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|
*> \brief \b DCHKBD
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
* ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
* Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
* IWORK, NOUT, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
* $ NSIZES, NTYPES
* DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
* LOGICAL DOTYPE( * )
* INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), NVAL( * )
* DOUBLE PRECISION A( LDA, * ), BD( * ), BE( * ), PT( LDPT, * ),
* $ Q( LDQ, * ), S1( * ), S2( * ), U( LDPT, * ),
* $ VT( LDPT, * ), WORK( * ), X( LDX, * ),
* $ Y( LDX, * ), Z( LDX, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*>
*> 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.
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] NSIZES
*> \verbatim
*> 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).
*> \endverbatim
*>
*> \param[in] MVAL
*> \verbatim
*> MVAL is INTEGER array, dimension (NM)
*> The values of the matrix row dimension M.
*> \endverbatim
*>
*> \param[in] NVAL
*> \verbatim
*> NVAL is INTEGER array, dimension (NM)
*> The values of the matrix column dimension N.
*> \endverbatim
*>
*> \param[in] NTYPES
*> \verbatim
*> 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. .
*> \endverbatim
*>
*> \param[in] DOTYPE
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] THRESH
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,NMAX)
*> where NMAX is the maximum value of N in NVAL.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,MMAX),
*> where MMAX is the maximum value of M in MVAL.
*> \endverbatim
*>
*> \param[out] BD
*> \verbatim
*> BD is DOUBLE PRECISION array, dimension
*> (max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] BE
*> \verbatim
*> BE is DOUBLE PRECISION array, dimension
*> (max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] S1
*> \verbatim
*> S1 is DOUBLE PRECISION array, dimension
*> (max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] S2
*> \verbatim
*> S2 is DOUBLE PRECISION array, dimension
*> (max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the arrays X, Y, and Z.
*> LDX >= max(1,MMAX)
*> \endverbatim
*>
*> \param[out] Y
*> \verbatim
*> Y is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is DOUBLE PRECISION array, dimension (LDQ,MMAX)
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= max(1,MMAX).
*> \endverbatim
*>
*> \param[out] PT
*> \verbatim
*> PT is DOUBLE PRECISION array, dimension (LDPT,NMAX)
*> \endverbatim
*>
*> \param[in] LDPT
*> \verbatim
*> LDPT is INTEGER
*> The leading dimension of the arrays PT, U, and V.
*> LDPT >= max(1, max(min(MVAL(j),NVAL(j)))).
*> \endverbatim
*>
*> \param[out] U
*> \verbatim
*> U is DOUBLE PRECISION array, dimension
*> (LDPT,max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] VT
*> \verbatim
*> VT is DOUBLE PRECISION array, dimension
*> (LDPT,max(min(MVAL(j),NVAL(j))))
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> 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))
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension at least 8*min(M,N)
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The FORTRAN unit number for printing out error messages
*> (e.g., if a routine returns IINFO not equal to 0.)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> 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) )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DCHKBD( NSIZES, MVAL, NVAL, NTYPES, DOTYPE, NRHS,
$ ISEED, THRESH, A, LDA, BD, BE, S1, S2, X, LDX,
$ Y, Z, Q, LDQ, PT, LDPT, U, VT, WORK, LWORK,
$ IWORK, NOUT, INFO )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDPT, LDQ, LDX, LWORK, NOUT, NRHS,
$ NSIZES, NTYPES
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER ISEED( 4 ), IWORK( * ), MVAL( * ), NVAL( * )
DOUBLE PRECISION A( LDA, * ), BD( * ), BE( * ), PT( LDPT, * ),
$ Q( LDQ, * ), S1( * ), S2( * ), U( LDPT, * ),
$ VT( LDPT, * ), WORK( * ), X( LDX, * ),
$ Y( LDX, * ), Z( LDX, * )
* ..
*
* ======================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TWO, HALF
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0,
$ HALF = 0.5D0 )
INTEGER MAXTYP
PARAMETER ( MAXTYP = 16 )
* ..
* .. Local Scalars ..
LOGICAL BADMM, BADNN, BIDIAG
CHARACTER UPLO
CHARACTER*3 PATH
INTEGER I, IINFO, IMODE, ITYPE, J, JCOL, JSIZE, JTYPE,
$ LOG2UI, M, MINWRK, MMAX, MNMAX, MNMIN, MQ,
$ MTYPES, N, NFAIL, NMAX, NTEST
DOUBLE PRECISION AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL,
$ TEMP1, TEMP2, ULP, ULPINV, UNFL
* ..
