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SUBROUTINE CCHKGG( NSIZES, NN, NTYPES, DOTYPE, ISEED, THRESH,
$ TSTDIF, THRSHN, NOUNIT, A, LDA, B, H, T, S1, $ S2, P1, P2, U, LDU, V, Q, Z, ALPHA1, BETA1, $ ALPHA3, BETA3, EVECTL, EVECTR, WORK, LWORK, $ RWORK, LLWORK, RESULT, INFO ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL TSTDIF INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES REAL THRESH, THRSHN * .. * .. Array Arguments .. LOGICAL DOTYPE( * ), LLWORK( * ) INTEGER ISEED( 4 ), NN( * ) REAL RESULT( 15 ), RWORK( * ) COMPLEX A( LDA, * ), ALPHA1( * ), ALPHA3( * ), $ B( LDA, * ), BETA1( * ), BETA3( * ), $ EVECTL( LDU, * ), EVECTR( LDU, * ), $ H( LDA, * ), P1( LDA, * ), P2( LDA, * ), $ Q( LDU, * ), S1( LDA, * ), S2( LDA, * ), $ T( LDA, * ), U( LDU, * ), V( LDU, * ), $ WORK( * ), Z( LDU, * ) * .. * * Purpose * ======= * * CCHKGG checks the nonsymmetric generalized eigenvalue problem * routines. * H H H * CGGHRD factors A and B as U H V and U T V , where means conjugate * transpose, H is hessenberg, T is triangular and U and V are unitary. * * H H * CHGEQZ factors H and T as Q S Z and Q P Z , where P and S are upper * triangular and Q and Z are unitary. It also computes the generalized * eigenvalues (alpha(1),beta(1)),...,(alpha(n),beta(n)), where * alpha(j)=S(j,j) and beta(j)=P(j,j) -- thus, w(j) = alpha(j)/beta(j) * is a root of the generalized eigenvalue problem * * det( A - w(j) B ) = 0 * * and m(j) = beta(j)/alpha(j) is a root of the essentially equivalent * problem * * det( m(j) A - B ) = 0 * * CTGEVC computes the matrix L of left eigenvectors and the matrix R * of right eigenvectors for the matrix pair ( S, P ). In the * description below, l and r are left and right eigenvectors * corresponding to the generalized eigenvalues (alpha,beta). * * When CCHKGG 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, 13 * tests will be performed. The first twelve "test ratios" should be * small -- O(1). They will be compared with the threshhold THRESH: * * H * (1) | A - U H V | / ( |A| n ulp ) * * H * (2) | B - U T V | / ( |B| n ulp ) * * H * (3) | I - UU | / ( n ulp ) * * H * (4) | I - VV | / ( n ulp ) * * H * (5) | H - Q S Z | / ( |H| n ulp ) * * H * (6) | T - Q P Z | / ( |T| n ulp ) * * H * (7) | I - QQ | / ( n ulp ) * * H * (8) | I - ZZ | / ( n ulp ) * * (9) max over all left eigenvalue/-vector pairs (beta/alpha,l) of * H * | (beta A - alpha B) l | / ( ulp max( |beta A|, |alpha B| ) ) * * (10) max over all left eigenvalue/-vector pairs (beta/alpha,l') of * H * | (beta H - alpha T) l' | / ( ulp max( |beta H|, |alpha T| ) ) * * where the eigenvectors l' are the result of passing Q to * STGEVC and back transforming (JOB='B'). * * (11) max over all right eigenvalue/-vector pairs (beta/alpha,r) of * * | (beta A - alpha B) r | / ( ulp max( |beta A|, |alpha B| ) ) * * (12) max over all right eigenvalue/-vector pairs (beta/alpha,r') of * * | (beta H - alpha T) r' | / ( ulp max( |beta H|, |alpha T| ) ) * * where the