.TH "SRC/zlalsd.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/zlalsd.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzlalsd\fP (uplo, smlsiz, n, nrhs, d, e, b, ldb, rcond, rank, work, rwork, iwork, info)"
.br
.RI "\fBZLALSD\fP uses the singular value decomposition of A to solve the least squares problem\&. "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zlalsd (character uplo, integer smlsiz, integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, double precision rcond, integer rank, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)"

.PP
\fBZLALSD\fP uses the singular value decomposition of A to solve the least squares problem\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
         = 'U': D and E define an upper bidiagonal matrix\&.
         = 'L': D and E define a  lower bidiagonal matrix\&.
.fi
.PP
.br
\fISMLSIZ\fP 
.PP
.nf
          SMLSIZ is INTEGER
         The maximum size of the subproblems at the bottom of the
         computation tree\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
         The dimension of the  bidiagonal matrix\&.  N >= 0\&.
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
          NRHS is INTEGER
         The number of columns of B\&. NRHS must be at least 1\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
         Contains the super-diagonal entries of the bidiagonal matrix\&.
         On exit, E has been destroyed\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
         The leading dimension of B in the calling subprogram\&.
         LDB must be at least max(1,N)\&.
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
          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)\&.
.fi
.PP
.br
\fIRANK\fP 
.PP
.nf
          RANK is INTEGER
         The number of singular values of A greater than RCOND times
         the largest singular value\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (N * NRHS)
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          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 )
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension at least
         (3*N*NLVL + 11*N)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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)\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Ming Gu and Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA 
.br
 Osni Marques, LBNL/NERSC, USA 
.br
.RE
.PP

.PP
Definition at line \fB179\fP of file \fBzlalsd\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.