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NAG[f07fgc] NAG[nag_dpocon] - Estimate condition number of real symmetric positive-definite matrix, matrix already factorized by f07fdc (nag_dpotrf)
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Calling Sequence
f07fgc(uplo, a, anorm, rcond, 'n'=n, 'fail'=fail)
nag_dpocon(. . .)
Parameters
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uplo - String;
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Constraint:   "Nag_Upper" or "Nag_Lower". .
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a - Matrix(1..dim1, 1..dim2, datatype=float[8], order=order);
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Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
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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 f16rcc (nag_dsy_norm). anorm must be computed either before calling f07fdc (nag_dpotrf) 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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'n'=n - integer; (optional)
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Default value: the dimension of the array a.
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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_dpocon (f07fgc) estimates the condition number of a real symmetric positive-definite matrix  , where  has been factorized by f07fdc (nag_dpotrf).
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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_dpocon (f07fgc) 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 f07fec (nag_dpotrs) with one right-hand side, because extra care is taken to avoid overflow when  is approximately singular.
The complex analogue of this function is f07fuc (nag_zpocon).
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Examples
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uplo := "Nag_Lower":
n := 4:
anorm := 10.16:
a := Matrix([[2.039607805437114, 0, 0, 0], [-1.529705854077835, 1.640121946685673, 0, 0], [0.2745625891934577, -0.2499814119483738, 0.7887488055748053, 0], [-0.04902903378454601, 0.6737303907389101, 0.6616575633742563, 0.5346894269298686]], datatype=float[8], order='C_order'):
NAG:-f07fgc(uplo, a, anorm, rcond, 'n' = n):
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