SUBROUTINE DDRVLS( DOTYPE, NM, MVAL, NN, NVAL, NNS, NSVAL, NNB,
$ NBVAL, NXVAL, THRESH, TSTERR, A, COPYA, B,
$ COPYB, C, S, COPYS, WORK, IWORK, NOUT )
*
* -- LAPACK test routine (version 3.1.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* January 2007
*
* .. Scalar Arguments ..
LOGICAL TSTERR
INTEGER NM, NN, NNB, NNS, NOUT
DOUBLE PRECISION THRESH
* ..
* .. Array Arguments ..
LOGICAL DOTYPE( * )
INTEGER IWORK( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
$ NVAL( * ), NXVAL( * )
DOUBLE PRECISION A( * ), B( * ), C( * ), COPYA( * ), COPYB( * ),
$ COPYS( * ), S( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DDRVLS tests the least squares driver routines DGELS, DGELSS, DGELSX,
* DGELSY and DGELSD.
*
* Arguments
* =========
*
* DOTYPE (input) LOGICAL array, dimension (NTYPES)
* The matrix types to be used for testing. Matrices of type j
* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
* The matrix of type j is generated as follows:
* j=1: A = U*D*V where U and V are random orthogonal matrices
* and D has random entries (> 0.1) taken from a uniform
* distribution (0,1). A is full rank.
* j=2: The same of 1, but A is scaled up.
* j=3: The same of 1, but A is scaled down.
* j=4: A = U*D*V where U and V are random orthogonal matrices
* and D has 3*min(M,N)/4 random entries (> 0.1) taken
* from a uniform distribution (0,1) and the remaining
* entries set to 0. A is rank-deficient.
* j=5: The same of 4, but A is scaled up.
* j=6: The same of 5, but A is scaled down.
*
* NM (input) INTEGER
* The number of values of M contained in the vector MVAL.
*
* MVAL (input) INTEGER array, dimension (NM)
* The values of the matrix row dimension M.
*
* NN (input) INTEGER
* The number of values of N contained in the vector NVAL.
*
* NVAL (input) INTEGER array, dimension (NN)
* The values of the matrix column dimension N.
*
* NNS (input) INTEGER
* The number of values of NRHS contained in the vector NSVAL.
*
* NSVAL (input) INTEGER array, dimension (NNS)
* The values of the number of right hand sides NRHS.
*
* NNB (input) INTEGER
* The number of values of NB and NX contained in the
* vectors NBVAL and NXVAL. The blocking parameters are used
* in pairs (NB,NX).
*
* NBVAL (input) INTEGER array, dimension (NNB)
* The values of the blocksize NB.
*
* NXVAL (input) INTEGER array, dimension (NNB)
* The values of the crossover point NX.
*
* THRESH (input) 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.
*
* TSTERR (input) LOGICAL
* Flag that indicates whether error exits are to be tested.
*
* A (workspace) DOUBLE PRECISION array, dimension (MMAX*NMAX)
* where MMAX is the maximum value of M in MVAL and NMAX is the
* maximum value of N in NVAL.
*
* COPYA (workspace) DOUBLE PRECISION array, dimension (MMAX*NMAX)
*
* B (workspace) DOUBLE PRECISION array, dimension (MMAX*NSMAX)
* where MMAX is the maximum value of M in MVAL and NSMAX is the
* maximum value of NRHS in NSVAL.
*
* COPYB (workspace) DOUBLE PRECISION array, dimension (MMAX*NSMAX)
*
* C (workspace) DOUBLE PRECISION array, dimension (MMAX*NSMAX)
*
* S (workspace) DOUBLE PRECISION array, dimension
* (min(MMAX,NMAX))
*
* COPYS (workspace) DOUBLE PRECISION array, dimension
* (min(MMAX,NMAX))
*
* WORK (workspace) DOUBLE PRECISION array,
* dimension (MMAX*NMAX + 4*NMAX + MMAX).
*
* IWORK (workspace) INTEGER array, dimension (15*NMAX)
*
* NOUT (input) INTEGER
* The unit number for output.
*
* =====================================================================
*
* .. Parameters ..
INTEGER NTESTS
PARAMETER ( NTESTS = 18 )
INTEGER SMLSIZ
PARAMETER ( SMLSIZ = 25 )
DOUBLE PRECISION ONE, TWO, ZERO
PARAMETER ( ONE = 1.0D0, TWO = 2.0D0, ZERO = 0.0D0 )
* ..
