---
name: "axpy"
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/axpy"
---

# axpy(3)

axpy: y = ax + y

## NAME

axpy - axpy: y = ax + y

## SYNOPSIS

### Functions

subroutine **caxpy** (n, ca, cx, incx, cy, incy)\
 **CAXPY**  subroutine **daxpy** (n, da, dx, incx, dy, incy)\
 **DAXPY**  subroutine **saxpy** (n, sa, sx, incx, sy, incy)\
 **SAXPY**  subroutine **zaxpy** (n, za, zx, incx, zy, incy)\
 **ZAXPY**

## Detailed Description

## Function Documentation

### subroutine caxpy (integer n, complex ca, complex, dimension(\*) cx, integer incx, complex, dimension(\*) cy, integer incy)

**CAXPY**

**Purpose:**

```
!>
!>    CAXPY constant times a vector plus a vector.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>         number of elements in input vector(s)
!>
```

*CA*

```
!>          CA is COMPLEX
!>           On entry, CA specifies the scalar alpha.
!>
```

*CX*

```
!>          CX is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
!>
```

*INCX*

```
!>          INCX is INTEGER
!>         storage spacing between elements of CX
!>
```

*CY*

```
!>          CY is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
!>
```

*INCY*

```
!>          INCY is INTEGER
!>         storage spacing between elements of CY
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>     jack dongarra, linpack, 3/11/78.
!>     modified 12/3/93, array(1) declarations changed to array(*)
!>
```

Definition at line **87** of file **caxpy.f**.

### subroutine daxpy (integer n, double precision da, double precision, dimension(\*) dx, integer incx, double precision, dimension(\*) dy, integer incy)

**DAXPY**

**Purpose:**

```
!>
!>    DAXPY constant times a vector plus a vector.
!>    uses unrolled loops for increments equal to one.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>         number of elements in input vector(s)
!>
```

*DA*

```
!>          DA is DOUBLE PRECISION
!>           On entry, DA specifies the scalar alpha.
!>
```

*DX*

```
!>          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
!>
```

*INCX*

```
!>          INCX is INTEGER
!>         storage spacing between elements of DX
!>
```

*DY*

```
!>          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
!>
```

*INCY*

```
!>          INCY is INTEGER
!>         storage spacing between elements of DY
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>     jack dongarra, linpack, 3/11/78.
!>     modified 12/3/93, array(1) declarations changed to array(*)
!>
```

Definition at line **88** of file **daxpy.f**.

### subroutine saxpy (integer n, real sa, real, dimension(\*) sx, integer incx, real, dimension(\*) sy, integer incy)

**SAXPY**

**Purpose:**

```
!>
!>    SAXPY constant times a vector plus a vector.
!>    uses unrolled loops for increments equal to one.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>         number of elements in input vector(s)
!>
```

*SA*

```
!>          SA is REAL
!>           On entry, SA specifies the scalar alpha.
!>
```

*SX*

```
!>          SX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
!>
```

*INCX*

```
!>          INCX is INTEGER
!>         storage spacing between elements of SX
!>
```

*SY*

```
!>          SY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
!>
```

*INCY*

```
!>          INCY is INTEGER
!>         storage spacing between elements of SY
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>     jack dongarra, linpack, 3/11/78.
!>     modified 12/3/93, array(1) declarations changed to array(*)
!>
```

Definition at line **88** of file **saxpy.f**.

### subroutine zaxpy (integer n, complex\*16 za, complex\*16, dimension(\*) zx, integer incx, complex\*16, dimension(\*) zy, integer incy)

**ZAXPY**

**Purpose:**

```
!>
!>    ZAXPY constant times a vector plus a vector.
!>
```

**Parameters**

*N*

```
!>          N is INTEGER
!>         number of elements in input vector(s)
!>
```

*ZA*

```
!>          ZA is COMPLEX*16
!>           On entry, ZA specifies the scalar alpha.
!>
```

*ZX*

```
!>          ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
!>
```

*INCX*

```
!>          INCX is INTEGER
!>         storage spacing between elements of ZX
!>
```

*ZY*

```
!>          ZY is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
!>
```

*INCY*

```
!>          INCY is INTEGER
!>         storage spacing between elements of ZY
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>     jack dongarra, 3/11/78.
!>     modified 12/3/93, array(1) declarations changed to array(*)
!>
```

Definition at line **87** of file **zaxpy.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.