---
name: "slasr"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slasr/3lapack"
---

# slasr(3lapack)

applies a sequence of plane rotations to a real matrix A,

## NAME

SLASR - applies a sequence of plane rotations to a real matrix A,

## SYNOPSIS

- SUBROUTINE SLASR(

  SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )

- CHARACTER

  DIRECT, PIVOT, SIDE

- INTEGER

  LDA, M, N

- REAL

  A( LDA, \* ), C( \* ), S( \* )

## PURPOSE

SLASR applies a sequence of plane rotations to a real matrix A, from either the left or the right.\
\
 When SIDE = 'L', the transformation takes the form\
\
\
    A := P\*A\
\
 and when SIDE = 'R', the transformation takes the form\
\
\
    A := A\*P\*\*T\
\
 where P is an orthogonal matrix consisting of a sequence of z plane rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', and P\*\*T is the transpose of P.\
\
 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 rotation\
\
    R(k) = (  c(k)  s(k) )\
\
         \= ( -s(k)  c(k) ).\
\
 When PIVOT = 'V' (Variable pivot), the rotation is performed for the plane (k,k+1), i.e., P(k) has the form\
\
\
    P(k) = (  1                                            )\
           (       ...                                     )\
           (              1                                )\
           (                   c(k)  s(k)                  )\
           (                  -s(k)  c(k)                  )\
           (                                1              )\
           (                                     ...       )\
           (                                            1  )\
 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\
\
\
    P(k) = (  c(k)                    s(k)                 )\
           (         1                                     )\
           (              ...                              )\
           (                     1                         )\
           ( -s(k)                    c(k)                 )\
           (                                 1             )\
           (                                      ...      )\
           (                                             1 )\
 where R(k) appears in rows and columns 1 and k+1.\
\
 Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is performed for the plane (k,z), giving P(k) the form\
\
\
    P(k) = ( 1                                             )\
           (      ...                                      )\
           (             1                                 )\
           (                  c(k)                    s(k) )\
           (                         1                     )\
           (                              ...              )\
           (                                     1         )\
           (                 -s(k)                    c(k) )\
 where R(k) appears in rows and columns k and z.  The rotations are performed without ever forming P(k) explicitly.\

## ARGUMENTS

- SIDE (input) 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\*\*T

- PIVOT (input) 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)

- DIRECT (input) 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)

- M (input) INTEGER

  The number of rows of the matrix A.  If m \<= 1, an immediate return is effected.

- N (input) INTEGER

  The number of columns of the matrix A.  If n \<= 1, an immediate return is effected.

- C (input) REAL array, dimension

  (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' The cosines c(k) of the plane rotations.

- S (input) REAL array, dimension

  (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' The sines s(k) of the plane rotations.  The 2-by-2 plane rotation part of the matrix P(k), R(k), has the form R(k) = (  c(k)  s(k) ) ( -s(k)  c(k) ).

- A (input/output) REAL array, dimension (LDA,N)

  The M-by-N matrix A.  On exit, A is overwritten by P\*A if SIDE = 'R' or by A\*P\*\*T if SIDE = 'L'.

- LDA (input) INTEGER

  The leading dimension of the array A.  LDA \>= max(1,M).