* .. Local Scalars ..
CHARACTER TRANS
CHARACTER*3 PATH
INTEGER CRANK, I, IM, IN, INB, INFO, INS, IRANK,
$ ISCALE, ITRAN, ITYPE, J, K, LDA, LDB, LDWORK,
$ LWLSY, LWORK, M, MNMIN, N, NB, NCOLS, NERRS,
$ NFAIL, NLVL, NRHS, NROWS, NRUN, RANK
DOUBLE PRECISION EPS, NORMA, NORMB, RCOND
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 ), ISEEDY( 4 )
DOUBLE PRECISION RESULT( NTESTS )
* ..
* .. External Functions ..
DOUBLE PRECISION DASUM, DLAMCH, DQRT12, DQRT14, DQRT17
EXTERNAL DASUM, DLAMCH, DQRT12, DQRT14, DQRT17
* ..
* .. External Subroutines ..
EXTERNAL ALAERH, ALAHD, ALASVM, DAXPY, DERRLS, DGELS,
$ DGELSD, DGELSS, DGELSX, DGELSY, DGEMM, DLACPY,
$ DLARNV, DLASRT, DQRT13, DQRT15, DQRT16, DSCAL,
$ XLAENV
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, INT, LOG, MAX, MIN, SQRT
* ..
* .. Scalars in Common ..
LOGICAL LERR, OK
CHARACTER*32 SRNAMT
INTEGER INFOT, IOUNIT
* ..
* .. Common blocks ..
COMMON / INFOC / INFOT, IOUNIT, OK, LERR
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEEDY / 1988, 1989, 1990, 1991 /
* ..
* .. Executable Statements ..
*
* Initialize constants and the random number seed.
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'LS'
NRUN = 0
NFAIL = 0
NERRS = 0
DO 10 I = 1, 4
ISEED( I ) = ISEEDY( I )
10 CONTINUE
EPS = DLAMCH( 'Epsilon' )
*
* Threshold for rank estimation
*
RCOND = SQRT( EPS ) - ( SQRT( EPS )-EPS ) / 2
*
* Test the error exits
*
CALL XLAENV( 2, 2 )
CALL XLAENV( 9, SMLSIZ )
IF( TSTERR )
$ CALL DERRLS( PATH, NOUT )
*
* Print the header if NM = 0 or NN = 0 and THRESH = 0.
*
IF( ( NM.EQ.0 .OR. NN.EQ.0 ) .AND. THRESH.EQ.ZERO )
$ CALL ALAHD( NOUT, PATH )
INFOT = 0
CALL XLAENV( 2, 2 )
CALL XLAENV( 9, SMLSIZ )
*
DO 150 IM = 1, NM
M = MVAL( IM )
LDA = MAX( 1, M )
*
DO 140 IN = 1, NN
N = NVAL( IN )
MNMIN = MIN( M, N )
LDB = MAX( 1, M, N )
*
DO 130 INS = 1, NNS
NRHS = NSVAL( INS )
NLVL = MAX( INT( LOG( MAX( ONE, DBLE( MNMIN ) ) /
$ DBLE( SMLSIZ+1 ) ) / LOG( TWO ) ) + 1, 0 )
LWORK = MAX( 1, ( M+NRHS )*( N+2 ), ( N+NRHS )*( M+2 ),
$ M*N+4*MNMIN+MAX( M, N ), 12*MNMIN+2*MNMIN*SMLSIZ+
$ 8*MNMIN*NLVL+MNMIN*NRHS+(SMLSIZ+1)**2 )
*
DO 120 IRANK = 1, 2
DO 110 ISCALE = 1, 3
ITYPE = ( IRANK-1 )*3 + ISCALE
IF( .NOT.DOTYPE( ITYPE ) )
$ GO TO 110
*
IF( IRANK.EQ.1 ) THEN
*
* Test DGELS
*
* Generate a matrix of scaling type ISCALE
*
CALL DQRT13( ISCALE, M, N, COPYA, LDA, NORMA,
$ ISEED )
DO 40 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
CALL XLAENV( 3, NXVAL( INB ) )
*
DO 30 ITRAN = 1, 2
IF( ITRAN.EQ.1 ) THEN
TRANS = 'N'
NROWS = M
NCOLS = N
ELSE
TRANS = 'T'
NROWS = N
NCOLS = M
END IF
LDWORK = MAX( 1, NCOLS )
*
* Set up a consistent rhs
*
IF( NCOLS.GT.0 ) THEN
CALL DLARNV( 2, ISEED, NCOLS*NRHS,
$ WORK )
CALL DSCAL( NCOLS*NRHS,
$ ONE / DBLE( NCOLS ), WORK,
$ 1 )
END IF
CALL DGEMM( TRANS, 'No transpose', NROWS,
$ NRHS, NCOLS, ONE, COPYA, LDA,
$ WORK, LDWORK, ZERO, B, LDB )
CALL DLACPY( 'Full', NROWS, NRHS, B, LDB,
$ COPYB, LDB )
*
* Solve LS or overdetermined system
