# slantp.f (3) - Linux Manuals

slantp.f -

## SYNOPSIS

### Functions/Subroutines

REAL function slantp (NORM, UPLO, DIAG, N, AP, WORK)
SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.

## Function/Subroutine Documentation

### REAL function slantp (characterNORM, characterUPLO, characterDIAG, integerN, real, dimension( * )AP, real, dimension( * )WORK)

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

Purpose:

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

Returns:

SLANTP

```    SLANTP = ( 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 SLANTP as described
above.
```

UPLO

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

DIAG

```          DIAG is CHARACTER*1
Specifies whether or not the matrix A is unit triangular.
= 'N':  Non-unit triangular
= 'U':  Unit triangular
```

N

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

AP

```          AP is REAL array, dimension (N*(N+1)/2)
The upper or lower triangular 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.
Note that when DIAG = 'U', the elements of the array AP
corresponding to the diagonal elements of the matrix A are
not referenced, but are assumed to be one.
```

WORK

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

Author:

Univ. of Tennessee

Univ. of California Berkeley