 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ cchkgg()

 subroutine cchkgg ( integer NSIZES, integer, dimension( * ) NN, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, real THRESH, logical TSTDIF, real THRSHN, integer NOUNIT, complex, dimension( lda, * ) A, integer LDA, complex, dimension( lda, * ) B, complex, dimension( lda, * ) H, complex, dimension( lda, * ) T, complex, dimension( lda, * ) S1, complex, dimension( lda, * ) S2, complex, dimension( lda, * ) P1, complex, dimension( lda, * ) P2, complex, dimension( ldu, * ) U, integer LDU, complex, dimension( ldu, * ) V, complex, dimension( ldu, * ) Q, complex, dimension( ldu, * ) Z, complex, dimension( * ) ALPHA1, complex, dimension( * ) BETA1, complex, dimension( * ) ALPHA3, complex, dimension( * ) BETA3, complex, dimension( ldu, * ) EVECTL, complex, dimension( ldu, * ) EVECTR, complex, dimension( * ) WORK, integer LWORK, real, dimension( * ) RWORK, logical, dimension( * ) LLWORK, real, dimension( 15 ) RESULT, integer INFO )

CCHKGG

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 threshold 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 threshold 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.
Parameters
 [in] NSIZES NSIZES is INTEGER The number of sizes of matrices to use. If it is zero, CCHKGG does nothing. It must be at least zero. [in] NN 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. [in] NTYPES NTYPES is 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. . [in] DOTYPE 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. [in,out] ISEED 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 CCHKGG to continue the same random number sequence. [in] THRESH 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. [in] TSTDIF TSTDIF is 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. [in] THRSHN THRSHN is REAL Threshold 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.) [in] NOUNIT NOUNIT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.) [in,out] A A is 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. [in] LDA LDA is 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 ). [in,out] B B is 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. [out] H H is COMPLEX array, dimension (LDA, max(NN)) The upper Hessenberg matrix computed from A by CGGHRD. [out] T T is COMPLEX array, dimension (LDA, max(NN)) The upper triangular matrix computed from B by CGGHRD. [out] S1 S1 is COMPLEX array, dimension (LDA, max(NN)) The Schur (upper triangular) matrix computed from H by CHGEQZ when Q and Z are also computed. [out] S2 S2 is COMPLEX array, dimension (LDA, max(NN)) The Schur (upper triangular) matrix computed from H by CHGEQZ when Q and Z are not computed. [out] P1 P1 is COMPLEX array, dimension (LDA, max(NN)) The upper triangular matrix computed from T by CHGEQZ when Q and Z are also computed. [out] P2 P2 is COMPLEX array, dimension (LDA, max(NN)) The upper triangular matrix computed from T by CHGEQZ when Q and Z are not computed. [out] U U is COMPLEX array, dimension (LDU, max(NN)) The (left) unitary matrix computed by CGGHRD. [in] LDU LDU is INTEGER The leading dimension of U, V, Q, Z, EVECTL, and EVECTR. It must be at least 1 and at least max( NN ). [out] V V is COMPLEX array, dimension (LDU, max(NN)) The (right) unitary matrix computed by CGGHRD. [out] Q Q is COMPLEX array, dimension (LDU, max(NN)) The (left) unitary matrix computed by CHGEQZ. [out] Z Z is COMPLEX array, dimension (LDU, max(NN)) The (left) unitary matrix computed by CHGEQZ. [out] ALPHA1 ALPHA1 is COMPLEX array, dimension (max(NN)) [out] BETA1 BETA1 is COMPLEX array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by CHGEQZ when Q, Z, and the full Schur matrices are computed. [out] ALPHA3 ALPHA3 is COMPLEX array, dimension (max(NN)) [out] BETA3 BETA3 is COMPLEX array, dimension (max(NN)) The generalized eigenvalues of (A,B) computed by CHGEQZ when neither Q, Z, nor the Schur matrices are computed. [out] EVECTL EVECTL is COMPLEX array, dimension (LDU, max(NN)) The (lower triangular) left eigenvector matrix for the matrices in S1 and P1. [out] EVECTR EVECTR is COMPLEX array, dimension (LDU, max(NN)) The (upper triangular) right eigenvector matrix for the matrices in S1 and P1. [out] WORK WORK is COMPLEX array, dimension (LWORK) [in] LWORK LWORK is INTEGER The number of entries in WORK. This must be at least max( 4*N, 2 * N**2, 1 ), for all N=NN(j). [out] RWORK RWORK is REAL array, dimension (2*max(NN)) [out] LLWORK LLWORK is LOGICAL array, dimension (max(NN)) [out] RESULT RESULT is REAL array, dimension (15) The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow. [out] INFO 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.

Definition at line 498 of file cchkgg.f.

503 *
504 * -- LAPACK test routine --
505 * -- LAPACK is a software package provided by Univ. of Tennessee, --
506 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
507 *
508 * .. Scalar Arguments ..
509  LOGICAL TSTDIF
510  INTEGER INFO, LDA, LDU, LWORK, NOUNIT, NSIZES, NTYPES
511  REAL THRESH, THRSHN
512 * ..