* .. Local Arrays ..
INTEGER IDUM( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
$ KMODE( MAXTYP ), KTYPE( MAXTYP )
DOUBLE PRECISION DUM( 1 ), DUMMA( 1 ), RESULT( 19 )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLARND
EXTERNAL DLAMCH, DLARND
* ..
* .. External Subroutines ..
EXTERNAL ALASUM, DBDSDC, DBDSQR, DBDT01, DBDT02, DBDT03,
$ DCOPY, DGEBRD, DGEMM, DLABAD, DLACPY, DLAHD2,
$ DLASET, DLATMR, DLATMS, DORGBR, DORT01, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, EXP, INT, LOG, MAX, MIN, SQRT
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, NUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, NUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA KTYPE / 1, 2, 5*4, 5*6, 3*9, 10 /
DATA KMAGN / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3, 0 /
DATA KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
$ 0, 0, 0 /
* ..
* .. Executable Statements ..
*
* Check for errors
*
INFO = 0
*
BADMM = .FALSE.
BADNN = .FALSE.
MMAX = 1
NMAX = 1
MNMAX = 1
MINWRK = 1
DO 10 J = 1, NSIZES
MMAX = MAX( MMAX, MVAL( J ) )
IF( MVAL( J ).LT.0 )
$ BADMM = .TRUE.
NMAX = MAX( NMAX, NVAL( J ) )
IF( NVAL( J ).LT.0 )
$ BADNN = .TRUE.
MNMAX = MAX( MNMAX, MIN( MVAL( J ), NVAL( J ) ) )
MINWRK = MAX( MINWRK, 3*( MVAL( J )+NVAL( J ) ),
$ MVAL( J )*( MVAL( J )+MAX( MVAL( J ), NVAL( J ),
$ NRHS )+1 )+NVAL( J )*MIN( NVAL( J ), MVAL( J ) ) )
10 CONTINUE
*
* Check for errors
*
IF( NSIZES.LT.0 ) THEN
INFO = -1
ELSE IF( BADMM ) THEN
INFO = -2
ELSE IF( BADNN ) THEN
INFO = -3
ELSE IF( NTYPES.LT.0 ) THEN
INFO = -4
ELSE IF( NRHS.LT.0 ) THEN
INFO = -6
ELSE IF( LDA.LT.MMAX ) THEN
INFO = -11
ELSE IF( LDX.LT.MMAX ) THEN
INFO = -17
ELSE IF( LDQ.LT.MMAX ) THEN
INFO = -21
ELSE IF( LDPT.LT.MNMAX ) THEN
INFO = -23
ELSE IF( MINWRK.GT.LWORK ) THEN
INFO = -27
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DCHKBD', -INFO )
RETURN
END IF
*
* Initialize constants
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'BD'
NFAIL = 0
NTEST = 0
UNFL = DLAMCH( 'Safe minimum' )
OVFL = DLAMCH( 'Overflow' )
CALL DLABAD( UNFL, OVFL )
ULP = DLAMCH( 'Precision' )
ULPINV = ONE / ULP
LOG2UI = INT( LOG( ULPINV ) / LOG( TWO ) )
RTUNFL = SQRT( UNFL )
RTOVFL = SQRT( OVFL )
INFOT = 0
*
* Loop over sizes, types
*
DO 200 JSIZE = 1, NSIZES
M = MVAL( JSIZE )
N = NVAL( JSIZE )
MNMIN = MIN( M, N )
AMNINV = ONE / MAX( M, N, 1 )
*
IF( NSIZES.NE.1 ) THEN
MTYPES = MIN( MAXTYP, NTYPES )
ELSE
MTYPES = MIN( MAXTYP+1, NTYPES )
END IF
*
DO 190 JTYPE = 1, MTYPES
IF( .NOT.DOTYPE( JTYPE ) )
$ GO TO 190
*
DO 20 J = 1, 4
IOLDSD( J ) = ISEED( J )
20 CONTINUE
*
DO 30 J = 1, 14
RESULT( J ) = -ONE
30 CONTINUE
*
UPLO = ' '
*
* Compute "A"
*
* Control parameters:
*
* KMAGN KMODE KTYPE
* =1 O(1) clustered 1 zero
* =2 large clustered 2 identity
* =3 small exponential (none)
* =4 arithmetic diagonal, (w/ eigenvalues)
* =5 random symmetric, w/ eigenvalues
* =6 nonsymmetric, w/ singular values
* =7 random diagonal
* =8 random symmetric
* =9 random nonsymmetric
* =10 random bidiagonal (log. distrib.)
