?orm2l/?unm2l

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?orm2l/?unm2l

Multiplies a general matrix by the orthogonal/unitary matrix from a QL factorization determined by ?geqlf (unblocked algorithm).

Syntax

call sorm2l ( side , trans , m , n , k , a , lda , tau , c , ldc , work , info )

call dorm2l ( side , trans , m , n , k , a , lda , tau , c , ldc , work , info )

call cunm2l ( side , trans , m , n , k , a , lda , tau , c , ldc , work , info )

call zunm2l ( side , trans , m , n , k , a , lda , tau , c , ldc , work , info )

Include Files

mkl.fi

Description

The routine ?orm2l / ?unm2l overwrites the general real/complex m -by- n matrix C with

Q*C if side = 'L' and trans = 'N' , or

Q^{T}*C / Q^{H}*C if side = 'L' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors), or

C*Q if side = 'R ‘ and trans = 'N' , or

C*Q^{T} / C*Q^{H} if side = 'R' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors).

Here Q is a real orthogonal or complex unitary matrix defined as the product of k elementary reflectors

Q = H(k)*...*H(2)*H(1) as returned by ?geqlf .

Q is of order m if side = 'L' and of order n if side = 'R' .

Input Parameters

side: CHARACTER*1 . = ‘L’ : apply Q or Q^{T} / Q^{H} from the left = ‘R’ : apply Q or Q^{T} / Q^{H} from the right
trans: CHARACTER*1 . = ‘N’ : apply Q (no transpose) = ‘T’ : apply Q^:code:`T` (transpose, for real flavors) = ‘C’ : apply Q^:code:`H` (conjugate transpose, for complex flavors)
m: INTEGER . The number of rows of the matrix C . m≥ 0 .
n: INTEGER . The number of columns of the matrix C . n≥ 0 .
k: INTEGER . The number of elementary reflectors whose product defines the matrix Q . If side = 'L' , m≥k≥ 0 ; if side = 'R' , n≥k≥ 0 .
a: REAL for sorm2l DOUBLE PRECISION for dorm2l COMPLEX for cunm2l DOUBLE COMPLEX for zunm2l . Array, DIMENSION ( lda , k ). The i -th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,..., k , as returned by ?geqlf in the last k columns of its array argument a . The array a is modified by the routine but restored on exit.
lda: INTEGER . The leading dimension of the array a . If side = 'L' , lda≥ max(1, m) if side = 'R' , lda≥ max(1, n) .
tau: REAL for sorm2l DOUBLE PRECISION for dorm2l COMPLEX for cunm2l DOUBLE COMPLEX for zunm2l . Array, DIMENSION ( k ). tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by ?geqlf .
c: REAL for sorm2l DOUBLE PRECISION for dorm2l COMPLEX for cunm2l DOUBLE COMPLEX for zunm2l . 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 sorm2l DOUBLE PRECISION for dorm2l COMPLEX for cunm2l DOUBLE COMPLEX for zunm2l . Workspace array, DIMENSION : ( n ) if side = 'L' , ( m ) if side = 'R' .

Output Parameters

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

info

INTEGER .

= 0: successful exit
< 0: if info = -i , the i -th argument had an illegal value

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?orm2l/?unm2l

Syntax

Include Files

Description

Input Parameters

Output Parameters