?laref

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?laref

Applies Householder reflectors to matrices on their rows or columns.

Syntax

void slaref(const char *type, float *a, const MKL_INT *lda, const MKL_INT *wantz,
            float *z, const MKL_INT *ldz, const MKL_INT *block, MKL_INT *irow1,
            MKL_INT *icol1, const MKL_INT *istart, const MKL_INT *istop,
            const MKL_INT *itmp1, const MKL_INT *itmp2, const MKL_INT *liloz,
            const MKL_INT *lihiz, const float *vecs, float *v2, float *v3, float *t1,
            float *t2, float *t3);

void dlaref(const char *type, double *a, const MKL_INT *lda, const MKL_INT *wantz,
            double *z, const MKL_INT *ldz, const MKL_INT *block, MKL_INT *irow1,
            MKL_INT *icol1, const MKL_INT *istart, const MKL_INT *istop,
            const MKL_INT *itmp1, const MKL_INT *itmp2, const MKL_INT *liloz,
            const MKL_INT *lihiz, const double *vecs, double *v2, double *v3, double *t1,
            double *t2, double *t3);

void claref(const char *type, MKL_Complex8 *a, const MKL_INT *lda, const MKL_INT *wantz,
            MKL_Complex8 *z, const MKL_INT *ldz, const MKL_INT *block, MKL_INT *irow1,
            MKL_INT *icol1, const MKL_INT *istart, const MKL_INT *istop,
            const MKL_INT *itmp1, const MKL_INT *itmp2, const MKL_INT *liloz,
            const MKL_INT *lihiz, const MKL_Complex8 *vecs, MKL_Complex8 *v2,
            MKL_Complex8 *v3, MKL_Complex8 *t1, MKL_Complex8 *t2, MKL_Complex8 *t3);

void zlaref(const char *type, MKL_Complex16 *a, const MKL_INT *lda, const MKL_INT *wantz,
            MKL_Complex16 *z, const MKL_INT *ldz, const MKL_INT *block, MKL_INT *irow1,
            MKL_INT *icol1, const MKL_INT *istart, const MKL_INT *istop,
            const MKL_INT *itmp1, const MKL_INT *itmp2, const MKL_INT *liloz,
            const MKL_INT *lihiz, const MKL_Complex16 *vecs, MKL_Complex16 *v2,
            MKL_Complex16 *v3, MKL_Complex16 *t1, MKL_Complex16 *t2, MKL_Complex16 *t3);

Include Files

mkl_scalapack.h

Description

slaref dlaref ?laref applies one or several Householder reflectors of size 3 to one or two matrices (if column is specified) on either their rows or columns.

Input Parameters

type

(local)

If ‘R’: Apply reflectors to the rows of the matrix (apply from left) Otherwise: Apply reflectors to the columns of the matrix Unchanged on exit.

a

(local) REAL for slaref DOUBLE PRECISION for dlaref COMPLEX for claref DOUBLE COMPLEX for zlaref

Array, (lld_a,LOCc(ja+n-1))lld_a * LOCc ( ja + n -1)

On entry, the matrix to receive the reflections.

lda

(local)

On entry, the leading dimension of a . Unchanged on exit.

wantz

(local)

If wantz ≠ 0 , then apply any column reflections to z as well.

If wantz = 0 , then do no additional work on z .

z

(local) REAL for slaref DOUBLE PRECISION for dlaref COMPLEX for claref DOUBLE COMPLEX for zlaref

Array, ldz * ncols , where the value ncols depends on other arguments. If wantzwantz ≠ 0 and type ≠ ‘R’ then ncols = icol1 + 3*( lihiz - liloz + 1). Otherwise, ncols is unused.

On entry, the second matrix to receive column reflections. This is changed only if wantz is set.

ldz

(local)

On entry, the leading dimension of z . Unchanged on exit.

block

(local)

If nonzero , then apply several reflectors at once and read their data from the vecs array.

If zero , apply the single reflector given by v2 , v3 , t1 , t2 , and t3 .

irow1

(local)

On entry, the local row element of a .

icol1

(local)

On entry, the local column element of a .

istart

(local)

Specifies the “number” of the first reflector. This is used as an index into vecs if block is set. istart is ignored if block is zero .

istop

(local)

Specifies the “number” of the last reflector. This is used as an index into vecs if block is set. istop is ignored if block is zero .

itmp1

(local)

Starting range into a . For rows, this is the local first column. For columns, this is the local first row.

itmp2

(local)

Ending range into a . For rows, this is the local last column. For columns, this is the local last row.

liloz , lihiz

(local)

These serve the same purpose as itmp1 , itmp2 but for z when wantz is set.

vecs

(local) REAL for slaref DOUBLE PRECISION for dlaref COMPLEX for claref DOUBLE COMPLEX for zlaref Array of size 3*N (matrix size)

This holds the size 3 reflectors one after another and this is only accessed when block is nonzero

v2 , v3 , t1 , t2 , t3

(local) REAL for slaref DOUBLE PRECISION for dlaref COMPLEX for claref DOUBLE COMPLEX for zlaref

This holds information on a single size 3 Householder reflector and is read when block is zero , and overwritten when block is nonzero

Output Parameters

a: The updated matrix on exit.
z: This is changed only if wantz is set.
irow1: Undefined on output.
icol1: Undefined on output.

v2 , v3 , t1 , t2 , t3

Overwritten when block is nonzero.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?laref

Syntax

Include Files

Description

Input Parameters

Output Parameters