ddrvbd.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 663 行 · 第 1/2 页

      SUBROUTINE DDRVBD( NSIZES, MM, NN, NTYPES, DOTYPE, ISEED, THRESH,
     $                   A, LDA, U, LDU, VT, LDVT, ASAV, USAV, VTSAV, S,
     $                   SSAV, E, WORK, LWORK, IWORK, NOUT, INFO )
*
*  -- LAPACK test routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDU, LDVT, LWORK, NOUT, NSIZES,
     $                   NTYPES
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            ISEED( 4 ), IWORK( * ), MM( * ), NN( * )
      DOUBLE PRECISION   A( LDA, * ), ASAV( LDA, * ), E( * ), S( * ),
     $                   SSAV( * ), U( LDU, * ), USAV( LDU, * ),
     $                   VT( LDVT, * ), VTSAV( LDVT, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DDRVBD checks the singular value decomposition (SVD) drivers
*  DGESVD and SGESDD.
*  Both DGESVD and SGESDD factor A = U diag(S) VT, where U and VT are
*  orthogonal and diag(S) is diagonal with the entries of the array S
*  on its diagonal. The entries of S are the singular values,
*  nonnegative and stored in decreasing order.  U and VT can be
*  optionally not computed, overwritten on A, or computed partially.
*
*  A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN.
*  U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N.
*
*  When DDRVBD is called, a number of matrix "sizes" (M's and N's)
*  and a number of matrix "types" are specified.  For each size (M,N)
*  and each type of matrix, and for the minimal workspace as well as
*  workspace adequate to permit blocking, an  M x N  matrix "A" will be
*  generated and used to test the SVD routines.  For each matrix, A will
*  be factored as A = U diag(S) VT and the following 12 tests computed:
*
*  Test for DGESVD:
*
*  (1)    | A - U diag(S) VT | / ( |A| max(M,N) ulp )
*
*  (2)    | I - U'U | / ( M ulp )
*
*  (3)    | I - VT VT' | / ( N ulp )
*
*  (4)    S contains MNMIN nonnegative values in decreasing order.
*         (Return 0 if true, 1/ULP if false.)
*
*  (5)    | U - Upartial | / ( M ulp ) where Upartial is a partially
*         computed U.
*
*  (6)    | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
*         computed VT.
*
*  (7)    | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
*         vector of singular values from the partial SVD
*
*  Test for DGESDD:
*
*  (8)    | A - U diag(S) VT | / ( |A| max(M,N) ulp )
*
*  (9)    | I - U'U | / ( M ulp )
*
*  (10)   | I - VT VT' | / ( N ulp )
*
*  (11)   S contains MNMIN nonnegative values in decreasing order.
*         (Return 0 if true, 1/ULP if false.)
*
*  (12)   | U - Upartial | / ( M ulp ) where Upartial is a partially
*         computed U.
*
*  (13)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
*         computed VT.
*
*  (14)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
*         vector of singular values from the partial SVD
*
*  The "sizes" are specified by the arrays MM(1:NSIZES) and
*  NN(1:NSIZES); the value of each element pair (MM(j),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)  The zero matrix.
*  (2)  The identity matrix.
*  (3)  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.
*  (4)  Same as (3), but multiplied by the underflow-threshold / ULP.
*  (5)  Same as (3), but multiplied by the overflow-threshold * ULP.
*
*  Arguments
*  ==========
*
*  NSIZES  (input) INTEGER
*          The number of matrix sizes (M,N) contained in the vectors
*          MM and NN.
*
*  MM      (input) INTEGER array, dimension (NSIZES)
*          The values of the matrix row dimension M.
*
*  NN      (input) INTEGER array, dimension (NSIZES)
*          The values of the matrix column dimension N.
*
*  NTYPES  (input) INTEGER
*          The number of elements in DOTYPE.   If it is zero, DDRVBD
*          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. .
*
*  DOTYPE  (input) 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.
*
*  ISEED   (input/output) INTEGER array, dimension (4)
*          On entry, 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.
*          On exit, ISEED is changed and can be used in the next call to
*          DDRVBD to continue the same random number sequence.
*
*  THRESH  (input) DOUBLE PRECISION
*          The threshold value for the test ratios.  A result is
*          included in the output file if RESULT >= THRESH.  The test
*          ratios are scaled to be O(1), so THRESH should be a small
*          multiple of 1, e.g., 10 or 100.  To have every test ratio
*          printed, use THRESH = 0.
*
*  A       (workspace) DOUBLE PRECISION array, dimension (LDA,NMAX)
*          where NMAX is the maximum value of N in NN.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,MMAX),
*          where MMAX is the maximum value of M in MM.
*
*  U       (workspace) DOUBLE PRECISION array, dimension (LDU,MMAX)
*
*  LDU     (input) INTEGER
*          The leading dimension of the array U.  LDU >= max(1,MMAX).
*
*  VT      (workspace) DOUBLE PRECISION array, dimension (LDVT,NMAX)
*
*  LDVT    (input) INTEGER
*          The leading dimension of the array VT.  LDVT >= max(1,NMAX).
