?laqps

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?laqps

Computes a step of QR factorization with column pivoting of a real m -by- n matrix A by using BLAS level 3.

Syntax

call slaqps ( m , n , offset , nb , kb , a , lda , jpvt , tau , vn1 , vn2 , auxv , f , ldf )

call dlaqps ( m , n , offset , nb , kb , a , lda , jpvt , tau , vn1 , vn2 , auxv , f , ldf )

call claqps ( m , n , offset , nb , kb , a , lda , jpvt , tau , vn1 , vn2 , auxv , f , ldf )

call zlaqps ( m , n , offset , nb , kb , a , lda , jpvt , tau , vn1 , vn2 , auxv , f , ldf )

Include Files

mkl.fi

Description

slaqps dlaqps claqps zlaqps

The routine computes a step of QR factorization with column pivoting of a real m -by- n matrix A by using BLAS level 3. The routine tries to factorize NB columns from A starting from the row offset +1, and updates all of the matrix with BLAS level 3 routine ?gemm .

In some cases, due to catastrophic cancellations, ?laqps 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.

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 A that have been factorized in previous steps.
nb: INTEGER . The number of columns to factorize.
a: REAL for slaqps DOUBLE PRECISION for dlaqps COMPLEX for claqps DOUBLE COMPLEX for zlaqps 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 ). If jpvt ( I ) = k then column k of the full matrix A has been permuted into position i in AP.
vn1 , vn2: REAL for slaqps / claqps DOUBLE PRECISION for dlaqps / zlaqps Arrays, DIMENSION ( n ) each. Contain the vectors with the partial and exact column norms, respectively.
auxv: REAL for slaqps DOUBLE PRECISION for dlaqps COMPLEX for claqps DOUBLE COMPLEX for zlaqps Array, DIMENSION ( nb ). Auxiliary vector.
f: REAL for slaqps DOUBLE PRECISION for dlaqps COMPLEX for claqps DOUBLE COMPLEX for zlaqps Array, DIMENSION ( ldf , nb ). For real flavors, matrix F^:code:`T` = L * Y^:code:`T` * A . For complex flavors, matrix F^:code:`H` = L * Y^:code:`H` * A .
ldf: INTEGER . The leading dimension of the array f . ldf≥ max(1,n) .

Output Parameters

kb: INTEGER . The number of columns actually factorized.
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.
jpvt: INTEGER array, DIMENSION ( n ). If jpvt(I) = k then column k of the full matrix A has been permuted into position i in AP.
tau: REAL for slaqps DOUBLE PRECISION for dlaqps COMPLEX for claqps DOUBLE COMPLEX for zlaqps Array, DIMENSION ( kb ). The scalar factors of the elementary reflectors.
vn1 , vn2: The vectors with the partial and exact column norms, respectively.
auxv: Auxiliary vector.
f: Matrix F' = L * Y' * A .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laqps

Syntax

Include Files

Description

Input Parameters

Output Parameters