?larzt

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 7/13/2023

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Public

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?larzt

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

Syntax

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

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

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

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

Include Files

mkl.fi

Description

The routine 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).

Currently, only storev = 'R' and direct = 'B' are supported.

Input Parameters

direct

CHARACTER*1.

Specifies the order in which the elementary reflectors are multiplied to form the block reflector:

If direct = 'F': H = H(1)*H(2)*...*H(k) (forward, not supported)

If direct = '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):

If storev = 'C': column-wise (not supported)

If storev = '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 slarzt

DOUBLE PRECISION for dlarzt

COMPLEX for clarzt

DOUBLE COMPLEX for zlarzt

Array, DIMENSION

(ldv, k) if storev = 'C'

(ldv, n) if storev = 'R' The matrix V.

ldv

INTEGER. The leading dimension of the array v.

If storev = 'C', ldv≥ max(1,n);

if storev = 'R', ldv≥k.

tau

REAL for slarzt

DOUBLE PRECISION for dlarzt

COMPLEX for clarzt

DOUBLE COMPLEX for zlarzt

Array, DIMENSION (k). tau(i) 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 slarzt

DOUBLE PRECISION for dlarzt

COMPLEX for clarzt

DOUBLE COMPLEX for zlarzt

Array, DIMENSION (ldt,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. See Application Notes below.

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.