?larzb

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?larzb

Applies a block reflector or its transpose/conjugate-transpose to a general matrix.

Syntax

call slarzb ( side , trans , direct , storev , m , n , k , l , v , ldv , t , ldt , c , ldc , work , ldwork )

call dlarzb ( side , trans , direct , storev , m , n , k , l , v , ldv , t , ldt , c , ldc , work , ldwork )

call clarzb ( side , trans , direct , storev , m , n , k , l , v , ldv , t , ldt , c , ldc , work , ldwork )

call zlarzb ( side , trans , direct , storev , m , n , k , l , v , ldv , t , ldt , c , ldc , work , ldwork )

Include Files

mkl.fi

Description

slarzb dlarzb clarzb zlarzb

The routine applies a real/complex block reflector H or its transpose H^:code:`T` (or the conjugate transpose H^:code:`H` for complex flavors) to a real/complex distributed m -by- n matrix C from the left or the right. Currently, only storev = 'R' and direct = 'B' are supported.

Input Parameters

side: CHARACTER*1 . If side = 'L' : apply H or H^:code:`T` / H^:code:`H` from the left If side = 'R' : apply H or H^:code:`T` / H^:code:`H` from the right
trans: CHARACTER*1 . If trans = 'N' : apply H (No transpose) If trans='C' : apply H^:code:`H` (conjugate transpose) If trans='T' : apply H^:code:`T` (transpose transpose)
direct: CHARACTER*1 . Indicates how H is formed from a product of elementary reflectors = ‘F’ : H = H(1)*H(2)*...*H(k) (forward, not supported) = ‘B’ : H = H(k)*...*H(2)*H(1) (backward)
storev: CHARACTER*1 . Indicates how the vectors which define the elementary reflectors are stored: = ‘C’ : Column-wise (not supported) = ‘R’ : Row-wise.
m: INTEGER . The number of rows of the matrix C .
n: INTEGER . The number of columns of the matrix C .
k: INTEGER . The order of the matrix T (equal to the number of elementary reflectors whose product defines the block reflector).
l: INTEGER . The number of columns of the matrix V containing the meaningful part of the Householder reflectors. If side = 'L' , m≥l≥ 0 , if side = 'R' , n≥l≥ 0 .
v: REAL for slarzb DOUBLE PRECISION for dlarzb COMPLEX for clarzb DOUBLE COMPLEX for zlarzb Array, DIMENSION ( ldv , nv ). If storev = 'C' , nv = k ; if storev = 'R' , nv = l .
ldv: INTEGER . The leading dimension of the array v . If storev = 'C' , ldv≥l ; if storev = 'R' , ldv≥k .
t: REAL for slarzb DOUBLE PRECISION for dlarzb COMPLEX for clarzb DOUBLE COMPLEX for zlarzb Array, DIMENSION ( ldt , k ). The triangular k -by- k matrix T in the representation of the block reflector.
ldt: INTEGER . The leading dimension of the array t . ldt≥k .
c: REAL for slarzb DOUBLE PRECISION for dlarzb COMPLEX for clarzb DOUBLE COMPLEX for zlarzb 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 slarzb DOUBLE PRECISION for dlarzb COMPLEX for clarzb DOUBLE COMPLEX for zlarzb Workspace array, DIMENSION ( ldwork , k ).
ldwork: INTEGER . The leading dimension of the array work . If side = 'L' , ldwork≥ max(1, n) ; if side = 'R' , ldwork≥ max(1, m) .

Output Parameters

c: On exit, C is overwritten by H * C, or H^:code:`T` / H^:code:`H` * C, or C * H, or C * H^:code:`T` / H^:code:`H` .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?larzb

Syntax

Include Files

Description

Input Parameters

Output Parameters