laqp2 - laqp2: step of geqp3

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subroutineclaqp2(integerm,integern,integeroffset,complex,dimension(lda,*)a,integerlda,integer,dimension(*)jpvt,complex,dimension(*)tau,real,dimension(*)vn1,real,dimension(*)vn2,complex,dimension(*)work)CLAQP2 computes a QR factorization with column pivoting of the matrix block. Purpose: 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. 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 the matrix A that must be pivoted but no factorized. OFFSET >= 0. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT 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. TAU TAU is COMPLEX array, dimension (min(M,N)) 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. WORK WORK is COMPLEX array, dimension (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 subroutinedlaqp2(integerm,integern,integeroffset,doubleprecision,dimension(lda,*)a,integerlda,integer,dimension(*)jpvt,doubleprecision,dimension(*)tau,doubleprecision,dimension(*)vn1,doubleprecision,dimension(*)vn2,doubleprecision,dimension(*)work)DLAQP2 computes a QR factorization with column pivoting of the matrix block. Purpose: 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. 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 the matrix A that must be pivoted but no factorized. OFFSET >= 0. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT 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. TAU TAU is DOUBLE PRECISION array, dimension (min(M,N)) 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. WORK WORK is DOUBLE PRECISION array, dimension (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 subroutineslaqp2(integerm,integern,integeroffset,real,dimension(lda,*)a,integerlda,integer,dimension(*)jpvt,real,dimension(*)tau,real,dimension(*)vn1,real,dimension(*)vn2,real,dimension(*)work)SLAQP2 computes a QR factorization with column pivoting of the matrix block. Purpose: 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. 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 the matrix A that must be pivoted but no factorized. OFFSET >= 0. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT 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. TAU TAU is REAL array, dimension (min(M,N)) 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. WORK WORK is REAL array, dimension (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 subroutinezlaqp2(integerm,integern,integeroffset,complex*16,dimension(lda,*)a,integerlda,integer,dimension(*)jpvt,complex*16,dimension(*)tau,doubleprecision,dimension(*)vn1,doubleprecision,dimension(*)vn2,complex*16,dimension(*)work)ZLAQP2 computes a QR factorization with column pivoting of the matrix block. Purpose: 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. 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 the matrix A that must be pivoted but no factorized. OFFSET >= 0. A 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. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). JPVT 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. TAU TAU is COMPLEX*16 array, dimension (min(M,N)) 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. WORK WORK is COMPLEX*16 array, dimension (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

laqp2 - laqp2: step of geqp3

Functions subroutine claqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) CLAQP2 computes a QR factorization with column pivoting of the matrix block. subroutine dlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) DLAQP2 computes a QR factorization with column pivoting of the matrix block. subroutine slaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) SLAQP2 computes a QR factorization with column pivoting of the matrix block. subroutine zlaqp2 (m, n, offset, a, lda, jpvt, tau, vn1, vn2, work) ZLAQP2 computes a QR factorization with column pivoting of the matrix block.