LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ dchkbd()

 subroutine dchkbd ( integer NSIZES, integer, dimension( * ) MVAL, integer, dimension( * ) NVAL, integer NTYPES, logical, dimension( * ) DOTYPE, integer NRHS, integer, dimension( 4 ) ISEED, double precision THRESH, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) BD, double precision, dimension( * ) BE, double precision, dimension( * ) S1, double precision, dimension( * ) S2, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( ldx, * ) Y, double precision, dimension( ldx, * ) Z, double precision, dimension( ldq, * ) Q, integer LDQ, double precision, dimension( ldpt, * ) PT, integer LDPT, double precision, dimension( ldpt, * ) U, double precision, dimension( ldpt, * ) VT, double precision, dimension( * ) WORK, integer LWORK, integer, dimension( * ) IWORK, integer NOUT, integer INFO )

DCHKBD

Purpose:
``` DCHKBD checks the singular value decomposition (SVD) routines.

DGEBRD reduces a real general m by n matrix A to upper or lower
bidiagonal form B by an orthogonal transformation:  Q' * A * P = B
(or A = Q * B * P').  The matrix B is upper bidiagonal if m >= n
and lower bidiagonal if m < n.

DORGBR generates the orthogonal matrices Q and P' from DGEBRD.
Note that Q and P are not necessarily square.

DBDSQR computes the singular value decomposition of the bidiagonal
matrix B as B = U S V'.  It is called three times to compute
1)  B = U S1 V', where S1 is the diagonal matrix of singular
values and the columns of the matrices U and V are the left
and right singular vectors, respectively, of B.
2)  Same as 1), but the singular values are stored in S2 and the
singular vectors are not computed.
3)  A = (UQ) S (P'V'), the SVD of the original matrix A.
In addition, DBDSQR has an option to apply the left orthogonal matrix
U to a matrix X, useful in least squares applications.

DBDSDC computes the singular value decomposition of the bidiagonal
matrix B as B = U S V' using divide-and-conquer. It is called twice
to compute
1) B = U S1 V', where S1 is the diagonal matrix of singular
values and the columns of the matrices U and V are the left
and right singular vectors, respectively, of B.
2) Same as 1), but the singular values are stored in S2 and the
singular vectors are not computed.

DBDSVDX computes the singular value decomposition of the bidiagonal
matrix B as B = U S V' using bisection and inverse iteration. It is
called six times to compute
1) B = U S1 V', RANGE='A', where S1 is the diagonal matrix of singular
values and the columns of the matrices U and V are the left
and right singular vectors, respectively, of B.
2) Same as 1), but the singular values are stored in S2 and the
singular vectors are not computed.
3) B = U S1 V', RANGE='I', with where S1 is the diagonal matrix of singular
values and the columns of the matrices U and V are the left
and right singular vectors, respectively, of B
4) Same as 3), but the singular values are stored in S2 and the
singular vectors are not computed.
5) B = U S1 V', RANGE='V', with where S1 is the diagonal matrix of singular
values and the columns of the matrices U and V are the left
and right singular vectors, respectively, of B
6) Same as 5), but the singular values are stored in S2 and the
singular vectors are not computed.

For each pair of matrix dimensions (M,N) and each selected matrix
type, an M by N matrix A and an M by NRHS matrix X are generated.
The problem dimensions are as follows
A:          M x N
Q:          M x min(M,N) (but M x M if NRHS > 0)
P:          min(M,N) x N
B:          min(M,N) x min(M,N)
U, V:       min(M,N) x min(M,N)
S1, S2      diagonal, order min(M,N)
X:          M x NRHS

For each generated matrix, 14 tests are performed:

Test DGEBRD and DORGBR

(1)   | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'

(2)   | I - Q' Q | / ( M ulp )

(3)   | I - PT PT' | / ( N ulp )

Test DBDSQR on bidiagonal matrix B

(4)   | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'

(5)   | Y - U Z | / ( |Y| max(min(M,N),k) ulp ), where Y = Q' X
and   Z = U' Y.
(6)   | I - U' U | / ( min(M,N) ulp )

(7)   | I - VT VT' | / ( min(M,N) ulp )

(8)   S1 contains min(M,N) nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(9)   | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
computing U and V.

(10)  0 if the true singular values of B are within THRESH of
those in S1.  2*THRESH if they are not.  (Tested using
DSVDCH)

Test DBDSQR on matrix A

(11)  | A - (QU) S (VT PT) | / ( |A| max(M,N) ulp )

(12)  | X - (QU) Z | / ( |X| max(M,k) ulp )

(13)  | I - (QU)'(QU) | / ( M ulp )

(14)  | I - (VT PT) (PT'VT') | / ( N ulp )

Test DBDSDC on bidiagonal matrix B

(15)  | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'

(16)  | I - U' U | / ( min(M,N) ulp )

(17)  | I - VT VT' | / ( min(M,N) ulp )

(18)  S1 contains min(M,N) nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(19)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
computing U and V.
Test DBDSVDX on bidiagonal matrix B

(20)  | B - U S1 VT | / ( |B| min(M,N) ulp ), VT = V'

(21)  | I - U' U | / ( min(M,N) ulp )

(22)  | I - VT VT' | / ( min(M,N) ulp )

(23)  S1 contains min(M,N) nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(24)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
computing U and V.

(25)  | S1 - U' B VT' | / ( |S| n ulp )    DBDSVDX('V', 'I')

(26)  | I - U' U | / ( min(M,N) ulp )

(27)  | I - VT VT' | / ( min(M,N) ulp )

(28)  S1 contains min(M,N) nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(29)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
computing U and V.

(30)  | S1 - U' B VT' | / ( |S1| n ulp )   DBDSVDX('V', 'V')

(31)  | I - U' U | / ( min(M,N) ulp )

(32)  | I - VT VT' | / ( min(M,N) ulp )

(33)  S1 contains min(M,N) nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)

(34)  | S1 - S2 | / ( |S1| ulp ), where S2 is computed without
computing U and V.

The possible matrix types are

(1)  The zero matrix.
(2)  The identity matrix.

(3)  A diagonal matrix with evenly spaced entries
1, ..., ULP  and random signs.
(ULP = (first number larger than 1) - 1 )
(4)  A diagonal matrix with geometrically spaced entries
1, ..., ULP  and random signs.
(5)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
and random signs.

(6)  Same as (3), but multiplied by SQRT( overflow threshold )
(7)  Same as (3), but multiplied by SQRT( underflow threshold )

(8)  A matrix of the form  U D V, where U and V are orthogonal and
D has evenly spaced entries 1, ..., ULP with random signs
on the diagonal.

(9)  A matrix of the form  U D V, where U and V are orthogonal and
D has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal.

(10) A matrix of the form  U D V, where U and V are orthogonal and
D has "clustered" entries 1, ULP,..., ULP with random
signs on the diagonal.

(11) Same as (8), but multiplied by SQRT( overflow threshold )
(12) Same as (8), but multiplied by SQRT( underflow threshold )

(13) Rectangular matrix with random entries chosen from (-1,1).
(14) Same as (13), but multiplied by SQRT( overflow threshold )
(15) Same as (13), but multiplied by SQRT( underflow threshold )

Special case:
(16) A bidiagonal matrix with random entries chosen from a
logarithmic distribution on [ulp^2,ulp^(-2)]  (I.e., each
entry is  e^x, where x is chosen uniformly on
[ 2 log(ulp), -2 log(ulp) ] .)  For *this* type:
(a) DGEBRD is not called to reduce it to bidiagonal form.
(b) the bidiagonal is  min(M,N) x min(M,N); if M<N, the
matrix will be lower bidiagonal, otherwise upper.
(c) only tests 5--8 and 14 are performed.

A subset of the full set of matrix types may be selected through
the logical array DOTYPE.```
Parameters
 [in] NSIZES ``` NSIZES is INTEGER The number of values of M and N contained in the vectors MVAL and NVAL. The matrix sizes are used in pairs (M,N).``` [in] MVAL ``` MVAL is INTEGER array, dimension (NM) The values of the matrix row dimension M.``` [in] NVAL ``` NVAL is INTEGER array, dimension (NM) The values of the matrix column dimension N.``` [in] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, DCHKBD 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 matrices are in A and B. 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 (m,n), a matrix 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] NRHS ``` NRHS is INTEGER The number of columns in the "right-hand side" matrices X, Y, and Z, used in testing DBDSQR. If NRHS = 0, then the operations on the right-hand side will not be tested. NRHS must be at least 0.``` [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 values of ISEED are changed on exit, and can be used in the next call to DCHKBD to continue the same random number sequence.``` [in] THRESH ``` THRESH is DOUBLE PRECISION The threshold value for the test ratios. A result is included in the output file if RESULT >= THRESH. To have every test ratio printed, use THRESH = 0. Note that the expected value of the test ratios is O(1), so THRESH should be a reasonably small multiple of 1, e.g., 10 or 100.``` [out] A ``` A is DOUBLE PRECISION array, dimension (LDA,NMAX) where NMAX is the maximum value of N in NVAL.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,MMAX), where MMAX is the maximum value of M in MVAL.``` [out] BD ``` BD is DOUBLE PRECISION array, dimension (max(min(MVAL(j),NVAL(j))))``` [out] BE ``` BE is DOUBLE PRECISION array, dimension (max(min(MVAL(j),NVAL(j))))``` [out] S1 ``` S1 is DOUBLE PRECISION array, dimension (max(min(MVAL(j),NVAL(j))))``` [out] S2 ``` S2 is DOUBLE PRECISION array, dimension (max(min(MVAL(j),NVAL(j))))``` [out] X ` X is DOUBLE PRECISION array, dimension (LDX,NRHS)` [in] LDX ``` LDX is INTEGER The leading dimension of the arrays X, Y, and Z. LDX >= max(1,MMAX)``` [out] Y ` Y is DOUBLE PRECISION array, dimension (LDX,NRHS)` [out] Z ` Z is DOUBLE PRECISION array, dimension (LDX,NRHS)` [out] Q ` Q is DOUBLE PRECISION array, dimension (LDQ,MMAX)` [in] LDQ ``` LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,MMAX).``` [out] PT ` PT is DOUBLE PRECISION array, dimension (LDPT,NMAX)` [in] LDPT ``` LDPT is INTEGER The leading dimension of the arrays PT, U, and V. LDPT >= max(1, max(min(MVAL(j),NVAL(j)))).``` [out] U ``` U is DOUBLE PRECISION array, dimension (LDPT,max(min(MVAL(j),NVAL(j))))``` [out] VT ``` VT is DOUBLE PRECISION array, dimension (LDPT,max(min(MVAL(j),NVAL(j))))``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The number of entries in WORK. This must be at least 3(M+N) and M(M + max(M,N,k) + 1) + N*min(M,N) for all pairs (M,N)=(MM(j),NN(j))``` [out] IWORK ` IWORK is INTEGER array, dimension at least 8*min(M,N)` [in] NOUT ``` NOUT is INTEGER The FORTRAN unit number for printing out error messages (e.g., if a routine returns IINFO not equal to 0.)``` [out] INFO ``` INFO is INTEGER If 0, then everything ran OK. -1: NSIZES < 0 -2: Some MM(j) < 0 -3: Some NN(j) < 0 -4: NTYPES < 0 -6: NRHS < 0 -8: THRESH < 0 -11: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ). -17: LDB < 1 or LDB < MMAX. -21: LDQ < 1 or LDQ < MMAX. -23: LDPT< 1 or LDPT< MNMAX. -27: LWORK too small. If DLATMR, SLATMS, DGEBRD, DORGBR, or DBDSQR, returns an error code, the absolute value of it is returned. ----------------------------------------------------------------------- Some Local Variables and Parameters: ---- ----- --------- --- ---------- ZERO, ONE Real 0 and 1. MAXTYP The number of types defined. NTEST The number of tests performed, or which can be performed so far, for the current matrix. MMAX Largest value in NN. NMAX Largest value in NN. MNMIN min(MM(j), NN(j)) (the dimension of the bidiagonal matrix.) MNMAX The maximum value of MNMIN for j=1,...,NSIZES. NFAIL The number of tests which have exceeded THRESH COND, IMODE Values to be passed to the matrix generators. ANORM Norm of A; passed to matrix generators. OVFL, UNFL Overflow and underflow thresholds. RTOVFL, RTUNFL Square roots of the previous 2 values. ULP, ULPINV Finest relative precision and its inverse. The following four arrays decode JTYPE: KTYPE(j) The general type (1-10) for type "j". KMODE(j) The MODE value to be passed to the matrix generator for type "j". KMAGN(j) The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) )```

Definition at line 489 of file dchkbd.f.

493*
494* -- LAPACK test routine --
495* -- LAPACK is a software package provided by Univ. of Tennessee, --
496* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
497*
498* .. Scalar Arguments ..
499 INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
500 \$ NSIZES, NTYPES
501 DOUBLE PRECISION THRESH
502* ..
503* .. Array Arguments ..
504 LOGICAL DOTYPE( * )
505 INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), NVAL( * )
506 DOUBLE PRECISION A( LDA, * ), BD( * ), BE( * ), PT( LDPT, * ),
507 \$ Q( LDQ, * ), S1( * ), S2( * ), U( LDPT, * ),
508 \$ VT( LDPT, * ), WORK( * ), X( LDX, * ),
509 \$ Y( LDX, * ), Z( LDX, * )
510* ..
511*
512* ======================================================================
513*
514* .. Parameters ..
515 DOUBLE PRECISION ZERO, ONE, TWO, HALF
516 parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
517 \$ half = 0.5d0 )
518 INTEGER MAXTYP
519 parameter( maxtyp = 16 )
520* ..
521* .. Local Scalars ..
523 CHARACTER UPLO
524 CHARACTER*3 PATH
525 INTEGER I, IINFO, IL, IMODE, ITEMP, ITYPE, IU, IWBD,
526 \$ IWBE, IWBS, IWBZ, IWWORK, J, JCOL, JSIZE,
527 \$ JTYPE, LOG2UI, M, MINWRK, MMAX, MNMAX, MNMIN,
528 \$ MNMIN2, MQ, MTYPES, N, NFAIL, NMAX,
529 \$ NS1, NS2, NTEST
530 DOUBLE PRECISION ABSTOL, AMNINV, ANORM, COND, OVFL, RTOVFL,
531 \$ RTUNFL, TEMP1, TEMP2, ULP, ULPINV, UNFL,
532 \$ VL, VU
533* ..
534* .. Local Arrays ..
535 INTEGER IDUM( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
536 \$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
537 \$ KTYPE( MAXTYP )
538 DOUBLE PRECISION DUM( 1 ), DUMMA( 1 ), RESULT( 40 )
539* ..
540* .. External Functions ..
541 DOUBLE PRECISION DLAMCH, DLARND, DSXT1
542 EXTERNAL dlamch, dlarnd, dsxt1
543* ..
544* .. External Subroutines ..
545 EXTERNAL alasum, dbdsdc, dbdsqr, dbdsvdx, dbdt01,
549* ..
550* .. Intrinsic Functions ..
551 INTRINSIC abs, exp, int, log, max, min, sqrt
552* ..
553* .. Scalars in Common ..
554 LOGICAL LERR, OK
555 CHARACTER*32 SRNAMT
556 INTEGER INFOT, NUNIT
557* ..
558* .. Common blocks ..
559 COMMON / infoc / infot, nunit, ok, lerr
560 COMMON / srnamc / srnamt
561* ..
562* .. Data statements ..
563 DATA ktype / 1, 2, 5*4, 5*6, 3*9, 10 /
564 DATA kmagn / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
565 DATA kmode / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
566 \$ 0, 0, 0 /
567* ..
568* .. Executable Statements ..
569*
570* Check for errors
571*
572 info = 0
573*
576 mmax = 1
577 nmax = 1
578 mnmax = 1
579 minwrk = 1
580 DO 10 j = 1, nsizes
581 mmax = max( mmax, mval( j ) )
582 IF( mval( j ).LT.0 )
584 nmax = max( nmax, nval( j ) )
585 IF( nval( j ).LT.0 )
587 mnmax = max( mnmax, min( mval( j ), nval( j ) ) )
588 minwrk = max( minwrk, 3*( mval( j )+nval( j ) ),
589 \$ mval( j )*( mval( j )+max( mval( j ), nval( j ),
590 \$ nrhs )+1 )+nval( j )*min( nval( j ), mval( j ) ) )
591 10 CONTINUE
592*
593* Check for errors
594*
595 IF( nsizes.LT.0 ) THEN
596 info = -1
597 ELSE IF( badmm ) THEN
598 info = -2
599 ELSE IF( badnn ) THEN
600 info = -3
601 ELSE IF( ntypes.LT.0 ) THEN
602 info = -4
603 ELSE IF( nrhs.LT.0 ) THEN
604 info = -6
605 ELSE IF( lda.LT.mmax ) THEN
606 info = -11
607 ELSE IF( ldx.LT.mmax ) THEN
608 info = -17
609 ELSE IF( ldq.LT.mmax ) THEN
610 info = -21
611 ELSE IF( ldpt.LT.mnmax ) THEN
612 info = -23
613 ELSE IF( minwrk.GT.lwork ) THEN
614 info = -27
615 END IF
616*
617 IF( info.NE.0 ) THEN
618 CALL xerbla( 'DCHKBD', -info )
619 RETURN
620 END IF
621*
622* Initialize constants
623*
624 path( 1: 1 ) = 'Double precision'
625 path( 2: 3 ) = 'BD'
626 nfail = 0
627 ntest = 0
628 unfl = dlamch( 'Safe minimum' )
629 ovfl = dlamch( 'Overflow' )
630 CALL dlabad( unfl, ovfl )
631 ulp = dlamch( 'Precision' )
632 ulpinv = one / ulp
633 log2ui = int( log( ulpinv ) / log( two ) )
634 rtunfl = sqrt( unfl )
635 rtovfl = sqrt( ovfl )
636 infot = 0
637 abstol = 2*unfl
638*
639* Loop over sizes, types
640*
641 DO 300 jsize = 1, nsizes
642 m = mval( jsize )
643 n = nval( jsize )
644 mnmin = min( m, n )
645 amninv = one / max( m, n, 1 )
646*
647 IF( nsizes.NE.1 ) THEN
648 mtypes = min( maxtyp, ntypes )
649 ELSE
650 mtypes = min( maxtyp+1, ntypes )
651 END IF
652*
653 DO 290 jtype = 1, mtypes
654 IF( .NOT.dotype( jtype ) )
655 \$ GO TO 290
656*
657 DO 20 j = 1, 4
658 ioldsd( j ) = iseed( j )
659 20 CONTINUE
660*
661 DO 30 j = 1, 34
662 result( j ) = -one
663 30 CONTINUE
664*
665 uplo = ' '
666*
667* Compute "A"
668*
669* Control parameters:
670*
671* KMAGN KMODE KTYPE
672* =1 O(1) clustered 1 zero
673* =2 large clustered 2 identity
674* =3 small exponential (none)
675* =4 arithmetic diagonal, (w/ eigenvalues)
676* =5 random symmetric, w/ eigenvalues
677* =6 nonsymmetric, w/ singular values
678* =7 random diagonal
679* =8 random symmetric
680* =9 random nonsymmetric
681* =10 random bidiagonal (log. distrib.)
682*
683 IF( mtypes.GT.maxtyp )
684 \$ GO TO 100
685*
686 itype = ktype( jtype )
687 imode = kmode( jtype )
688*
689* Compute norm
690*
691 GO TO ( 40, 50, 60 )kmagn( jtype )
692*
693 40 CONTINUE
694 anorm = one
695 GO TO 70
696*
697 50 CONTINUE
698 anorm = ( rtovfl*ulp )*amninv
699 GO TO 70
700*
701 60 CONTINUE
702 anorm = rtunfl*max( m, n )*ulpinv
703 GO TO 70
704*
705 70 CONTINUE
706*
707 CALL dlaset( 'Full', lda, n, zero, zero, a, lda )
708 iinfo = 0
709 cond = ulpinv
710*
711 bidiag = .false.