513 * .. Array Arguments ..
514  LOGICAL DOTYPE( * ), LLWORK( * )
515  INTEGER ISEED( 4 ), NN( * )
516  REAL RESULT( 15 ), RWORK( * )
517  COMPLEX A( LDA, * ), ALPHA1( * ), ALPHA3( * ),
518  \$ B( LDA, * ), BETA1( * ), BETA3( * ),
519  \$ EVECTL( LDU, * ), EVECTR( LDU, * ),
520  \$ H( LDA, * ), P1( LDA, * ), P2( LDA, * ),
521  \$ Q( LDU, * ), S1( LDA, * ), S2( LDA, * ),
522  \$ T( LDA, * ), U( LDU, * ), V( LDU, * ),
523  \$ WORK( * ), Z( LDU, * )
524 * ..
525 *
526 * =====================================================================
527 *
528 * .. Parameters ..
529  REAL ZERO, ONE
530  parameter( zero = 0.0e+0, one = 1.0e+0 )
531  COMPLEX CZERO, CONE
532  parameter( czero = ( 0.0e+0, 0.0e+0 ),
533  \$ cone = ( 1.0e+0, 0.0e+0 ) )
534  INTEGER MAXTYP
535  parameter( maxtyp = 26 )
536 * ..
537 * .. Local Scalars ..
539  INTEGER I1, IADD, IINFO, IN, J, JC, JR, JSIZE, JTYPE,
540  \$ LWKOPT, MTYPES, N, N1, NERRS, NMATS, NMAX,
541  \$ NTEST, NTESTT
542  REAL ANORM, BNORM, SAFMAX, SAFMIN, TEMP1, TEMP2,
543  \$ ULP, ULPINV
544  COMPLEX CTEMP
545 * ..
546 * .. Local Arrays ..
547  LOGICAL LASIGN( MAXTYP ), LBSIGN( MAXTYP )
548  INTEGER IOLDSD( 4 ), KADD( 6 ), KAMAGN( MAXTYP ),
549  \$ KATYPE( MAXTYP ), KAZERO( MAXTYP ),
550  \$ KBMAGN( MAXTYP ), KBTYPE( MAXTYP ),
551  \$ KBZERO( MAXTYP ), KCLASS( MAXTYP ),
552  \$ KTRIAN( MAXTYP ), KZ1( 6 ), KZ2( 6 )
553  REAL DUMMA( 4 ), RMAGN( 0: 3 )
554  COMPLEX CDUMMA( 4 )
555 * ..
556 * .. External Functions ..
557  REAL CLANGE, SLAMCH
558  COMPLEX CLARND
559  EXTERNAL clange, slamch, clarnd
560 * ..
561 * .. External Subroutines ..
562  EXTERNAL cgeqr2, cget51, cget52, cgghrd, chgeqz, clacpy,
564  \$ slasum, xerbla
565 * ..
566 * .. Intrinsic Functions ..
567  INTRINSIC abs, conjg, max, min, real, sign
568 * ..
569 * .. Data statements ..
570  DATA kclass / 15*1, 10*2, 1*3 /
571  DATA kz1 / 0, 1, 2, 1, 3, 3 /
572  DATA kz2 / 0, 0, 1, 2, 1, 1 /
573  DATA kadd / 0, 0, 0, 0, 3, 2 /
574  DATA katype / 0, 1, 0, 1, 2, 3, 4, 1, 4, 4, 1, 1, 4,
575  \$ 4, 4, 2, 4, 5, 8, 7, 9, 4*4, 0 /
576  DATA kbtype / 0, 0, 1, 1, 2, -3, 1, 4, 1, 1, 4, 4,
577  \$ 1, 1, -4, 2, -4, 8*8, 0 /
578  DATA kazero / 6*1, 2, 1, 2*2, 2*1, 2*2, 3, 1, 3,
579  \$ 4*5, 4*3, 1 /
580  DATA kbzero / 6*1, 1, 2, 2*1, 2*2, 2*1, 4, 1, 4,
581  \$ 4*6, 4*4, 1 /
582  DATA kamagn / 8*1, 2, 3, 2, 3, 2, 3, 7*1, 2, 3, 3,
583  \$ 2, 1 /
584  DATA kbmagn / 8*1, 3, 2, 3, 2, 2, 3, 7*1, 3, 2, 3,
585  \$ 2, 1 /
586  DATA ktrian / 16*0, 10*1 /
587  DATA lasign / 6*.false., .true., .false., 2*.true.,
588  \$ 2*.false., 3*.true., .false., .true.,
589  \$ 3*.false., 5*.true., .false. /
590  DATA lbsign / 7*.false., .true., 2*.false.,
591  \$ 2*.true., 2*.false., .true., .false., .true.,
592  \$ 9*.false. /
593 * ..
594 * .. Executable Statements ..
