.TH "SRC/DEPRECATED/zgelsx.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
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.SH NAME
SRC/DEPRECATED/zgelsx.f
.SH SYNOPSIS
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.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzgelsx\fP (m, n, nrhs, a, lda, b, ldb, jpvt, rcond, rank, work, rwork, info)"
.br
.RI "\fB ZGELSX solves overdetermined or underdetermined systems for GE matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zgelsx (integer m, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer, dimension( * ) jpvt, double precision rcond, integer rank, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)"

.PP
\fB ZGELSX solves overdetermined or underdetermined systems for GE matrices\fP  
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\fBPurpose:\fP
.RS 4

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.nf
!>
!> This routine is deprecated and has been replaced by routine ZGELSY\&.
!>
!> ZGELSX computes the minimum-norm solution to a complex linear least
!> squares problem:
!>     minimize || A * X - B ||
!> using a complete orthogonal factorization 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 routine first computes a QR factorization with column pivoting:
!>     A * P = Q * [ R11 R12 ]
!>                 [  0  R22 ]
!> with R11 defined as the largest leading submatrix whose estimated
!> condition number is less than 1/RCOND\&.  The order of R11, RANK,
!> is the effective rank of A\&.
!>
!> Then, R22 is considered to be negligible, and R12 is annihilated
!> by unitary transformations from the right, arriving at the
!> complete orthogonal factorization:
!>    A * P = Q * [ T11 0 ] * Z
!>                [  0  0 ]
!> The minimum-norm solution is then
!>    X = P * Z**H [ inv(T11)*Q1**H*B ]
!>                 [        0         ]
!> where Q1 consists of the first RANK columns of Q\&.
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIM\fP 
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!>          M is INTEGER
!>          The number of rows of the matrix A\&.  M >= 0\&.
!> 
.fi
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\fIN\fP 
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!>          N is INTEGER
!>          The number of columns of the matrix A\&.  N >= 0\&.
!> 
.fi
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\fINRHS\fP 
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!>          NRHS is INTEGER
!>          The number of right hand sides, i\&.e\&., the number of
!>          columns of matrices B and X\&. NRHS >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
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!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A\&.
!>          On exit, A has been overwritten by details of its
!>          complete orthogonal factorization\&.
!> 
.fi
.PP
.br
\fILDA\fP 
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!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,M)\&.
!> 
.fi
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\fIB\fP 
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.nf
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the M-by-NRHS right hand side matrix B\&.
!>          On exit, 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 elements N+1:M in that column\&.
!> 
.fi
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.br
\fILDB\fP 
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!>          LDB is INTEGER
!>          The leading dimension of the array B\&. LDB >= max(1,M,N)\&.
!> 
.fi
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\fIJPVT\fP 
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!>          JPVT is INTEGER array, dimension (N)
!>          On entry, if JPVT(i) \&.ne\&. 0, the i-th column of A is an
!>          initial column, otherwise it is a free column\&.  Before
!>          the QR factorization of A, all initial columns are
!>          permuted to the leading positions; only the remaining
!>          free columns are moved as a result of column pivoting
!>          during the factorization\&.
!>          On exit, if JPVT(i) = k, then the i-th column of A*P
!>          was the k-th column of A\&.
!> 
.fi
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.br
\fIRCOND\fP 
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!>          RCOND is DOUBLE PRECISION
!>          RCOND is used to determine the effective rank of A, which
!>          is defined as the order of the largest leading triangular
!>          submatrix R11 in the QR factorization with pivoting of A,
!>          whose estimated condition number < 1/RCOND\&.
!> 
.fi
.PP
.br
\fIRANK\fP 
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.nf
!>          RANK is INTEGER
!>          The effective rank of A, i\&.e\&., the order of the submatrix
!>          R11\&.  This is the same as the order of the submatrix T11
!>          in the complete orthogonal factorization of A\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
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!>          WORK is COMPLEX*16 array, dimension
!>                      (min(M,N) + max( N, 2*min(M,N)+NRHS )),
!> 
.fi
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\fIRWORK\fP 
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!>          RWORK is DOUBLE PRECISION array, dimension (2*N)
!> 
.fi
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\fIINFO\fP 
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!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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Definition at line \fB182\fP of file \fBzgelsx\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.