random eigenvalues * CALL SLATMR( N, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE, $ 'T', 'N', WORK( N+1 ), 1, ONE, $ WORK( 2*N+1 ), 1, ONE, 'N', IDUMMA, N, 0, $ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO ) * ELSE * IINFO = 1 END IF * IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9993 )'Generator', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) RETURN END IF * 90 CONTINUE * * Test for minimal and generous workspace * DO 250 IWK = 1, 2 IF( IWK.EQ.1 ) THEN NNWORK = 4*N ELSE NNWORK = 5*N + 2*N**2 END IF NNWORK = MAX( NNWORK, 1 ) * * Initialize RESULT * DO 100 J = 1, 7 RESULT( J ) = -ONE 100 CONTINUE * * Compute eigenvalues and eigenvectors, and test them * CALL SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEV( 'V', 'V', N, H, LDA, WR, WI, VL, LDVL, VR, $ LDVR, WORK, NNWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9993 )'SGEEV1', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (1) * CALL SGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, WR, WI, $ WORK, RES ) RESULT( 1 ) = RES( 1 ) * * Do Test (2) * CALL SGET22( 'T', 'N', 'T', N, A, LDA, VL, LDVL, WR, WI, $ WORK, RES ) RESULT( 2 ) = RES( 1 ) * * Do Test (3) * DO 120 J = 1, N TNRM = ONE IF( WI( J ).EQ.ZERO ) THEN TNRM = SNRM2( N, VR( 1, J ), 1 ) ELSE IF( WI( J ).GT.ZERO ) THEN TNRM = SLAPY2( SNRM2( N, VR( 1, J ), 1 ), $ SNRM2( N, VR( 1, J+1 ), 1 ) ) END IF RESULT( 3 ) = MAX( RESULT( 3 ), $ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) ) IF( WI( J ).GT.ZERO ) THEN VMX = ZERO VRMX = ZERO DO 110 JJ = 1, N VTST = SLAPY2( VR( JJ, J ), VR( JJ, J+1 ) ) IF( VTST.GT.VMX ) $ VMX = VTST IF( VR( JJ, J+1 ).EQ.ZERO .AND. $ ABS( VR( JJ, J ) ).GT.VRMX ) $ VRMX = ABS( VR( JJ, J ) ) 110 CONTINUE IF( VRMX / VMX.LT.ONE-TWO*ULP ) $ RESULT( 3 ) = ULPINV END IF 120 CONTINUE * * Do Test (4) * DO 140 J = 1, N TNRM = ONE IF( WI( J ).EQ.ZERO ) THEN TNRM = SNRM2( N, VL( 1, J ), 1 ) ELSE IF( WI( J ).GT.ZERO ) THEN TNRM = SLAPY2( SNRM2( N, VL( 1, J ), 1 ), $ SNRM2( N, VL( 1, J+1 ), 1 ) ) END IF RESULT( 4 ) = MAX( RESULT( 4 ), $ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) ) IF( WI( J ).GT.ZERO ) THEN VMX = ZERO VRMX = ZERO DO 130 JJ = 1, N VTST = SLAPY2( VL( JJ, J ), VL( JJ, J+1 ) ) IF( VTST.GT.VMX ) $ VMX = VTST IF( VL( JJ, J+1 ).EQ.ZERO .AND. $ ABS( VL( JJ, J ) ).GT.VRMX ) $ VRMX = ABS( VL( JJ, J ) ) 130 CONTINUE IF( VRMX / VMX.LT.ONE-TWO*ULP ) $ RESULT( 4 ) = ULPINV END IF 140 CONTINUE * * Compute eigenvalues only, and test them * CALL SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEV( 'N', 'N', N, H, LDA, WR1, WI1, DUM, 1, DUM, $ 1, WORK, NNWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9993 )'SGEEV2', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (5) * DO 150 J = 1, N IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) ) $ RESULT( 5 ) = ULPINV 150 CONTINUE * * Compute eigenvalues and right eigenvectors, and test them * CALL SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEV( 'N', 'V', N, H, LDA, WR1, WI1, DUM, 1, LRE, $ LDLRE, WORK, NNWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9993 )'SGEEV3', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (5) again * DO 160 J = 1, N IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) ) $ RESULT( 5 ) = ULPINV 160 CONTINUE * * Do Test (6) * DO 180 J = 1, N DO 170 JJ = 1, N IF( VR( J, JJ ).NE.LRE( J, JJ ) ) $ RESULT( 6 ) = ULPINV 170 CONTINUE 180 CONTINUE * * Compute eigenvalues and left eigenvectors, and test them * CALL SLACPY( 'F', N, N, A, LDA, H, LDA ) CALL SGEEV( 'V', 'N', N, H, LDA, WR1, WI1, LRE, LDLRE, $ DUM, 1, WORK, NNWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9993 )'SGEEV4', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (5) again * DO 190 J = 1, N IF( WR( J ).NE.WR1( J ) .OR. WI( J ).NE.WI1( J ) ) $ RESULT( 5 ) = ULPINV 190 CONTINUE * * Do Test (7) * DO 210 J = 1, N DO 200 JJ = 1, N IF( VL( J, JJ ).NE.LRE( J, JJ ) ) $ RESULT( 7 ) = ULPINV 200 CONTINUE 210 CONTINUE * * End of Loop -- Check for RESULT(j) > THRESH * 220 CONTINUE * NTEST = 0 NFAIL = 0 DO 230 J = 1, 7 IF( RESULT( J ).GE.ZERO ) $ NTEST = NTEST + 1 IF( RESULT( J ).GE.THRESH ) $ NFAIL = NFAIL + 1 230 CONTINUE * IF( NFAIL.GT.0 ) $ NTESTF = NTESTF + 1 IF( NTESTF.EQ.1 ) THEN WRITE( NOUNIT, FMT = 9999 )PATH WRITE( NOUNIT, FMT = 9998 ) WRITE( NOUNIT, FMT = 9997 ) WRITE( NOUNIT, FMT = 9996 ) WRITE( NOUNIT, FMT = 9995 )THRESH NTESTF = 2 END IF * DO 240 J = 1, 7 IF( RESULT( J ).GE.THRESH ) THEN WRITE( NOUNIT, FMT = 9994 )N, IWK, IOLDSD, JTYPE, $ J, RESULT( J ) END IF 240 CONTINUE * NERRS = NERRS + NFAIL NTESTT = NTESTT + NTEST * 250 CONTINUE 260 CONTINUE 270 CONTINUE * * Summary * CALL SLASUM( PATH, NOUNIT, NERRS, NTESTT ) * 9999 FORMAT( / 1X, A3, ' -- Real Eigenvalue-Eigenvector Decomposition', $ ' Driver', / ' Matrix types (see SDRVEV for details): ' ) * 9998 FORMAT( / ' Special Matrices:', / ' 1=Zero matrix. ', $ ' ', ' 5=Diagonal: geometr. spaced entries.', $ / ' 2=Identity matrix. ', ' 6=Diagona', $ 'l: clustered entries.', / ' 3=Transposed Jordan block. ', $ ' ', ' 7=Diagonal: large, evenly spaced.', / ' ', $ '4=Diagonal: evenly spaced entries. ', ' 8=Diagonal: s', $ 'mall, evenly spaced.' ) 9997 FORMAT( ' Dense, Non-Symmetric Matrices:', / ' 9=Well-cond., ev', $ 'enly spaced eigenvals.', ' 14=Ill-cond., geomet. spaced e', $ 'igenals.', / ' 10=Well-cond., geom. spaced eigenvals. ', $ ' 15=Ill-conditioned, clustered e.vals.', / ' 11=Well-cond', $ 'itioned, clustered e.vals. ', ' 16=Ill-cond., random comp', $ 'lex ', / ' 12=Well-cond., random complex ', 6X, ' ', $ ' 17=Ill-cond., large rand. complx ', / ' 13=Ill-condi', $ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.', $ ' complx ' ) 9996 FORMAT( ' 19=Matrix with random O(1) entries. ', ' 21=Matrix ', $ 'with small random entries.', / ' 20=Matrix with large ran', $ 'dom entries. ', / ) 9995 FORMAT( ' Tests performed with test threshold =', F8.2, $ / / ' 1 = | A VR - VR W | / ( n |A| ulp ) ', $ / ' 2 = | transpose(A) VL - VL W | / ( n |A| ulp ) ', $ / ' 3 = | |VR(i)| - 1 | / ulp ', $ / ' 4 = | |VL(i)| - 1 | / ulp ', $ / ' 5 = 0 if W same no matter if VR or VL computed,', $ ' 1/ulp otherwise', / $ ' 6 = 0 if VR same no matter if VL computed,', $ ' 1/ulp otherwise', / $ ' 7 = 0 if VL same no matter if VR computed,', $ ' 1/ulp otherwise', / ) 9994 FORMAT( ' N=', I5, ', IWK=', I2, ', seed=', 4( I4, ',' ), $ ' type ', I2, ', test(', I2, ')=', G10.3 ) 9993 FORMAT( ' SDRVEV: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of SDRVEV * END