eigenvectors r' are the result of passing Z to * STGEVC and back transforming (JOB='B'). * * The last three test ratios will usually be small, but there is no * mathematical requirement that they be so. They are therefore * compared with THRESH only if TSTDIF is .TRUE. * * (13) | S(Q,Z computed) - S(Q,Z not computed) | / ( |S| ulp ) * * (14) | P(Q,Z computed) - P(Q,Z not computed) | / ( |P| ulp ) * * (15) max( |alpha(Q,Z computed) - alpha(Q,Z not computed)|/|S| , * |beta(Q,Z computed) - beta(Q,Z not computed)|/|P| ) / ulp * * In addition, the normalization of L and R are checked, and compared * with the threshhold THRSHN. * * 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 P*D1, P is a random unitary diagonal * matrix (i.e., with random magnitude 1 entries * on the diagonal), and D1=diag( 0, 1,..., N-1 ) * (i.e., a diagonal matrix with D1(1,1)=0, * D1(2,2)=1, ..., D1(N,N)=N-1.) * (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=P*diag( 0, 0, 1, ..., N-3, 0 ) and * D2=Q*diag( 0, N-3, N-4,..., 1, 0, 0 ), and * P and Q are random unitary diagonal matrices. * t t * (16) U ( J , J ) V where U and V are random unitary matrices. * * (17) U ( T1, T2 ) V where T1 and T2 are upper triangular matrices * with random O(1) entries above the diagonal * and diagonal entries diag(T1) = * P*( 0, 0, 1, ..., N-3, 0 ) and diag(T2) = * Q*( 0, N-3, N-4,..., 1, 0, 0 ) * * (18) U ( T1, T2 ) V diag(T1) = ( 0, 0, 1, 1, s, ..., s, 0 ) * diag(T2) = ( 0, 1, 0, 1,..., 1, 0 ) * s = machine precision. * * (19) U ( T1, T2 ) V 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) U ( T1, T2 ) V diag(T1)=( 0, 0, 1, 1, a, ..., a =s, 0 ) * diag(T2) = ( 0, 1, 0, 1, ..., 1, 0, 0 ) * * (21) U ( T1, T2 ) V 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) U ( big*T1, small*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) * * (23) U ( small*T1, big*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) * * (24) U ( small*T1, small*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) * * (25) U ( big*T1, big*T2 ) V diag(T1) = P*( 0, 0, 1, ..., N-3, 0 ) * diag(T2) = ( 0, 1, ..., 1, 0, 0 ) * * (26) U ( T1, T2 ) V where T1 and T2 are random upper-triangular * matrices. * * Arguments * ========= * * NSIZES (input) INTEGER * The number of sizes of matrices to use. If it is zero, * CCHKGG 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, CCHKGG * 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 CCHKGG to continue the same random number * sequence. * * THRESH (input) 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. * * TSTDIF (input) LOGICAL * Specifies whether test ratios 13-15 will be computed and * compared with THRESH. * = .FALSE.: Only test ratios 1-12 will be computed and tested. * Ratios 13-15 will be set to zero. * = .TRUE.: All the test ratios 1-15 will be computed and * tested. * * THRSHN (input) REAL * Threshhold for reporting eigenvector normalization error. * If the normalization of any eigenvector differs from 1 by * more than