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NAG[f07tgc] NAG[nag_dtrcon] - Estimate condition number of real triangular matrix
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Calling Sequence
f07tgc(norm_type, uplo, diag, a, rcond, 'n'=n, 'fail'=fail)
nag_dtrcon(. . .)
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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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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If , is upper triangular and the elements of the array below the diagonal are not referenced.
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If , is lower triangular and the elements of the array above the diagonal are not referenced.
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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 if the estimate underflows. If rcond is less than machine precision, then 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_dtrcon (f07tgc) estimates the condition number of a real triangular matrix.
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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_dtrcon (f07tgc) 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 f07tec (nag_dtrtrs) with one right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The complex analogue of this function is f07tuc (nag_ztrcon).
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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:
a := Matrix([[4.3, 0, 0, 0], [-3.96, -4.87, 0, 0], [0.4, 0.31, -8.02, 0], [-0.27, 0.07000000000000001, -5.95, 0.12]], datatype=float[8], order='C_order'):
NAG:-f07tgc(norm_type, uplo, diag, a, rcond, 'n' = n):
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