*
IF( MTYPES.GT.MAXTYP )
$ GO TO 100
*
ITYPE = KTYPE( JTYPE )
IMODE = KMODE( JTYPE )
*
* Compute norm
*
GO TO ( 40, 50, 60 )KMAGN( JTYPE )
*
40 CONTINUE
ANORM = ONE
GO TO 70
*
50 CONTINUE
ANORM = ( RTOVFL*ULP )*AMNINV
GO TO 70
*
60 CONTINUE
ANORM = RTUNFL*MAX( M, N )*ULPINV
GO TO 70
*
70 CONTINUE
*
CALL DLASET( 'Full', LDA, N, ZERO, ZERO, A, LDA )
IINFO = 0
COND = ULPINV
*
BIDIAG = .FALSE.
IF( ITYPE.EQ.1 ) THEN
*
* Zero matrix
*
IINFO = 0
*
ELSE IF( ITYPE.EQ.2 ) THEN
*
* Identity
*
DO 80 JCOL = 1, MNMIN
A( JCOL, JCOL ) = ANORM
80 CONTINUE
*
ELSE IF( ITYPE.EQ.4 ) THEN
*
* Diagonal Matrix, [Eigen]values Specified
*
CALL DLATMS( MNMIN, MNMIN, 'S', ISEED, 'N', WORK, IMODE,
$ COND, ANORM, 0, 0, 'N', A, LDA,
$ WORK( MNMIN+1 ), IINFO )
*
ELSE IF( ITYPE.EQ.5 ) THEN
*
* Symmetric, eigenvalues specified
*
CALL DLATMS( MNMIN, MNMIN, 'S', ISEED, 'S', WORK, IMODE,
$ COND, ANORM, M, N, 'N', A, LDA,
$ WORK( MNMIN+1 ), IINFO )
*
ELSE IF( ITYPE.EQ.6 ) THEN
*
* Nonsymmetric, singular values specified
*
CALL DLATMS( M, N, 'S', ISEED, 'N', WORK, IMODE, COND,
$ ANORM, M, N, 'N', A, LDA, WORK( MNMIN+1 ),
$ IINFO )
*
ELSE IF( ITYPE.EQ.7 ) THEN
*
* Diagonal, random entries
*
CALL DLATMR( MNMIN, MNMIN, 'S', ISEED, 'N', WORK, 6, ONE,
$ ONE, 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
$ WORK( 2*MNMIN+1 ), 1, ONE, 'N', IWORK, 0, 0,
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
*
ELSE IF( ITYPE.EQ.8 ) THEN
*
* Symmetric, random entries
*
CALL DLATMR( MNMIN, MNMIN, 'S', ISEED, 'S', WORK, 6, ONE,
$ ONE, 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
$ WORK( M+MNMIN+1 ), 1, ONE, 'N', IWORK, M, N,
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
*
ELSE IF( ITYPE.EQ.9 ) THEN
*
* Nonsymmetric, random entries
*
CALL DLATMR( M, N, 'S', ISEED, 'N', WORK, 6, ONE, ONE,
$ 'T', 'N', WORK( MNMIN+1 ), 1, ONE,
$ WORK( M+MNMIN+1 ), 1, ONE, 'N', IWORK, M, N,
$ ZERO, ANORM, 'NO', A, LDA, IWORK, IINFO )
*
ELSE IF( ITYPE.EQ.10 ) THEN
*
* Bidiagonal, random entries
*
TEMP1 = -TWO*LOG( ULP )
DO 90 J = 1, MNMIN
BD( J ) = EXP( TEMP1*DLARND( 2, ISEED ) )
IF( J.LT.MNMIN )
$ BE( J ) = EXP( TEMP1*DLARND( 2, ISEED ) )
90 CONTINUE
*
IINFO = 0
BIDIAG = .TRUE.