*
IF( M.GT.0 .AND. N.GT.0 ) THEN
CALL DLACPY( 'Full', M, N, COPYA, LDA,
$ A, LDA )
CALL DLACPY( 'Full', NROWS, NRHS,
$ COPYB, LDB, B, LDB )
END IF
SRNAMT = 'DGELS '
CALL DGELS( TRANS, M, N, NRHS, A, LDA, B,
$ LDB, WORK, LWORK, INFO )
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DGELS ', INFO, 0,
$ TRANS, M, N, NRHS, -1, NB,
$ ITYPE, NFAIL, NERRS,
$ NOUT )
*
* Check correctness of results
*
LDWORK = MAX( 1, NROWS )
IF( NROWS.GT.0 .AND. NRHS.GT.0 )
$ CALL DLACPY( 'Full', NROWS, NRHS,
$ COPYB, LDB, C, LDB )
CALL DQRT16( TRANS, M, N, NRHS, COPYA,
$ LDA, B, LDB, C, LDB, WORK,
$ RESULT( 1 ) )
*
IF( ( ITRAN.EQ.1 .AND. M.GE.N ) .OR.
$ ( ITRAN.EQ.2 .AND. M.LT.N ) ) THEN
*
* Solving LS system
*
RESULT( 2 ) = DQRT17( TRANS, 1, M, N,
$ NRHS, COPYA, LDA, B, LDB,
$ COPYB, LDB, C, WORK,
$ LWORK )
ELSE
*
* Solving overdetermined system
*
RESULT( 2 ) = DQRT14( TRANS, M, N,
$ NRHS, COPYA, LDA, B, LDB,
$ WORK, LWORK )
END IF
*
* Print information about the tests that
* did not pass the threshold.
*
DO 20 K = 1, 2
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9999 )TRANS, M,
$ N, NRHS, NB, ITYPE, K,
$ RESULT( K )
NFAIL = NFAIL + 1
END IF
20 CONTINUE
NRUN = NRUN + 2
30 CONTINUE
40 CONTINUE
END IF
*
* Generate a matrix of scaling type ISCALE and rank
* type IRANK.
*
CALL DQRT15( ISCALE, IRANK, M, N, NRHS, COPYA, LDA,
$ COPYB, LDB, COPYS, RANK, NORMA, NORMB,
$ ISEED, WORK, LWORK )
*
* workspace used: MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
*
* Initialize vector IWORK.
*
DO 50 J = 1, N
IWORK( J ) = 0
50 CONTINUE
LDWORK = MAX( 1, M )
*
* Test DGELSX
*
* DGELSX: Compute the minimum-norm solution X
* to min( norm( A * X - B ) ) using a complete
* orthogonal factorization.
*
CALL DLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, B, LDB )
*
SRNAMT = 'DGELSX'
CALL DGELSX( M, N, NRHS, A, LDA, B, LDB, IWORK,
$ RCOND, CRANK, WORK, INFO )
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DGELSX', INFO, 0, ' ', M, N,
$ NRHS, -1, NB, ITYPE, NFAIL, NERRS,
$ NOUT )
*
* workspace used: MAX( MNMIN+3*N, 2*MNMIN+NRHS )
*
* Test 3: Compute relative error in svd
* workspace: M*N + 4*MIN(M,N) + MAX(M,N)
*
RESULT( 3 ) = DQRT12( CRANK, CRANK, A, LDA, COPYS,
$ WORK, LWORK )
*
* Test 4: Compute error in solution
* workspace: M*NRHS + M
*
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
$ LDWORK )
CALL DQRT16( 'No transpose', M, N, NRHS, COPYA,
$ LDA, B, LDB, WORK, LDWORK,
$ WORK( M*NRHS+1 ), RESULT( 4 ) )
*
* Test 5: Check norm of r'*A
* workspace: NRHS*(M+N)
*
RESULT( 5 ) = ZERO
IF( M.GT.CRANK )
$ RESULT( 5 ) = DQRT17( 'No transpose', 1, M, N,
$ NRHS, COPYA, LDA, B, LDB, COPYB,
$ LDB, C, WORK, LWORK )
*
* Test 6: Check if x is in the rowspace of A
* workspace: (M+NRHS)*(N+2)
*
RESULT( 6 ) = ZERO
*
IF( N.GT.CRANK )
$ RESULT( 6 ) = DQRT14( 'No transpose', M, N,
$ NRHS, COPYA, LDA, B, LDB, WORK,
$ LWORK )
*
* Print information about the tests that did not
* pass the threshold.
