---
name: "crot.f"
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/crot.f"
---

# crot.f(3)

## NAME

SRC/crot.f

## SYNOPSIS

### Functions/Subroutines

subroutine **crot** (n, cx, incx, cy, incy, c, s)\
 **CROT** applies a plane rotation with real cosine and complex sine to a pair of complex vectors.

## Function/Subroutine Documentation

### subroutine crot (integer n, complex, dimension( \* ) cx, integer incx, complex, dimension( \* ) cy, integer incy, real c, complex s)

**CROT** applies a plane rotation with real cosine and complex sine to a pair of complex vectors.

**Purpose:**

```
!>
!> CROT applies a plane rotation, where the cos (C) is real and the
!> sin (S) is complex, and the vectors CX and CY are complex.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>          The number of elements in the vectors CX and CY.
!>
```

*CX*

```
!>          CX is COMPLEX array, dimension (N)
!>          On input, the vector X.
!>          On output, CX is overwritten with C*X + S*Y.
!>
```

*INCX*

```
!>          INCX is INTEGER
!>          The increment between successive values of CX.  INCX <> 0.
!>
```

*CY*

```
!>          CY is COMPLEX array, dimension (N)
!>          On input, the vector Y.
!>          On output, CY is overwritten with -CONJG(S)*X + C*Y.
!>
```

*INCY*

```
!>          INCY is INTEGER
!>          The increment between successive values of CY.  INCX <> 0.
!>
```

*C*

```
!>          C is REAL
!>
```

*S*

```
!>          S is COMPLEX
!>          C and S define a rotation
!>             [  C          S  ]
!>             [ -conjg(S)   C  ]
!>          where C*C + S*CONJG(S) = 1.0.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **102** of file **crot.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.