?lasr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

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

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 in the matrix A. The value of m must be at least zero.

n: INTEGER. The number of columns in the matrix A. The value of n must be at least zero.

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