?larzt

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?larzt

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

slarzt dlarzt clarzt zlarzt

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.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?larzt

Syntax

Include Files

Description

Input Parameters

Output Parameters

Application Notes