712 IF( itype.EQ.1 ) THEN
713*
714* Zero matrix
715*
716 iinfo = 0
717*
718 ELSE IF( itype.EQ.2 ) THEN
719*
720* Identity
721*
722 DO 80 jcol = 1, mnmin
723 a( jcol, jcol ) = anorm
724 80 CONTINUE
725*
726 ELSE IF( itype.EQ.4 ) THEN
727*
728* Diagonal Matrix, [Eigen]values Specified
729*
730 CALL dlatms( mnmin, mnmin, 'S', iseed, 'N', work, imode,
731 \$ cond, anorm, 0, 0, 'N', a, lda,
732 \$ work( mnmin+1 ), iinfo )
733*
734 ELSE IF( itype.EQ.5 ) THEN
735*
736* Symmetric, eigenvalues specified
737*
738 CALL dlatms( mnmin, mnmin, 'S', iseed, 'S', work, imode,
739 \$ cond, anorm, m, n, 'N', a, lda,
740 \$ work( mnmin+1 ), iinfo )
741*
742 ELSE IF( itype.EQ.6 ) THEN
743*
744* Nonsymmetric, singular values specified
745*
746 CALL dlatms( m, n, 'S', iseed, 'N', work, imode, cond,
747 \$ anorm, m, n, 'N', a, lda, work( mnmin+1 ),
748 \$ iinfo )
749*
750 ELSE IF( itype.EQ.7 ) THEN
751*
752* Diagonal, random entries
753*
754 CALL dlatmr( mnmin, mnmin, 'S', iseed, 'N', work, 6, one,
755 \$ one, 'T', 'N', work( mnmin+1 ), 1, one,
756 \$ work( 2*mnmin+1 ), 1, one, 'N', iwork, 0, 0,
757 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
758*
759 ELSE IF( itype.EQ.8 ) THEN
760*
761* Symmetric, random entries
762*
763 CALL dlatmr( mnmin, mnmin, 'S', iseed, 'S', work, 6, one,
764 \$ one, 'T', 'N', work( mnmin+1 ), 1, one,
765 \$ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
766 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
767*
768 ELSE IF( itype.EQ.9 ) THEN
769*
770* Nonsymmetric, random entries
771*
772 CALL dlatmr( m, n, 'S', iseed, 'N', work, 6, one, one,
773 \$ 'T', 'N', work( mnmin+1 ), 1, one,
774 \$ work( m+mnmin+1 ), 1, one, 'N', iwork, m, n,
775 \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
776*
777 ELSE IF( itype.EQ.10 ) THEN
778*
779* Bidiagonal, random entries
780*
781 temp1 = -two*log( ulp )
782 DO 90 j = 1, mnmin
783 bd( j ) = exp( temp1*dlarnd( 2, iseed ) )
784 IF( j.LT.mnmin )
785 \$ be( j ) = exp( temp1*dlarnd( 2, iseed ) )
786 90 CONTINUE
787*
788 iinfo = 0
789 bidiag = .true.
790 IF( m.GE.n ) THEN
791 uplo = 'U'
792 ELSE
793 uplo = 'L'
794 END IF
795 ELSE
796 iinfo = 1
797 END IF
798*
799 IF( iinfo.EQ.0 ) THEN
800*
801* Generate Right-Hand Side
802*
803 IF( bidiag ) THEN
804 CALL dlatmr( mnmin, nrhs, 'S', iseed, 'N', work, 6,
805 \$ one, one, 'T', 'N', work( mnmin+1 ), 1,
806 \$ one, work( 2*mnmin+1 ), 1, one, 'N',
807 \$ iwork, mnmin, nrhs, zero, one, 'NO', y,
808 \$ ldx, iwork, iinfo )
809 ELSE
810 CALL dlatmr( m, nrhs, 'S', iseed, 'N', work, 6, one,
811 \$ one, 'T', 'N', work( m+1 ), 1, one,
812 \$ work( 2*m+1 ), 1, one, 'N', iwork, m,
813 \$ nrhs, zero, one, 'NO', x, ldx, iwork,
814 \$ iinfo )
815 END IF
816 END IF
817*
818* Error Exit
819*
820 IF( iinfo.NE.0 ) THEN
821 WRITE( nout, fmt = 9998 )'Generator', iinfo, m, n,
822 \$ jtype, ioldsd
823 info = abs( iinfo )
824 RETURN
825 END IF
826*
827 100 CONTINUE
828*
829* Call DGEBRD and DORGBR to compute B, Q, and P, do tests.
830*
831 IF( .NOT.bidiag ) THEN
832*
833* Compute transformations to reduce A to bidiagonal form:
834* B := Q' * A * P.
835*
836 CALL dlacpy( ' ', m, n, a, lda, q, ldq )
837 CALL dgebrd( m, n, q, ldq, bd, be, work, work( mnmin+1 ),
838 \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
839*
840* Check error code from DGEBRD.
841*
842 IF( iinfo.NE.0 ) THEN
843 WRITE( nout, fmt = 9998 )'DGEBRD', iinfo, m, n,
844 \$ jtype, ioldsd
845 info = abs( iinfo )
846 RETURN
847 END IF
848*
849 CALL dlacpy( ' ', m, n, q, ldq, pt, ldpt )
850 IF( m.GE.n ) THEN
851 uplo = 'U'
852 ELSE
853 uplo = 'L'
854 END IF
855*
856* Generate Q
857*
858 mq = m
859 IF( nrhs.LE.0 )
860 \$ mq = mnmin
861 CALL dorgbr( 'Q', m, mq, n, q, ldq, work,
862 \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
863*
864* Check error code from DORGBR.
865*
866 IF( iinfo.NE.0 ) THEN
867 WRITE( nout, fmt = 9998 )'DORGBR(Q)', iinfo, m, n,
868 \$ jtype, ioldsd
869 info = abs( iinfo )
870 RETURN
871 END IF
872*
873* Generate P'
874*
875 CALL dorgbr( 'P', mnmin, n, m, pt, ldpt, work( mnmin+1 ),
876 \$ work( 2*mnmin+1 ), lwork-2*mnmin, iinfo )
877*
878* Check error code from DORGBR.
879*
880 IF( iinfo.NE.0 ) THEN
881 WRITE( nout, fmt = 9998 )'DORGBR(P)', iinfo, m, n,
882 \$ jtype, ioldsd
883 info = abs( iinfo )
884 RETURN
885 END IF
886*
887* Apply Q' to an M by NRHS matrix X: Y := Q' * X.
888*
889 CALL dgemm( 'Transpose', 'No transpose', m, nrhs, m, one,
890 \$ q, ldq, x, ldx, zero, y, ldx )
891*
892* Test 1: Check the decomposition A := Q * B * PT
893* 2: Check the orthogonality of Q
894* 3: Check the orthogonality of PT
895*
896 CALL dbdt01( m, n, 1, a, lda, q, ldq, bd, be, pt, ldpt,
897 \$ work, result( 1 ) )
898 CALL dort01( 'Columns', m, mq, q, ldq, work, lwork,
899 \$ result( 2 ) )
900 CALL dort01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
901 \$ result( 3 ) )
902 END IF
903*
904* Use DBDSQR to form the SVD of the bidiagonal matrix B:
905* B := U * S1 * VT, and compute Z = U' * Y.
906*
907 CALL dcopy( mnmin, bd, 1, s1, 1 )
908 IF( mnmin.GT.0 )
909 \$ CALL dcopy( mnmin-1, be, 1, work, 1 )
910 CALL dlacpy( ' ', m, nrhs, y, ldx, z, ldx )
911 CALL dlaset( 'Full', mnmin, mnmin, zero, one, u, ldpt )
912 CALL dlaset( 'Full', mnmin, mnmin, zero, one, vt, ldpt )
913*
914 CALL dbdsqr( uplo, mnmin, mnmin, mnmin, nrhs, s1, work, vt,
915 \$ ldpt, u, ldpt, z, ldx, work( mnmin+1 ), iinfo )
916*
917* Check error code from DBDSQR.
918*
919 IF( iinfo.NE.0 ) THEN
920 WRITE( nout, fmt = 9998 )'DBDSQR(vects)', iinfo, m, n,
921 \$ jtype, ioldsd
922 info = abs( iinfo )
923 IF( iinfo.LT.0 ) THEN
924 RETURN
925 ELSE
926 result( 4 ) = ulpinv
927 GO TO 270
928 END IF
929 END IF
930*
931* Use DBDSQR to compute only the singular values of the
932* bidiagonal matrix B; U, VT, and Z should not be modified.
