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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute

```NAME
LAPACK-3 - 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

SYNOPSIS
DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )

CHARACTER    DIAG, NORM, UPLO

INTEGER      N

DOUBLE       PRECISION WORK( * )

COMPLEX*16   AP( * )

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.

DESCRIPTION
ZLANTP returns the value
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.

ARGUMENTS
NORM    (input) CHARACTER*1
Specifies the value to be returned in ZLANTP as described
above.

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

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

N       (input) INTEGER
The order of the matrix A.  N >= 0.  When N = 0, ZLANTP is
set to zero.

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

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```