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NAG[f07puc] NAG[nag_zhpcon] - Estimate condition number of complex Hermitian indefinite matrix, matrix already factorized by f07prc (nag_zhptrf), packed storage
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Calling Sequence
f07puc(uplo, n, ap, ipiv, anorm, rcond, 'fail'=fail)
nag_zhpcon(. . .)
Parameters
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uplo - String;
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On entry: indicates how has been factorized.
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Constraint: "Nag_Upper" or "Nag_Lower". .
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n - integer;
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On entry: , the order of the matrix .
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Constraint: . .
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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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On entry: details of the factorization of stored in packed form, as returned by f07prc (nag_zhptrf).
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ipiv - Vector(1..dim, datatype=integer[kernelopts('wordsize')/8]);
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Note: the dimension, dim, of the array ipiv must be at least .
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On entry: details of the interchanges and the block structure of , as returned by f07prc (nag_zhptrf).
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anorm - float;
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On entry: the 1-norm of the original matrix , which may be computed by calling f16udc (nag_zhp_norm). anorm must be computed either before calling f07prc (nag_zhptrf) or else from a copy of the original matrix .
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Constraint: . .
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rcond - assignable;
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Note: On exit the variable rcond will have a value of type float.
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On exit: an estimate of the reciprocal of the condition number of . rcond is set to zero if exact singularity is detected or the estimate underflows. If rcond is less than machine precision, is singular to working precision.
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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_zhpcon (f07puc) estimates the condition number of a complex Hermitian indefinite matrix , where has been factorized by f07prc (nag_zhptrf), using packed storage.
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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: .
"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.
"NE_REAL"
On entry, . Constraint: .
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Accuracy
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The computed estimate rcond is never less than the true value , and in practice is nearly always less than , although examples can be constructed where rcond is much larger.
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Further Comments
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A call to nag_zhpcon (f07puc) involves solving a number of systems of linear equations of the form ; the number is usually 5 and never more than 11. Each solution involves approximately real floating-point operations but takes considerably longer than a call to f07psc (nag_zhptrs) with one right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The real analogue of this function is f07pgc (nag_dspcon).
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Examples
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>
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uplo := "Nag_Lower":
n := 4:
anorm := 14.6641984095488:
ap := Vector([-4.981630459440283 +0*I, 0.210214907090655 +0.1106935130516159*I, -7.724450141995383 +0*I, 0.3100287981271241 -0.04333020743962702*I, -0.1518120207240102 -0.3742958425613706*I, -1.36 +0*I, 0.5637050486508776 -0.2850349501519716*I, 0.339658279960361 -0.03031451811355639*I, 3.91 -1.5*I, -1.84 +0*I], datatype=complex[8], order='C_order'):
ipiv := Vector([1, 2, -1, -1], datatype=integer[kernelopts('wordsize')/8]):
NAG:-f07puc(uplo, n, ap, ipiv, anorm, rcond):
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