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NAG[f07bgc] NAG[nag_dgbcon] - Estimate condition number of real band matrix, matrix already factorized by f07bdc (nag_dgbtrf)
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Calling Sequence
f07bgc(norm_type, kl, ku, ab, ipiv, anorm, rcond, 'n'=n, 'fail'=fail)
nag_dgbcon(. . .)
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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kl - integer;
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On entry: , the number of subdiagonals within the band of the matrix .
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Constraint: . .
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ku - integer;
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On entry: , the number of superdiagonals within the band 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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ipiv - Vector(1..dim, datatype=integer[kernelopts('wordsize')/8]);
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Note: the dimension, dim, of the array ipiv must be at least .
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anorm - float;
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anorm must be computed either before calling f07bdc (nag_dgbtrf) 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_dgbcon (f07bgc) estimates the condition number of a real band matrix , where has been factorized by f07bdc (nag_dgbtrf).
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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: .
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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Examples
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>
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norm_type := "Nag_OneNorm":
n := 4:
kl := 1:
ku := 2:
anorm := 13.63:
ab := Matrix([[0, -6.98, 2.46, -2.73, -2.13], [0.0329512893982808, 2.56, 2.46, 4.07, 0], [0.9605233703438396, -5.932930470988539, -3.839143870881089, 0, 0], [0.8056726812110376, -0.7269066639923109, 0, 0, 0]], datatype=float[8], order='C_order'):
ipiv := Vector([2, 3, 3, 4], datatype=integer[kernelopts('wordsize')/8]):
NAG:-f07bgc(norm_type, kl, ku, ab, ipiv, anorm, rcond, 'n' = n):
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