THRSHN*ulp, then a special error message will be * printed. (This is handled separately from the other tests, * since only a compiler or programming error should cause an * error message, at least if THRSHN is at least 5--10.) * * NOUNIT (input) INTEGER * The FORTRAN unit number for printing out error messages * (e.g., if a routine returns IINFO not equal to 0.) * * A (input/workspace) COMPLEX 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. * * LDA (input) INTEGER * The leading dimension of A, B, H, T, S1, P1, S2, and P2. * It must be at least 1 and at least max( NN ). * * B (input/workspace) COMPLEX 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. * * H (workspace) COMPLEX array, dimension (LDA, max(NN)) * The upper Hessenberg matrix computed from A by CGGHRD. * * T (workspace) COMPLEX array, dimension (LDA, max(NN)) * The upper triangular matrix computed from B by CGGHRD. * * S1 (workspace) COMPLEX array, dimension (LDA, max(NN)) * The Schur (upper triangular) matrix computed from H by CHGEQZ * when Q and Z are also computed. * * S2 (workspace) COMPLEX array, dimension (LDA, max(NN)) * The Schur (upper triangular) matrix computed from H by CHGEQZ * when Q and Z are not computed. * * P1 (workspace) COMPLEX array, dimension (LDA, max(NN)) * The upper triangular matrix computed from T by CHGEQZ * when Q and Z are also computed. * * P2 (workspace) COMPLEX array, dimension (LDA, max(NN)) * The upper triangular matrix computed from T by CHGEQZ * when Q and Z are not computed. * * U (workspace) COMPLEX array, dimension (LDU, max(NN)) * The (left) unitary matrix computed by CGGHRD. * * LDU (input) INTEGER * The leading dimension of U, V, Q, Z, EVECTL, and EVECTR. It * must be at least 1 and at least max( NN ). * * V (workspace) COMPLEX array, dimension (LDU, max(NN)) * The (right) unitary matrix computed by CGGHRD. * * Q (workspace) COMPLEX array, dimension (LDU, max(NN)) * The (left) unitary matrix computed by CHGEQZ. * * Z (workspace) COMPLEX array, dimension (LDU, max(NN)) * The (left) unitary matrix computed by CHGEQZ. * * ALPHA1 (workspace) COMPLEX array, dimension (max(NN)) * BETA1 (workspace) COMPLEX array, dimension (max(NN)) * The generalized eigenvalues of (A,B) computed by CHGEQZ * when Q, Z, and the full Schur matrices are computed. * * ALPHA3 (workspace) COMPLEX array, dimension (max(NN)) * BETA3 (workspace) COMPLEX array, dimension (max(NN)) * The generalized eigenvalues of (A,B) computed by CHGEQZ * when neither Q, Z, nor the Schur matrices are computed. * * EVECTL (workspace) COMPLEX array, dimension (LDU, max(NN)) * The (lower triangular) left eigenvector matrix for the * matrices in S1 and P1. * * EVECTR (workspace) COMPLEX array, dimension (LDU, max(NN)) * The (upper triangular) right eigenvector matrix for the * matrices in S1 and P1. * * WORK (workspace) COMPLEX array, dimension (LWORK) * * LWORK (input) INTEGER * The number of entries in WORK. This must be at least * max( 4*N, 2 * N**2, 1 ), for all N=NN(j). * * RWORK (workspace) REAL array, dimension (2*max(NN)) * * LLWORK (workspace) LOGICAL array, dimension (max(NN)) * * RESULT (output) REAL array, dimension (15) * The values computed by the tests described above. * The values are currently limited to 1/ulp, to avoid * overflow. * * INFO (output) 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. