SUBROUTINE ZDRVEV( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH, \$ NOUNIT, A, LDA, H, W, W1, VL, LDVL, VR, LDVR, \$ LRE, LDLRE, RESULT, WORK, NWORK, RWORK, IWORK, \$ INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, LDLRE, LDVL, LDVR, NOUNIT, NSIZES, \$ NTYPES, NWORK DOUBLE PRECISION THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER ISEED( 4 ), IWORK( * ), NN( * ) DOUBLE PRECISION RESULT( 7 ), RWORK( * ) COMPLEX*16 A( LDA, * ), H( LDA, * ), LRE( LDLRE, * ), \$ VL( LDVL, * ), VR( LDVR, * ), W( * ), W1( * ), \$ WORK( * ) * .. * * Purpose * ======= * * ZDRVEV checks the nonsymmetric eigenvalue problem driver ZGEEV. * * When ZDRVEV 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 diagonal matrix with diagonal entries W(j). * * (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 complex angles. * (ULP = (first number larger than 1) - 1 ) * (5) A diagonal matrix with geometrically spaced entries * 1, ..., ULP and random complex angles. * (6) A diagonal matrix with "clustered" entries 1, ULP, ..., ULP * and random complex angles. * * (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 unitary and * T has evenly spaced entries 1, ..., ULP with random complex * angles on the diagonal and random O(1) entries in the upper * triangle. * * (10) A matrix of the form U' T U, where U is unitary and * T has geometrically spaced entries 1, ..., ULP with random * complex angles on the diagonal and random O(1) entries in * the upper triangle. * * (11) A matrix of the form U' T U, where U is unitary and * T has "clustered" entries 1, ULP,..., ULP with random * complex angles on the diagonal and random O(1) entries in * the upper triangle. * * (12) A matrix of the form U' T U, where U is unitary and * T has complex eigenvalues randomly chosen from * ULP < |z| < 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 complex angles 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 complex angles 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 complex angles 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 complex eigenvalues randomly chosen * from ULP < |z| < 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 |z| < 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 * * Arguments * ========== * * NSIZES (input) INTEGER * The number of sizes of matrices to use. If it is zero, * ZDRVEV does nothing. It must be at least zero. * * NN (input) 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. * * NTYPES (input) INTEGER * The number of elements in DOTYPE. If it is zero, ZDRVEV * 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. . * * DOTYPE (input) 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. * * ISEED (input/output) 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 ZDRVEV to continue the same random number * sequence. * * THRESH (input) 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. * * NOUNIT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns INFO not equal to 0.) * * A (workspace) COMPLEX*16 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. * * LDA (input) INTEGER * The leading dimension of A, and H. LDA must be at * least 1 and at least max(NN). * * H (workspace) COMPLEX*16 array, dimension (LDA, max(NN)) * Another copy of the test matrix A, modified by ZGEEV. * * W (workspace) COMPLEX*16 array, dimension (max(NN)) * The eigenvalues of A. On exit, W are the eigenvalues of * the matrix in A. * * W1 (workspace) COMPLEX*16 array, dimension (max(NN)) * Like W, this array contains the eigenvalues of A, * but those computed when ZGEEV only computes a partial * eigendecomposition, i.e. not the eigenvalues and left * and right eigenvectors. * * VL (workspace) COMPLEX*16 array, dimension (LDVL, max(NN)) * VL holds the computed left eigenvectors. * * LDVL (input) INTEGER * Leading dimension of VL. Must be at least max(1,max(NN)). * * VR (workspace) COMPLEX*16 array, dimension (LDVR, max(NN)) * VR holds the computed right eigenvectors. * * LDVR (input) INTEGER * Leading dimension of VR. Must be at least max(1,max(NN)). * * LRE (workspace) COMPLEX*16 array, dimension (LDLRE, max(NN)) * LRE holds the computed right or left eigenvectors. * * LDLRE (input) INTEGER * Leading dimension of LRE. Must be at least max(1,max(NN)). * * RESULT (output) DOUBLE PRECISION array, dimension (7) * The values computed by the seven tests described above. * The values are currently limited to 1/ulp, to avoid * overflow. * * WORK (workspace) COMPLEX*16 array, dimension (NWORK) * * NWORK (input) INTEGER * The number of entries in WORK. This must be at least * 5*NN(j)+2*NN(j)**2 for all j. * * RWORK (workspace) DOUBLE PRECISION array, dimension (2*max(NN)) * * IWORK (workspace) INTEGER array, dimension (max(NN)) * * INFO (output) 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) ). * -14: LDVL < 1 or LDVL < NMAX, where NMAX is max( NN(j) ). * -16: LDVR < 1 or LDVR < NMAX, where NMAX is max( NN(j) ). * -18: LDLRE < 1 or LDLRE < NMAX, where NMAX is max( NN(j) ). * -21: NWORK too small. * If ZLATMR, CLATMS, CLATME or ZGEEV 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.) * * ===================================================================== * * .. Parameters .. COMPLEX*16 CZERO PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) ) COMPLEX*16 CONE PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) DOUBLE PRECISION TWO PARAMETER ( TWO = 2.0D+0 ) 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 DOUBLE PRECISION ANORM, COND, CONDS, OVFL, RTULP, RTULPI, TNRM, \$ ULP, ULPINV, UNFL, VMX, VRMX, VTST * .. * .. Local Arrays .. INTEGER IDUMMA( 1 ), IOLDSD( 4 ), KCONDS( MAXTYP ), \$ KMAGN( MAXTYP ), KMODE( MAXTYP ), \$ KTYPE( MAXTYP ) DOUBLE PRECISION RES( 2 ) COMPLEX*16 DUM( 1 ) * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DZNRM2 EXTERNAL DLAMCH, DZNRM2 * .. * .. External Subroutines .. EXTERNAL DLABAD, DLASUM, XERBLA, ZGEEV, ZGET22, ZLACPY, \$ ZLASET, ZLATME, ZLATMR, ZLATMS * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DIMAG, 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 ) = 'Zomplex 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 = -14 ELSE IF( LDVR.LT.1 .OR. LDVR.LT.NMAX ) THEN INFO = -16 ELSE IF( LDLRE.LT.1 .OR. LDLRE.LT.NMAX ) THEN INFO = -28 ELSE IF( 5*NMAX+2*NMAX**2.GT.NWORK ) THEN INFO = -21 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZDRVEV', -INFO ) RETURN END IF * * Quick return if nothing to do * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) \$ RETURN * * More Important constants * UNFL = DLAMCH( 'Safe minimum' ) OVFL = ONE / UNFL CALL DLABAD( UNFL, OVFL ) ULP = DLAMCH( '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 ZLASET( 'Full', LDA, N, CZERO, CZERO, 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 ) = DCMPLX( ANORM ) 70 CONTINUE * ELSE IF( ITYPE.EQ.3 ) THEN * * Jordan Block * DO 80 JCOL = 1, N A( JCOL, JCOL ) = DCMPLX( ANORM ) IF( JCOL.GT.1 ) \$ A( JCOL, JCOL-1 ) = CONE 80 CONTINUE * ELSE IF( ITYPE.EQ.4 ) THEN * * Diagonal Matrix, [Eigen]values Specified * CALL ZLATMS( N, N, 'S', ISEED, 'H', RWORK, IMODE, COND, \$ ANORM, 0, 0, 'N', A, LDA, WORK( N+1 ), \$ IINFO ) * ELSE IF( ITYPE.EQ.5 ) THEN * * Hermitian, eigenvalues specified * CALL ZLATMS( N, N, 'S', ISEED, 'H', RWORK, 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 * CALL ZLATME( N, 'D', ISEED, WORK, IMODE, COND, CONE, ' ', \$ 'T', 'T', 'T', RWORK, 4, CONDS, N, N, ANORM, \$ A, LDA, WORK( 2*N+1 ), IINFO ) * ELSE IF( ITYPE.EQ.7 ) THEN * * Diagonal, random eigenvalues * CALL ZLATMR( N, N, 'D', ISEED, 'N', WORK, 6, ONE, CONE, \$ '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 ZLATMR( N, N, 'D', ISEED, 'H', WORK, 6, ONE, CONE, \$ '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 ZLATMR( N, N, 