?laqp2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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

slaqp2 dlaqp2 claqp2 zlaqp2

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 of the matrix A . m≥ 0 .
n: INTEGER . The number of columns of the matrix A . n≥ 0 .
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