dchkbb.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 584 行 · 第 1/2 页

      SUBROUTINE DCHKBB( NSIZES, MVAL, NVAL, NWDTHS, KK, NTYPES, DOTYPE,
     $                   NRHS, ISEED, THRESH, NOUNIT, A, LDA, AB, LDAB,
     $                   BD, BE, Q, LDQ, P, LDP, C, LDC, CC, WORK,
     $                   LWORK, RESULT, INFO )
*
*  -- LAPACK test routine (release 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, LDAB, LDC, LDP, LDQ, LWORK, NOUNIT,
     $                   NRHS, NSIZES, NTYPES, NWDTHS
      DOUBLE PRECISION   THRESH
*     ..
*     .. Array Arguments ..
      LOGICAL            DOTYPE( * )
      INTEGER            ISEED( 4 ), KK( * ), MVAL( * ), NVAL( * )
      DOUBLE PRECISION   A( LDA, * ), AB( LDAB, * ), BD( * ), BE( * ),
     $                   C( LDC, * ), CC( LDC, * ), P( LDP, * ),
     $                   Q( LDQ, * ), RESULT( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DCHKBB tests the reduction of a general real rectangular band
*  matrix to bidiagonal form.
*
*  DGBBRD factors a general band matrix A as  Q B P* , where * means
*  transpose, B is upper bidiagonal, and Q and P are orthogonal;
*  DGBBRD can also overwrite a given matrix C with Q* C .
*
*  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 C are generated.
*  The problem dimensions are as follows
*     A:          M x N
*     Q:          M x M
*     P:          N x N
*     B:          min(M,N) x min(M,N)
*     C:          M x NRHS
*
*  For each generated matrix, 4 tests are performed:
*
*  (1)   | A - Q B PT | / ( |A| max(M,N) ulp ), PT = P'
*
*  (2)   | I - Q' Q | / ( M ulp )
*
*  (3)   | I - PT PT' | / ( N ulp )
*
*  (4)   | Y - Q' C | / ( |Y| max(M,NRHS) ulp ), where Y = Q' C.
*
*  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:
*
*  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 )
*
*  Arguments
*  =========
*
*  NSIZES  (input) 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).
*          If NSIZES is zero, DCHKBB does nothing.  NSIZES must be at
*          least zero.
*
*  MVAL    (input) INTEGER array, dimension (NSIZES)
*          The values of the matrix row dimension M.
*
*  NVAL    (input) INTEGER array, dimension (NSIZES)
*          The values of the matrix column dimension N.
*
*  NWDTHS  (input) INTEGER
*          The number of bandwidths to use.  If it is zero,
*          DCHKBB does nothing.  It must be at least zero.
*
*  KK      (input) INTEGER array, dimension (NWDTHS)
*          An array containing the bandwidths to be used for the band
*          matrices.  The values must be at least zero.
*
*  NTYPES  (input) INTEGER
*          The number of elements in DOTYPE.   If it is zero, DCHKBB
*          does nothing.  It must be at least zero.  If it is MAXTYP+1
*          and NSIZES is 1, then an additional type, MAXTYP+1 is
*          defined, which is to use whatever matrix is in A.  This
*          is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
*          DOTYPE(MAXTYP+1) is .TRUE. .
*
*  DOTYPE  (input) LOGICAL array, dimension (NTYPES)
*          If DOTYPE(j) is .TRUE., then for each size in NN a
*          matrix of that size and of type j will be generated.
*          If NTYPES is smaller than the maximum number of types
*          defined (PARAMETER MAXTYP), then types NTYPES+1 through
*          MAXTYP will not be generated.  If NTYPES is larger
*          than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
*          will be ignored.
*
*  NRHS    (input) INTEGER
*          The number of columns in the "right-hand side" matrix C.
*          If NRHS = 0, then the operations on the right-hand side will
*          not be tested. NRHS must be at least 0.
*
*  ISEED   (input/output) INTEGER array, dimension (4)
*          On entry ISEED specifies the seed of the random number
*          generator. The array elements should be between 0 and 4095;
*          if not they will be reduced mod 4096.  Also, ISEED(4) must
*          be odd.  The random number generator uses a linear
*          congruential sequence limited to small integers, and so
*          should produce machine independent random numbers. The
*          values of ISEED are changed on exit, and can be used in the
*          next call to DCHKBB to continue the same random number
*          sequence.
*
*  THRESH  (input) DOUBLE PRECISION
*          A test will count as "failed" if the "error", computed as
*          described above, exceeds THRESH.  Note that the error
*          is scaled to be O(1), so THRESH should be a reasonably
*          small multiple of 1, e.g., 10 or 100.  In particular,
*          it should not depend on the precision (single vs. double)
*          or the size of the matrix.  It must be at least zero.