*
*  ASAV    (workspace) DOUBLE PRECISION array, dimension (LDA,NMAX)
*
*  USAV    (workspace) DOUBLE PRECISION array, dimension (LDU,MMAX)
*
*  VTSAV   (workspace) DOUBLE PRECISION array, dimension (LDVT,NMAX)
*
*  S       (workspace) DOUBLE PRECISION array, dimension
*                      (max(min(MM,NN)))
*
*  SSAV    (workspace) DOUBLE PRECISION array, dimension
*                      (max(min(MM,NN)))
*
*  E       (workspace) DOUBLE PRECISION array, dimension
*                      (max(min(MM,NN)))
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK)
*
*  LWORK   (input) INTEGER
*          The number of entries in WORK.  This must be at least
*          max(3*MN+MX,5*MN-4)+2*MN**2 for all pairs
*          pairs  (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) )
*
*  IWORK   (workspace) INTEGER array, dimension at least 8*min(M,N)
*
*  NOUT    (input) INTEGER
*          The FORTRAN unit number for printing out error messages
*          (e.g., if a routine returns IINFO not equal to 0.)
*
*  INFO    (output) INTEGER
*          If 0, then everything ran OK.
*           -1: NSIZES < 0
*           -2: Some MM(j) < 0
*           -3: Some NN(j) < 0
*           -4: NTYPES < 0
*           -7: THRESH < 0
*          -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
*          -12: LDU < 1 or LDU < MMAX.
*          -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ).
*          -21: LWORK too small.
*          If  DLATMS, or DGESVD returns an error code, the
*              absolute value of it is returned.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
      INTEGER            MAXTYP
      PARAMETER          ( MAXTYP = 5 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BADMM, BADNN
      CHARACTER          JOBQ, JOBU, JOBVT
      CHARACTER*3        PATH
      INTEGER            I, IINFO, IJQ, IJU, IJVT, IWS, IWTMP, J, JSIZE,
     $                   JTYPE, LSWORK, M, MINWRK, MMAX, MNMAX, MNMIN,
     $                   MTYPES, N, NFAIL, NMAX, NTEST
      DOUBLE PRECISION   ANORM, DIF, DIV, OVFL, ULP, ULPINV, UNFL
*     ..
*     .. Local Arrays ..
      CHARACTER          CJOB( 4 )
      INTEGER            IOLDSD( 4 )
      DOUBLE PRECISION   RESULT( 14 )
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           ALASVM, DBDT01, DGESDD, DGESVD, DLABAD, DLACPY,
     $                   DLASET, DLATMS, DORT01, DORT03, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, MAX, MIN
*     ..
*     .. Scalars in Common ..
      LOGICAL            LERR, OK
      CHARACTER*6        SRNAMT
      INTEGER            INFOT, NUNIT
*     ..
*     .. Common blocks ..
      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
      COMMON             / SRNAMC / SRNAMT
*     ..
*     .. Data statements ..
      DATA               CJOB / 'N', 'O', 'S', 'A' /
*     ..
*     .. 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, MM( J ) )
         IF( MM( J ).LT.0 )
     $      BADMM = .TRUE.
         NMAX = MAX( NMAX, NN( J ) )
         IF( NN( J ).LT.0 )
     $      BADNN = .TRUE.
         MNMAX = MAX( MNMAX, MIN( MM( J ), NN( J ) ) )
         MINWRK = MAX( MINWRK, MAX( 3*MIN( MM( J ),
     $            NN( J ) )+MAX( MM( J ), NN( J ) ), 5*MIN( MM( J ),
     $            NN( J )-4 ) )+2*MIN( MM( J ), NN( J ) )**2 )
   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( LDA.LT.MAX( 1, MMAX ) ) THEN
         INFO = -10
      ELSE IF( LDU.LT.MAX( 1, MMAX ) ) THEN
         INFO = -12
      ELSE IF( LDVT.LT.MAX( 1, NMAX ) ) THEN
         INFO = -14
      ELSE IF( MINWRK.GT.LWORK ) THEN
         INFO = -21
      END IF
*
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DDRVBD', -INFO )
         RETURN
      END IF
*
*     Initialize constants
*
      PATH( 1: 1 ) = 'Double precision'
      PATH( 2: 3 ) = 'BD'
      NFAIL = 0
      NTEST = 0
      UNFL = DLAMCH( 'Safe minimum' )
      OVFL = ONE / UNFL
      CALL DLABAD( UNFL, OVFL )
      ULP = DLAMCH( 'Precision' )
      ULPINV = ONE / ULP
      INFOT = 0
*
*     Loop over sizes, types
*
      DO 150 JSIZE = 1, NSIZES
         M = MM( JSIZE )
         N = NN( JSIZE )
         MNMIN = MIN( M, N )
*
         IF( NSIZES.NE.1 ) THEN
            MTYPES = MIN( MAXTYP, NTYPES )
         ELSE
            MTYPES = MIN( MAXTYP+1, NTYPES )
         END IF
*
         DO 140 JTYPE = 1, MTYPES
            IF( .NOT.DOTYPE( JTYPE ) )
     $         GO TO 140
*
            DO 20 J = 1, 4
               IOLDSD( J ) = ISEED( J )
   20       CONTINUE
*
*           Compute "A"
*
            IF( MTYPES.GT.MAXTYP )
     $         GO TO 30
*