*
DO 60 K = 3, 6
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )M, N, NRHS, NB,
$ ITYPE, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
60 CONTINUE
NRUN = NRUN + 4
*
* Loop for testing different block sizes.
*
DO 100 INB = 1, NNB
NB = NBVAL( INB )
CALL XLAENV( 1, NB )
CALL XLAENV( 3, NXVAL( INB ) )
*
* Test DGELSY
*
* DGELSY: Compute the minimum-norm solution X
* to min( norm( A * X - B ) )
* using the rank-revealing orthogonal
* factorization.
*
* Initialize vector IWORK.
*
DO 70 J = 1, N
IWORK( J ) = 0
70 CONTINUE
*
* Set LWLSY to the adequate value.
*
LWLSY = MAX( 1, MNMIN+2*N+NB*( N+1 ),
$ 2*MNMIN+NB*NRHS )
*
CALL DLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, B,
$ LDB )
*
SRNAMT = 'DGELSY'
CALL DGELSY( M, N, NRHS, A, LDA, B, LDB, IWORK,
$ RCOND, CRANK, WORK, LWLSY, INFO )
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DGELSY', INFO, 0, ' ', M,
$ N, NRHS, -1, NB, ITYPE, NFAIL,
$ NERRS, NOUT )
*
* Test 7: Compute relative error in svd
* workspace: M*N + 4*MIN(M,N) + MAX(M,N)
*
RESULT( 7 ) = DQRT12( CRANK, CRANK, A, LDA,
$ COPYS, WORK, LWORK )
*
* Test 8: Compute error in solution
* workspace: M*NRHS + M
*
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
$ LDWORK )
CALL DQRT16( 'No transpose', M, N, NRHS, COPYA,
$ LDA, B, LDB, WORK, LDWORK,
$ WORK( M*NRHS+1 ), RESULT( 8 ) )
*
* Test 9: Check norm of r'*A
* workspace: NRHS*(M+N)
*
RESULT( 9 ) = ZERO
IF( M.GT.CRANK )
$ RESULT( 9 ) = DQRT17( 'No transpose', 1, M,
$ N, NRHS, COPYA, LDA, B, LDB,
$ COPYB, LDB, C, WORK, LWORK )
*
* Test 10: Check if x is in the rowspace of A
* workspace: (M+NRHS)*(N+2)
*
RESULT( 10 ) = ZERO
*
IF( N.GT.CRANK )
$ RESULT( 10 ) = DQRT14( 'No transpose', M, N,
$ NRHS, COPYA, LDA, B, LDB,
$ WORK, LWORK )
*
* Test DGELSS
*
* DGELSS: Compute the minimum-norm solution X
* to min( norm( A * X - B ) )
* using the SVD.