IF( M.GE.N ) THEN
UPLO = 'U'
ELSE
UPLO = 'L'
END IF
ELSE
IINFO = 1
END IF
*
IF( IINFO.EQ.0 ) THEN
*
* Generate Right-Hand Side
*
IF( BIDIAG ) THEN
CALL DLATMR( MNMIN, NRHS, 'S', ISEED, 'N', WORK, 6,
$ ONE, ONE, 'T', 'N', WORK( MNMIN+1 ), 1,
$ ONE, WORK( 2*MNMIN+1 ), 1, ONE, 'N',
$ IWORK, MNMIN, NRHS, ZERO, ONE, 'NO', Y,
$ LDX, IWORK, IINFO )
ELSE
CALL DLATMR( M, NRHS, 'S', ISEED, 'N', WORK, 6, ONE,
$ ONE, 'T', 'N', WORK( M+1 ), 1, ONE,
$ WORK( 2*M+1 ), 1, ONE, 'N', IWORK, M,
$ NRHS, ZERO, ONE, 'NO', X, LDX, IWORK,
$ IINFO )
END IF
END IF
*
* Error Exit
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUT, FMT = 9998 )'Generator', IINFO, M, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
100 CONTINUE
*
* Call DGEBRD and DORGBR to compute B, Q, and P, do tests.
*
IF( .NOT.BIDIAG ) THEN
*
* Compute transformations to reduce A to bidiagonal form:
* B := Q' * A * P.
*
CALL DLACPY( ' ', M, N, A, LDA, Q, LDQ )
CALL DGEBRD( M, N, Q, LDQ, BD, BE, WORK, WORK( MNMIN+1 ),
$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
*
* Check error code from DGEBRD.
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUT, FMT = 9998 )'DGEBRD', IINFO, M, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
CALL DLACPY( ' ', M, N, Q, LDQ, PT, LDPT )
IF( M.GE.N ) THEN
UPLO = 'U'
ELSE
UPLO = 'L'
END IF
*
* Generate Q
*
MQ = M
IF( NRHS.LE.0 )
$ MQ = MNMIN
CALL DORGBR( 'Q', M, MQ, N, Q, LDQ, WORK,
$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
*
* Check error code from DORGBR.
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUT, FMT = 9998 )'DORGBR(Q)', IINFO, M, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
* Generate P'
*
CALL DORGBR( 'P', MNMIN, N, M, PT, LDPT, WORK( MNMIN+1 ),
$ WORK( 2*MNMIN+1 ), LWORK-2*MNMIN, IINFO )
*
* Check error code from DORGBR.
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUT, FMT = 9998 )'DORGBR(P)', IINFO, M, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
RETURN
END IF
*
* Apply Q' to an M by NRHS matrix X: Y := Q' * X.
*
CALL DGEMM( 'Transpose', 'No transpose', M, NRHS, M, ONE,
$ Q, LDQ, X, LDX, ZERO, Y, LDX )
*
* Test 1: Check the decomposition A := Q * B * PT
* 2: Check the orthogonality of Q
* 3: Check the orthogonality of PT
*
CALL DBDT01( M, N, 1, A, LDA, Q, LDQ, BD, BE, PT, LDPT,
$ WORK, RESULT( 1 ) )
CALL DORT01( 'Columns', M, MQ, Q, LDQ, WORK, LWORK,
$ RESULT( 2 ) )
CALL DORT01( 'Rows', MNMIN, N, PT, LDPT, WORK, LWORK,
$ RESULT( 3 ) )
END IF
*
* Use DBDSQR to form the SVD of the bidiagonal matrix B:
* B := U * S1 * VT, and compute Z = U' * Y.
*
CALL DCOPY( MNMIN, BD, 1, S1, 1 )
IF( MNMIN.GT.0 )
$ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
CALL DLACPY( ' ', M, NRHS, Y, LDX, Z, LDX )
CALL DLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, U, LDPT )
CALL DLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, VT, LDPT )
*
CALL DBDSQR( UPLO, MNMIN, MNMIN, MNMIN, NRHS, S1, WORK, VT,
$ LDPT, U, LDPT, Z, LDX, WORK( MNMIN+1 ), IINFO )
*
* Check error code from DBDSQR.
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUT, FMT = 9998 )'DBDSQR(vects)', IINFO, M, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 4 ) = ULPINV
GO TO 170
END IF
END IF
*
* Use DBDSQR to compute only the singular values of the
* bidiagonal matrix B; U, VT, and Z should not be modified.
*
CALL DCOPY( MNMIN, BD, 1, S2, 1 )
IF( MNMIN.GT.0 )
$ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
*
CALL DBDSQR( UPLO, MNMIN, 0, 0, 0, S2, WORK, VT, LDPT, U,
$ LDPT, Z, LDX, WORK( MNMIN+1 ), IINFO )
*
* Check error code from DBDSQR.
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUT, FMT = 9998 )'DBDSQR(values)', IINFO, M, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 9 ) = ULPINV
GO TO 170
END IF
END IF
*
* Test 4: Check the decomposition B := U * S1 * VT
* 5: Check the computation Z := U' * Y
* 6: Check the orthogonality of U
* 7: Check the orthogonality of VT
*
CALL DBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT,
$ WORK, RESULT( 4 ) )
CALL DBDT02( MNMIN, NRHS, Y, LDX, Z, LDX, U, LDPT, WORK,
$ RESULT( 5 ) )
CALL DORT01( 'Columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK,
$ RESULT( 6 ) )
CALL DORT01( 'Rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK,
$ RESULT( 7 ) )
*
* Test 8: Check that the singular values are sorted in
* non-increasing order and are non-negative
*
RESULT( 8 ) = ZERO
DO 110 I = 1, MNMIN - 1
IF( S1( I ).LT.S1( I+1 ) )
$ RESULT( 8 ) = ULPINV
IF( S1( I ).LT.ZERO )
$ RESULT( 8 ) = ULPINV
110 CONTINUE
IF( MNMIN.GE.1 ) THEN
IF( S1( MNMIN ).LT.ZERO )
$ RESULT( 8 ) = ULPINV
END IF
*
* Test 9: Compare DBDSQR with and without singular vectors
*
TEMP2 = ZERO
*
DO 120 J = 1, MNMIN
TEMP1 = ABS( S1( J )-S2( J ) ) /
$ MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
$ ULP*MAX( ABS( S1( J ) ), ABS( S2( J ) ) ) )
TEMP2 = MAX( TEMP1, TEMP2 )
120 CONTINUE
*
RESULT( 9 ) = TEMP2
*
* Test 10: Sturm sequence test of singular values
* Go up by factors of two until it succeeds
*
TEMP1 = THRESH*( HALF-ULP )
*
DO 130 J = 0, LOG2UI
* CALL DSVDCH( MNMIN, BD, BE, S1, TEMP1, IINFO )
IF( IINFO.EQ.0 )
$ GO TO 140
TEMP1 = TEMP1*TWO
130 CONTINUE
*
140 CONTINUE
RESULT( 10 ) = TEMP1
*
* Use DBDSQR to form the decomposition A := (QU) S (VT PT)
* from the bidiagonal form A := Q B PT.
*
IF( .NOT.BIDIAG ) THEN
CALL DCOPY( MNMIN, BD, 1, S2, 1 )
IF( MNMIN.GT.0 )
$ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
*
CALL DBDSQR( UPLO, MNMIN, N, M, NRHS, S2, WORK, PT, LDPT,
$ Q, LDQ, Y, LDX, WORK( MNMIN+1 ), IINFO )
*
* Test 11: Check the decomposition A := Q*U * S2 * VT*PT
* 12: Check the computation Z := U' * Q' * X
* 13: Check the orthogonality of Q*U
* 14: Check the orthogonality of VT*PT
*
CALL DBDT01( M, N, 0, A, LDA, Q, LDQ, S2, DUMMA, PT,
$ LDPT, WORK, RESULT( 11 ) )
CALL DBDT02( M, NRHS, X, LDX, Y, LDX, Q, LDQ, WORK,
$ RESULT( 12 ) )
CALL DORT01( 'Columns', M, MQ, Q, LDQ, WORK, LWORK,
$ RESULT( 13 ) )
CALL DORT01( 'Rows', MNMIN, N, PT, LDPT, WORK, LWORK,
$ RESULT( 14 ) )
END IF
*
* Use DBDSDC to form the SVD of the bidiagonal matrix B:
* B := U * S1 * VT
*
CALL DCOPY( MNMIN, BD, 1, S1, 1 )
IF( MNMIN.GT.0 )
$ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
CALL DLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, U, LDPT )
CALL DLASET( 'Full', MNMIN, MNMIN, ZERO, ONE, VT, LDPT )
*
CALL DBDSDC( UPLO, 'I', MNMIN, S1, WORK, U, LDPT, VT, LDPT,
$ DUM, IDUM, WORK( MNMIN+1 ), IWORK, IINFO )
*
* Check error code from DBDSDC.
