.TH "laqps" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laqps \- laqps: step of geqp3 .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclaqps\fP (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)" .br .RI "\fBCLAQPS\fP computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3\&. " .ti -1c .RI "subroutine \fBdlaqps\fP (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)" .br .RI "\fBDLAQPS\fP computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3\&. " .ti -1c .RI "subroutine \fBslaqps\fP (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)" .br .RI "\fBSLAQPS\fP computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3\&. " .ti -1c .RI "subroutine \fBzlaqps\fP (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf)" .br .RI "\fBZLAQPS\fP computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine claqps (integer m, integer n, integer offset, integer nb, integer kb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, complex, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, complex, dimension( * ) auxv, complex, dimension( ldf, * ) f, integer ldf)" .PP \fBCLAQPS\fP computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLAQPS computes a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3\&. It tries to factorize NB columns from A starting from the row OFFSET+1, and updates all of the matrix with Blas-3 xGEMM\&. In some cases, due to catastrophic cancellations, it cannot factorize NB columns\&. Hence, the actual number of factorized columns is returned in KB\&. 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 A that have been factorized in previous steps\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The number of columns to factorize\&. .fi .PP .br \fIKB\fP .PP .nf KB is INTEGER The number of columns actually factorized\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, block A(OFFSET+1:M,1:KB) is the triangular factor obtained and block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized\&. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated\&. .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) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP\&. .fi .PP .br \fITAU\fP .PP .nf TAU is COMPLEX array, dimension (KB) 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 \fIAUXV\fP .PP .nf AUXV is COMPLEX array, dimension (NB) Auxiliary vector\&. .fi .PP .br \fIF\fP .PP .nf F is COMPLEX array, dimension (LDF,NB) Matrix F**H = L * Y**H * A\&. .fi .PP .br \fILDF\fP .PP .nf LDF is INTEGER The leading dimension of the array F\&. LDF >= max(1,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 .RE .PP .br Partial column norm updating strategy modified on April 2011 Z\&. Drmac and Z\&. Bujanovic, Dept\&. of Mathematics, University of Zagreb, Croatia\&. .PP \fBReferences:\fP .RS 4 LAPACK Working Note 176 .RE .PP .SS "subroutine dlaqps (integer m, integer n, integer offset, integer nb, integer kb, 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( * ) auxv, double precision, dimension( ldf, * ) f, integer ldf)" .PP \fBDLAQPS\fP computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLAQPS computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3\&. It tries to factorize NB columns from A starting from the row OFFSET+1, and updates all of the matrix with Blas-3 xGEMM\&. In some cases, due to catastrophic cancellations, it cannot factorize NB columns\&. Hence, the actual number of factorized columns is returned in KB\&. 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 A that have been factorized in previous steps\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The number of columns to factorize\&. .fi .PP .br \fIKB\fP .PP .nf KB is INTEGER The number of columns actually factorized\&. .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, block A(OFFSET+1:M,1:KB) is the triangular factor obtained and block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized\&. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated\&. .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) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP\&. .fi .PP .br \fITAU\fP .PP .nf TAU is DOUBLE PRECISION array, dimension (KB) 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 \fIAUXV\fP .PP .nf AUXV is DOUBLE PRECISION array, dimension (NB) Auxiliary vector\&. .fi .PP .br \fIF\fP .PP .nf F is DOUBLE PRECISION array, dimension (LDF,NB) Matrix F**T = L*Y**T*A\&. .fi .PP .br \fILDF\fP .PP .nf LDF is INTEGER The leading dimension of the array F\&. LDF >= max(1,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 slaqps (integer m, integer n, integer offset, integer nb, integer kb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) jpvt, real, dimension( * ) tau, real, dimension( * ) vn1, real, dimension( * ) vn2, real, dimension( * ) auxv, real, dimension( ldf, * ) f, integer ldf)" .PP \fBSLAQPS\fP computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLAQPS computes a step of QR factorization with column pivoting of a real M-by-N matrix A by using Blas-3\&. It tries to factorize NB columns from A starting from the row OFFSET+1, and updates all of the matrix with Blas-3 xGEMM\&. In some cases, due to catastrophic cancellations, it cannot factorize NB columns\&. Hence, the actual number of factorized columns is returned in KB\&. 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 A that have been factorized in previous steps\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The number of columns to factorize\&. .fi .PP .br \fIKB\fP .PP .nf KB is INTEGER The number of columns actually factorized\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A\&. On exit, block A(OFFSET+1:M,1:KB) is the triangular factor obtained and block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized\&. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated\&. .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) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP\&. .fi .PP .br \fITAU\fP .PP .nf TAU is REAL array, dimension (KB) 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 \fIAUXV\fP .PP .nf AUXV is REAL array, dimension (NB) Auxiliary vector\&. .fi .PP .br \fIF\fP .PP .nf F is REAL array, dimension (LDF,NB) Matrix F**T = L*Y**T*A\&. .fi .PP .br \fILDF\fP .PP .nf LDF is INTEGER The leading dimension of the array F\&. LDF >= max(1,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 .RE .PP .br Partial column norm updating strategy modified on April 2011 Z\&. Drmac and Z\&. Bujanovic, Dept\&. of Mathematics, University of Zagreb, Croatia\&. .PP \fBReferences:\fP .RS 4 LAPACK Working Note 176 .RE .PP .SS "subroutine zlaqps (integer m, integer n, integer offset, integer nb, integer kb, 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( * ) auxv, complex*16, dimension( ldf, * ) f, integer ldf)" .PP \fBZLAQPS\fP computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAQPS computes a step of QR factorization with column pivoting of a complex M-by-N matrix A by using Blas-3\&. It tries to factorize NB columns from A starting from the row OFFSET+1, and updates all of the matrix with Blas-3 xGEMM\&. In some cases, due to catastrophic cancellations, it cannot factorize NB columns\&. Hence, the actual number of factorized columns is returned in KB\&. 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 A that have been factorized in previous steps\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The number of columns to factorize\&. .fi .PP .br \fIKB\fP .PP .nf KB is INTEGER The number of columns actually factorized\&. .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, block A(OFFSET+1:M,1:KB) is the triangular factor obtained and block A(1:OFFSET,1:N) has been accordingly pivoted, but no factorized\&. The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has been updated\&. .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) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP\&. .fi .PP .br \fITAU\fP .PP .nf TAU is COMPLEX*16 array, dimension (KB) 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 \fIAUXV\fP .PP .nf AUXV is COMPLEX*16 array, dimension (NB) Auxiliary vector\&. .fi .PP .br \fIF\fP .PP .nf F is COMPLEX*16 array, dimension (LDF,NB) Matrix F**H = L * Y**H * A\&. .fi .PP .br \fILDF\fP .PP .nf LDF is INTEGER The leading dimension of the array F\&. LDF >= max(1,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\&.