|
NAG[f07quc] NAG[nag_zspcon] - Estimate condition number of complex symmetric matrix, matrix already factorized by f07qrc (nag_zsptrf), packed storage
|
|
Calling Sequence
f07quc(uplo, n, ap, ipiv, anorm, rcond, 'fail'=fail)
nag_zspcon(. . .)
Parameters
|
uplo - String;
|
|
|
On entry: indicates how has been factorized.
|
|
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 .
|
|
On entry: details of the factorization of stored in packed form, as returned by f07qrc (nag_zsptrf).
|
|
|
ipiv - Vector(1..dim, datatype=integer[kernelopts('wordsize')/8]);
|
|
|
Note: the dimension, dim, of the array ipiv must be at least .
|
|
On entry: details of the interchanges and the block structure of , as returned by f07qrc (nag_zsptrf).
|
|
|
anorm - float;
|
|
|
On entry: the 1-norm of the original matrix , which may be computed by calling f16ugc (nag_zsp_norm). anorm must be computed either before calling f07qrc (nag_zsptrf) 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_zspcon (f07quc) estimates the condition number of a complex symmetric matrix , where has been factorized by f07qrc (nag_zsptrf), 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_zspcon (f07quc) 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 f07qsc (nag_zsptrs) with one right-hand side, because extra care is taken to avoid overflow when is approximately singular.
The real analogue of this function is f07pgc (nag_dspcon).
|
|
|
Examples
|
|
>
|
uplo := "Nag_Lower":
n := 4:
anorm := 23.34266890690333:
ap := Vector([-2.095414887840057 -2.201139281440786*I, 0.6163476554930588 +0.3205087519415588*I, -3.062435063227829 +0.5785222871831118*I, -0.6361017242414988 -0.1467934997322617*I, -6.055798556294841 -3.919323319763695*I, -4.045615983721325 +0.6791946874193678*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:-f07quc(uplo, n, ap, ipiv, anorm, rcond):
|
|
|