|
|
NAG[f08uec] NAG[nag_dsbgst] - Reduction of real symmetric-definite banded generalized eigenproblem  to standard form  , such that  has the same bandwidth as 
|
|
Calling Sequence
f08uec(vect, uplo, n, ka, kb, ab, bb, x, 'fail'=fail)
nag_dsbgst(. . .)
Parameters
|
|
vect - String;
|
|
|
|
On entry: indicates whether  is to be returned.
|
|
|
  is not returned.
|
|
|
  is returned.
|
|
|
Constraint:   "Nag_DoNotForm" or "Nag_FormX". .
|
|
|
|
uplo - String;
|
|
|
|
On entry: indicates whether the upper or lower triangular part of  is stored.
|
|
|
 The upper triangular part of  is stored.
|
|
|
 The lower triangular part of  is stored.
|
|
|
Constraint:   "Nag_Upper" or "Nag_Lower". .
|
|
|
|
n - integer;
|
|
|
|
Constraint:  . .
|
|
|
|
ka - integer;
|
|
|
|
Constraint:  . .
|
|
|
|
kb - integer;
|
|
|
|
Constraint:  . .
|
|
|
|
ab - Matrix(1..dim1, 1..dim2, datatype=float[8], order=order);
|
|
|
|
Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
|
|
|
On exit: the upper or lower triangle of  is overwritten by the corresponding upper or lower triangle of  as specified by uplo.
|
|
|
|
bb - Matrix(1..dim1, 1..dim2, datatype=float[8], order=order);
|
|
|
|
Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
|
|
|
On entry: the banded split Cholesky factor of  as specified by uplo, n and kb and returned by f08ufc (nag_dpbstf).
|
|
|
|
x - Matrix(1..dim1, 1..dim2, datatype=float[8], order=order);
|
|
|
|
Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
|
|
|
If  , x is not referenced.
|
|
|
|
'fail'=fail - table; (optional)
|
|
|
|
The NAG error argument, see the documentation for NagError.
|
|
|
|
|
Description
|
|
|
|
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:  .
On entry,  . Constraint:  .
"NE_INT_2"
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.
|
|
|
Accuracy
|
|
Forming the reduced matrix  is a stable procedure. However it involves implicit multiplication by  . When nag_dsbgst (f08uec) is used as a step in the computation of eigenvalues and eigenvectors of the original problem, there may be a significant loss of accuracy if  is ill-conditioned with respect to inversion.
|
|
|
|
Examples
|
|
|
>
|
vect := "Nag_DoNotForm":
uplo := "Nag_Lower":
n := 4:
ka := 2:
kb := 1:
ab := Matrix([[0, 0, 0.24, 0], [0.39, -0.11, 0.42, 0.79], [-0.25, 0.63, 0.48, -0.03]], datatype=float[8], order='C_order'):
bb := Matrix([[0, 1.438749456993816, 0.6602956445140701, 1.050238722644967], [-0.3885978477717261, 0.7462727898852248, -0.3050851079238761, 1.081665382639197]], datatype=float[8], order='C_order'):
x := Matrix(1, 1, datatype=float[8], order='C_order'):
NAG:-f08uec(vect, uplo, n, ka, kb, ab, bb, x):
|
|
|
