?larft

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?larft

Forms the triangular factor T of a block reflector H = I - V * T * V ** H .

Syntax

call slarft ( direct , storev , n , k , v , ldv , tau , t , ldt )

call dlarft ( direct , storev , n , k , v , ldv , tau , t , ldt )

call clarft ( direct , storev , n , k , v , ldv , tau , t , ldt )

call zlarft ( direct , storev , n , k , v , ldv , tau , t , ldt )

Include Files

mkl.fi

Description

The routine ?larft forms the triangular factor T of a real/complex block reflector H of order n , which is defined as a product of k elementary reflectors.

If direct = 'F' , H = H(1)*H(2)* . . .*H(k) and T is upper triangular;

If direct = 'B' , H = H(k)*. . .*H(2)*H(1) and T is lower triangular.

If storev = 'C' , the vector which defines the elementary reflector H(i) is stored in the i -th column of the array v , and H = I - V*T*V^{T} (for real flavors) or H = I - V*T*V^{H} (for complex flavors) .

If storev = 'R' , the vector which defines the elementary reflector H(i) is stored in the i -th row of the array v , and H = I - V^{T}*T*V (for real flavors) or H = I - V^{H}*T*V (for complex flavors).

Input Parameters

The data types are given for the Fortran interface.

direct

CHARACTER*1 .

Specifies the order in which the elementary reflectors are multiplied to form the block reflector: = ‘F’ : H = H(1)*H(2)*. . . *H(k) (forward) = ‘B’ : H = H(k)*. . .*H(2)*H(1) (backward)

storev

CHARACTER*1 .

Specifies how the vectors which define the elementary reflectors are stored (see also Application Notes below) : = ‘C’ : column-wise = ‘R’ : row-wise.

n

INTEGER . The order of the block reflector H . n≥ 0 .

k

INTEGER . The order of the triangular factor T (equal to the number of elementary reflectors). k≥ 1 .

v: REAL for slarft DOUBLE PRECISION for dlarft COMPLEX for clarft DOUBLE COMPLEX for zlarft Array, DIMENSION ( ldv , k ) if storev = 'C' or ( ldv , n ) if storev = 'R' . The matrix V .
v: The size limitations depend on values of parameters storev and side as described in the following table: The matrix v . See Application Notes below.

ldv

INTEGER . The leading dimension of the array v .

If storev = 'C' , ldv≥ max(1,n)

if storev = 'R' , ldv≥k .

tau: REAL for slarft DOUBLE PRECISION for dlarft COMPLEX for clarft DOUBLE COMPLEX for zlarft Array, size ( k ). tau(i)[i-1] must contain the scalar factor of the elementary reflector H(i).

ldt

INTEGER . The leading dimension of the output array t . ldt≥k .

Output Parameters

t

REAL for slarft DOUBLE PRECISION for dlarft COMPLEX for clarft DOUBLE COMPLEX for zlarft

Array, size ldt by k . The k -by- k triangular factor T of the block reflector. If direct = 'F' , T is upper triangular; if direct = 'B' , T is lower triangular. The rest of the array is not used.

v

The matrix V .

Application Notes

The shape of the matrix \(V\) and the storage of the vectors which define the \(H(i)\) is best illustrated by the following example with n = 5 and k = 3 . The elements equal to 1 are not stored; the corresponding array elements are modified but restored on exit. The rest of the array is not used.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?larft

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes