complex_blas_level1(3) LAPACK complex_blas_level1(3)

# NAME¶

complex_blas_level1

# SYNOPSIS¶

## Functions¶

subroutine caxpy (N, CA, CX, INCX, CY, INCY)
CAXPY subroutine ccopy (N, CX, INCX, CY, INCY)
CCOPY complex function cdotc (N, CX, INCX, CY, INCY)
CDOTC complex function cdotu (N, CX, INCX, CY, INCY)
CDOTU subroutine crotg (CA, CB, C, S)
CROTG subroutine cscal (N, CA, CX, INCX)
CSCAL subroutine csrot (N, CX, INCX, CY, INCY, C, S)
CSROT subroutine csscal (N, SA, CX, INCX)
CSSCAL subroutine cswap (N, CX, INCX, CY, INCY)
CSWAP

# Detailed Description¶

This is the group of complex LEVEL 1 BLAS routines.

# 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

NAG Ltd.

Date

November 2017

Further Details:

```
jack dongarra, linpack, 3/11/78.

modified 12/3/93, array(1) declarations changed to array(*)```

## subroutine ccopy (integer N, complex, dimension(*) CX, integer INCX, complex, dimension(*) CY, integer INCY)¶

CCOPY

Purpose:

```
CCOPY copies a vector x to a vector y.```

Parameters

N

```
N is INTEGER

number of elements in input vector(s)```

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

NAG Ltd.

Date

November 2017

Further Details:

```
jack dongarra, linpack, 3/11/78.

modified 12/3/93, array(1) declarations changed to array(*)```

## complex function cdotc (integer N, complex, dimension(*) CX, integer INCX, complex, dimension(*) CY, integer INCY)¶

CDOTC

Purpose:

```
CDOTC forms the dot product of two complex vectors

CDOTC = X^H * Y```

Parameters

N

```
N is INTEGER

number of elements in input vector(s)```

CX

```
CX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )```

INCX

```
INCX is INTEGER

storage spacing between elements of CX```

CY

```
CY is REAL 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

NAG Ltd.

Date

November 2017

Further Details:

```
jack dongarra, linpack,  3/11/78.

modified 12/3/93, array(1) declarations changed to array(*)```

## complex function cdotu (integer N, complex, dimension(*) CX, integer INCX, complex, dimension(*) CY, integer INCY)¶

CDOTU

Purpose:

```
CDOTU forms the dot product of two complex vectors

CDOTU = X^T * Y```

Parameters

N

```
N is INTEGER

number of elements in input vector(s)```

CX

```
CX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )```

INCX

```
INCX is INTEGER

storage spacing between elements of CX```

CY

```
CY is REAL 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

NAG Ltd.

Date

November 2017

Further Details:

```
jack dongarra, linpack, 3/11/78.

modified 12/3/93, array(1) declarations changed to array(*)```

## subroutine crotg (complex CA, complex CB, real C, complex S)¶

CROTG

Purpose:

```
CROTG determines a complex Givens rotation.```

Parameters

CA

```
CA is COMPLEX```

CB

```
CB is COMPLEX```

C

```
C is REAL```

S

```
S is COMPLEX```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

November 2017

## subroutine cscal (integer N, complex CA, complex, dimension(*) CX, integer INCX)¶

CSCAL

Purpose:

```
CSCAL scales a vector by a constant.```

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```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

November 2017

Further Details:

```
jack dongarra, linpack,  3/11/78.

modified 3/93 to return if incx .le. 0.

modified 12/3/93, array(1) declarations changed to array(*)```

## subroutine csrot (integer N, complex, dimension( * ) CX, integer INCX, complex, dimension( * ) CY, integer INCY, real C, real S)¶

CSROT

Purpose:

```
CSROT applies a plane rotation, where the cos and sin (c and s) are real

and the vectors cx and cy are complex.

jack dongarra, linpack, 3/11/78.```

Parameters

N

```
N is INTEGER

On entry, N specifies the order of the vectors cx and cy.

N must be at least zero.```

CX

```
CX is COMPLEX array, dimension at least

( 1 + ( N - 1 )*abs( INCX ) ).

Before entry, the incremented array CX must contain the n

element vector cx. On exit, CX is overwritten by the updated

vector cx.```

INCX

```
INCX is INTEGER

On entry, INCX specifies the increment for the elements of

CX. INCX must not be zero.```

CY

```
CY is COMPLEX array, dimension at least

( 1 + ( N - 1 )*abs( INCY ) ).

Before entry, the incremented array CY must contain the n

element vector cy. On exit, CY is overwritten by the updated

vector cy.```

INCY

```
INCY is INTEGER

On entry, INCY specifies the increment for the elements of

CY. INCY must not be zero.```

C

```
C is REAL

On entry, C specifies the cosine, cos.```

S

```
S is REAL

On entry, S specifies the sine, sin.```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

December 2016

## subroutine csscal (integer N, real SA, complex, dimension(*) CX, integer INCX)¶

CSSCAL

Purpose:

```
CSSCAL scales a complex vector by a real constant.```

Parameters

N

```
N is INTEGER

number of elements in input vector(s)```

SA

```
SA is REAL

On entry, SA 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```

Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date

November 2017

Further Details:

```
jack dongarra, linpack, 3/11/78.

modified 3/93 to return if incx .le. 0.

modified 12/3/93, array(1) declarations changed to array(*)```

## subroutine cswap (integer N, complex, dimension(*) CX, integer INCX, complex, dimension(*) CY, integer INCY)¶

CSWAP

Purpose:

```
CSWAP interchanges two vectors.```

Parameters

N

```
N is INTEGER

number of elements in input vector(s)```

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

NAG Ltd.

Date

November 2017

Further Details:

```
jack dongarra, linpack, 3/11/78.

modified 12/3/93, array(1) declarations changed to array(*)```

# Author¶

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