# lartv - Man Page

lartv: apply vector of plane rotations to vectors

## Synopsis

### Functions

subroutine clartv (n, x, incx, y, incy, c, s, incc)
CLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.
subroutine dlartv (n, x, incx, y, incy, c, s, incc)
DLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.
subroutine slartv (n, x, incx, y, incy, c, s, incc)
SLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.
subroutine zlartv (n, x, incx, y, incy, c, s, incc)
ZLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

## Function Documentation

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

CLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

Purpose:

``` CLARTV applies a vector of complex plane rotations with real cosines
to elements of the complex vectors x and y. For i = 1,2,...,n

( x(i) ) := (        c(i)   s(i) ) ( x(i) )
( y(i) )    ( -conjg(s(i))  c(i) ) ( y(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.```

INCX

```          INCX is INTEGER
The increment between elements of X. INCX > 0.```

Y

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

INCY

```          INCY is INTEGER
The increment between elements of Y. INCY > 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 106 of file clartv.f.

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

DLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.

Purpose:

``` DLARTV applies a vector of real plane rotations to elements of the
real vectors x and y. For i = 1,2,...,n

( x(i) ) := (  c(i)  s(i) ) ( x(i) )
( y(i) )    ( -s(i)  c(i) ) ( y(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.```

INCX

```          INCX is INTEGER
The increment between elements of X. INCX > 0.```

Y

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

INCY

```          INCY is INTEGER
The increment between elements of Y. INCY > 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 107 of file dlartv.f.

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

SLARTV applies a vector of plane rotations with real cosines and real sines to the elements of a pair of vectors.

Purpose:

``` SLARTV applies a vector of real plane rotations to elements of the
real vectors x and y. For i = 1,2,...,n

( x(i) ) := (  c(i)  s(i) ) ( x(i) )
( y(i) )    ( -s(i)  c(i) ) ( y(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.```

INCX

```          INCX is INTEGER
The increment between elements of X. INCX > 0.```

Y

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

INCY

```          INCY is INTEGER
The increment between elements of Y. INCY > 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 107 of file slartv.f.

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

ZLARTV applies a vector of plane rotations with real cosines and complex sines to the elements of a pair of vectors.

Purpose:

``` ZLARTV applies a vector of complex plane rotations with real cosines
to elements of the complex vectors x and y. For i = 1,2,...,n

( x(i) ) := (        c(i)   s(i) ) ( x(i) )
( y(i) )    ( -conjg(s(i))  c(i) ) ( y(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.```

INCX

```          INCX is INTEGER
The increment between elements of X. INCX > 0.```

Y

```          Y is COMPLEX*16 array, dimension (1+(N-1)*INCY)
The vector y.```

INCY

```          INCY is INTEGER
The increment between elements of Y. INCY > 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