f16ukc returns the value of the -norm, the -norm, the Frobenius norm, or the maximum absolute value of the elements of a complex Hermitian matrix stored in Rectangular Full Packed (RFP) format.
The function may be called by the names: f16ukc, nag_blast_zhf_norm or nag_zhf_norm.
3Description
Given a complex symmetric matrix, ,
f16ukc calculates one of the values given by
(the -norm of ),
(the -norm of ),
(the Frobenius norm of ), or
(the maximum absolute element value of ).
is stored in compact form using the RFP format.
The RFP storage format is described in Section 3.4.3 in the F07 Chapter Introduction.
4References
Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee https://www.netlib.org/blas/blast-forum/blas-report.pdf
Gustavson F G, Waśniewski J, Dongarra J J and Langou J (2010) Rectangular full packed format for Cholesky's algorithm: factorization, solution, and inversion ACM Trans. Math. Software37, 2
5Arguments
1: – Nag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by . See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint:
or .
2: – Nag_NormTypeInput
On entry: specifies the value to be returned.
The -norm.
The -norm.
The Frobenius (or Euclidean) norm.
The value (not a norm).
Constraint:
, , or .
3: – Nag_RFP_StoreInput
On entry: specifies whether the normal RFP representation of or its conjugate transpose is stored.
The matrix is stored in normal RFP format.
The conjugate transpose of the RFP representation of the matrix is stored.
Constraint:
or .
4: – Nag_UploTypeInput
On entry: specifies whether the upper or lower triangular part of is stored.
The upper triangular part of is stored.
The lower triangular part of is stored.
Constraint:
or .
5: – IntegerInput
On entry: , the order of the matrix .
If , f16ukc returns immediately.
Constraint:
.
6: – const ComplexInput
On entry: the upper or lower triangular part (as specified by uplo) of the Hermitian matrix , in either normal or transposed RFP format (as specified by transr). The storage format is described in detail in Section 3.4.3 in the F07 Chapter Introduction.
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument had an illegal value.
NE_INT
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 contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
Background information to multithreading can be found in the Multithreading documentation.
f16ukc is not threaded in any implementation.
9Further Comments
None.
10Example
This example reads in the lower triangular part of a symmetric matrix, converts this to RFP format, then calculates the norm of the matrix for each of the available norm types.