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NAG[f07auc] NAG[nag_zgecon] - Estimate condition number of complex matrix, matrix already factorized by f07arc (nag_zgetrf)
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Calling Sequence
f07auc(norm_type, a, anorm, rcond, 'n'=n, 'fail'=fail)
nag_zgecon(. . .)
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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a - Matrix(1..dim1, 1..dim2, datatype=complex[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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anorm must be computed either before calling f07arc (nag_zgetrf) 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_zgecon (f07auc) estimates the condition number of a complex matrix , where has been factorized by f07arc (nag_zgetrf).
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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_zgecon (f07auc) involves solving a number of systems of linear equations of the form or ; the number is usually 5 and never more than 11. Each solution involves approximately real floating-point operations but takes considerably longer than a call to f07asc (nag_zgetrs) with 1 right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The real analogue of this function is f07agc (nag_dgecon).
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Examples
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>
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norm_type := "Nag_OneNorm":
n := 4:
anorm := 12.88382186360408:
a := Matrix([[-3.29 -2.39*I , -1.91 +4.42*I , -0.14 -1.35*I , 1.72 +1.35*I ], [0.2376120269469406 +0.2559596521570857*I , 4.895180634002975 -0.711362223485444*I , -0.462279846639494 +1.696610587680362*I , 1.226852844063328 +0.6189731619114427*I ], [-0.1019520808892006 -0.7010135339437114*I , -0.6691496431943212 +0.3688698547971655*I , -5.141410913810232 -1.129969734660953*I , 0.9982579915199449 +0.3850152275763778*I ], [-0.5358546703595748 +0.2707272529359829*I , -0.2040217794587079 +0.8601180679984047*I , 0.008233047063940029 +0.1210636819910635*I , 0.1482391810748419 -0.1252239986075848*I ]], datatype=complex[8]):
NAG:-f07auc(norm_type, a, anorm, rcond, 'n' = n):
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