---
name: "lartv"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/lartv"
---

# lartv(3)

lartv: apply vector of plane rotations to vectors

## NAME

lartv - 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.

## Detailed Description

## 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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **106** of file **zlartv.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.