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NAG[f16ugc] NAG[nag_zsp_norm] -  -norm,  -norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage
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Calling Sequence
f16ugc(norm_type, uplo, ap, r, 'n'=n, 'fail'=fail)
nag_zsp_norm(. . .)
Parameters
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norm_type - String;
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On entry: specifies the value to be returned.
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  or "Nag_OneNorm" The 1-norm.
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 The  -norm.
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 The Frobenius (or Euclidean) norm.
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 The value ![max |a[ij]|](/support/helpjp/helpview.aspx?si=10241/file08351/math41.png) (not a norm).
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Constraint:   "Nag_OneNorm", "Nag_InfNorm", "Nag_FrobeniusNorm" or "Nag_MaxNorm". .
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uplo - String;
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On entry: specifies whether the upper or lower triangular part of  is stored.
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 The upper triangular part of  is stored.
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 The lower triangular part of  is stored.
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Constraint:   "Nag_Upper" or "Nag_Lower". .
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ap - Vector(1..dim, datatype=complex[8]);
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Note: the dimension, dim, of the array ap must be at least  .
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r - assignable;
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Note: On exit the variable r will have a value of type float.
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On exit: the value of the norm specified by norm.
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'n'=n - integer; (optional)
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Default value: the first dimension of the array ap.
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On entry:  , the order of the matrix  .
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Constraint:  . .
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_zsp_norm (f16ugc) calculates the value of the 1-norm, the  -norm, the Frobenius norm or the maximum absolute value of the elements of a complex  by  symmetric matrix, stored in packed form.
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Description
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Given a complex  by  symmetric matrix,  , in packed storage, nag_zsp_norm (f16ugc) calculates one of the values given by
![||A||[F]=((∑),(∑)|a[ij]|^2)^(1/2)](/support/helpjp/helpview.aspx?si=10241/file08351/math220.png)
or
![max |a[ij]|](/support/helpjp/helpview.aspx?si=10241/file08351/math224.png)
Note that, since  is symmetric,  = LinearAlgebra[Norm](A, infinity)](/support/helpjp/helpview.aspx?si=10241/file08351/math229.png) .
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Error Indicators and Warnings
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"NE_ALLOC_FAIL"
Dynamic memory allocation failed.
"NE_BAD_PARAM"
On entry, argument  had an illegal value.
"NE_INT"
On entry,  . Constraint:  .
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Accuracy
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The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of The BLAS Technical Forum Standard (2001)).
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Examples
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norm_type := "Nag_OneNorm":
uplo := "Nag_Lower":
n := 4:
ap := Vector([-0.39 -0.71*I, 5.14 -0.64*I, 8.859999999999999 +1.81*I, -7.86 -2.96*I, -3.52 +0.58*I, -2.83 -0.03*I, 3.8 +0.92*I, 5.32 -1.59*I, -1.54 -2.86*I, -0.5600000000000001 +0.12*I], datatype=complex[8], order='C_order'):
NAG:-f16ugc(norm_type, uplo, ap, r, 'n' = n):
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