595 *
596 * Check for errors
597 *
598  info = 0
599 *
601  nmax = 1
602  DO 10 j = 1, nsizes
603  nmax = max( nmax, nn( j ) )
604  IF( nn( j ).LT.0 )
606  10 CONTINUE
607 *
608  lwkopt = max( 2*nmax*nmax, 4*nmax, 1 )
609 *
610 * Check for errors
611 *
612  IF( nsizes.LT.0 ) THEN
613  info = -1
614  ELSE IF( badnn ) THEN
615  info = -2
616  ELSE IF( ntypes.LT.0 ) THEN
617  info = -3
618  ELSE IF( thresh.LT.zero ) THEN
619  info = -6
620  ELSE IF( lda.LE.1 .OR. lda.LT.nmax ) THEN
621  info = -10
622  ELSE IF( ldu.LE.1 .OR. ldu.LT.nmax ) THEN
623  info = -19
624  ELSE IF( lwkopt.GT.lwork ) THEN
625  info = -30
626  END IF
627 *
628  IF( info.NE.0 ) THEN
629  CALL xerbla( 'CCHKGG', -info )
630  RETURN
631  END IF
632 *
633 * Quick return if possible
634 *
635  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
636  \$ RETURN
637 *
638  safmin = slamch( 'Safe minimum' )
639  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
640  safmin = safmin / ulp
641  safmax = one / safmin
642  CALL slabad( safmin, safmax )
643  ulpinv = one / ulp
644 *
645 * The values RMAGN(2:3) depend on N, see below.
646 *
647  rmagn( 0 ) = zero
648  rmagn( 1 ) = one
649 *
650 * Loop over sizes, types
651 *
652  ntestt = 0
653  nerrs = 0
654  nmats = 0
655 *
656  DO 240 jsize = 1, nsizes
657  n = nn( jsize )
658  n1 = max( 1, n )
659  rmagn( 2 ) = safmax*ulp / real( n1 )
660  rmagn( 3 ) = safmin*ulpinv*n1
661 *
662  IF( nsizes.NE.1 ) THEN
663  mtypes = min( maxtyp, ntypes )
664  ELSE
665  mtypes = min( maxtyp+1, ntypes )
666  END IF
667 *
668  DO 230 jtype = 1, mtypes
669  IF( .NOT.dotype( jtype ) )
670  \$ GO TO 230
671  nmats = nmats + 1
672  ntest = 0
673 *
674 * Save ISEED in case of an error.
675 *
676  DO 20 j = 1, 4
677  ioldsd( j ) = iseed( j )
678  20 CONTINUE
679 *
680 * Initialize RESULT
681 *
682  DO 30 j = 1, 15
683  result( j ) = zero
684  30 CONTINUE
685 *
686 * Compute A and B
687 *
688 * Description of control parameters:
689 *
690 * KCLASS: =1 means w/o rotation, =2 means w/ rotation,
691 * =3 means random.
692 * KATYPE: the "type" to be passed to CLATM4 for computing A.
693 * KAZERO: the pattern of zeros on the diagonal for A:
694 * =1: ( xxx ), =2: (0, xxx ) =3: ( 0, 0, xxx, 0 ),
695 * =4: ( 0, xxx, 0, 0 ), =5: ( 0, 0, 1, xxx, 0 ),
696 * =6: ( 0, 1, 0, xxx, 0 ). (xxx means a string of
697 * non-zero entries.)
698 * KAMAGN: the magnitude of the matrix: =0: zero, =1: O(1),
699 * =2: large, =3: small.
700 * LASIGN: .TRUE. if the diagonal elements of A are to be
701 * multiplied by a random magnitude 1 number.
702 * KBTYPE, KBZERO, KBMAGN, LBSIGN: the same, but for B.
703 * KTRIAN: =0: don't fill in the upper triangle, =1: do.
704 * KZ1, KZ2, KADD: used to implement KAZERO and KBZERO.
705 * RMAGN: used to implement KAMAGN and KBMAGN.
706 *
707  IF( mtypes.GT.maxtyp )
708  \$ GO TO 110
709  iinfo = 0
710  IF( kclass( jtype ).LT.3 ) THEN
711 *
712 * Generate A (w/o rotation)
713 *
714  IF( abs( katype( jtype ) ).EQ.3 ) THEN
715  in = 2*( ( n-1 ) / 2 ) + 1
716  IF( in.NE.n )
717  \$ CALL claset( 'Full', n, n, czero, czero, a, lda )
718  ELSE
719  in = n
720  END IF
721  CALL clatm4( katype( jtype ), in, kz1( kazero( jtype ) ),
722  \$ kz2( kazero( jtype ) ), lasign( jtype ),
723  \$ rmagn( kamagn( jtype ) ), ulp,
724  \$ rmagn( ktrian( jtype )*kamagn( jtype ) ), 4,
725  \$ iseed, a, lda )
728  \$ a( iadd, iadd ) = rmagn( kamagn( jtype ) )
729 *
730 * Generate B (w/o rotation)
731 *
732  IF( abs( kbtype( jtype ) ).EQ.3 ) THEN
733  in = 2*( ( n-1 ) / 2 ) + 1
734  IF( in.NE.n )
735  \$ CALL claset( 'Full', n, n, czero, czero, b, lda )
736  ELSE
737  in = n
738  END IF
739  CALL clatm4( kbtype( jtype ), in, kz1( kbzero( jtype ) ),
740  \$ kz2( kbzero( jtype ) ), lbsign( jtype ),
741  \$ rmagn( kbmagn( jtype ) ), one,
742  \$ rmagn( ktrian( jtype )*kbmagn( jtype ) ), 4,
743  \$ iseed, b, lda )
746  \$ b( iadd, iadd ) = rmagn( kbmagn( jtype ) )
747 *
748  IF( kclass( jtype ).EQ.2 .AND. n.GT.0 ) THEN
749 *
750 * Include rotations
751 *
752 * Generate U, V as Householder transformations times a
753 * diagonal matrix. (Note that CLARFG makes U(j,j) and
754 * V(j,j) real.)
