.TH "laqp2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
laqp2 \- laqp2: step of geqp3
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclaqp2\fP (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)"
.br
.RI "\fBCLAQP2\fP computes a QR factorization with column pivoting of the matrix block\&. "
.ti -1c
.RI "subroutine \fBdlaqp2\fP (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)"
.br
.RI "\fBDLAQP2\fP computes a QR factorization with column pivoting of the matrix block\&. "
.ti -1c
.RI "subroutine \fBslaqp2\fP (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)"
.br
.RI "\fBSLAQP2\fP computes a QR factorization with column pivoting of the matrix block\&. "
.ti -1c
.RI "subroutine \fBzlaqp2\fP (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)"
.br
.RI "\fBZLAQP2\fP computes a QR factorization with column pivoting of the matrix block\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine claqp2 (integer m, integer n, integer offset, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, complex, dimension( * ) work)"

.PP
\fBCLAQP2\fP computes a QR factorization with column pivoting of the matrix block\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLAQP2 computes a QR factorization with column pivoting of
 the block A(OFFSET+1:M,1:N)\&.
 The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized\&.
.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
\fIOFFSET\fP 
.PP
.nf
          OFFSET is INTEGER
          The number of rows of the matrix A that must be pivoted
          but no factorized\&. OFFSET >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          On entry, the M-by-N matrix A\&.
          On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
          the triangular factor obtained; the elements in block
          A(OFFSET+1:M,1:N) below the diagonal, together with the
          array TAU, represent the orthogonal matrix Q as a product of
          elementary reflectors\&. Block A(1:OFFSET,1:N) has been
          accordingly pivoted, but no factorized\&.
.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(i) \&.ne\&. 0, the i-th column of A is permuted
          to the front of A*P (a leading column); if JPVT(i) = 0,
          the i-th column of A is a free column\&.
          On exit, if JPVT(i) = k, then the i-th column of A*P
          was the k-th column of A\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors\&.
.fi
.PP
.br
\fIVN1\fP 
.PP
.nf
          VN1 is REAL array, dimension (N)
          The vector with the partial column norms\&.
.fi
.PP
.br
\fIVN2\fP 
.PP
.nf
          VN2 is REAL array, dimension (N)
          The vector with the exact column norms\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (N)
.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
G\&. Quintana-Orti, Depto\&. de Informatica, Universidad Jaime I, Spain X\&. Sun, Computer Science Dept\&., Duke University, USA 
.br
 Partial column norm updating strategy modified on April 2011 Z\&. Drmac and Z\&. Bujanovic, Dept\&. of Mathematics, University of Zagreb, Croatia\&. 
.RE
.PP
\fBReferences:\fP
.RS 4
LAPACK Working Note 176  
.RE
.PP

.SS "subroutine dlaqp2 (integer m, integer n, integer offset, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, double precision, dimension( * ) tau, double precision, dimension( * ) vn1, double precision, dimension( * ) vn2, double precision, dimension( * ) work)"

.PP
\fBDLAQP2\fP computes a QR factorization with column pivoting of the matrix block\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAQP2 computes a QR factorization with column pivoting of
 the block A(OFFSET+1:M,1:N)\&.
 The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized\&.
.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
\fIOFFSET\fP 
.PP
.nf
          OFFSET is INTEGER
          The number of rows of the matrix A that must be pivoted
          but no factorized\&. OFFSET >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the M-by-N matrix A\&.
          On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
          the triangular factor obtained; the elements in block
          A(OFFSET+1:M,1:N) below the diagonal, together with the
          array TAU, represent the orthogonal matrix Q as a product of
          elementary reflectors\&. Block A(1:OFFSET,1:N) has been
          accordingly pivoted, but no factorized\&.
.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(i) \&.ne\&. 0, the i-th column of A is permuted
          to the front of A*P (a leading column); if JPVT(i) = 0,
          the i-th column of A is a free column\&.
          On exit, if JPVT(i) = k, then the i-th column of A*P
          was the k-th column of A\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is DOUBLE PRECISION array, dimension (min(M,N))
          The scalar factors of the elementary reflectors\&.
.fi
.PP
.br
\fIVN1\fP 
.PP
.nf
          VN1 is DOUBLE PRECISION array, dimension (N)
          The vector with the partial column norms\&.
.fi
.PP
.br
\fIVN2\fP 
.PP
.nf
          VN2 is DOUBLE PRECISION array, dimension (N)
          The vector with the exact column norms\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (N)
.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
G\&. Quintana-Orti, Depto\&. de Informatica, Universidad Jaime I, Spain X\&. Sun, Computer Science Dept\&., Duke University, USA 
.br
 Partial column norm updating strategy modified on April 2011 Z\&. Drmac and Z\&. Bujanovic, Dept\&. of Mathematics, University of Zagreb, Croatia\&. 
.RE
.PP
\fBReferences:\fP
.RS 4
LAPACK Working Note 176  
.RE
.PP