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUT, FMT = 9998 )'DBDSDC(vects)', IINFO, M, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 15 ) = ULPINV
GO TO 170
END IF
END IF
*
* Use DBDSDC to compute only the singular values of the
* bidiagonal matrix B; U and VT should not be modified.
*
CALL DCOPY( MNMIN, BD, 1, S2, 1 )
IF( MNMIN.GT.0 )
$ CALL DCOPY( MNMIN-1, BE, 1, WORK, 1 )
*
CALL DBDSDC( UPLO, 'N', MNMIN, S2, WORK, DUM, 1, DUM, 1,
$ DUM, IDUM, WORK( MNMIN+1 ), IWORK, IINFO )
*
* Check error code from DBDSDC.
*
IF( IINFO.NE.0 ) THEN
WRITE( NOUT, FMT = 9998 )'DBDSDC(values)', IINFO, M, N,
$ JTYPE, IOLDSD
INFO = ABS( IINFO )
IF( IINFO.LT.0 ) THEN
RETURN
ELSE
RESULT( 18 ) = ULPINV
GO TO 170
END IF
END IF
*
* Test 15: Check the decomposition B := U * S1 * VT
* 16: Check the orthogonality of U
* 17: Check the orthogonality of VT
*
CALL DBDT03( UPLO, MNMIN, 1, BD, BE, U, LDPT, S1, VT, LDPT,
$ WORK, RESULT( 15 ) )
CALL DORT01( 'Columns', MNMIN, MNMIN, U, LDPT, WORK, LWORK,
$ RESULT( 16 ) )
CALL DORT01( 'Rows', MNMIN, MNMIN, VT, LDPT, WORK, LWORK,
$ RESULT( 17 ) )
*
* Test 18: Check that the singular values are sorted in
* non-increasing order and are non-negative
*
RESULT( 18 ) = ZERO
DO 150 I = 1, MNMIN - 1
IF( S1( I ).LT.S1( I+1 ) )
$ RESULT( 18 ) = ULPINV
IF( S1( I ).LT.ZERO )
$ RESULT( 18 ) = ULPINV
150 CONTINUE
IF( MNMIN.GE.1 ) THEN
IF( S1( MNMIN ).LT.ZERO )
$ RESULT( 18 ) = ULPINV
END IF
*
* Test 19: Compare DBDSQR with and without singular vectors
*
TEMP2 = ZERO
*
DO 160 J = 1, MNMIN
TEMP1 = ABS( S1( J )-S2( J ) ) /
$ MAX( SQRT( UNFL )*MAX( S1( 1 ), ONE ),
$ ULP*MAX( ABS( S1( 1 ) ), ABS( S2( 1 ) ) ) )
TEMP2 = MAX( TEMP1, TEMP2 )
160 CONTINUE
*
RESULT( 19 ) = TEMP2
*
* End of Loop -- Check for RESULT(j) > THRESH
*
170 CONTINUE
DO 180 J = 1, 19
IF( RESULT( J ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 )
$ CALL DLAHD2( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )M, N, JTYPE, IOLDSD, J,
$ RESULT( J )
NFAIL = NFAIL + 1
END IF
180 CONTINUE
IF( .NOT.BIDIAG ) THEN
NTEST = NTEST + 19
ELSE
NTEST = NTEST + 5
END IF
*
190 CONTINUE
200 CONTINUE
*
* Summary
*
CALL ALASUM( PATH, NOUT, NFAIL, NTEST, 0 )
*
RETURN
*
* End of DCHKBD
*
9999 FORMAT( ' M=', I5, ', N=', I5, ', type ', I2, ', seed=',
$ 4( I4, ',' ), ' test(', I2, ')=', G11.4 )
9998 FORMAT( ' DCHKBD: ', A, ' returned INFO=', I6, '.', / 9X, 'M=',
$ I6, ', N=', I6, ', JTYPE=', I6, ', ISEED=(', 3( I5, ',' ),
$ I5, ')' )
*
END
|