755 *
756  DO 50 jc = 1, n - 1
757  DO 40 jr = jc, n
758  u( jr, jc ) = clarnd( 3, iseed )
759  v( jr, jc ) = clarnd( 3, iseed )
760  40 CONTINUE
761  CALL clarfg( n+1-jc, u( jc, jc ), u( jc+1, jc ), 1,
762  \$ work( jc ) )
763  work( 2*n+jc ) = sign( one, real( u( jc, jc ) ) )
764  u( jc, jc ) = cone
765  CALL clarfg( n+1-jc, v( jc, jc ), v( jc+1, jc ), 1,
766  \$ work( n+jc ) )
767  work( 3*n+jc ) = sign( one, real( v( jc, jc ) ) )
768  v( jc, jc ) = cone
769  50 CONTINUE
770  ctemp = clarnd( 3, iseed )
771  u( n, n ) = cone
772  work( n ) = czero
773  work( 3*n ) = ctemp / abs( ctemp )
774  ctemp = clarnd( 3, iseed )
775  v( n, n ) = cone
776  work( 2*n ) = czero
777  work( 4*n ) = ctemp / abs( ctemp )
778 *
779 * Apply the diagonal matrices
780 *
781  DO 70 jc = 1, n
782  DO 60 jr = 1, n
783  a( jr, jc ) = work( 2*n+jr )*
784  \$ conjg( work( 3*n+jc ) )*
785  \$ a( jr, jc )
786  b( jr, jc ) = work( 2*n+jr )*
787  \$ conjg( work( 3*n+jc ) )*
788  \$ b( jr, jc )
789  60 CONTINUE
790  70 CONTINUE
791  CALL cunm2r( 'L', 'N', n, n, n-1, u, ldu, work, a,
792  \$ lda, work( 2*n+1 ), iinfo )
793  IF( iinfo.NE.0 )
794  \$ GO TO 100
795  CALL cunm2r( 'R', 'C', n, n, n-1, v, ldu, work( n+1 ),
796  \$ a, lda, work( 2*n+1 ), iinfo )
797  IF( iinfo.NE.0 )
798  \$ GO TO 100
799  CALL cunm2r( 'L', 'N', n, n, n-1, u, ldu, work, b,
800  \$ lda, work( 2*n+1 ), iinfo )
801  IF( iinfo.NE.0 )
802  \$ GO TO 100
803  CALL cunm2r( 'R', 'C', n, n, n-1, v, ldu, work( n+1 ),
804  \$ b, lda, work( 2*n+1 ), iinfo )
805  IF( iinfo.NE.0 )
806  \$ GO TO 100
807  END IF
808  ELSE
809 *
810 * Random matrices
811 *
812  DO 90 jc = 1, n
813  DO 80 jr = 1, n
814  a( jr, jc ) = rmagn( kamagn( jtype ) )*
815  \$ clarnd( 4, iseed )
816  b( jr, jc ) = rmagn( kbmagn( jtype ) )*
817  \$ clarnd( 4, iseed )
818  80 CONTINUE
819  90 CONTINUE
820  END IF
821 *
822  anorm = clange( '1', n, n, a, lda, rwork )
823  bnorm = clange( '1', n, n, b, lda, rwork )
824 *
825  100 CONTINUE
826 *
827  IF( iinfo.NE.0 ) THEN
828  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n, jtype,
829  \$ ioldsd
830  info = abs( iinfo )
831  RETURN
832  END IF
833 *
834  110 CONTINUE
835 *
836 * Call CGEQR2, CUNM2R, and CGGHRD to compute H, T, U, and V
837 *
838  CALL clacpy( ' ', n, n, a, lda, h, lda )
839  CALL clacpy( ' ', n, n, b, lda, t, lda )
840  ntest = 1
841  result( 1 ) = ulpinv
842 *
843  CALL cgeqr2( n, n, t, lda, work, work( n+1 ), iinfo )
844  IF( iinfo.NE.0 ) THEN
845  WRITE( nounit, fmt = 9999 )'CGEQR2', iinfo, n, jtype,
846  \$ ioldsd
847  info = abs( iinfo )
848  GO TO 210
849  END IF
850 *
851  CALL cunm2r( 'L', 'C', n, n, n, t, lda, work, h, lda,
852  \$ work( n+1 ), iinfo )
853  IF( iinfo.NE.0 ) THEN
854  WRITE( nounit, fmt = 9999 )'CUNM2R', iinfo, n, jtype,
855  \$ ioldsd
856  info = abs( iinfo )
857  GO TO 210
858  END IF
859 *
860  CALL claset( 'Full', n, n, czero, cone, u, ldu )
861  CALL cunm2r( 'R', 'N', n, n, n, t, lda, work, u, ldu,
862  \$ work( n+1 ), iinfo )
863  IF( iinfo.NE.0 ) THEN
864  WRITE( nounit, fmt = 9999 )'CUNM2R', iinfo, n, jtype,
