# zspmv.f man page

zspmv.f —

## Synopsis

### Functions/Subroutines

subroutinezspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)ZSPMVcomputes a matrix-vector product for complex vectors using a complex symmetric packed matrix

## Function/Subroutine Documentation

### subroutine zspmv (characterUPLO, integerN, complex*16ALPHA, complex*16, dimension( * )AP, complex*16, dimension( * )X, integerINCX, complex*16BETA, complex*16, dimension( * )Y, integerINCY)

**ZSPMV** computes a matrix-vector product for complex vectors using a complex symmetric packed matrix

**Purpose:**

```
ZSPMV performs the matrix-vector operation
y := alpha*A*x + beta*y,
where alpha and beta are scalars, x and y are n element vectors and
A is an n by n symmetric matrix, supplied in packed form.
```

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the matrix A is supplied in the packed
array AP as follows:
UPLO = 'U' or 'u' The upper triangular part of A is
supplied in AP.
UPLO = 'L' or 'l' The lower triangular part of A is
supplied in AP.
Unchanged on exit.
```

*N*

```
N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
```

*ALPHA*

```
ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
```

*AP*

```
AP is COMPLEX*16 array, dimension at least
( ( N*( N + 1 ) )/2 ).
Before entry, with UPLO = 'U' or 'u', the array AP must
contain the upper triangular part of the symmetric matrix
packed sequentially, column by column, so that AP( 1 )
contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
and a( 2, 2 ) respectively, and so on.
Before entry, with UPLO = 'L' or 'l', the array AP must
contain the lower triangular part of the symmetric matrix
packed sequentially, column by column, so that AP( 1 )
contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
and a( 3, 1 ) respectively, and so on.
Unchanged on exit.
```

*X*

```
X is COMPLEX*16 array, dimension at least
( 1 + ( N - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the N-
element vector x.
Unchanged on exit.
```

*INCX*

```
INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
```

*BETA*

```
BETA is COMPLEX*16
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
Unchanged on exit.
```

*Y*

```
Y is COMPLEX*16 array, dimension at least
( 1 + ( N - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
```

*INCY*

```
INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
Unchanged on exit.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 152 of file zspmv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zspmv(3) is an alias of zspmv.f(3).