*
*  NOUNIT  (input) INTEGER
*          The FORTRAN unit number for printing out error messages
*          (e.g., if a routine returns IINFO not equal to 0.)
*
*  A       (input/workspace) DOUBLE PRECISION array, dimension
*                            (LDA, max(NN))
*          Used to hold the matrix A.
*
*  LDA     (input) INTEGER
*          The leading dimension of A.  It must be at least 1
*          and at least max( NN ).
*
*  AB      (workspace) DOUBLE PRECISION array, dimension (LDAB, max(NN))
*          Used to hold A in band storage format.
*
*  LDAB    (input) INTEGER
*          The leading dimension of AB.  It must be at least 2 (not 1!)
*          and at least max( KK )+1.
*
*  BD      (workspace) DOUBLE PRECISION array, dimension (max(NN))
*          Used to hold the diagonal of the bidiagonal matrix computed
*          by DGBBRD.
*
*  BE      (workspace) DOUBLE PRECISION array, dimension (max(NN))
*          Used to hold the off-diagonal of the bidiagonal matrix
*          computed by DGBBRD.
*
*  Q       (workspace) DOUBLE PRECISION array, dimension (LDQ, max(NN))
*          Used to hold the orthogonal matrix Q computed by DGBBRD.
*
*  LDQ     (input) INTEGER
*          The leading dimension of Q.  It must be at least 1
*          and at least max( NN ).
*
*  P       (workspace) DOUBLE PRECISION array, dimension (LDP, max(NN))
*          Used to hold the orthogonal matrix P computed by DGBBRD.
*
*  LDP     (input) INTEGER
*          The leading dimension of P.  It must be at least 1
*          and at least max( NN ).
*
*  C       (workspace) DOUBLE PRECISION array, dimension (LDC, max(NN))
*          Used to hold the matrix C updated by DGBBRD.
*
*  LDC     (input) INTEGER
*          The leading dimension of U.  It must be at least 1
*          and at least max( NN ).
*
*  CC      (workspace) DOUBLE PRECISION array, dimension (LDC, max(NN))
*          Used to hold a copy of the matrix C.
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK)
*
*  LWORK   (input) INTEGER
*          The number of entries in WORK.  This must be at least
*          max( LDA+1, max(NN)+1 )*max(NN).
*
*  RESULT  (output) DOUBLE PRECISION array, dimension (4)
*          The values computed by the tests described above.
*          The values are currently limited to 1/ulp, to avoid
*          overflow.
*
*  INFO    (output) INTEGER
*          If 0, then everything ran OK.
*
*-----------------------------------------------------------------------
*
*       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.
*       NTESTT          The total number of tests performed so far.
*       NMAX            Largest value in NN.
*       NMATS           The number of matrices generated so far.
*       NERRS           The number of tests which have exceeded THRESH
*                       so far.
*       COND, IMODE     Values to be passed to the matrix generators.
*       ANORM           Norm of A; passed to matrix generators.
*
*       OVFL, UNFL      Overflow and underflow thresholds.
*       ULP, ULPINV     Finest relative precision and its inverse.
*       RTOVFL, RTUNFL  Square roots of the previous 2 values.
*               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) )
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
      INTEGER            MAXTYP
      PARAMETER          ( MAXTYP = 15 )
*     ..
*     .. Local Scalars ..
      LOGICAL            BADMM, BADNN, BADNNB
      INTEGER            I, IINFO, IMODE, ITYPE, J, JCOL, JR, JSIZE,
     $                   JTYPE, JWIDTH, K, KL, KMAX, KU, M, MMAX, MNMAX,
     $                   MNMIN, MTYPES, N, NERRS, NMATS, NMAX, NTEST,
     $                   NTESTT
      DOUBLE PRECISION   AMNINV, ANORM, COND, OVFL, RTOVFL, RTUNFL, ULP,
     $                   ULPINV, UNFL
*     ..
*     .. Local Arrays ..
      INTEGER            IDUMMA( 1 ), IOLDSD( 4 ), KMAGN( MAXTYP ),
     $                   KMODE( MAXTYP ), KTYPE( MAXTYP )
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           DLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           DBDT01, DBDT02, DGBBRD, DLACPY, DLAHD2, DLASET,
     $                   DLASUM, DLATMR, DLATMS, DORT01, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, MAX, MIN, SQRT
*     ..
*     .. Data statements ..
      DATA               KTYPE / 1, 2, 5*4, 5*6, 3*9 /
      DATA               KMAGN / 2*1, 3*1, 2, 3, 3*1, 2, 3, 1, 2, 3 /
      DATA               KMODE / 2*0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
     $                   0, 0 /
*     ..
*     .. Executable Statements ..
*
*     Check for errors
*
      NTESTT = 0
      INFO = 0
*
*     Important constants
*