?larfx

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?larfx

Applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order less than or equal to 10.

Syntax

lapack_int LAPACKE_slarfx(int matrix_layout, char side, lapack_int m, lapack_int n,
                          const float *v, float tau, float *c, lapack_int ldc,
                          float *work);

lapack_int LAPACKE_dlarfx(int matrix_layout, char side, lapack_int m, lapack_int n,
                          const double *v, double tau, double *c, lapack_int ldc,
                          double *work);

lapack_int LAPACKE_clarfx(int matrix_layout, char side, lapack_int m, lapack_int n,
                          const lapack_complex_float *v, lapack_complex_float tau,
                          lapack_complex_float *c, lapack_int ldc,
                          lapack_complex_float *work);

lapack_int LAPACKE_zlarfx(int matrix_layout, char side, lapack_int m, lapack_int n,
                          const lapack_complex_double *v, lapack_complex_double tau,
                          lapack_complex_double *c, lapack_int ldc,
                          lapack_complex_double *work);

Include Files

mkl.h

Description

The routine ?larfx applies a real/complex elementary reflector H to a real/complex m -by- n matrix C , from either the left or the right.

H is represented in the following forms:

H = I - tau*v*v^{T} , where tau is a real scalar and v is a real vector. H = I - tau*v*v^{H} , where tau is a complex scalar and v is a complex vector.

If tau = 0 , then H is taken to be the unit matrix.

Input Parameters

A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

side

If side = 'L' : form H*C If side = 'R' : form C*H .

m

The number of rows of the matrix C .

n

The number of columns of the matrix C .

v

REAL for slarfx DOUBLE PRECISION for dlarfx COMPLEX for clarfx DOUBLE COMPLEX for zlarfx Array, size ( m ) if side = 'L' or ( n ) if side = 'R' . The vector v in the representation of H .

tau

REAL for slarfx DOUBLE PRECISION for dlarfx COMPLEX for clarfx DOUBLE COMPLEX for zlarfx The value tau in the representation of H .

c

REAL for slarfx DOUBLE PRECISION for dlarfx COMPLEX for clarfx DOUBLE COMPLEX for zlarfx

Array, size at least max(1, ldc * n ) for column major layout and max (1, ldc * m ) for row major layout . On entry, the m -by- n matrix C .

ldc

The leading dimension of the array c . lda ≥ (1, m ).

work: REAL for slarfx DOUBLE PRECISION for dlarfx COMPLEX for clarfx DOUBLE COMPLEX for zlarfx Workspace array, size ( n ) if side = 'L' or ( m ) if side = 'R' . work is not referenced if H has order < 11.

Output Parameters

c: On exit, C is overwritten by the matrix H*C if side = 'L' , or C*H if side = 'R' .

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?larfx

Syntax

Include Files

Description

Input Parameters

Output Parameters