933*
934 CALL dcopy( mnmin, bd, 1, s2, 1 )
935 IF( mnmin.GT.0 )
936 \$ CALL dcopy( mnmin-1, be, 1, work, 1 )
937*
938 CALL dbdsqr( uplo, mnmin, 0, 0, 0, s2, work, vt, ldpt, u,
939 \$ ldpt, z, ldx, work( mnmin+1 ), iinfo )
940*
941* Check error code from DBDSQR.
942*
943 IF( iinfo.NE.0 ) THEN
944 WRITE( nout, fmt = 9998 )'DBDSQR(values)', iinfo, m, n,
945 \$ jtype, ioldsd
946 info = abs( iinfo )
947 IF( iinfo.LT.0 ) THEN
948 RETURN
949 ELSE
950 result( 9 ) = ulpinv
951 GO TO 270
952 END IF
953 END IF
954*
955* Test 4: Check the decomposition B := U * S1 * VT
956* 5: Check the computation Z := U' * Y
957* 6: Check the orthogonality of U
958* 7: Check the orthogonality of VT
959*
960 CALL dbdt03( uplo, mnmin, 1, bd, be, u, ldpt, s1, vt, ldpt,
961 \$ work, result( 4 ) )
962 CALL dbdt02( mnmin, nrhs, y, ldx, z, ldx, u, ldpt, work,
963 \$ result( 5 ) )
964 CALL dort01( 'Columns', mnmin, mnmin, u, ldpt, work, lwork,
965 \$ result( 6 ) )
966 CALL dort01( 'Rows', mnmin, mnmin, vt, ldpt, work, lwork,
967 \$ result( 7 ) )
968*
969* Test 8: Check that the singular values are sorted in
970* non-increasing order and are non-negative
971*
972 result( 8 ) = zero
973 DO 110 i = 1, mnmin - 1
974 IF( s1( i ).LT.s1( i+1 ) )
975 \$ result( 8 ) = ulpinv
976 IF( s1( i ).LT.zero )
977 \$ result( 8 ) = ulpinv
978 110 CONTINUE
979 IF( mnmin.GE.1 ) THEN
980 IF( s1( mnmin ).LT.zero )
981 \$ result( 8 ) = ulpinv
982 END IF
983*
984* Test 9: Compare DBDSQR with and without singular vectors
985*
986 temp2 = zero
987*
988 DO 120 j = 1, mnmin
989 temp1 = abs( s1( j )-s2( j ) ) /
990 \$ max( sqrt( unfl )*max( s1( 1 ), one ),
991 \$ ulp*max( abs( s1( j ) ), abs( s2( j ) ) ) )
992 temp2 = max( temp1, temp2 )
993 120 CONTINUE
994*
995 result( 9 ) = temp2
996*
997* Test 10: Sturm sequence test of singular values
998* Go up by factors of two until it succeeds
999*
1000 temp1 = thresh*( half-ulp )
1001*
1002 DO 130 j = 0, log2ui
1003* CALL DSVDCH( MNMIN, BD, BE, S1, TEMP1, IINFO )
1004 IF( iinfo.EQ.0 )
1005 \$ GO TO 140
1006 temp1 = temp1*two
1007 130 CONTINUE
1008*
1009 140 CONTINUE
1010 result( 10 ) = temp1
1011*
1012* Use DBDSQR to form the decomposition A := (QU) S (VT PT)
1013* from the bidiagonal form A := Q B PT.
1014*
1015 IF( .NOT.bidiag ) THEN
1016 CALL dcopy( mnmin, bd, 1, s2, 1 )
1017 IF( mnmin.GT.0 )
1018 \$ CALL dcopy( mnmin-1, be, 1, work, 1 )
1019*
1020 CALL dbdsqr( uplo, mnmin, n, m, nrhs, s2, work, pt, ldpt,
1021 \$ q, ldq, y, ldx, work( mnmin+1 ), iinfo )
1022*
1023* Test 11: Check the decomposition A := Q*U * S2 * VT*PT
1024* 12: Check the computation Z := U' * Q' * X
1025* 13: Check the orthogonality of Q*U
1026* 14: Check the orthogonality of VT*PT
1027*
1028 CALL dbdt01( m, n, 0, a, lda, q, ldq, s2, dumma, pt,
1029 \$ ldpt, work, result( 11 ) )
1030 CALL dbdt02( m, nrhs, x, ldx, y, ldx, q, ldq, work,
1031 \$ result( 12 ) )
1032 CALL dort01( 'Columns', m, mq, q, ldq, work, lwork,
1033 \$ result( 13 ) )
1034 CALL dort01( 'Rows', mnmin, n, pt, ldpt, work, lwork,
1035 \$ result( 14 ) )
1036 END IF
1037*
1038* Use DBDSDC to form the SVD of the bidiagonal matrix B:
1039* B := U * S1 * VT
1040*
1041 CALL dcopy( mnmin, bd, 1, s1, 1 )
1042 IF( mnmin.GT.0 )
1043 \$ CALL dcopy( mnmin-1, be, 1, work, 1 )
1044 CALL dlaset( 'Full', mnmin, mnmin, zero, one, u, ldpt )
1045 CALL dlaset( 'Full', mnmin, mnmin, zero, one, vt, ldpt )
1046*
1047 CALL dbdsdc( uplo, 'I', mnmin, s1, work, u, ldpt, vt, ldpt,
1048 \$ dum, idum, work( mnmin+1 ), iwork, iinfo )
1049*
1050* Check error code from DBDSDC.
1051*
1052 IF( iinfo.NE.0 ) THEN
1053 WRITE( nout, fmt = 9998 )'DBDSDC(vects)', iinfo, m, n,
1054 \$ jtype, ioldsd
1055 info = abs( iinfo )
1056 IF( iinfo.LT.0 ) THEN
1057 RETURN
1058 ELSE
1059 result( 15 ) = ulpinv
1060 GO TO 270
1061 END IF
1062 END IF
1063*
1064* Use DBDSDC to compute only the singular values of the
1065* bidiagonal matrix B; U and VT should not be modified.
1066*
1067 CALL dcopy( mnmin, bd, 1, s2, 1 )
1068 IF( mnmin.GT.0 )
1069 \$ CALL dcopy( mnmin-1, be, 1, work, 1 )
1070*
1071 CALL dbdsdc( uplo, 'N', mnmin, s2, work, dum, 1, dum, 1,
1072 \$ dum, idum, work( mnmin+1 ), iwork, iinfo )
1073*
1074* Check error code from DBDSDC.