865  \$ ioldsd
866  info = abs( iinfo )
867  GO TO 210
868  END IF
869 *
870  CALL cgghrd( 'V', 'I', n, 1, n, h, lda, t, lda, u, ldu, v,
871  \$ ldu, iinfo )
872  IF( iinfo.NE.0 ) THEN
873  WRITE( nounit, fmt = 9999 )'CGGHRD', iinfo, n, jtype,
874  \$ ioldsd
875  info = abs( iinfo )
876  GO TO 210
877  END IF
878  ntest = 4
879 *
880 * Do tests 1--4
881 *
882  CALL cget51( 1, n, a, lda, h, lda, u, ldu, v, ldu, work,
883  \$ rwork, result( 1 ) )
884  CALL cget51( 1, n, b, lda, t, lda, u, ldu, v, ldu, work,
885  \$ rwork, result( 2 ) )
886  CALL cget51( 3, n, b, lda, t, lda, u, ldu, u, ldu, work,
887  \$ rwork, result( 3 ) )
888  CALL cget51( 3, n, b, lda, t, lda, v, ldu, v, ldu, work,
889  \$ rwork, result( 4 ) )
890 *
891 * Call CHGEQZ to compute S1, P1, S2, P2, Q, and Z, do tests.
892 *
893 * Compute T1 and UZ
894 *
895 * Eigenvalues only
896 *
897  CALL clacpy( ' ', n, n, h, lda, s2, lda )
898  CALL clacpy( ' ', n, n, t, lda, p2, lda )
899  ntest = 5
900  result( 5 ) = ulpinv
901 *
902  CALL chgeqz( 'E', 'N', 'N', n, 1, n, s2, lda, p2, lda,
903  \$ alpha3, beta3, q, ldu, z, ldu, work, lwork,
904  \$ rwork, iinfo )
905  IF( iinfo.NE.0 ) THEN
906  WRITE( nounit, fmt = 9999 )'CHGEQZ(E)', iinfo, n, jtype,
907  \$ ioldsd
908  info = abs( iinfo )
909  GO TO 210
910  END IF
911 *
912 * Eigenvalues and Full Schur Form
913 *
914  CALL clacpy( ' ', n, n, h, lda, s2, lda )
915  CALL clacpy( ' ', n, n, t, lda, p2, lda )
916 *
917  CALL chgeqz( 'S', 'N', 'N', n, 1, n, s2, lda, p2, lda,
918  \$ alpha1, beta1, q, ldu, z, ldu, work, lwork,
919  \$ rwork, iinfo )
920  IF( iinfo.NE.0 ) THEN
921  WRITE( nounit, fmt = 9999 )'CHGEQZ(S)', iinfo, n, jtype,
922  \$ ioldsd
923  info = abs( iinfo )
924  GO TO 210
925  END IF
926 *
927 * Eigenvalues, Schur Form, and Schur Vectors
928 *
929  CALL clacpy( ' ', n, n, h, lda, s1, lda )
930  CALL clacpy( ' ', n, n, t, lda, p1, lda )
931 *
932  CALL chgeqz( 'S', 'I', 'I', n, 1, n, s1, lda, p1, lda,
933  \$ alpha1, beta1, q, ldu, z, ldu, work, lwork,
934  \$ rwork, iinfo )
935  IF( iinfo.NE.0 ) THEN
936  WRITE( nounit, fmt = 9999 )'CHGEQZ(V)', iinfo, n, jtype,
937  \$ ioldsd
938  info = abs( iinfo )
939  GO TO 210
940  END IF
941 *
942  ntest = 8
943 *
944 * Do Tests 5--8
945 *
946  CALL cget51( 1, n, h, lda, s1, lda, q, ldu, z, ldu, work,
947  \$ rwork, result( 5 ) )
948  CALL cget51( 1, n, t, lda, p1, lda, q, ldu, z, ldu, work,
949  \$ rwork, result( 6 ) )
950  CALL cget51( 3, n, t, lda, p1, lda, q, ldu, q, ldu, work,
951  \$ rwork, result( 7 ) )
952  CALL cget51( 3, n, t, lda, p1, lda, z, ldu, z, ldu, work,
953  \$ rwork, result( 8 ) )
954 *
955 * Compute the Left and Right Eigenvectors of (S1,P1)
956 *
957 * 9: Compute the left eigenvector Matrix without
958 * back transforming:
959 *
960  ntest = 9
961  result( 9 ) = ulpinv
962 *
963 * To test "SELECT" option, compute half of the eigenvectors
964 * in one call, and half in another
965 *
966  i1 = n / 2
967  DO 120 j = 1, i1
968  llwork( j ) = .true.
969  120 CONTINUE
970  DO 130 j = i1 + 1, n
971  llwork( j ) = .false.
