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NAG[f07pgc] NAG[nag_dspcon] - Estimate condition number of real symmetric indefinite matrix, matrix already factorized by f07pdc (nag_dsptrf), packed storage
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Calling Sequence
f07pgc(uplo, n, ap, ipiv, anorm, rcond, 'fail'=fail)
nag_dspcon(. . .)
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=float[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 f07pdc (nag_dsptrf).
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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 f07pdc (nag_dsptrf).
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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 f16rdc (nag_dsp_norm). anorm must be computed either before calling f07pdc (nag_dsptrf) 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_dspcon (f07pgc) estimates the condition number of a real symmetric indefinite matrix  , where  has been factorized by f07pdc (nag_dsptrf), 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_dspcon (f07pgc) involves solving a number of systems of linear equations of the form  ; the number is usually 4 or 5 and never more than 11. Each solution involves approximately  floating-point operations but takes considerably longer than a call to f07pec (nag_dsptrs) with one right-hand side, because extra care is taken to avoid overflow when  is approximately singular.
The complex analogues of this function are f07puc (nag_zhpcon) for Hermitian matrices and f07quc (nag_zspcon) for symmetric matrices.
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Examples
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uplo := "Nag_Lower":
n := 4:
anorm := 11.29:
ap := Vector([1.335954681697555, -0.6975109160126703, -1.905898246668038, 0.8273386982024001, 0.7403045011146071, 3.494530386740331, 0.6353591160220995, -0.3480662983425414, -1.138121546961326, -1.81], datatype=float[8], order='C_order'):
ipiv := Vector([1, 2, 3, 4], datatype=integer[kernelopts('wordsize')/8]):
NAG:-f07pgc(uplo, n, ap, ipiv, anorm, rcond):
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