LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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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