# slasr.f man page

slasr.f —

## Synopsis

### Functions/Subroutines

subroutineslasr(SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA)SLASRapplies a sequence of plane rotations to a general rectangular matrix.

## Function/Subroutine Documentation

### subroutine slasr (characterSIDE, characterPIVOT, characterDIRECT, integerM, integerN, real, dimension( * )C, real, dimension( * )S, real, dimension( lda, * )A, integerLDA)

**SLASR** applies a sequence of plane rotations to a general rectangular matrix.

**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.
```

**Parameters:**

*SIDE*

```
SIDE is 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*

```
PIVOT is 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*

```
DIRECT is 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*

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

*N*

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

*C*

```
C is REAL array, dimension
(M-1) if SIDE = 'L'
(N-1) if SIDE = 'R'
The cosines c(k) of the plane rotations.
```

*S*

```
S is 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*

```
A is 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*

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

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 200 of file slasr.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

slasr(3) is an alias of slasr.f(3).