972  130 CONTINUE
973 *
974  CALL ctgevc( 'L', 'S', llwork, n, s1, lda, p1, lda, evectl,
975  \$ ldu, cdumma, ldu, n, in, work, rwork, iinfo )
976  IF( iinfo.NE.0 ) THEN
977  WRITE( nounit, fmt = 9999 )'CTGEVC(L,S1)', iinfo, n,
978  \$ jtype, ioldsd
979  info = abs( iinfo )
980  GO TO 210
981  END IF
982 *
983  i1 = in
984  DO 140 j = 1, i1
985  llwork( j ) = .false.
986  140 CONTINUE
987  DO 150 j = i1 + 1, n
988  llwork( j ) = .true.
989  150 CONTINUE
990 *
991  CALL ctgevc( 'L', 'S', llwork, n, s1, lda, p1, lda,
992  \$ evectl( 1, i1+1 ), ldu, cdumma, ldu, n, in,
993  \$ work, rwork, iinfo )
994  IF( iinfo.NE.0 ) THEN
995  WRITE( nounit, fmt = 9999 )'CTGEVC(L,S2)', iinfo, n,
996  \$ jtype, ioldsd
997  info = abs( iinfo )
998  GO TO 210
999  END IF
1000 *
1001  CALL cget52( .true., n, s1, lda, p1, lda, evectl, ldu,
1002  \$ alpha1, beta1, work, rwork, dumma( 1 ) )
1003  result( 9 ) = dumma( 1 )
1004  IF( dumma( 2 ).GT.thrshn ) THEN
1005  WRITE( nounit, fmt = 9998 )'Left', 'CTGEVC(HOWMNY=S)',
1006  \$ dumma( 2 ), n, jtype, ioldsd
1007  END IF
1008 *
1009 * 10: Compute the left eigenvector Matrix with
1010 * back transforming:
1011 *
1012  ntest = 10
1013  result( 10 ) = ulpinv
1014  CALL clacpy( 'F', n, n, q, ldu, evectl, ldu )
1015  CALL ctgevc( 'L', 'B', llwork, n, s1, lda, p1, lda, evectl,
1016  \$ ldu, cdumma, ldu, n, in, work, rwork, iinfo )
1017  IF( iinfo.NE.0 ) THEN
1018  WRITE( nounit, fmt = 9999 )'CTGEVC(L,B)', iinfo, n,
1019  \$ jtype, ioldsd
1020  info = abs( iinfo )
1021  GO TO 210
1022  END IF
1023 *
1024  CALL cget52( .true., n, h, lda, t, lda, evectl, ldu, alpha1,
1025  \$ beta1, work, rwork, dumma( 1 ) )
1026  result( 10 ) = dumma( 1 )
1027  IF( dumma( 2 ).GT.thrshn ) THEN
1028  WRITE( nounit, fmt = 9998 )'Left', 'CTGEVC(HOWMNY=B)',
1029  \$ dumma( 2 ), n, jtype, ioldsd
1030  END IF
1031 *
1032 * 11: Compute the right eigenvector Matrix without
1033 * back transforming:
1034 *
1035  ntest = 11
1036  result( 11 ) = ulpinv
1037 *
1038 * To test "SELECT" option, compute half of the eigenvectors
1039 * in one call, and half in another
1040 *
1041  i1 = n / 2
1042  DO 160 j = 1, i1
1043  llwork( j ) = .true.
1044  160 CONTINUE
1045  DO 170 j = i1 + 1, n
1046  llwork( j ) = .false.
1047  170 CONTINUE
1048 *
1049  CALL ctgevc( 'R', 'S', llwork, n, s1, lda, p1, lda, cdumma,
1050  \$ ldu, evectr, ldu, n, in, work, rwork, iinfo )
1051  IF( iinfo.NE.0 ) THEN
1052  WRITE( nounit, fmt = 9999 )'CTGEVC(R,S1)', iinfo, n,
1053  \$ jtype, ioldsd
1054  info = abs( iinfo )
1055  GO TO 210
1056  END IF
1057 *
1058  i1 = in
1059  DO 180 j = 1, i1
1060  llwork( j ) = .false.
1061  180 CONTINUE
1062  DO 190 j = i1 + 1, n
1063  llwork( j ) = .true.
