?larfg

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?larfg

Generates an elementary reflector (Householder matrix).

Syntax

lapack_int LAPACKE_slarfg(lapack_int n, float *alpha, float *x, lapack_int incx,
                          float *tau);

lapack_int LAPACKE_dlarfg(lapack_int n, double *alpha, double *x, lapack_int incx,
                          double *tau);

lapack_int LAPACKE_clarfg(lapack_int n, lapack_complex_float *alpha,
                          lapack_complex_float *x, lapack_int incx,
                          lapack_complex_float *tau);

lapack_int LAPACKE_zlarfg(lapack_int n, lapack_complex_double *alpha,
                          lapack_complex_double *x, lapack_int incx,
                          lapack_complex_double *tau);

Include Files

mkl.h

Description

The routine ?larfg generates a real/complex elementary reflector H of order n , such that

for real flavors and

for complex flavors, where alpha and beta are scalars (with beta real for all flavors), and x is an ( n -1)-element real/complex vector. H is represented in the form

for real flavors and

for complex flavors, where tau is a real/complex scalar and v is a real/complex ( n -1)-element vector, respectively. Note that for clarfg / zlarfg , H is not Hermitian.

If the elements of x are all zero (and, for complex flavors, alpha is real), then tau = 0 and H is taken to be the unit matrix.

Otherwise, 1 ≤ tau ≤ 2 (for real flavors), or

1 ≤ Re(tau) ≤ 2 and abs(tau-1) ≤ 1 (for complex flavors).

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.

n

The order of the elementary reflector.

alpha: REAL for slarfg DOUBLE PRECISION for dlarfg COMPLEX for clarfg DOUBLE COMPLEX for zlarfg On entry, the value alpha.
x: REAL for slarfg DOUBLE PRECISION for dlarfg COMPLEX for clarfg DOUBLE COMPLEX for zlarfg Array, size (1+( n -2)*abs( incx )). On entry, the vector x .

incx

The increment between elements of x . incx > 0 .

Output Parameters

alpha: On exit, it is overwritten with the value beta .
x: On exit, it is overwritten with the vector v .
tau: REAL for slarfg DOUBLE PRECISION for dlarfg COMPLEX for clarfg DOUBLE COMPLEX for zlarfg The value tau .

Return Values

This function returns a value, info.

If info = 0 , the execution is successful.
If info = -2 , alpha is NaN
If info = -3 , array x contains NaN components.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?larfg

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values