1075*
1076 IF( iinfo.NE.0 ) THEN
1077 WRITE( nout, fmt = 9998 )'DBDSDC(values)', iinfo, m, n,
1078 \$ jtype, ioldsd
1079 info = abs( iinfo )
1080 IF( iinfo.LT.0 ) THEN
1081 RETURN
1082 ELSE
1083 result( 18 ) = ulpinv
1084 GO TO 270
1085 END IF
1086 END IF
1087*
1088* Test 15: Check the decomposition B := U * S1 * VT
1089* 16: Check the orthogonality of U
1090* 17: Check the orthogonality of VT
1091*
1092 CALL dbdt03( uplo, mnmin, 1, bd, be, u, ldpt, s1, vt, ldpt,
1093 \$ work, result( 15 ) )
1094 CALL dort01( 'Columns', mnmin, mnmin, u, ldpt, work, lwork,
1095 \$ result( 16 ) )
1096 CALL dort01( 'Rows', mnmin, mnmin, vt, ldpt, work, lwork,
1097 \$ result( 17 ) )
1098*
1099* Test 18: Check that the singular values are sorted in
1100* non-increasing order and are non-negative
1101*
1102 result( 18 ) = zero
1103 DO 150 i = 1, mnmin - 1
1104 IF( s1( i ).LT.s1( i+1 ) )
1105 \$ result( 18 ) = ulpinv
1106 IF( s1( i ).LT.zero )
1107 \$ result( 18 ) = ulpinv
1108 150 CONTINUE
1109 IF( mnmin.GE.1 ) THEN
1110 IF( s1( mnmin ).LT.zero )
1111 \$ result( 18 ) = ulpinv
1112 END IF
1113*
1114* Test 19: Compare DBDSQR with and without singular vectors
1115*
1116 temp2 = zero
1117*
1118 DO 160 j = 1, mnmin
1119 temp1 = abs( s1( j )-s2( j ) ) /
1120 \$ max( sqrt( unfl )*max( s1( 1 ), one ),
1121 \$ ulp*max( abs( s1( 1 ) ), abs( s2( 1 ) ) ) )
1122 temp2 = max( temp1, temp2 )
1123 160 CONTINUE
1124*
1125 result( 19 ) = temp2
1126*
1127*
1128* Use DBDSVDX to compute the SVD of the bidiagonal matrix B:
1129* B := U * S1 * VT
1130*
1131 IF( jtype.EQ.10 .OR. jtype.EQ.16 ) THEN
1132* =================================
1133* Matrix types temporarily disabled
1134* =================================
1135 result( 20:34 ) = zero
1136 GO TO 270
1137 END IF
1138*
1139 iwbs = 1
1140 iwbd = iwbs + mnmin
1141 iwbe = iwbd + mnmin
1142 iwbz = iwbe + mnmin
1143 iwwork = iwbz + 2*mnmin*(mnmin+1)
1144 mnmin2 = max( 1,mnmin*2 )
1145*
1146 CALL dcopy( mnmin, bd, 1, work( iwbd ), 1 )
1147 IF( mnmin.GT.0 )
1148 \$ CALL dcopy( mnmin-1, be, 1, work( iwbe ), 1 )
1149*
1150 CALL dbdsvdx( uplo, 'V', 'A', mnmin, work( iwbd ),
1151 \$ work( iwbe ), zero, zero, 0, 0, ns1, s1,
1152 \$ work( iwbz ), mnmin2, work( iwwork ),
1153 \$ iwork, iinfo)
1154*
1155* Check error code from DBDSVDX.
1156*
1157 IF( iinfo.NE.0 ) THEN
1158 WRITE( nout, fmt = 9998 )'DBDSVDX(vects,A)', iinfo, m, n,
1159 \$ jtype, ioldsd
1160 info = abs( iinfo )
1161 IF( iinfo.LT.0 ) THEN
1162 RETURN
1163 ELSE
1164 result( 20 ) = ulpinv
1165 GO TO 270
1166 END IF
1167 END IF
1168*
1169 j = iwbz
1170 DO 170 i = 1, ns1
1171 CALL dcopy( mnmin, work( j ), 1, u( 1,i ), 1 )
1172 j = j + mnmin
1173 CALL dcopy( mnmin, work( j ), 1, vt( i,1 ), ldpt )
1174 j = j + mnmin
1175 170 CONTINUE
1176*
1177* Use DBDSVDX to compute only the singular values of the
1178* bidiagonal matrix B; U and VT should not be modified.
1179*
1180 IF( jtype.EQ.9 ) THEN
1181* =================================
1182* Matrix types temporarily disabled
1183* =================================
1184 result( 24 ) = zero
1185 GO TO 270
1186 END IF
1187*
1188 CALL dcopy( mnmin, bd, 1, work( iwbd ), 1 )
1189 IF( mnmin.GT.0 )
1190 \$ CALL dcopy( mnmin-1, be, 1, work( iwbe ), 1 )
1191*
1192 CALL dbdsvdx( uplo, 'N', 'A', mnmin, work( iwbd ),
1193 \$ work( iwbe ), zero, zero, 0, 0, ns2, s2,
1194 \$ work( iwbz ), mnmin2, work( iwwork ),
1195 \$ iwork, iinfo )
1196*
1197* Check error code from DBDSVDX.
1198*
1199 IF( iinfo.NE.0 ) THEN
1200 WRITE( nout, fmt = 9998 )'DBDSVDX(values,A)', iinfo,
1201 \$ m, n, jtype, ioldsd
1202 info = abs( iinfo )
1203 IF( iinfo.LT.0 ) THEN
1204 RETURN
1205 ELSE
1206 result( 24 ) = ulpinv
1207 GO TO 270
1208 END IF
1209 END IF
1210*
1211* Save S1 for tests 30-34.
1212*
1213 CALL dcopy( mnmin, s1, 1, work( iwbs ), 1 )
1214*
1215* Test 20: Check the decomposition B := U * S1 * VT
1216* 21: Check the orthogonality of U
1217* 22: Check the orthogonality of VT
1218* 23: Check that the singular values are sorted in
1219* non-increasing order and are non-negative
1220* 24: Compare DBDSVDX with and without singular vectors
1221*
1222 CALL dbdt03( uplo, mnmin, 1, bd, be, u, ldpt, s1, vt,
1223 \$ ldpt, work( iwbs+mnmin ), result( 20 ) )
1224 CALL dort01( 'Columns', mnmin, mnmin, u, ldpt,
1225 \$ work( iwbs+mnmin ), lwork-mnmin,
1226 \$ result( 21 ) )
1227 CALL dort01( 'Rows', mnmin, mnmin, vt, ldpt,
1228 \$ work( iwbs+mnmin ), lwork-mnmin,
1229 \$ result( 22) )
1230*
1231 result( 23 ) = zero
1232 DO 180 i = 1, mnmin - 1
1233 IF( s1( i ).LT.s1( i+1 ) )
1234 \$ result( 23 ) = ulpinv
1235 IF( s1( i ).LT.zero )
1236 \$ result( 23 ) = ulpinv
1237 180 CONTINUE
1238 IF( mnmin.GE.1 ) THEN
1239 IF( s1( mnmin ).LT.zero )
1240 \$ result( 23 ) = ulpinv
1241 END IF
1242*
1243 temp2 = zero
1244 DO 190 j = 1, mnmin
1245 temp1 = abs( s1( j )-s2( j ) ) /
1246 \$ max( sqrt( unfl )*max( s1( 1 ), one ),
1247 \$ ulp*max( abs( s1( 1 ) ), abs( s2( 1 ) ) ) )
1248 temp2 = max( temp1, temp2 )
1249 190 CONTINUE
1250 result( 24 ) = temp2
1251 anorm = s1( 1 )
1252*
1253* Use DBDSVDX with RANGE='I': choose random values for IL and
1254* IU, and ask for the IL-th through IU-th singular values
1255* and corresponding vectors.
