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NAG[f07ugc] NAG[nag_dtpcon] - Estimate condition number of real triangular matrix, packed storage
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Calling Sequence
f07ugc(norm_type, uplo, diag, n, ap, rcond, 'fail'=fail)
nag_dtpcon(. . .)
Parameters
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norm_type - String;
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On entry: indicates whether or is estimated.
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is estimated.
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Constraint: , "Nag_OneNorm" or "Nag_InfNorm". .
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uplo - String;
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On entry: indicates whether is upper or lower triangular.
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is upper triangular.
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is lower triangular.
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Constraint: "Nag_Upper" or "Nag_Lower". .
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diag - String;
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On entry: indicates whether is a non-unit or unit triangular matrix.
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is a non-unit triangular matrix.
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Constraint: "Nag_NonUnitDiag" or "Nag_UnitDiag". .
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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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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_dtpcon (f07ugc) estimates the condition number of a real triangular matrix, 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.
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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_dtpcon (f07ugc) involves solving a number of systems of linear equations of the form or ; 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 f07uec (nag_dtptrs) with one right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The complex analogue of this function is f07uuc (nag_ztpcon).
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Examples
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>
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norm_type := "Nag_OneNorm":
uplo := "Nag_Lower":
diag := "Nag_NonUnitDiag":
n := 4:
ap := Vector([4.3, -3.96, -4.87, 0.4, 0.31, -8.02, -0.27, 0.07000000000000001, -5.95, 0.12], datatype=float[8], order='C_order'):
NAG:-f07ugc(norm_type, uplo, diag, n, ap, rcond):
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