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

.in +1c
.ti -1c
.RI "subroutine \fBzgelsd\fP (m, n, nrhs, a, lda, b, ldb, s, rcond, rank, work, lwork, rwork, iwork, info)"
.br
.RI "\fB ZGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgelsd (integer m, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) s, double precision rcond, integer rank, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)"

.PP
\fB ZGELSD computes the minimum-norm solution to a linear least squares problem for GE matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZGELSD computes the minimum-norm solution to a real linear least
!> squares problem:
!>     minimize 2-norm(| b - A*x |)
!> using the singular value decomposition (SVD) of A\&. A is an M-by-N
!> matrix which may be rank-deficient\&.
!>
!> Several right hand side vectors b and solution vectors x can be
!> handled in a single call; they are stored as the columns of the
!> M-by-NRHS right hand side matrix B and the N-by-NRHS solution
!> matrix X\&.
!>
!> The problem is solved in three steps:
!> (1) Reduce the coefficient matrix A to bidiagonal form with
!>     Householder transformations, reducing the original problem
!>     into a  (BLS)
!> (2) Solve the BLS using a divide and conquer approach\&.
!> (3) Apply back all the Householder transformations to solve
!>     the original least squares problem\&.
!>
!> The effective rank of A is determined by treating as zero those
!> singular values which are less than RCOND times the largest singular
!> value\&.
!>
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix A\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
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.nf
!>          N is INTEGER
!>          The number of columns of the matrix A\&. N >= 0\&.
!> 
.fi
.PP
.br
\fINRHS\fP 
.PP
.nf
!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of columns
!>          of the matrices B and X\&. NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
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.nf
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A\&.
!>          On exit, A has been destroyed\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the M-by-NRHS right hand side matrix B\&.
!>          On exit, B is overwritten by the N-by-NRHS solution matrix X\&.
!>          If m >= n and RANK = n, the residual sum-of-squares for
!>          the solution in the i-th column is given by the sum of
!>          squares of the modulus of elements n+1:m in that column\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= max(1,M,N)\&.
!> 
.fi
.PP
.br
\fIS\fP 
.PP
.nf
!>          S is DOUBLE PRECISION array, dimension (min(M,N))
!>          The singular values of A in decreasing order\&.
!>          The condition number of A in the 2-norm = S(1)/S(min(m,n))\&.
!> 
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
!>          RCOND is DOUBLE PRECISION
!>          RCOND is used to determine the effective rank of A\&.
!>          Singular values S(i) <= RCOND*S(1) are treated as zero\&.
!>          If RCOND < 0, machine precision is used instead\&.
!> 
.fi
.PP
.br
\fIRANK\fP 
.PP
.nf
!>          RANK is INTEGER
!>          The effective rank of A, i\&.e\&., the number of singular values
!>          which are greater than RCOND*S(1)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&. LWORK must be at least 1\&.
!>          The exact minimum amount of workspace needed depends on M,
!>          N and NRHS\&. As long as LWORK is at least
!>              2*N + N*NRHS
!>          if M is greater than or equal to N or
!>              2*M + M*NRHS
!>          if M is less than N, the code will execute correctly\&.
!>          For good performance, LWORK should generally be larger\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the array WORK and the
!>          minimum sizes of the arrays RWORK and IWORK, and returns
!>          these values as the first entries of the WORK, RWORK and
!>          IWORK arrays, and no error message related to LWORK is issued
!>          by XERBLA\&.
!> 
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
!>          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
!>          LRWORK >=
!>             10*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
!>             MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
!>          if M is greater than or equal to N or
!>             10*M + 2*M*SMLSIZ + 8*M*NLVL + 3*SMLSIZ*NRHS +
!>             MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS )
!>          if M is less than N, the code will execute correctly\&.
!>          SMLSIZ is returned by ILAENV and is equal to the maximum
!>          size of the subproblems at the bottom of the computation
!>          tree (usually about 25), and
!>             NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
!>          On exit, if INFO = 0, RWORK(1) returns the minimum LRWORK\&.
!> 
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
!>          LIWORK >= max(1, 3*MINMN*NLVL + 11*MINMN),
!>          where MINMN = MIN( M,N )\&.
!>          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK\&.
!> 
.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 for computing the SVD failed to converge;
!>                if INFO = i, i off-diagonal elements of an intermediate
!>                bidiagonal form did not converge to zero\&.
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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\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

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Definition at line \fB217\fP of file \fBzgelsd\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.