.SS "subroutine slaqp2 (integer m, integer n, integer offset, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real, dimension( * ) work)"

.PP
\fBSLAQP2\fP computes a QR factorization with column pivoting of the matrix block\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLAQP2 computes a QR factorization with column pivoting of
 the block A(OFFSET+1:M,1:N)\&.
 The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized\&.
.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
\fIOFFSET\fP 
.PP
.nf
          OFFSET is INTEGER
          The number of rows of the matrix A that must be pivoted
          but no factorized\&. OFFSET >= 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 block A(OFFSET+1:M,1:N) is
          the triangular factor obtained; the elements in block
          A(OFFSET+1:M,1:N) below the diagonal, together with the
          array TAU, represent the orthogonal matrix Q as a product of
          elementary reflectors\&. Block A(1:OFFSET,1:N) has been
          accordingly pivoted, but no factorized\&.
.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(i) \&.ne\&. 0, the i-th column of A is permuted
          to the front of A*P (a leading column); if JPVT(i) = 0,
          the i-th column of A is a free column\&.
          On exit, if JPVT(i) = k, then the i-th column of A*P
          was 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
\fIVN1\fP 
.PP
.nf
          VN1 is REAL array, dimension (N)
          The vector with the partial column norms\&.
.fi
.PP
.br
\fIVN2\fP 
.PP
.nf
          VN2 is REAL array, dimension (N)
          The vector with the exact column norms\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (N)
.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
G\&. Quintana-Orti, Depto\&. de Informatica, Universidad Jaime I, Spain X\&. Sun, Computer Science Dept\&., Duke University, USA 
.br
 Partial column norm updating strategy modified on April 2011 Z\&. Drmac and Z\&. Bujanovic, Dept\&. of Mathematics, University of Zagreb, Croatia\&. 
.RE
.PP
\fBReferences:\fP
.RS 4
LAPACK Working Note 176  
.RE
.PP

.SS "subroutine zlaqp2 (integer m, integer n, integer offset, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, complex*16, dimension( * ) tau, double precision, dimension( * ) vn1, double precision, dimension( * ) vn2, complex*16, dimension( * ) work)"

.PP
\fBZLAQP2\fP computes a QR factorization with column pivoting of the matrix block\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLAQP2 computes a QR factorization with column pivoting of
 the block A(OFFSET+1:M,1:N)\&.
 The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized\&.
.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
\fIOFFSET\fP 
.PP
.nf
          OFFSET is INTEGER
          The number of rows of the matrix A that must be pivoted
          but no factorized\&. OFFSET >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the M-by-N matrix A\&.
          On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
          the triangular factor obtained; the elements in block
          A(OFFSET+1:M,1:N) below the diagonal, together with the
          array TAU, represent the orthogonal matrix Q as a product of
          elementary reflectors\&. Block A(1:OFFSET,1:N) has been
          accordingly pivoted, but no factorized\&.
.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(i) \&.ne\&. 0, the i-th column of A is permuted
          to the front of A*P (a leading column); if JPVT(i) = 0,
          the i-th column of A is a free column\&.
          On exit, if JPVT(i) = k, then the i-th column of A*P
          was the k-th column of A\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors\&.
.fi
.PP
.br
\fIVN1\fP 
.PP
.nf
          VN1 is DOUBLE PRECISION array, dimension (N)
          The vector with the partial column norms\&.
.fi
.PP
.br
\fIVN2\fP 
.PP
.nf
          VN2 is DOUBLE PRECISION array, dimension (N)
          The vector with the exact column norms\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (N)
.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
G\&. Quintana-Orti, Depto\&. de Informatica, Universidad Jaime I, Spain X\&. Sun, Computer Science Dept\&., Duke University, USA 
.br
 Partial column norm updating strategy modified on April 2011 Z\&. Drmac and Z\&. Bujanovic, Dept\&. of Mathematics, University of Zagreb, Croatia\&. 
.RE
.PP
\fBReferences:\fP
.RS 4
LAPACK Working Note 176  
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.