slasd1.f(3)							      LAPACK							       slasd1.f(3)

NAME

       slasd1.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slasd1 (NL, NR, SQRE, D, ALPHA, BETA, U, LDU, VT, LDVT, IDXQ, IWORK, WORK, INFO)
	   SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.

Function/Subroutine Documentation
   subroutine slasd1 (integerNL, integerNR, integerSQRE, real, dimension( * )D, realALPHA, realBETA, real, dimension( ldu, * )U, integerLDU, real,
       dimension( ldvt, * )VT, integerLDVT, integer, dimension( * )IDXQ, integer, dimension( * )IWORK, real, dimension( * )WORK, integerINFO)
       SLASD1 computes the SVD of an upper bidiagonal matrix B of the specified size. Used by sbdsdc.

       Purpose:

	    SLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B,
	    where N = NL + NR + 1 and M = N + SQRE. SLASD1 is called from SLASD0.

	    A related subroutine SLASD7 handles the case in which the singular
	    values (and the singular vectors in factored form) are desired.

	    SLASD1 computes the SVD as follows:

			  ( D1(in)    0    0	   0 )
	      B = U(in) * (   Z1**T   a   Z2**T    b ) * VT(in)
			  (   0       0   D2(in)   0 )

		= U(out) * ( D(out) 0) * VT(out)

	    where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M
	    with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros
	    elsewhere; and the entry b is empty if SQRE = 0.

	    The left singular vectors of the original matrix are stored in U, and
	    the transpose of the right singular vectors are stored in VT, and the
	    singular values are in D.  The algorithm consists of three stages:

	       The first stage consists of deflating the size of the problem
	       when there are multiple singular values or when there are zeros in
	       the Z vector.  For each such occurence the dimension of the
	       secular equation problem is reduced by one.  This stage is
	       performed by the routine SLASD2.

	       The second stage consists of calculating the updated
	       singular values. This is done by finding the square roots of the
	       roots of the secular equation via the routine SLASD4 (as called
	       by SLASD3). This routine also calculates the singular vectors of
	       the current problem.

	       The final stage consists of computing the updated singular vectors
	       directly using the updated singular values.  The singular vectors
	       for the current problem are multiplied with the singular vectors
	       from the overall problem.

       Parameters:
	   NL

		     NL is INTEGER
		    The row dimension of the upper block.  NL >= 1.

	   NR

		     NR is INTEGER
		    The row dimension of the lower block.  NR >= 1.

	   SQRE

		     SQRE is INTEGER
		    = 0: the lower block is an NR-by-NR square matrix.
		    = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

		    The bidiagonal matrix has row dimension N = NL + NR + 1,
		    and column dimension M = N + SQRE.

	   D

		     D is REAL array, dimension (NL+NR+1).
		    N = NL+NR+1
		    On entry D(1:NL,1:NL) contains the singular values of the
		    upper block; and D(NL+2:N) contains the singular values of
		    the lower block. On exit D(1:N) contains the singular values
		    of the modified matrix.

	   ALPHA

		     ALPHA is REAL
		    Contains the diagonal element associated with the added row.

	   BETA

		     BETA is REAL
		    Contains the off-diagonal element associated with the added
		    row.

	   U

		     U is REAL array, dimension (LDU,N)
		    On entry U(1:NL, 1:NL) contains the left singular vectors of
		    the upper block; U(NL+2:N, NL+2:N) contains the left singular
		    vectors of the lower block. On exit U contains the left
		    singular vectors of the bidiagonal matrix.

	   LDU

		     LDU is INTEGER
		    The leading dimension of the array U.  LDU >= max( 1, N ).

	   VT

		     VT is REAL array, dimension (LDVT,M)
		    where M = N + SQRE.
		    On entry VT(1:NL+1, 1:NL+1)**T contains the right singular
		    vectors of the upper block; VT(NL+2:M, NL+2:M)**T contains
		    the right singular vectors of the lower block. On exit
		    VT**T contains the right singular vectors of the
		    bidiagonal matrix.

	   LDVT

		     LDVT is INTEGER
		    The leading dimension of the array VT.  LDVT >= max( 1, M ).

	   IDXQ

		     IDXQ is INTEGER array, dimension (N)
		    This contains the permutation which will reintegrate the
		    subproblem just solved back into sorted order, i.e.
		    D( IDXQ( I = 1, N ) ) will be in ascending order.

	   IWORK

		     IWORK is INTEGER array, dimension (4*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:
	   September 2012

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

       Definition at line 204 of file slasd1.f.

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

Version 3.4.2							  Tue Sep 25 2012						       slasd1.f(3)