1064  190 CONTINUE
1065 *
1066  CALL ctgevc( 'R', 'S', llwork, n, s1, lda, p1, lda, cdumma,
1067  \$ ldu, evectr( 1, i1+1 ), ldu, n, in, work,
1068  \$ rwork, iinfo )
1069  IF( iinfo.NE.0 ) THEN
1070  WRITE( nounit, fmt = 9999 )'CTGEVC(R,S2)', iinfo, n,
1071  \$ jtype, ioldsd
1072  info = abs( iinfo )
1073  GO TO 210
1074  END IF
1075 *
1076  CALL cget52( .false., n, s1, lda, p1, lda, evectr, ldu,
1077  \$ alpha1, beta1, work, rwork, dumma( 1 ) )
1078  result( 11 ) = dumma( 1 )
1079  IF( dumma( 2 ).GT.thresh ) THEN
1080  WRITE( nounit, fmt = 9998 )'Right', 'CTGEVC(HOWMNY=S)',
1081  \$ dumma( 2 ), n, jtype, ioldsd
1082  END IF
1083 *
1084 * 12: Compute the right eigenvector Matrix with
1085 * back transforming:
1086 *
1087  ntest = 12
1088  result( 12 ) = ulpinv
1089  CALL clacpy( 'F', n, n, z, ldu, evectr, ldu )
1090  CALL ctgevc( 'R', 'B', llwork, n, s1, lda, p1, lda, cdumma,
1091  \$ ldu, evectr, ldu, n, in, work, rwork, iinfo )
1092  IF( iinfo.NE.0 ) THEN
1093  WRITE( nounit, fmt = 9999 )'CTGEVC(R,B)', iinfo, n,
1094  \$ jtype, ioldsd
1095  info = abs( iinfo )
1096  GO TO 210
1097  END IF
1098 *
1099  CALL cget52( .false., n, h, lda, t, lda, evectr, ldu,
1100  \$ alpha1, beta1, work, rwork, dumma( 1 ) )
1101  result( 12 ) = dumma( 1 )
1102  IF( dumma( 2 ).GT.thresh ) THEN
1103  WRITE( nounit, fmt = 9998 )'Right', 'CTGEVC(HOWMNY=B)',
1104  \$ dumma( 2 ), n, jtype, ioldsd
1105  END IF
1106 *
1107 * Tests 13--15 are done only on request
1108 *
1109  IF( tstdif ) THEN
1110 *
1111 * Do Tests 13--14
1112 *
1113  CALL cget51( 2, n, s1, lda, s2, lda, q, ldu, z, ldu,
1114  \$ work, rwork, result( 13 ) )
1115  CALL cget51( 2, n, p1, lda, p2, lda, q, ldu, z, ldu,
1116  \$ work, rwork, result( 14 ) )
1117 *
1118 * Do Test 15
1119 *
1120  temp1 = zero
1121  temp2 = zero
1122  DO 200 j = 1, n
1123  temp1 = max( temp1, abs( alpha1( j )-alpha3( j ) ) )
1124  temp2 = max( temp2, abs( beta1( j )-beta3( j ) ) )
1125  200 CONTINUE
1126 *
1127  temp1 = temp1 / max( safmin, ulp*max( temp1, anorm ) )
1128  temp2 = temp2 / max( safmin, ulp*max( temp2, bnorm ) )
1129  result( 15 ) = max( temp1, temp2 )
1130  ntest = 15
1131  ELSE
1132  result( 13 ) = zero
1133  result( 14 ) = zero
1134  result( 15 ) = zero
1135  ntest = 12
1136  END IF
1137 *
1138 * End of Loop -- Check for RESULT(j) > THRESH
1139 *
1140  210 CONTINUE
1141 *
1142  ntestt = ntestt + ntest
1143 *
1144 * Print out tests which fail.
1145 *
1146  DO 220 jr = 1, ntest
1147  IF( result( jr ).GE.thresh ) THEN
1148 *
1149 * If this is the first test to fail,
1150 * print a header to the data file.
1151 *
1152  IF( nerrs.EQ.0 ) THEN
1153  WRITE( nounit, fmt = 9997 )'CGG'
1154 *
1155 * Matrix types
1156 *
1157  WRITE( nounit, fmt = 9996 )
1158  WRITE( nounit, fmt = 9995 )
1159  WRITE( nounit, fmt = 9994 )'Unitary'
1160 *
1161 * Tests performed
1162 *
1163  WRITE( nounit, fmt = 9993 )'unitary', '*',
1164  \$ 'conjugate transpose', ( '*', j = 1, 10 )
1165 *
1166  END IF
1167  nerrs = nerrs + 1
1168  IF( result( jr ).LT.10000.0 ) THEN
1169  WRITE( nounit, fmt = 9992 )n, jtype, ioldsd, jr,
1170  \$ result( jr )
1171  ELSE
1172  WRITE( nounit, fmt = 9991 )n, jtype, ioldsd, jr,
1173  \$ result( jr )
1174  END IF
1175  END IF
1176  220 CONTINUE
1177 *
1178  230 CONTINUE
1179  240 CONTINUE
1180 *
1181 * Summary
1182 *
1183  CALL slasum( 'CGG', nounit, nerrs, ntestt )
1184  RETURN
1185 *
1186  9999 FORMAT( ' CCHKGG: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1187  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1188 *
1189  9998 FORMAT( ' CCHKGG: ', a, ' Eigenvectors from ', a, ' incorrectly ',
1190  \$ 'normalized.', / ' Bits of error=', 0p, g10.3, ',', 9x,
1191  \$ 'N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5,
1192  \$ ')' )
1193 *
1194  9997 FORMAT( 1x, a3, ' -- Complex Generalized eigenvalue problem' )
1195 *
1196  9996 FORMAT( ' Matrix types (see CCHKGG for details): ' )
1197 *