1256*
1257 DO 200 i = 1, 4
1258 iseed2( i ) = iseed( i )
1259 200 CONTINUE
1260 IF( mnmin.LE.1 ) THEN
1261 il = 1
1262 iu = mnmin
1263 ELSE
1264 il = 1 + int( ( mnmin-1 )*dlarnd( 1, iseed2 ) )
1265 iu = 1 + int( ( mnmin-1 )*dlarnd( 1, iseed2 ) )
1266 IF( iu.LT.il ) THEN
1267 itemp = iu
1268 iu = il
1269 il = itemp
1270 END IF
1271 END IF
1272*
1273 CALL dcopy( mnmin, bd, 1, work( iwbd ), 1 )
1274 IF( mnmin.GT.0 )
1275 \$ CALL dcopy( mnmin-1, be, 1, work( iwbe ), 1 )
1276*
1277 CALL dbdsvdx( uplo, 'V', 'I', mnmin, work( iwbd ),
1278 \$ work( iwbe ), zero, zero, il, iu, ns1, s1,
1279 \$ work( iwbz ), mnmin2, work( iwwork ),
1280 \$ iwork, iinfo)
1281*
1282* Check error code from DBDSVDX.
1283*
1284 IF( iinfo.NE.0 ) THEN
1285 WRITE( nout, fmt = 9998 )'DBDSVDX(vects,I)', iinfo,
1286 \$ m, n, jtype, ioldsd
1287 info = abs( iinfo )
1288 IF( iinfo.LT.0 ) THEN
1289 RETURN
1290 ELSE
1291 result( 25 ) = ulpinv
1292 GO TO 270
1293 END IF
1294 END IF
1295*
1296 j = iwbz
1297 DO 210 i = 1, ns1
1298 CALL dcopy( mnmin, work( j ), 1, u( 1,i ), 1 )
1299 j = j + mnmin
1300 CALL dcopy( mnmin, work( j ), 1, vt( i,1 ), ldpt )
1301 j = j + mnmin
1302 210 CONTINUE
1303*
1304* Use DBDSVDX to compute only the singular values of the
1305* bidiagonal matrix B; U and VT should not be modified.
1306*
1307 CALL dcopy( mnmin, bd, 1, work( iwbd ), 1 )
1308 IF( mnmin.GT.0 )
1309 \$ CALL dcopy( mnmin-1, be, 1, work( iwbe ), 1 )
1310*
1311 CALL dbdsvdx( uplo, 'N', 'I', mnmin, work( iwbd ),
1312 \$ work( iwbe ), zero, zero, il, iu, ns2, s2,
1313 \$ work( iwbz ), mnmin2, work( iwwork ),
1314 \$ iwork, iinfo )
1315*
1316* Check error code from DBDSVDX.
1317*
1318 IF( iinfo.NE.0 ) THEN
1319 WRITE( nout, fmt = 9998 )'DBDSVDX(values,I)', iinfo,
1320 \$ m, n, jtype, ioldsd
1321 info = abs( iinfo )
1322 IF( iinfo.LT.0 ) THEN
1323 RETURN
1324 ELSE
1325 result( 29 ) = ulpinv
1326 GO TO 270
1327 END IF
1328 END IF
1329*
1330* Test 25: Check S1 - U' * B * VT'
1331* 26: Check the orthogonality of U
1332* 27: Check the orthogonality of VT
1333* 28: Check that the singular values are sorted in
1334* non-increasing order and are non-negative
1335* 29: Compare DBDSVDX with and without singular vectors
1336*
1337 CALL dbdt04( uplo, mnmin, bd, be, s1, ns1, u,
1338 \$ ldpt, vt, ldpt, work( iwbs+mnmin ),
1339 \$ result( 25 ) )
1340 CALL dort01( 'Columns', mnmin, ns1, u, ldpt,
1341 \$ work( iwbs+mnmin ), lwork-mnmin,
1342 \$ result( 26 ) )
1343 CALL dort01( 'Rows', ns1, mnmin, vt, ldpt,
1344 \$ work( iwbs+mnmin ), lwork-mnmin,
1345 \$ result( 27 ) )
1346*
1347 result( 28 ) = zero
1348 DO 220 i = 1, ns1 - 1
1349 IF( s1( i ).LT.s1( i+1 ) )
1350 \$ result( 28 ) = ulpinv
1351 IF( s1( i ).LT.zero )
1352 \$ result( 28 ) = ulpinv
1353 220 CONTINUE
1354 IF( ns1.GE.1 ) THEN
1355 IF( s1( ns1 ).LT.zero )
1356 \$ result( 28 ) = ulpinv
1357 END IF
1358*
1359 temp2 = zero
1360 DO 230 j = 1, ns1
1361 temp1 = abs( s1( j )-s2( j ) ) /
1362 \$ max( sqrt( unfl )*max( s1( 1 ), one ),
1363 \$ ulp*max( abs( s1( 1 ) ), abs( s2( 1 ) ) ) )
1364 temp2 = max( temp1, temp2 )
1365 230 CONTINUE
1366 result( 29 ) = temp2
1367*
1368* Use DBDSVDX with RANGE='V': determine the values VL and VU
1369* of the IL-th and IU-th singular values and ask for all
1370* singular values in this range.
1371*
1372 CALL dcopy( mnmin, work( iwbs ), 1, s1, 1 )
1373*
1374 IF( mnmin.GT.0 ) THEN
1375 IF( il.NE.1 ) THEN
1376 vu = s1( il ) + max( half*abs( s1( il )-s1( il-1 ) ),
1377 \$ ulp*anorm, two*rtunfl )
1378 ELSE
1379 vu = s1( 1 ) + max( half*abs( s1( mnmin )-s1( 1 ) ),
1380 \$ ulp*anorm, two*rtunfl )
1381 END IF
1382 IF( iu.NE.ns1 ) THEN
1383 vl = s1( iu ) - max( ulp*anorm, two*rtunfl,
1384 \$ half*abs( s1( iu+1 )-s1( iu ) ) )
1385 ELSE
1386 vl = s1( ns1 ) - max( ulp*anorm, two*rtunfl,
1387 \$ half*abs( s1( mnmin )-s1( 1 ) ) )
1388 END IF
1389 vl = max( vl,zero )
1390 vu = max( vu,zero )
1391 IF( vl.GE.vu ) vu = max( vu*2, vu+vl+half )
1392 ELSE
1393 vl = zero
1394 vu = one
1395 END IF
1396*
1397 CALL dcopy( mnmin, bd, 1, work( iwbd ), 1 )
1398 IF( mnmin.GT.0 )
1399 \$ CALL dcopy( mnmin-1, be, 1, work( iwbe ), 1 )
1400*
1401 CALL dbdsvdx( uplo, 'V', 'V', mnmin, work( iwbd ),
1402 \$ work( iwbe ), vl, vu, 0, 0, ns1, s1,
1403 \$ work( iwbz ), mnmin2, work( iwwork ),
1404 \$ iwork, iinfo )
1405*
1406* Check error code from DBDSVDX.