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), $ CONE = ( 1.0E+0, 0.0E+0 ) ) INTEGER MAXTYP PARAMETER ( MAXTYP = 26 ) * .. * .. Local Scalars .. LOGICAL BADNN INTEGER I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE, $ LWKOPT, MTYPES, N, N1, NERRS, NMATS, NMAX, $ NTEST, NTESTT REAL ANORM, BNORM, SAFMAX, SAFMIN, TEMP1, TEMP2, $ ULP, ULPINV COMPLEX CTEMP * .. * .. Local Arrays .. LOGICAL LASIGN( MAXTYP ), LBSIGN( MAXTYP ) INTEGER IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ), $ KATYPE( MAXTYP ), KAZERO( MAXTYP ), $ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ), $ KBZERO( MAXTYP ), KCLASS( MAXTYP ), $ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 ) REAL DUMMA( 4 ), RMAGN( 0: 3 ) COMPLEX CDUMMA( 4 ) * .. * .. External Functions .. REAL CLANGE, SLAMCH COMPLEX CLARND EXTERNAL CLANGE, SLAMCH, CLARND * .. * .. External Subroutines .. EXTERNAL CGEQR2, CGET51, CGET52, CGGHRD, CHGEQZ, CLACPY, $ CLARFG, CLASET, CLATM4, CTGEVC, CUNM2R, SLABAD, $ SLASUM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, CONJG, MAX, MIN, REAL, 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 LASIGN / 6*.FALSE., .TRUE., .FALSE., 2*.TRUE., $ 2*.FALSE., 3*.TRUE., .FALSE., .TRUE., $ 3*.FALSE., 5*.TRUE., .FALSE. / DATA LBSIGN / 7*.FALSE., .TRUE., 2*.FALSE., $ 2*.TRUE., 2*.FALSE., .TRUE., .FALSE., .TRUE., $ 9*.FALSE. / * .. * .. 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 * LWKOPT = MAX( 2*NMAX*NMAX, 4*NMAX, 1 ) * * 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( LDA.LE.1 .OR. LDA.LT.NMAX ) THEN INFO = -10 ELSE IF( LDU.LE.1 .OR. LDU.LT.NMAX ) THEN INFO = -19 ELSE IF( LWKOPT.GT.LWORK ) THEN INFO = -30 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CCHKGG', -INFO ) RETURN END IF * * Quick return if possible * IF( NSIZES.EQ.0 .OR. NTYPES.EQ.0 ) $ RETURN * SAFMIN = SLAMCH( 'Safe minimum' ) ULP = SLAMCH( 'Epsilon' )*SLAMCH( 'Base' ) SAFMIN = SAFMIN / ULP SAFMAX = ONE / SAFMIN CALL SLABAD( SAFMIN, SAFMAX ) 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 240 JSIZE = 1, NSIZES N = NN( JSIZE ) N1 = MAX( 1, N ) RMAGN( 2 ) = SAFMAX*ULP / REAL( N1 ) RMAGN( 3 ) = SAFMIN*ULPINV*N1 * IF( NSIZES.NE.1 ) THEN MTYPES = MIN( MAXTYP, NTYPES ) ELSE MTYPES = MIN( MAXTYP+1, NTYPES ) END IF * DO 230 JTYPE = 1, MTYPES IF( .NOT.DOTYPE( JTYPE ) ) $ GO TO 230 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, 15 RESULT( J ) = ZERO 30 CONTINUE * * Compute A and B * * Description of control parameters: * * KCLASS: =1 means w/o rotation, =2 means w/ rotation, * =3 means random. * KATYPE: the "type" to be passed to CLATM4 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. * LASIGN: .TRUE. if the diagonal elements of A are to be * multiplied by a random magnitude 1 number. * KBTYPE, KBZERO, KBMAGN, LBSIGN: 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 CLASET( 'Full', N, N, CZERO, CZERO, A, LDA ) ELSE IN = N END IF CALL CLATM4( KATYPE( JTYPE ), IN, KZ1( KAZERO( JTYPE ) ), $ KZ2( KAZERO( JTYPE ) ), LASIGN( JTYPE ), $ RMAGN( KAMAGN( JTYPE ) ), ULP, $ RMAGN( KTRIAN( JTYPE )*KAMAGN( JTYPE ) ), 4, $ ISEED, A, LDA ) IADD = KADD( KAZERO( JTYPE ) ) IF( IADD.GT.0 .AND. IADD.LE.N ) $ A( IADD, IADD ) = RMAGN( KAMAGN( JTYPE ) ) * * Generate B (w/o rotation) * IF( ABS( KBTYPE( JTYPE ) ).EQ.3 ) THEN IN = 2*( ( N-1 ) / 2 ) + 1 IF( IN.NE.N ) $ CALL CLASET( 'Full', N, N, CZERO, CZERO, B, LDA ) ELSE IN = N END IF CALL CLATM4( KBTYPE( JTYPE ), IN, KZ1( KBZERO( JTYPE ) ), $ KZ2( KBZERO( JTYPE ) ), LBSIGN( JTYPE ), $ RMAGN( KBMAGN( JTYPE ) ), ONE, $ RMAGN( KTRIAN( JTYPE )*KBMAGN( JTYPE ) ), 4, $ ISEED, B, LDA ) IADD = KADD( KBZERO( JTYPE ) ) IF( IADD.NE.0 ) $ B( IADD, IADD ) = RMAGN( KBMAGN( JTYPE ) ) * IF( KCLASS( JTYPE ).EQ.2 .AND. N.GT.0 ) THEN * * Include rotations * * Generate U, V as Householder transformations times a * diagonal matrix. (Note that CLARFG makes U(j,j) and * V(j,j) real.) * DO 50 JC = 1, N - 1 DO 40 JR = JC, N U( JR, JC ) = CLARND( 3, ISEED ) V( JR, JC ) = CLARND( 3, ISEED ) 40 CONTINUE CALL CLARFG( N+1-JC, U( JC, JC ), U( JC+1, JC ), 1, $ WORK( JC ) ) WORK( 2*N+JC ) = SIGN( ONE, REAL( U( JC, JC ) ) ) U( JC, JC ) = CONE CALL CLARFG( N+1-JC, V( JC, JC ), V( JC+1, JC ), 1, $ WORK( N+JC ) ) WORK( 3*N+JC ) = SIGN( ONE, REAL( V( JC, JC ) ) ) V( JC, JC ) = CONE 50 CONTINUE CTEMP = CLARND( 3, ISEED ) U( N, N ) = CONE WORK( N ) = CZERO WORK( 3*N ) = CTEMP / ABS( CTEMP ) CTEMP = CLARND( 3, ISEED ) V( N, N ) = CONE WORK( 2*N ) = CZERO WORK( 4*N ) = CTEMP / ABS( CTEMP ) * * Apply the diagonal matrices * DO 70 JC = 1, N DO 60 JR = 1, N A( JR, JC ) = WORK( 2*N+JR )* $ CONJG( WORK( 3*N+JC ) )* $ A( JR, JC ) B( JR, JC ) = WORK( 2*N+JR )* $ CONJG( WORK( 3*N+JC ) )* $ B( JR, JC ) 60 CONTINUE 70 CONTINUE CALL CUNM2R( 'L', 'N', N, N, N-1, U, LDU, WORK, A, $ LDA, WORK( 2*N+1 ), IINFO ) IF( IINFO.NE.0 ) $ GO TO 100 CALL CUNM2R( 'R', 'C', N, N, N-1, V, LDU, WORK( N+1 ), $ A, LDA, WORK( 2*N+1 ), IINFO ) IF( IINFO.NE.0 ) $ GO TO 100 CALL CUNM2R( 'L', 'N', N, N, N-1, U, LDU, WORK, B, $ LDA, WORK( 2*N+1 ), IINFO ) IF( IINFO.NE.0 ) $ GO TO 100 CALL CUNM2R( 'R', 'C', N, N, N-1, V, LDU, 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 ) )* $ CLARND( 4, ISEED ) B( JR, JC ) = RMAGN( KBMAGN( JTYPE ) )* $ CLARND( 4, ISEED ) 80 CONTINUE 90 CONTINUE END IF * ANORM = CLANGE( '1', N, N, A, LDA, RWORK ) BNORM = CLANGE( '1', N, N, B, LDA, RWORK ) * 100 CONTINUE * IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'Generator', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) RETURN END IF * 110 CONTINUE * * Call CGEQR2, CUNM2R, and CGGHRD to compute H, T, U, and V * CALL CLACPY( ' ', N, N, A, LDA, H, LDA ) CALL CLACPY( ' ', N, N, B, LDA, T, LDA ) NTEST = 1 RESULT( 1 ) = ULPINV * CALL CGEQR2( N, N, T, LDA, WORK, WORK( N+1 ), IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CGEQR2', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * CALL CUNM2R( 'L', 'C', N, N, N, T, LDA, WORK, H, LDA, $ WORK( N+1 ), IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CUNM2R', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * CALL CLASET( 'Full', N, N, CZERO, CONE, U, LDU ) CALL CUNM2R( 'R', 'N', N, N, N, T, LDA, WORK, U, LDU, $ WORK( N+1 ), IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CUNM2R', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * CALL CGGHRD( 'V', 'I', N, 1, N, H, LDA, T, LDA, U, LDU, V, $ LDU, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CGGHRD', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF NTEST = 4 * * Do tests 1--4 * CALL CGET51( 1, N, A, LDA, H, LDA, U, LDU, V, LDU, WORK, $ RWORK, RESULT( 1 ) ) CALL CGET51( 1, N, B, LDA, T, LDA, U, LDU, V, LDU, WORK, $ RWORK, RESULT( 2 ) ) CALL CGET51( 3, N, B, LDA, T, LDA, U, LDU, U, LDU, WORK, $ RWORK, RESULT( 3 ) ) CALL CGET51( 3, N, B, LDA, T, LDA, V, LDU, V, LDU, WORK, $ RWORK, RESULT( 4 ) ) * * Call CHGEQZ to compute S1, P1, S2, P2, Q, and Z, do tests. * * Compute T1 and UZ * * Eigenvalues only * CALL CLACPY( ' ', N, N, H, LDA, S2, LDA ) CALL CLACPY( ' ', N, N, T, LDA, P2, LDA ) NTEST = 5 RESULT( 5 ) = ULPINV * CALL CHGEQZ( 'E', 'N', 'N', N, 1, N, S2, LDA, P2, LDA, $ ALPHA3, BETA3, Q, LDU, Z, LDU, WORK, LWORK, $ RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CHGEQZ(E)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * * Eigenvalues and Full Schur Form * CALL CLACPY( ' ', N, N, H, LDA, S2, LDA ) CALL CLACPY( ' ', N, N, T, LDA, P2, LDA ) * CALL CHGEQZ( 'S', 'N', 'N', N, 1, N, S2, LDA, P2, LDA, $ ALPHA1, BETA1, Q, LDU, Z, LDU, WORK, LWORK, $ RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CHGEQZ(S)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * * Eigenvalues, Schur Form, and Schur Vectors * CALL CLACPY( ' ', N, N, H, LDA, S1, LDA ) CALL CLACPY( ' ', N, N, T, LDA, P1, LDA ) * CALL CHGEQZ( 'S', 'I', 'I', N, 1, N, S1, LDA, P1, LDA, $ ALPHA1, BETA1, Q, LDU, Z, LDU, WORK, LWORK, $ RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CHGEQZ(V)', IINFO, N, JTYPE, $ IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * NTEST = 8 * * Do Tests 5--8 * CALL CGET51( 1, N, H, LDA, S1, LDA, Q, LDU, Z, LDU, WORK, $ RWORK, RESULT( 5 ) ) CALL CGET51( 1, N, T, LDA, P1, LDA, Q, LDU, Z, LDU, WORK, $ RWORK, RESULT( 6 ) ) CALL CGET51( 3, N, T, LDA, P1, LDA, Q, LDU, Q, LDU, WORK, $ RWORK, RESULT( 7 ) ) CALL CGET51( 3, N, T, LDA, P1, LDA, Z, LDU, Z, LDU, WORK, $ RWORK, RESULT( 8 ) ) * * Compute the Left and Right Eigenvectors of (S1,P1) * * 9: Compute the left eigenvector Matrix without * back transforming: * NTEST = 9 RESULT( 9 ) = ULPINV * * To test "SELECT" option, compute half of the eigenvectors * in one call, and half in another * I1 = N / 2 DO 120 J = 1, I1 LLWORK( J ) = .TRUE. 120 CONTINUE DO 130 J = I1 + 1, N LLWORK( J ) = .FALSE. 