?laqp2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?laqp2

Computes a QR factorization with column pivoting of the matrix block.

Syntax

call slaqp2(m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
call dlaqp2(m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
call claqp2(m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)
call zlaqp2(m, n, offset, a, lda, jpvt, tau, vn1, vn2, work)

Include Files

mkl.fi

Description

The routine 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.

Input Parameters

m: INTEGER. The number of rows in the matrix A. The value of m must be at least zero.

n: INTEGER. The number of columns in the matrix A. The value of n must be at least zero.

offset: INTEGER . The number of rows of the matrix A that must be pivoted but no factorized. offset≥ 0 .
a: REAL for slaqp2 DOUBLE PRECISION for dlaqp2 COMPLEX for claqp2 DOUBLE COMPLEX for zlaqp2 Array, DIMENSION ( lda , n ). On entry, the m -by- n matrix A .
lda: INTEGER . The leading dimension of the array a . lda≥ max(1,m) .
jpvt: INTEGER . Array, DIMENSION ( n ). On entry, if jpvt(i) ≠ 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.
vn1 , vn2: REAL for slaqp2 / claqp2 DOUBLE PRECISION for dlaqp2 / zlaqp2 Arrays, DIMENSION ( n ) each. Contain the vectors with the partial and exact column norms, respectively.
work: REAL for slaqp2 DOUBLE PRECISION for dlaqp2 COMPLEX for claqp2 DOUBLE COMPLEX for zlaqp2 Workspace array, DIMENSION ( n ).

Output Parameters

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 not factorized.
jpvt: On exit, if jpvt(i) = k , then the i -th column of A * P was the k -th column of A .
tau: REAL for slaqp2 DOUBLE PRECISION for dlaqp2 COMPLEX for claqp2 DOUBLE COMPLEX for zlaqp2 Array, DIMENSION (min(m,n)) . The scalar factors of the elementary reflectors.
vn1 , vn2: Contain the vectors with the partial and exact column norms, respectively.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laqp2

Syntax

Include Files

Description

Input Parameters

Output Parameters