1407*
1408 IF( iinfo.NE.0 ) THEN
1409 WRITE( nout, fmt = 9998 )'DBDSVDX(vects,V)', iinfo,
1410 \$ m, n, jtype, ioldsd
1411 info = abs( iinfo )
1412 IF( iinfo.LT.0 ) THEN
1413 RETURN
1414 ELSE
1415 result( 30 ) = ulpinv
1416 GO TO 270
1417 END IF
1418 END IF
1419*
1420 j = iwbz
1421 DO 240 i = 1, ns1
1422 CALL dcopy( mnmin, work( j ), 1, u( 1,i ), 1 )
1423 j = j + mnmin
1424 CALL dcopy( mnmin, work( j ), 1, vt( i,1 ), ldpt )
1425 j = j + mnmin
1426 240 CONTINUE
1427*
1428* Use DBDSVDX to compute only the singular values of the
1429* bidiagonal matrix B; U and VT should not be modified.
1430*
1431 CALL dcopy( mnmin, bd, 1, work( iwbd ), 1 )
1432 IF( mnmin.GT.0 )
1433 \$ CALL dcopy( mnmin-1, be, 1, work( iwbe ), 1 )
1434*
1435 CALL dbdsvdx( uplo, 'N', 'V', mnmin, work( iwbd ),
1436 \$ work( iwbe ), vl, vu, 0, 0, ns2, s2,
1437 \$ work( iwbz ), mnmin2, work( iwwork ),
1438 \$ iwork, iinfo )
1439*
1440* Check error code from DBDSVDX.
1441*
1442 IF( iinfo.NE.0 ) THEN
1443 WRITE( nout, fmt = 9998 )'DBDSVDX(values,V)', iinfo,
1444 \$ m, n, jtype, ioldsd
1445 info = abs( iinfo )
1446 IF( iinfo.LT.0 ) THEN
1447 RETURN
1448 ELSE
1449 result( 34 ) = ulpinv
1450 GO TO 270
1451 END IF
1452 END IF
1453*
1454* Test 30: Check S1 - U' * B * VT'
1455* 31: Check the orthogonality of U
1456* 32: Check the orthogonality of VT
1457* 33: Check that the singular values are sorted in
1458* non-increasing order and are non-negative
1459* 34: Compare DBDSVDX with and without singular vectors
1460*
1461 CALL dbdt04( uplo, mnmin, bd, be, s1, ns1, u,
1462 \$ ldpt, vt, ldpt, work( iwbs+mnmin ),
1463 \$ result( 30 ) )
1464 CALL dort01( 'Columns', mnmin, ns1, u, ldpt,
1465 \$ work( iwbs+mnmin ), lwork-mnmin,
1466 \$ result( 31 ) )
1467 CALL dort01( 'Rows', ns1, mnmin, vt, ldpt,
1468 \$ work( iwbs+mnmin ), lwork-mnmin,
1469 \$ result( 32 ) )
1470*
1471 result( 33 ) = zero
1472 DO 250 i = 1, ns1 - 1
1473 IF( s1( i ).LT.s1( i+1 ) )
1474 \$ result( 28 ) = ulpinv
1475 IF( s1( i ).LT.zero )
1476 \$ result( 28 ) = ulpinv
1477 250 CONTINUE
1478 IF( ns1.GE.1 ) THEN
1479 IF( s1( ns1 ).LT.zero )
1480 \$ result( 28 ) = ulpinv
1481 END IF
1482*
1483 temp2 = zero
1484 DO 260 j = 1, ns1
1485 temp1 = abs( s1( j )-s2( j ) ) /
1486 \$ max( sqrt( unfl )*max( s1( 1 ), one ),
1487 \$ ulp*max( abs( s1( 1 ) ), abs( s2( 1 ) ) ) )
1488 temp2 = max( temp1, temp2 )
1489 260 CONTINUE
1490 result( 34 ) = temp2
1491*
1492* End of Loop -- Check for RESULT(j) > THRESH
1493*
1494 270 CONTINUE
1495*
1496 DO 280 j = 1, 34
1497 IF( result( j ).GE.thresh ) THEN
1498 IF( nfail.EQ.0 )
1499 \$ CALL dlahd2( nout, path )
1500 WRITE( nout, fmt = 9999 )m, n, jtype, ioldsd, j,
1501 \$ result( j )
1502 nfail = nfail + 1
1503 END IF
1504 280 CONTINUE
1505 IF( .NOT.bidiag ) THEN
1506 ntest = ntest + 34
1507 ELSE
1508 ntest = ntest + 30
1509 END IF
1510*
1511 290 CONTINUE
1512 300 CONTINUE
1513*
1514* Summary
1515*
1516 CALL alasum( path, nout, nfail, ntest, 0 )
1517*
1518 RETURN
1519*
1520* End of DCHKBD
1521*
1522 9999 FORMAT( ' M=', i5, ', N=', i5, ', type ', i2, ', seed=',
1523 \$ 4( i4, ',' ), ' test(', i2, ')=', g11.4 )
1524 9998 FORMAT( ' DCHKBD: ', a, ' returned INFO=', i6, '.', / 9x, 'M=',
1525 \$ i6, ', N=', i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ),
1526 \$ i5, ')' )
1527*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: dlaset.f:110
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine alasum(TYPE, NOUT, NFAIL, NRUN, NERRS)
ALASUM
Definition: alasum.f:73
subroutine dbdsdc(UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO)
DBDSDC
Definition: dbdsdc.f:205
subroutine dbdsqr(UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK, INFO)
DBDSQR
Definition: dbdsqr.f:241
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
double precision function dsxt1(IJOB, D1, N1, D2, N2, ABSTOL, ULP, UNFL)
DSXT1
Definition: dsxt1.f:106
subroutine dbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RESID)
DBDT01
Definition: dbdt01.f:141
subroutine dbdt02(M, N, B, LDB, C, LDC, U, LDU, WORK, RESID)
DBDT02
Definition: dbdt02.f:112
subroutine dort01(ROWCOL, M, N, U, LDU, WORK, LWORK, RESID)
DORT01
Definition: dort01.f:116
subroutine dbdt03(UPLO, N, KD, D, E, U, LDU, S, VT, LDVT, WORK, RESID)
DBDT03
Definition: dbdt03.f:135
subroutine dbdt04(UPLO, N, D, E, S, NS, U, LDU, VT, LDVT, WORK, RESID)
DBDT04
Definition: dbdt04.f:131
subroutine dlahd2(IOUNIT, PATH)
DLAHD2
Definition: dlahd2.f:65
subroutine dlatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
DLATMR
Definition: dlatmr.f:471
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:73
subroutine dlatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
DLATMS
Definition: dlatms.f:321
subroutine dorgbr(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
DORGBR
Definition: dorgbr.f:157
subroutine dgebrd(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, LWORK, INFO)
DGEBRD
Definition: dgebrd.f:205
subroutine dbdsvdx(UPLO, JOBZ, RANGE, N, D, E, VL, VU, IL, IU, NS, S, Z, LDZ, WORK, IWORK, INFO)
DBDSVDX
Definition: dbdsvdx.f:226
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