---
name: "lar2v"
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/lar2v"
---

# lar2v(3)

lar2v: apply vector of plane rotations to 2x2 matrices

## NAME

lar2v - 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.

## Detailed Description

## 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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **110** of file **zlar2v.f**.

## Author

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