# lar2v - Man Page

lar2v: apply vector of plane rotations to 2x2 matrices

## Synopsis

### Functions

subroutine clar2v (n, x, y, z, incx, c, s, incc)
CLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.
subroutine dlar2v (n, x, y, z, incx, c, s, incc)
DLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.
subroutine slar2v (n, x, y, z, incx, c, s, incc)
SLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.
subroutine zlar2v (n, x, y, z, incx, c, s, incc)
ZLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

## Function Documentation

### subroutine clar2v (integer n, complex, dimension( * ) x, complex, dimension( * ) y, complex, dimension( * ) z, integer incx, real, dimension( * ) c, complex, dimension( * ) s, integer incc)

CLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:

``` CLAR2V applies a vector of complex plane rotations with real cosines
from both sides to a sequence of 2-by-2 complex Hermitian matrices,
defined by the elements of the vectors x, y and z. For i = 1,2,...,n

(       x(i)  z(i) ) :=
( conjg(z(i)) y(i) )

(  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )```
Parameters

N

```          N is INTEGER
The number of plane rotations to be applied.```

X

```          X is COMPLEX array, dimension (1+(N-1)*INCX)
The vector x; the elements of x are assumed to be real.```

Y

```          Y is COMPLEX array, dimension (1+(N-1)*INCX)
The vector y; the elements of y are assumed to be real.```

Z

```          Z is COMPLEX array, dimension (1+(N-1)*INCX)
The vector z.```

INCX

```          INCX is INTEGER
The increment between elements of X, Y and Z. INCX > 0.```

C

```          C is REAL array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.```

S

```          S is COMPLEX array, dimension (1+(N-1)*INCC)
The sines of the plane rotations.```

INCC

```          INCC is INTEGER
The increment between elements of C and S. INCC > 0.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 110 of file clar2v.f.

### subroutine dlar2v (integer n, double precision, dimension( * ) x, double precision, dimension( * ) y, double precision, dimension( * ) z, integer incx, double precision, dimension( * ) c, double precision, dimension( * ) s, integer incc)

DLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:

``` DLAR2V applies a vector of real plane rotations from both sides to
a sequence of 2-by-2 real symmetric matrices, defined by the elements
of the vectors x, y and z. For i = 1,2,...,n

( x(i)  z(i) ) := (  c(i)  s(i) ) ( x(i)  z(i) ) ( c(i) -s(i) )
( z(i)  y(i) )    ( -s(i)  c(i) ) ( z(i)  y(i) ) ( s(i)  c(i) )```
Parameters

N

```          N is INTEGER
The number of plane rotations to be applied.```

X

```          X is DOUBLE PRECISION array,
dimension (1+(N-1)*INCX)
The vector x.```

Y

```          Y is DOUBLE PRECISION array,
dimension (1+(N-1)*INCX)
The vector y.```

Z

```          Z is DOUBLE PRECISION array,
dimension (1+(N-1)*INCX)
The vector z.```

INCX

```          INCX is INTEGER
The increment between elements of X, Y and Z. INCX > 0.```

C

```          C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.```

S

```          S is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
The sines of the plane rotations.```

INCC

```          INCC is INTEGER
The increment between elements of C and S. INCC > 0.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 109 of file dlar2v.f.

### subroutine slar2v (integer n, real, dimension( * ) x, real, dimension( * ) y, real, dimension( * ) z, integer incx, real, dimension( * ) c, real, dimension( * ) s, integer incc)

SLAR2V applies a vector of plane rotations with real cosines and real sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:

``` SLAR2V applies a vector of real plane rotations from both sides to
a sequence of 2-by-2 real symmetric matrices, defined by the elements
of the vectors x, y and z. For i = 1,2,...,n

( x(i)  z(i) ) := (  c(i)  s(i) ) ( x(i)  z(i) ) ( c(i) -s(i) )
( z(i)  y(i) )    ( -s(i)  c(i) ) ( z(i)  y(i) ) ( s(i)  c(i) )```
Parameters

N

```          N is INTEGER
The number of plane rotations to be applied.```

X

```          X is REAL array,
dimension (1+(N-1)*INCX)
The vector x.```

Y

```          Y is REAL array,
dimension (1+(N-1)*INCX)
The vector y.```

Z

```          Z is REAL array,
dimension (1+(N-1)*INCX)
The vector z.```

INCX

```          INCX is INTEGER
The increment between elements of X, Y and Z. INCX > 0.```

C

```          C is REAL array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.```

S

```          S is REAL array, dimension (1+(N-1)*INCC)
The sines of the plane rotations.```

INCC

```          INCC is INTEGER
The increment between elements of C and S. INCC > 0.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 109 of file slar2v.f.

### subroutine zlar2v (integer n, complex*16, dimension( * ) x, complex*16, dimension( * ) y, complex*16, dimension( * ) z, integer incx, double precision, dimension( * ) c, complex*16, dimension( * ) s, integer incc)

ZLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:

``` ZLAR2V applies a vector of complex plane rotations with real cosines
from both sides to a sequence of 2-by-2 complex Hermitian matrices,
defined by the elements of the vectors x, y and z. For i = 1,2,...,n

(       x(i)  z(i) ) :=
( conjg(z(i)) y(i) )

(  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )```
Parameters

N

```          N is INTEGER
The number of plane rotations to be applied.```

X

```          X is COMPLEX*16 array, dimension (1+(N-1)*INCX)
The vector x; the elements of x are assumed to be real.```

Y

```          Y is COMPLEX*16 array, dimension (1+(N-1)*INCX)
The vector y; the elements of y are assumed to be real.```

Z

```          Z is COMPLEX*16 array, dimension (1+(N-1)*INCX)
The vector z.```

INCX

```          INCX is INTEGER
The increment between elements of X, Y and Z. INCX > 0.```

C

```          C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.```

S

```          S is COMPLEX*16 array, dimension (1+(N-1)*INCC)
The sines of the plane rotations.```

INCC

```          INCC is INTEGER
The increment between elements of C and S. INCC > 0.```
Author

Univ. of Tennessee

Univ. of California Berkeley