?lasr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?lasr

Applies a sequence of plane rotations to a general rectangular matrix.

Syntax

call slasr ( side , pivot , direct , m , n , c , s , a , lda )

call dlasr ( side , pivot , direct , m , n , c , s , a , lda )

call clasr ( side , pivot , direct , m , n , c , s , a , lda )

call zlasr ( side , pivot , direct , m , n , c , s , a , lda )

Include Files

mkl.fi

Description

slasr dlasr clasr zlasr

The routine applies a sequence of plane rotations to a real/complex matrix A , from the left or the right.

A := P*A , when side = 'L' ( Left-hand side )

A := A*P' , when side = 'R' ( Right-hand side )

where P is an orthogonal matrix consisting of a sequence of plane rotations with z = m when side = 'L' and z = n when side = 'R' .

When direct = 'F' (Forward sequence), then

P = P(z-1)*...P(2)*P(1) ,

and when direct = 'B' (Backward sequence), then

P = P(1)*P(2)*...*P(z-1) ,

where P ( k ) is a plane rotation matrix defined by the 2-by-2 plane rotation:

When pivot = 'V' ( Variable pivot ), the rotation is performed for the plane ( k , k + 1), that is, P ( k ) has the form

where R ( k ) appears as a rank-2 modification to the identity matrix in rows and columns k and k +1.

When pivot = 'T' ( Top pivot ), the rotation is performed for the plane (1,k+1) , so P ( k ) has the form

where R ( k ) appears in rows and columns k and k +1.

Similarly, when pivot = 'B' ( Bottom pivot ), the rotation is performed for the plane (k,z) , giving P ( k ) the form

where R ( k ) appears in rows and columns k and z . The rotations are performed without ever forming P ( k ) explicitly.

Input Parameters

side: CHARACTER*1 . Specifies whether the plane rotation matrix P is applied to A on the left or the right. = ‘L’ : left, compute A := P*A = ‘R’ : right, compute A:= A*P'
direct: CHARACTER*1 . Specifies whether P is a forward or backward sequence of plane rotations. = ‘F’ : forward, P = P(z-1)*...*P(2)*P(1) = ‘B’ : backward, P = P(1)*P(2)*...*P(z-1)
pivot: CHARACTER*1 . Specifies the plane for which P ( k ) is a plane rotation matrix. = ‘V’ : Variable pivot, the plane ( k , k +1) = ‘T’ : Top pivot, the plane (1, k +1) = ‘B’ : Bottom pivot, the plane ( k , z )
m: INTEGER . The number of rows of the matrix A . If m ≤ 1 , an immediate return is effected.
n: INTEGER . The number of columns of the matrix A . If n ≤ 1 , an immediate return is effected.
c , s: REAL for slasr / clasr DOUBLE PRECISION for dlasr / zlasr . Arrays, DIMENSION ( m -1) if side = 'L' , ( n -1) if side = ‘R’ . c(k) and s(k) contain the cosine and sine of the plane rotations respectively that define the 2-by-2 plane rotation part ( R ( k )) of the P ( k ) matrix as described above in Description .
a: REAL for slasr DOUBLE PRECISION for dlasr COMPLEX for clasr DOUBLE COMPLEX for zlasr . Array, DIMENSION ( lda, n ). The m -by- n matrix A .
lda: INTEGER . The leading dimension of the array a . lda≥ max(1,m) .

Output Parameters

a: On exit, A is overwritten by P*A if side = 'R', or by A*P ‘ if side = 'L' .

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lasr

Syntax

Include Files

Description

Input Parameters

Output Parameters