|
|
NAG[f16uac] NAG[nag_zge_norm] -  -norm,  -norm, Frobenius norm, largest absolute element, complex general matrix
|
|
Calling Sequence
f16uac(norm_type, a, r, 'm'=m, 'n'=n, 'fail'=fail)
nag_zge_norm(. . .)
Parameters
|
|
norm_type - String;
|
|
|
|
On entry: specifies the value to be returned.
|
|
|
  or "Nag_OneNorm" The 1-norm.
|
|
|
 The  -norm.
|
|
|
 The Frobenius (or Euclidean) norm.
|
|
|
 The value ![max |a[ij]|](/support/helpjp/helpview.aspx?si=10243/file08345/math41.png) (not a norm).
|
|
|
Constraint:   "Nag_OneNorm", "Nag_InfNorm", "Nag_FrobeniusNorm" or "Nag_MaxNorm". .
|
|
|
|
a - Matrix(1..dim1, 1..dim2, datatype=complex[8], order=order);
|
|
|
|
Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
|
|
|
|
r - assignable;
|
|
|
|
Note: On exit the variable r will have a value of type float.
|
|
|
On exit: the value of the norm specified by norm.
|
|
|
|
'm'=m - integer; (optional)
|
|
|
|
Default value: the first dimension of the array a.
|
|
|
On entry:  , the number of rows of the matrix  .
|
|
|
Constraint:  . .
|
|
|
|
'n'=n - integer; (optional)
|
|
|
|
Default value: the second dimension of the array a.
|
|
|
On entry:  , the number of columns of the matrix  .
|
|
|
Constraint:  . .
|
|
|
|
'fail'=fail - table; (optional)
|
|
|
|
The NAG error argument, see the documentation for NagError.
|
|
|
|
|
Description
|
|
|
|
Purpose
|
|
nag_zge_norm (f16uac) calculates the value of the 1-norm, the  -norm, the Frobenius norm or the maximum absolute value of the elements of a complex  by  matrix.
|
|
|
Description
|
|
Given a complex  by  matrix,  , nag_zge_norm (f16uac) calculates one of the values given by
![||A||[F]=((∑),(∑)|a[ij]|^2)^(1/2)](/support/helpjp/helpview.aspx?si=10243/file08345/math170.png)
or
![max |a[ij]|](/support/helpjp/helpview.aspx?si=10243/file08345/math174.png)
|
|
|
Error Indicators and Warnings
|
|
"NE_ALLOC_FAIL"
Dynamic memory allocation failed.
"NE_BAD_PARAM"
On entry, argument  had an illegal value.
"NE_INT"
On entry,  . Constraint:  .
On entry,  . Constraint:  .
"NE_INTERNAL_ERROR"
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.
|
|
|
Accuracy
|
|
The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of The BLAS Technical Forum Standard (2001)).
|
|
|
|
Examples
|
|
|
>
|
norm_type := "Nag_OneNorm":
m := 4:
n := 4:
a := Matrix([[-1.34 +2.55*I , 0.28 +3.17*I , -6.39 -2.2*I , 0.72 -0.92*I ], [-0.17 -1.41*I , 3.31 -0.15*I , -0.15 +1.34*I , 1.29 +1.38*I ], [-3.29 -2.39*I , -1.91 +4.42*I , -0.14 -1.35*I , 1.72 +1.35*I ], [2.41 +0.39*I , -0.5600000000000001 +1.47*I , -0.83 -0.6899999999999999*I , -1.96 +0.67*I ]], datatype=complex[8]):
NAG:-f16uac(norm_type, a, r, 'm' = m, 'n' = n):
|
|
|
