.TH "SRC/sgeqp3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/sgeqp3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBsgeqp3\fP (m, n, a, lda, jpvt, tau, work, lwork, info)"
.br
.RI "\fBSGEQP3\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine sgeqp3 (integer m, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)"

.PP
\fBSGEQP3\fP  
.PP
\fBPurpose:\fP
.RS 4

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.nf
!>
!> SGEQP3 computes a QR factorization with column pivoting of a
!> matrix A:  A*P = Q*R  using Level 3 BLAS\&.
!> 
.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 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is REAL array, dimension (LDA,N)
!>          On entry, the M-by-N matrix A\&.
!>          On exit, the upper triangle of the array contains the
!>          min(M,N)-by-N upper trapezoidal matrix R; the elements below
!>          the diagonal, together with the array TAU, represent the
!>          orthogonal matrix Q as a product of min(M,N) elementary
!>          reflectors\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIJPVT\fP 
.PP
.nf
!>          JPVT is INTEGER array, dimension (N)
!>          On entry, if JPVT(J)\&.ne\&.0, the J-th column of A is permuted
!>          to the front of A*P (a leading column); if JPVT(J)=0,
!>          the J-th column of A is a free column\&.
!>          On exit, if JPVT(J)=K, then the J-th column of A*P was the
!>          the K-th column of A\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is REAL array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL 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 >= 3*N+1\&.
!>          For optimal performance LWORK >= 2*N+( N+1 )*NB, where NB
!>          is the optimal blocksize\&.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA\&.
!> 
.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\&.
!> 
.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
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\fBFurther Details:\fP
.RS 4

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.nf
!>
!>  The matrix Q is represented as a product of elementary reflectors
!>
!>     Q = H(1) H(2) \&. \&. \&. H(k), where k = min(m,n)\&.
!>
!>  Each H(i) has the form
!>
!>     H(i) = I - tau * v * v**T
!>
!>  where tau is a real scalar, and v is a real/complex vector
!>  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
!>  A(i+1:m,i), and tau in TAU(i)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBContributors:\fP
.RS 4
G\&. Quintana-Orti, Depto\&. de Informatica, Universidad Jaime I, Spain X\&. Sun, Computer Science Dept\&., Duke University, USA 
.RE
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Definition at line \fB150\fP of file \fBsgeqp3\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.