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NAG[f07nuc] NAG[nag_zsycon] - Estimate condition number of complex symmetric matrix, matrix already factorized by f07nrc (nag_zsytrf)
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Calling Sequence
f07nuc(uplo, a, ipiv, anorm, rcond, 'n'=n, 'fail'=fail)
nag_zsycon(. . .)
Parameters
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uplo - String;
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On entry: indicates how has been factorized.
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Constraint: "Nag_Upper" or "Nag_Lower". .
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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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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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On entry: details of the interchanges and the block structure of , as returned by f07nrc (nag_zsytrf).
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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 f16ufc (nag_zsy_norm). anorm must be computed either before calling f07nrc (nag_zsytrf) 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_zsycon (f07nuc) estimates the condition number of a complex symmetric matrix , where has been factorized by f07nrc (nag_zsytrf).
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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_zsycon (f07nuc) involves solving a number of systems of linear equations of the form ; 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 f07nsc (nag_zsytrs) with one right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The real analogue of this function is f07mgc (nag_dsycon).
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Examples
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>
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uplo := "Nag_Lower":
n := 4:
anorm := 23.34266890690333:
a := Matrix([[-2.095414887840057 -2.201139281440786*I , 0 +0*I , 0 +0*I , 0 +0*I ], [0.6163476554930588 +0.3205087519415588*I , -3.062435063227829 +0.5785222871831118*I , 0 +0*I , 0 +0*I ], [-0.6361017242414988 -0.1467934997322617*I , -6.055798556294841 -3.919323319763695*I , -4.045615983721325 +0.6791946874193678*I , 0 +0*I ], [0.5427284633454681 -0.1831081849498078*I , 0.5412035604708979 -0.2900201404573731*I , -0.368537352783284 +0.1407508587514384*I , 8.859999999999999 +1.81*I ]], datatype=complex[8], order='C_order'):
ipiv := Vector([1, -1, -1, 2], datatype=integer[kernelopts('wordsize')/8]):
NAG:-f07nuc(uplo, a, ipiv, anorm, rcond, 'n' = n):
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