130 CONTINUE * CALL CTGEVC( 'L', 'S', LLWORK, N, S1, LDA, P1, LDA, EVECTL, $ LDU, CDUMMA, LDU, N, IN, WORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CTGEVC(L,S1)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * I1 = IN DO 140 J = 1, I1 LLWORK( J ) = .FALSE. 140 CONTINUE DO 150 J = I1 + 1, N LLWORK( J ) = .TRUE. 150 CONTINUE * CALL CTGEVC( 'L', 'S', LLWORK, N, S1, LDA, P1, LDA, $ EVECTL( 1, I1+1 ), LDU, CDUMMA, LDU, N, IN, $ WORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CTGEVC(L,S2)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * CALL CGET52( .TRUE., N, S1, LDA, P1, LDA, EVECTL, LDU, $ ALPHA1, BETA1, WORK, RWORK, DUMMA( 1 ) ) RESULT( 9 ) = DUMMA( 1 ) IF( DUMMA( 2 ).GT.THRSHN ) THEN WRITE( NOUNIT, FMT = 9998 )'Left', 'CTGEVC(HOWMNY=S)', $ DUMMA( 2 ), N, JTYPE, IOLDSD END IF * * 10: Compute the left eigenvector Matrix with * back transforming: * NTEST = 10 RESULT( 10 ) = ULPINV CALL CLACPY( 'F', N, N, Q, LDU, EVECTL, LDU ) CALL CTGEVC( 'L', 'B', LLWORK, N, S1, LDA, P1, LDA, EVECTL, $ LDU, CDUMMA, LDU, N, IN, WORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CTGEVC(L,B)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * CALL CGET52( .TRUE., N, H, LDA, T, LDA, EVECTL, LDU, ALPHA1, $ BETA1, WORK, RWORK, DUMMA( 1 ) ) RESULT( 10 ) = DUMMA( 1 ) IF( DUMMA( 2 ).GT.THRSHN ) THEN WRITE( NOUNIT, FMT = 9998 )'Left', 'CTGEVC(HOWMNY=B)', $ DUMMA( 2 ), N, JTYPE, IOLDSD END IF * * 11: Compute the right eigenvector Matrix without * back transforming: * NTEST = 11 RESULT( 11 ) = ULPINV * * To test "SELECT" option, compute half of the eigenvectors * in one call, and half in another * I1 = N / 2 DO 160 J = 1, I1 LLWORK( J ) = .TRUE. 160 CONTINUE DO 170 J = I1 + 1, N LLWORK( J ) = .FALSE. 170 CONTINUE * CALL CTGEVC( 'R', 'S', LLWORK, N, S1, LDA, P1, LDA, CDUMMA, $ LDU, EVECTR, LDU, N, IN, WORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CTGEVC(R,S1)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * I1 = IN DO 180 J = 1, I1 LLWORK( J ) = .FALSE. 180 CONTINUE DO 190 J = I1 + 1, N LLWORK( J ) = .TRUE. 190 CONTINUE * CALL CTGEVC( 'R', 'S', LLWORK, N, S1, LDA, P1, LDA, CDUMMA, $ LDU, EVECTR( 1, I1+1 ), LDU, N, IN, WORK, $ RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CTGEVC(R,S2)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * CALL CGET52( .FALSE., N, S1, LDA, P1, LDA, EVECTR, LDU, $ ALPHA1, BETA1, WORK, RWORK, DUMMA( 1 ) ) RESULT( 11 ) = DUMMA( 1 ) IF( DUMMA( 2 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Right', 'CTGEVC(HOWMNY=S)', $ DUMMA( 2 ), N, JTYPE, IOLDSD END IF * * 12: Compute the right eigenvector Matrix with * back transforming: * NTEST = 12 RESULT( 12 ) = ULPINV CALL CLACPY( 'F', N, N, Z, LDU, EVECTR, LDU ) CALL CTGEVC( 'R', 'B', LLWORK, N, S1, LDA, P1, LDA, CDUMMA, $ LDU, EVECTR, LDU, N, IN, WORK, RWORK, IINFO ) IF( IINFO.NE.0 ) THEN WRITE( NOUNIT, FMT = 9999 )'CTGEVC(R,B)', IINFO, N, $ JTYPE, IOLDSD INFO = ABS( IINFO ) GO TO 210 END IF * CALL CGET52( .FALSE., N, H, LDA, T, LDA, EVECTR, LDU, $ ALPHA1, BETA1, WORK, RWORK, DUMMA( 1 ) ) RESULT( 12 ) = DUMMA( 1 ) IF( DUMMA( 2 ).GT.THRESH ) THEN WRITE( NOUNIT, FMT = 9998 )'Right', 'CTGEVC(HOWMNY=B)', $ DUMMA( 2 ), N, JTYPE, IOLDSD END IF * * Tests 13--15 are done only on request * IF( TSTDIF ) THEN * * Do Tests 13--14 * CALL CGET51( 2, N, S1, LDA, S2, LDA, Q, LDU, Z, LDU, $ WORK, RWORK, RESULT( 13 ) ) CALL CGET51( 2, N, P1, LDA, P2, LDA, Q, LDU, Z, LDU, $ WORK, RWORK, RESULT( 14 ) ) * * Do Test 15 * TEMP1 = ZERO TEMP2 = ZERO DO 200 J = 1, N TEMP1 = MAX( TEMP1, ABS( ALPHA1( J )-ALPHA3( J ) ) ) TEMP2 = MAX( TEMP2, ABS( BETA1( J )-BETA3( J ) ) ) 200 CONTINUE * TEMP1 = TEMP1 / MAX( SAFMIN, ULP*MAX( TEMP1, ANORM ) ) TEMP2 = TEMP2 / MAX( SAFMIN, ULP*MAX( TEMP2, BNORM ) ) RESULT( 15 ) = MAX( TEMP1, TEMP2 ) NTEST = 15 ELSE RESULT( 13 ) = ZERO RESULT( 14 ) = ZERO RESULT( 15 ) = ZERO NTEST = 12 END IF * * End of Loop -- Check for RESULT(j) > THRESH * 210 CONTINUE * NTESTT = NTESTT + NTEST * * Print out tests which fail. * DO 220 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 = 9997 )'CGG' * * Matrix types * WRITE( NOUNIT, FMT = 9996 ) WRITE( NOUNIT, FMT = 9995 ) WRITE( NOUNIT, FMT = 9994 )'Unitary' * * Tests performed * WRITE( NOUNIT, FMT = 9993 )'unitary', '*', $ 'conjugate transpose', ( '*', J = 1, 10 ) * END IF NERRS = NERRS + 1 IF( RESULT( JR ).LT.10000.0 ) 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 220 CONTINUE * 230 CONTINUE 240 CONTINUE * * Summary * CALL SLASUM( 'CGG', NOUNIT, NERRS, NTESTT ) RETURN * 9999 FORMAT( ' CCHKGG: ', A, ' returned INFO=', I6, '.', / 9X, 'N=', $ I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, ')' ) * 9998 FORMAT( ' CCHKGG: ', A, ' Eigenvectors from ', A, ' incorrectly ', $ 'normalized.', / ' Bits of error=', 0P, G10.3, ',', 9X, $ 'N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ), I5, $ ')' ) * 9997 FORMAT( 1X, A3, ' -- Complex Generalized eigenvalue problem' ) * 9996 FORMAT( ' Matrix types (see CCHKGG 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: (H is Hessenberg, S is Schur, B, ', $ 'T, P are triangular,', / 20X, 'U, V, Q, and Z are ', A, $ ', l and r are the', / 20X, $ 'appropriate left and right eigenvectors, resp., a is', $ / 20X, 'alpha, b is beta, and ', A, ' means ', A, '.)', $ / ' 1 = | A - U H V', A, $ ' | / ( |A| n ulp ) 2 = | B - U T V', A, $ ' | / ( |B| n ulp )', / ' 3 = | I - UU', A, $ ' | / ( n ulp ) 4 = | I - VV', A, $ ' | / ( n ulp )', / ' 5 = | H - Q S Z', A, $ ' | / ( |H| n ulp )', 6X, '6 = | T - Q P Z', A, $ ' | / ( |T| n ulp )', / ' 7 = | I - QQ', A, $ ' | / ( n ulp ) 8 = | I - ZZ', A, $ ' | / ( n ulp )', / ' 9 = max | ( b S - a P )', A, $ ' l | / const. 10 = max | ( b H - a T )', A, $ ' l | / const.', / $ ' 11= max | ( b S - a P ) r | / const. 12 = max | ( b H', $ ' - a T ) r | / const.', / 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, E10.3 ) * * End of CCHKGG * END |