# zlantp.f - Man Page

## Synopsis

### Functions/Subroutines

double precision function **zlantp** (NORM, UPLO, DIAG, **N**, AP, WORK)**ZLANTP** 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

### double precision function zlantp (character NORM, character UPLO, character DIAG, integer N, complex*16, dimension( * ) AP, double precision, dimension( * ) WORK)

**ZLANTP** 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:**

ZLANTP 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:**ZLANTP

ZLANTP = ( 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 ZLANTP 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, ZLANTP is set to zero.

*AP*AP is COMPLEX*16 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 DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced.

**Author:**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 127 of file zlantp.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlantp(3) is an alias of zlantp.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK