slasq1.f(3) [debian man page]

slasq1.f(3)							      LAPACK							       slasq1.f(3)

NAME

       slasq1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slasq1 (N, D, E, WORK, INFO)
	   SLASQ1

Function/Subroutine Documentation
   subroutine slasq1 (integerN, real, dimension( * )D, real, dimension( * )E, real, dimension( * )WORK, integerINFO)
       SLASQ1

       Purpose:

	    SLASQ1 computes the singular values of a real N-by-N bidiagonal
	    matrix with diagonal D and off-diagonal E. The singular values
	    are computed to high relative accuracy, in the absence of
	    denormalization, underflow and overflow. The algorithm was first
	    presented in

	    "Accurate singular values and differential qd algorithms" by K. V.
	    Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230,
	    1994,

	    and the present implementation is described in "An implementation of
	    the dqds Algorithm (Positive Case)", LAPACK Working Note.

       Parameters:
	   N

		     N is INTEGER
		   The number of rows and columns in the matrix. N >= 0.

	   D

		     D is REAL array, dimension (N)
		   On entry, D contains the diagonal elements of the
		   bidiagonal matrix whose SVD is desired. On normal exit,
		   D contains the singular values in decreasing order.

	   E

		     E is REAL array, dimension (N)
		   On entry, elements E(1:N-1) contain the off-diagonal elements
		   of the bidiagonal matrix whose SVD is desired.
		   On exit, E is overwritten.

	   WORK

		     WORK is REAL array, dimension (4*N)

	   INFO

		     INFO is INTEGER
		   = 0: successful exit
		   < 0: if INFO = -i, the i-th argument had an illegal value
		   > 0: the algorithm failed
			= 1, a split was marked by a positive value in E
			= 2, current block of Z not diagonalized after 100*N
			     iterations (in inner while loop)  On exit D and E
			     represent a matrix with the same singular values
			     which the calling subroutine could use to finish the
			     computation, or even feed back into SLASQ1
			= 3, termination criterion of outer while loop not met
			     (program created more than N unreduced blocks)

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Definition at line 109 of file slasq1.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       slasq1.f(3)

slasd0.f(3)							      LAPACK							       slasd0.f(3)

NAME

       slasd0.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slasd0 (N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO)
	   SLASD0

Function/Subroutine Documentation
   subroutine slasd0 (integerN, integerSQRE, real, dimension( * )D, real, dimension( * )E, real, dimension( ldu, * )U, integerLDU, real,
       dimension( ldvt, * )VT, integerLDVT, integerSMLSIZ, integer, dimension( * )IWORK, real, dimension( * )WORK, integerINFO)
       SLASD0

       Purpose:

	    Using a divide and conquer approach, SLASD0 computes the singular
	    value decomposition (SVD) of a real upper bidiagonal N-by-M
	    matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
	    The algorithm computes orthogonal matrices U and VT such that
	    B = U * S * VT. The singular values S are overwritten on D.

	    A related subroutine, SLASDA, computes only the singular values,
	    and optionally, the singular vectors in compact form.

       Parameters:
	   N

		     N is INTEGER
		    On entry, the row dimension of the upper bidiagonal matrix.
		    This is also the dimension of the main diagonal array D.

	   SQRE

		     SQRE is INTEGER
		    Specifies the column dimension of the bidiagonal matrix.
		    = 0: The bidiagonal matrix has column dimension M = N;
		    = 1: The bidiagonal matrix has column dimension M = N+1;

	   D

		     D is REAL array, dimension (N)
		    On entry D contains the main diagonal of the bidiagonal
		    matrix.
		    On exit D, if INFO = 0, contains its singular values.

	   E

		     E is REAL array, dimension (M-1)
		    Contains the subdiagonal entries of the bidiagonal matrix.
		    On exit, E has been destroyed.

	   U

		     U is REAL array, dimension at least (LDQ, N)
		    On exit, U contains the left singular vectors.

	   LDU

		     LDU is INTEGER
		    On entry, leading dimension of U.

	   VT

		     VT is REAL array, dimension at least (LDVT, M)
		    On exit, VT**T contains the right singular vectors.

	   LDVT

		     LDVT is INTEGER
		    On entry, leading dimension of VT.

	   SMLSIZ

		     SMLSIZ is INTEGER
		    On entry, maximum size of the subproblems at the
		    bottom of the computation tree.

	   IWORK

		     IWORK is INTEGER array, dimension (8*N)

	   WORK

		     WORK is REAL array, dimension (3*M**2+2*M)

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     > 0:  if INFO = 1, a singular value did not converge

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

       Definition at line 150 of file slasd0.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       slasd0.f(3)