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NAG[f07ggc] NAG[nag_dppcon] - Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by f07gdc (nag_dpptrf), packed storage
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Calling Sequence
f07ggc(uplo, n, ap, anorm, rcond, 'fail'=fail)
nag_dppcon(. . .)
Parameters
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uplo - String;
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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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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 f07gdc (nag_dpptrf) 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_dppcon (f07ggc) estimates the condition number of a real symmetric positive-definite matrix , where has been factorized by f07gdc (nag_dpptrf), 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_dppcon (f07ggc) 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 f07gec (nag_dpptrs) with one right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The complex analogue of this function is f07guc (nag_zppcon).
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Examples
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>
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uplo := "Nag_Lower":
n := 4:
anorm := 10.16:
ap := Vector([2.039607805437114, -1.529705854077835, 1.640121946685673, 0.2745625891934577, -0.2499814119483738, 0.7887488055748053, -0.049029033784546, 0.6737303907389099, 0.6616575633742564, 0.5346894269298686], datatype=float[8], order='C_order'):
NAG:-f07ggc(uplo, n, ap, anorm, rcond):
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