'D', ISEED, 'N', WORK, 6, ONE, CONE, \$ '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 ZLASET( 'Full', 2, N, CZERO, CZERO, A, LDA ) CALL ZLASET( 'Full', N-3, 1, CZERO, CZERO, A( 3, 1 ), \$ LDA ) CALL ZLASET( 'Full', N-3, 2, CZERO, CZERO, \$ A( 3, N-1 ), LDA ) CALL ZLASET( 'Full', 1, N, CZERO, CZERO, A( N, 1 ), \$ LDA ) END IF * ELSE IF( ITYPE.EQ.10 ) THEN * * Triangular, random eigenvalues * CALL ZLATMR( N, N, 'D', ISEED, 'N', WORK, 6, ONE, CONE, \$ '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 = 2*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 ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEV( 'V', 'V', N, H, LDA, W, VL, LDVL, VR, LDVR, \$ WORK, NNWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9993 )'ZGEEV1', IINFO, N, JTYPE, \$ IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (1) * CALL ZGET22( 'N', 'N', 'N', N, A, LDA, VR, LDVR, W, WORK, \$ RWORK, RES ) RESULT( 1 ) = RES( 1 ) * * Do Test (2) * CALL ZGET22( 'C', 'N', 'C', N, A, LDA, VL, LDVL, W, WORK, \$ RWORK, RES ) RESULT( 2 ) = RES( 1 ) * * Do Test (3) * DO 120 J = 1, N TNRM = DZNRM2( N, VR( 1, J ), 1 ) RESULT( 3 ) = MAX( RESULT( 3 ), \$ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) ) VMX = ZERO VRMX = ZERO DO 110 JJ = 1, N VTST = ABS( VR( JJ, J ) ) IF( VTST.GT.VMX ) \$ VMX = VTST IF( DIMAG( VR( JJ, J ) ).EQ.ZERO .AND. \$ ABS( DBLE( VR( JJ, J ) ) ).GT.VRMX ) \$ VRMX = ABS( DBLE( VR( JJ, J ) ) ) 110 CONTINUE IF( VRMX / VMX.LT.ONE-TWO*ULP ) \$ RESULT( 3 ) = ULPINV 120 CONTINUE * * Do Test (4) * DO 140 J = 1, N TNRM = DZNRM2( N, VL( 1, J ), 1 ) RESULT( 4 ) = MAX( RESULT( 4 ), \$ MIN( ULPINV, ABS( TNRM-ONE ) / ULP ) ) VMX = ZERO VRMX = ZERO DO 130 JJ = 1, N VTST = ABS( VL( JJ, J ) ) IF( VTST.GT.VMX ) \$ VMX = VTST IF( DIMAG( VL( JJ, J ) ).EQ.ZERO .AND. \$ ABS( DBLE( VL( JJ, J ) ) ).GT.VRMX ) \$ VRMX = ABS( DBLE( VL( JJ, J ) ) ) 130 CONTINUE IF( VRMX / VMX.LT.ONE-TWO*ULP ) \$ RESULT( 4 ) = ULPINV 140 CONTINUE * * Compute eigenvalues only, and test them * CALL ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEV( 'N', 'N', N, H, LDA, W1, DUM, 1, DUM, 1, \$ WORK, NNWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9993 )'ZGEEV2', IINFO, N, JTYPE, \$ IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (5) * DO 150 J = 1, N IF( W( J ).NE.W1( J ) ) \$ RESULT( 5 ) = ULPINV 150 CONTINUE * * Compute eigenvalues and right eigenvectors, and test them * CALL ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEV( 'N', 'V', N, H, LDA, W1, DUM, 1, LRE, LDLRE, \$ WORK, NNWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9993 )'ZGEEV3', IINFO, N, JTYPE, \$ IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (5) again * DO 160 J = 1, N IF( W( J ).NE.W1( 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 ZLACPY( 'F', N, N, A, LDA, H, LDA ) CALL ZGEEV( 'V', 'N', N, H, LDA, W1, LRE, LDLRE, DUM, 1, \$ WORK, NNWORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN RESULT( 1 ) = ULPINV WRITE( NOUNIT, FMT = 9993 )'ZGEEV4', IINFO, N, JTYPE, \$ IOLDSD INFO = ABS( IINFO ) GO TO 220 END IF * * Do Test (5) again * DO 190 J = 1, N IF( W( J ).NE.W1( 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 DLASUM( PATH, NOUNIT, NERRS, NTESTT ) * 9999 FORMAT( / 1X, A3, ' -- Complex Eigenvalue-Eigenvector ', \$ 'Decomposition Driver', / \$ ' Matrix types (see ZDRVEV 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 ', A6, / ' 12=Well-cond., random complex ', A6, ' ', \$ ' 17=Ill-cond., large rand. complx ', A4, / ' 13=Ill-condi', \$ 'tioned, evenly spaced. ', ' 18=Ill-cond., small rand.', \$ ' complx ', A4 ) 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 = | conj-trans(A) VL - VL conj-trans(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( ' ZDRVEV: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', \$ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * RETURN * * End of ZDRVEV * END