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zlalsd

zlalsd.f(3)							      LAPACK							       zlalsd.f(3)

NAME

       zlalsd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlalsd (UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, RANK, WORK, RWORK, IWORK, INFO)
	   ZLALSD uses the singular value decomposition of A to solve the least squares problem.

Function/Subroutine Documentation
   subroutine zlalsd (characterUPLO, integerSMLSIZ, integerN, integerNRHS, double precision, dimension( * )D, double precision, dimension( * )E,
       complex*16, dimension( ldb, * )B, integerLDB, double precisionRCOND, integerRANK, complex*16, dimension( * )WORK, double precision,
       dimension( * )RWORK, integer, dimension( * )IWORK, integerINFO)
       ZLALSD uses the singular value decomposition of A to solve the least squares problem.

       Purpose:

	    ZLALSD uses the singular value decomposition of A to solve the least
	    squares problem of finding X to minimize the Euclidean norm of each
	    column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
	    are N-by-NRHS. The solution X overwrites B.

	    The singular values of A smaller than RCOND times the largest
	    singular value are treated as zero in solving the least squares
	    problem; in this case a minimum norm solution is returned.
	    The actual singular values are returned in D in ascending order.

	    This code makes very mild assumptions about floating point
	    arithmetic. It will work on machines with a guard digit in
	    add/subtract, or on those binary machines without guard digits
	    which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2.
	    It could conceivably fail on hexadecimal or decimal machines
	    without guard digits, but we know of none.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		    = 'U': D and E define an upper bidiagonal matrix.
		    = 'L': D and E define a  lower bidiagonal matrix.

	   SMLSIZ

		     SMLSIZ is INTEGER
		    The maximum size of the subproblems at the bottom of the
		    computation tree.

	   N

		     N is INTEGER
		    The dimension of the  bidiagonal matrix.  N >= 0.

	   NRHS

		     NRHS is INTEGER
		    The number of columns of B. NRHS must be at least 1.

	   D

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

	   E

		     E is DOUBLE PRECISION array, dimension (N-1)
		    Contains the super-diagonal entries of the bidiagonal matrix.
		    On exit, E has been destroyed.

	   B

		     B is COMPLEX*16 array, dimension (LDB,NRHS)
		    On input, B contains the right hand sides of the least
		    squares problem. On output, B contains the solution X.

	   LDB

		     LDB is INTEGER
		    The leading dimension of B in the calling subprogram.
		    LDB must be at least max(1,N).

	   RCOND

		     RCOND is DOUBLE PRECISION
		    The singular values of A less than or equal to RCOND times
		    the largest singular value are treated as zero in solving
		    the least squares problem. If RCOND is negative,
		    machine precision is used instead.
		    For example, if diag(S)*X=B were the least squares problem,
		    where diag(S) is a diagonal matrix of singular values, the
		    solution would be X(i) = B(i) / S(i) if S(i) is greater than
		    RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
		    RCOND*max(S).

	   RANK

		     RANK is INTEGER
		    The number of singular values of A greater than RCOND times
		    the largest singular value.

	   WORK

		     WORK is COMPLEX*16 array, dimension at least
		    (N * NRHS).

	   RWORK

		     RWORK is DOUBLE PRECISION array, dimension at least
		    (9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
		    MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ),
		    where
		    NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )

	   IWORK

		     IWORK is INTEGER array, dimension at least
		    (3*N*NLVL + 11*N).

	   INFO

		     INFO is INTEGER
		    = 0:  successful exit.
		    < 0:  if INFO = -i, the i-th argument had an illegal value.
		    > 0:  The algorithm failed to compute a singular value while
			  working on the submatrix lying in rows and columns
			  INFO/(N+1) through MOD(INFO,N+1).

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA
	    Osni Marques, LBNL/NERSC, USA

       Definition at line 188 of file zlalsd.f.

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

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