?larz

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?larz

Applies an elementary reflector (as returned by ?tzrzf ) to a general matrix.

Syntax

call slarz(side, m, n, l, v, incv, tau, c, ldc, work)
call dlarz(side, m, n, l, v, incv, tau, c, ldc, work)
call clarz(side, m, n, l, v, incv, tau, c, ldc, work)
call zlarz(side, m, n, l, v, incv, tau, c, ldc, work)

Include Files

mkl.fi

Description

The routine ?larz 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 forms

H = I-tau*v*v^{T} for real flavors and H = I-tau*v*v^{H} for complex flavors,

where tau is a real/complex scalar and v is a real/complex vector, respectively.

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

For complex flavors, to apply H^H (the conjugate transpose of H ), supply conjg( tau ) instead of tau .

H is a product of k elementary reflectors as returned by ?tzrzf .

Input Parameters

side: CHARACTER*1 . If side = 'L' : form H * C If side = 'R' : form C * H
m: INTEGER . The number of rows of the matrix C .
n: INTEGER . The number of columns of the matrix C .
l: INTEGER . The number of entries of the vector v containing the meaningful part of the Householder vectors. If side = 'L' , m≥L≥ 0 , if side = 'R' , n≥L≥ 0 .
v: REAL for slarz DOUBLE PRECISION for dlarz COMPLEX for clarz DOUBLE COMPLEX for zlarz Array, DIMENSION (1+( l -1)*abs( incv )). The vector v in the representation of H as returned by ?tzrzf . v is not used if tau = 0 .
incv: INTEGER . The increment between elements of v . incv≠ 0 .
tau: REAL for slarz DOUBLE PRECISION for dlarz COMPLEX for clarz DOUBLE COMPLEX for zlarz The value tau in the representation of H .
c: REAL for slarz DOUBLE PRECISION for dlarz COMPLEX for clarz DOUBLE COMPLEX for zlarz Array, DIMENSION ( ldc , n ). On entry, the m -by- n matrix C .
ldc: INTEGER . The leading dimension of the array c . ldc≥ max(1,m) .
work: REAL for slarz DOUBLE PRECISION for dlarz COMPLEX for clarz DOUBLE COMPLEX for zlarz Workspace array, DIMENSION ( n ) if side = 'L' or ( m ) if side = 'R' .

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 Fortran

?larz

Syntax

Include Files

Description

Input Parameters

Output Parameters