|
NAG[f07guc] NAG[nag_zppcon] - Estimate condition number of complex Hermitian positive-definite matrix, matrix already factorized by f07grc (nag_zpptrf), packed storage
|
|
Calling Sequence
f07guc(uplo, n, ap, anorm, rcond, 'fail'=fail)
nag_zppcon(. . .)
Parameters
|
uplo - String;
|
|
|
Constraint: "Nag_Upper" or "Nag_Lower". .
|
|
|
n - integer;
|
|
|
On entry: , the order of the matrix .
|
|
Constraint: . .
|
|
|
ap - Vector(1..dim, datatype=complex[8]);
|
|
|
Note: the dimension, dim, of the array ap must be at least .
|
|
|
anorm - float;
|
|
|
On entry: the 1-norm of the original matrix , which may be computed by calling f16udc (nag_zhp_norm). anorm must be computed either before calling f07grc (nag_zpptrf) or else from a copy of the original matrix .
|
|
Constraint: . .
|
|
|
rcond - assignable;
|
|
|
Note: On exit the variable rcond will have a value of type float.
|
|
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.
|
|
|
'fail'=fail - table; (optional)
|
|
|
The NAG error argument, see the documentation for NagError.
|
|
|
|
Description
|
|
|
Purpose
|
|
nag_zppcon (f07guc) estimates the condition number of a complex Hermitian positive-definite matrix , where has been factorized by f07grc (nag_zpptrf), using packed storage.
|
|
Error Indicators and Warnings
|
|
"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: .
|
|
Accuracy
|
|
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.
|
|
Further Comments
|
|
A call to nag_zppcon (f07guc) 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 f07gsc (nag_zpptrs) with one right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The real analogue of this function is f07ggc (nag_dppcon).
|
|
|
Examples
|
|
>
|
uplo := "Nag_Lower":
n := 4:
anorm := 10.96735730690591:
ap := Vector([1.797220075561143 +0*I, 0.8401864749527325 +1.068316577423342*I, 1.316353439509685 +0*I, 1.057188279741849 -0.467388502622712*I, -0.4701749470106329 +0.3130658155999466*I, 1.560392977137124 +0*I, 0.233694251311356 -1.391037210186643*I, 0.08335250923944192 +0.03676071443037458*I, 0.9359617337923402 +0.9899692192815736*I, 0.6603332973655891 +0*I], datatype=complex[8], order='C_order'):
NAG:-f07guc(uplo, n, ap, anorm, rcond):
|
|
|