# zlansp.f man page

zlansp.f —

## Synopsis

### Functions/Subroutines

DOUBLE PRECISION functionzlansp(NORM, UPLO, N, AP, WORK)ZLANSPreturns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.

## Function/Subroutine Documentation

### DOUBLE PRECISION function zlansp (characterNORM, characterUPLO, integerN, complex*16, dimension( * )AP, double precision, dimension( * )WORK)

**ZLANSP** returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.

**Purpose:**

```
ZLANSP returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
complex symmetric matrix A, supplied in packed form.
```

**Returns:**

ZLANSP

```
ZLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
```

**Parameters:**

*NORM*

```
NORM is CHARACTER*1
Specifies the value to be returned in ZLANSP as described
above.
```

*UPLO*

```
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is supplied.
= 'U': Upper triangular part of A is supplied
= 'L': Lower triangular part of A is supplied
```

*N*

```
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANSP is
set to zero.
```

*AP*

```
AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangle of the symmetric matrix A, packed
columnwise in a linear array. The j-th column of A is stored
in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
```

*WORK*

```
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 116 of file zlansp.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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