1198  9995 FORMAT( ' Special Matrices:', 23x,
1199  \$ '(J''=transposed Jordan block)',
1200  \$ / ' 1=(0,0) 2=(I,0) 3=(0,I) 4=(I,I) 5=(J'',J'') ',
1201  \$ '6=(diag(J'',I), diag(I,J''))', / ' Diagonal Matrices: ( ',
1202  \$ 'D=diag(0,1,2,...) )', / ' 7=(D,I) 9=(large*D, small*I',
1203  \$ ') 11=(large*I, small*D) 13=(large*D, large*I)', /
1204  \$ ' 8=(I,D) 10=(small*D, large*I) 12=(small*I, large*D) ',
1205  \$ ' 14=(small*D, small*I)', / ' 15=(D, reversed D)' )
1206  9994 FORMAT( ' Matrices Rotated by Random ', a, ' Matrices U, V:',
1207  \$ / ' 16=Transposed Jordan Blocks 19=geometric ',
1208  \$ 'alpha, beta=0,1', / ' 17=arithm. alpha&beta ',
1209  \$ ' 20=arithmetic alpha, beta=0,1', / ' 18=clustered ',
1210  \$ 'alpha, beta=0,1 21=random alpha, beta=0,1',
1211  \$ / ' Large & Small Matrices:', / ' 22=(large, small) ',
1212  \$ '23=(small,large) 24=(small,small) 25=(large,large)',
1213  \$ / ' 26=random O(1) matrices.' )
1214 *
1215  9993 FORMAT( / ' Tests performed: (H is Hessenberg, S is Schur, B, ',
1216  \$ 'T, P are triangular,', / 20x, 'U, V, Q, and Z are ', a,
1217  \$ ', l and r are the', / 20x,
1218  \$ 'appropriate left and right eigenvectors, resp., a is',
1219  \$ / 20x, 'alpha, b is beta, and ', a, ' means ', a, '.)',
1220  \$ / ' 1 = | A - U H V', a,
1221  \$ ' | / ( |A| n ulp ) 2 = | B - U T V', a,
1222  \$ ' | / ( |B| n ulp )', / ' 3 = | I - UU', a,
1223  \$ ' | / ( n ulp ) 4 = | I - VV', a,
1224  \$ ' | / ( n ulp )', / ' 5 = | H - Q S Z', a,
1225  \$ ' | / ( |H| n ulp )', 6x, '6 = | T - Q P Z', a,
1226  \$ ' | / ( |T| n ulp )', / ' 7 = | I - QQ', a,
1227  \$ ' | / ( n ulp ) 8 = | I - ZZ', a,
1228  \$ ' | / ( n ulp )', / ' 9 = max | ( b S - a P )', a,
1229  \$ ' l | / const. 10 = max | ( b H - a T )', a,
1230  \$ ' l | / const.', /
1231  \$ ' 11= max | ( b S - a P ) r | / const. 12 = max | ( b H',
1232  \$ ' - a T ) r | / const.', / 1x )
1233 *
1234  9992 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
1235  \$ 4( i4, ',' ), ' result ', i2, ' is', 0p, f8.2 )
1236  9991 FORMAT( ' Matrix order=', i5, ', type=', i2, ', seed=',
1237  \$ 4( i4, ',' ), ' result ', i2, ' is', 1p, e10.3 )
1238 *
1239 * End of CCHKGG
1240 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine clatm4(ITYPE, N, NZ1, NZ2, RSIGN, AMAGN, RCOND, TRIANG, IDIST, ISEED, A, LDA)
CLATM4
Definition: clatm4.f:171
subroutine cget52(LEFT, N, A, LDA, B, LDB, E, LDE, ALPHA, BETA, WORK, RWORK, RESULT)
CGET52
Definition: cget52.f:161
subroutine cget51(ITYPE, N, A, LDA, B, LDB, U, LDU, V, LDV, WORK, RWORK, RESULT)
CGET51
Definition: cget51.f:155
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:75
real function clange(NORM, M, N, A, LDA, WORK)
CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: clange.f:115
subroutine cgeqr2(M, N, A, LDA, TAU, WORK, INFO)
CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
Definition: cgeqr2.f:130
subroutine chgeqz(JOB, COMPQ, COMPZ, N, ILO, IHI, H, LDH, T, LDT, ALPHA, BETA, Q, LDQ, Z, LDZ, WORK, LWORK, RWORK, INFO)
CHGEQZ
Definition: chgeqz.f:284
subroutine ctgevc(SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL, LDVL, VR, LDVR, MM, M, WORK, RWORK, INFO)
CTGEVC
Definition: ctgevc.f:219
subroutine claset(UPLO, M, N, ALPHA, BETA, A, LDA)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: claset.f:106
subroutine clarfg(N, ALPHA, X, INCX, TAU)
CLARFG generates an elementary reflector (Householder matrix).
Definition: clarfg.f:106
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
subroutine cgghrd(COMPQ, COMPZ, N, ILO, IHI, A, LDA, B, LDB, Q, LDQ, Z, LDZ, INFO)
CGGHRD
Definition: cgghrd.f:204
subroutine cunm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
CUNM2R multiplies a general matrix by the unitary matrix from a QR factorization determined by cgeqrf...
Definition: cunm2r.f:159
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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