*
CALL DLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, B,
$ LDB )
SRNAMT = 'DGELSS'
CALL DGELSS( M, N, NRHS, A, LDA, B, LDB, S,
$ RCOND, CRANK, WORK, LWORK, INFO )
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DGELSS', INFO, 0, ' ', M,
$ N, NRHS, -1, NB, ITYPE, NFAIL,
$ NERRS, NOUT )
*
* workspace used: 3*min(m,n) +
* max(2*min(m,n),nrhs,max(m,n))
*
* Test 11: Compute relative error in svd
*
IF( RANK.GT.0 ) THEN
CALL DAXPY( MNMIN, -ONE, COPYS, 1, S, 1 )
RESULT( 11 ) = DASUM( MNMIN, S, 1 ) /
$ DASUM( MNMIN, COPYS, 1 ) /
$ ( EPS*DBLE( MNMIN ) )
ELSE
RESULT( 11 ) = ZERO
END IF
*
* Test 12: Compute error in solution
*
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
$ LDWORK )
CALL DQRT16( 'No transpose', M, N, NRHS, COPYA,
$ LDA, B, LDB, WORK, LDWORK,
$ WORK( M*NRHS+1 ), RESULT( 12 ) )
*
* Test 13: Check norm of r'*A
*
RESULT( 13 ) = ZERO
IF( M.GT.CRANK )
$ RESULT( 13 ) = DQRT17( 'No transpose', 1, M,
$ N, NRHS, COPYA, LDA, B, LDB,
$ COPYB, LDB, C, WORK, LWORK )
*
* Test 14: Check if x is in the rowspace of A
*
RESULT( 14 ) = ZERO
IF( N.GT.CRANK )
$ RESULT( 14 ) = DQRT14( 'No transpose', M, N,
$ NRHS, COPYA, LDA, B, LDB,
$ WORK, LWORK )
*
* Test DGELSD
*
* DGELSD: Compute the minimum-norm solution X
* to min( norm( A * X - B ) ) using a
* divide and conquer SVD.
*
* Initialize vector IWORK.
*
DO 80 J = 1, N
IWORK( J ) = 0
80 CONTINUE
*
CALL DLACPY( 'Full', M, N, COPYA, LDA, A, LDA )
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, B,
$ LDB )
*
SRNAMT = 'DGELSD'
CALL DGELSD( M, N, NRHS, A, LDA, B, LDB, S,
$ RCOND, CRANK, WORK, LWORK, IWORK,
$ INFO )
IF( INFO.NE.0 )
$ CALL ALAERH( PATH, 'DGELSD', INFO, 0, ' ', M,
$ N, NRHS, -1, NB, ITYPE, NFAIL,
$ NERRS, NOUT )
*
* Test 15: Compute relative error in svd
*
IF( RANK.GT.0 ) THEN
CALL DAXPY( MNMIN, -ONE, COPYS, 1, S, 1 )
RESULT( 15 ) = DASUM( MNMIN, S, 1 ) /
$ DASUM( MNMIN, COPYS, 1 ) /
$ ( EPS*DBLE( MNMIN ) )
ELSE
RESULT( 15 ) = ZERO
END IF
*
* Test 16: Compute error in solution
*
CALL DLACPY( 'Full', M, NRHS, COPYB, LDB, WORK,
$ LDWORK )
CALL DQRT16( 'No transpose', M, N, NRHS, COPYA,
$ LDA, B, LDB, WORK, LDWORK,
$ WORK( M*NRHS+1 ), RESULT( 16 ) )
*
* Test 17: Check norm of r'*A
*
RESULT( 17 ) = ZERO
IF( M.GT.CRANK )
$ RESULT( 17 ) = DQRT17( 'No transpose', 1, M,
$ N, NRHS, COPYA, LDA, B, LDB,
$ COPYB, LDB, C, WORK, LWORK )
*
* Test 18: Check if x is in the rowspace of A
*
RESULT( 18 ) = ZERO
IF( N.GT.CRANK )
$ RESULT( 18 ) = DQRT14( 'No transpose', M, N,
$ NRHS, COPYA, LDA, B, LDB,
$ WORK, LWORK )
*
* Print information about the tests that did not
* pass the threshold.
*
DO 90 K = 7, NTESTS
IF( RESULT( K ).GE.THRESH ) THEN
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
$ CALL ALAHD( NOUT, PATH )
WRITE( NOUT, FMT = 9998 )M, N, NRHS, NB,
$ ITYPE, K, RESULT( K )
NFAIL = NFAIL + 1
END IF
90 CONTINUE
NRUN = NRUN + 12
*
100 CONTINUE
110 CONTINUE
120 CONTINUE
130 CONTINUE
140 CONTINUE
150 CONTINUE
*
* Print a summary of the results.
*
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
*
9999 FORMAT( ' TRANS=''', A1, ''', M=', I5, ', N=', I5, ', NRHS=', I4,
$ ', NB=', I4, ', type', I2, ', test(', I2, ')=', G12.5 )
9998 FORMAT( ' M=', I5, ', N=', I5, ', NRHS=', I4, ', NB=', I4,
$ ', type', I2, ', test(', I2, ')=', G12.5 )
RETURN
*
* End of DDRVLS
*
END