laqps - laqps: step of geqp3

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subroutineclaqps(integerm,integern,integeroffset,integernb,integerkb,complex,dimension(lda,*)a,integerlda,integer,dimension(*)jpvt,complex,dimension(*)tau,real,dimension(*)vn1,real,dimension(*)vn2,complex,dimension(*)auxv,complex,dimension(ldf,*)f,integerldf)CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. Purpose: 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. ParametersM M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0 OFFSET OFFSET is INTEGER The number of rows of A that have been factorized in previous steps. NB NB is INTEGER The number of columns to factorize. KB KB is INTEGER The number of columns actually factorized. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT JPVT is INTEGER array, dimension (N) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP. TAU TAU is COMPLEX array, dimension (KB) The scalar factors of the elementary reflectors. VN1 VN1 is REAL array, dimension (N) The vector with the partial column norms. VN2 VN2 is REAL array, dimension (N) The vector with the exact column norms. AUXV AUXV is COMPLEX array, dimension (NB) Auxiliary vector. F F is COMPLEX array, dimension (LDF,NB) Matrix F**H = L * Y**H * A. LDF LDF is INTEGER The leading dimension of the array F. LDF >= max(1,N). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia. References: LAPACK Working Note 176 subroutinedlaqps(integerm,integern,integeroffset,integernb,integerkb,doubleprecision,dimension(lda,*)a,integerlda,integer,dimension(*)jpvt,doubleprecision,dimension(*)tau,doubleprecision,dimension(*)vn1,doubleprecision,dimension(*)vn2,doubleprecision,dimension(*)auxv,doubleprecision,dimension(ldf,*)f,integerldf)DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. Purpose: 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. ParametersM M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0 OFFSET OFFSET is INTEGER The number of rows of A that have been factorized in previous steps. NB NB is INTEGER The number of columns to factorize. KB KB is INTEGER The number of columns actually factorized. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT JPVT is INTEGER array, dimension (N) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP. TAU TAU is DOUBLE PRECISION array, dimension (KB) The scalar factors of the elementary reflectors. VN1 VN1 is DOUBLE PRECISION array, dimension (N) The vector with the partial column norms. VN2 VN2 is DOUBLE PRECISION array, dimension (N) The vector with the exact column norms. AUXV AUXV is DOUBLE PRECISION array, dimension (NB) Auxiliary vector. F F is DOUBLE PRECISION array, dimension (LDF,NB) Matrix F**T = L*Y**T*A. LDF LDF is INTEGER The leading dimension of the array F. LDF >= max(1,N). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia. References: LAPACK Working Note 176 subroutineslaqps(integerm,integern,integeroffset,integernb,integerkb,real,dimension(lda,*)a,integerlda,integer,dimension(*)jpvt,real,dimension(*)tau,real,dimension(*)vn1,real,dimension(*)vn2,real,dimension(*)auxv,real,dimension(ldf,*)f,integerldf)SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. Purpose: 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. ParametersM M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0 OFFSET OFFSET is INTEGER The number of rows of A that have been factorized in previous steps. NB NB is INTEGER The number of columns to factorize. KB KB is INTEGER The number of columns actually factorized. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT JPVT is INTEGER array, dimension (N) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP. TAU TAU is REAL array, dimension (KB) The scalar factors of the elementary reflectors. VN1 VN1 is REAL array, dimension (N) The vector with the partial column norms. VN2 VN2 is REAL array, dimension (N) The vector with the exact column norms. AUXV AUXV is REAL array, dimension (NB) Auxiliary vector. F F is REAL array, dimension (LDF,NB) Matrix F**T = L*Y**T*A. LDF LDF is INTEGER The leading dimension of the array F. LDF >= max(1,N). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia. References: LAPACK Working Note 176 subroutinezlaqps(integerm,integern,integeroffset,integernb,integerkb,complex*16,dimension(lda,*)a,integerlda,integer,dimension(*)jpvt,complex*16,dimension(*)tau,doubleprecision,dimension(*)vn1,doubleprecision,dimension(*)vn2,complex*16,dimension(*)auxv,complex*16,dimension(ldf,*)f,integerldf)ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. Purpose: 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. ParametersM M is INTEGER The number of rows of the matrix A. M >= 0. N N is INTEGER The number of columns of the matrix A. N >= 0 OFFSET OFFSET is INTEGER The number of rows of A that have been factorized in previous steps. NB NB is INTEGER The number of columns to factorize. KB KB is INTEGER The number of columns actually factorized. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT JPVT is INTEGER array, dimension (N) JPVT(I) = K <==> Column K of the full matrix A has been permuted into position I in AP. TAU TAU is COMPLEX*16 array, dimension (KB) The scalar factors of the elementary reflectors. VN1 VN1 is DOUBLE PRECISION array, dimension (N) The vector with the partial column norms. VN2 VN2 is DOUBLE PRECISION array, dimension (N) The vector with the exact column norms. AUXV AUXV is COMPLEX*16 array, dimension (NB) Auxiliary vector. F F is COMPLEX*16 array, dimension (LDF,NB) Matrix F**H = L * Y**H * A. LDF LDF is INTEGER The leading dimension of the array F. LDF >= max(1,N). Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain X. Sun, Computer Science Dept., Duke University, USA Partial column norm updating strategy modified on April 2011 Z. Drmac and Z. Bujanovic, Dept. of Mathematics, University of Zagreb, Croatia. References: LAPACK Working Note 176

laqps - laqps: step of geqp3

Functions subroutine claqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) CLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. subroutine dlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. subroutine slaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) SLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3. subroutine zlaqps (m, n, offset, nb, kb, a, lda, jpvt, tau, vn1, vn2, auxv, f, ldf) ZLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.