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NAG[f07hgc] NAG[nag_dpbcon] - Estimate condition number of real symmetric positive-definite band matrix, matrix already factorized by f07hdc (nag_dpbtrf)
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Calling Sequence
f07hgc(uplo, kd, ab, anorm, rcond, 'n'=n, 'fail'=fail)
nag_dpbcon(. . .)
Parameters
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uplo - String;
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Constraint: "Nag_Upper" or "Nag_Lower". .
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kd - integer;
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On entry: , the number of superdiagonals or subdiagonals of the matrix .
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Constraint: . .
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ab - 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 f16rec (nag_dsb_norm). anorm must be computed either before calling f07hdc (nag_dpbtrf) 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 second dimension of the array ab.
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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_dpbcon (f07hgc) estimates the condition number of a real symmetric positive-definite band matrix , where has been factorized by f07hdc (nag_dpbtrf).
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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: .
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_dpbcon (f07hgc) 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 (assuming ) but takes considerably longer than a call to f07hec (nag_dpbtrs) with one right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The complex analogue of this function is f07huc (nag_zpbcon).
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Examples
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>
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uplo := "Nag_Lower":
n := 4:
kd := 1:
anorm := 10.7:
ab := Matrix([[0, 2.343074902771996, 1.143796127400537, 2.078877201506509], [-1.149659055507477, 1.130612248337004, -1.963537900164584, 1.146524711734229]], datatype=float[8], order='C_order'):
NAG:-f07hgc(uplo, kd, ab, anorm, rcond, 'n' = n):
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