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NAG[f08qtc] NAG[nag_ztrexc] - Reorder Schur factorization of complex matrix using unitary similarity transformation
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Calling Sequence
f08qtc(compq, t, q, ifst, ilst, 'n'=n, 'fail'=fail)
nag_ztrexc(. . .)
Parameters
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compq - String;
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On entry: indicates whether the matrix  of Schur vectors is to be updated.
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 The matrix  of Schur vectors is updated.
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 No Schur vectors are updated.
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Constraint:   "Nag_UpdateSchur" or "Nag_NotQ". .
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t - 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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On exit: is overwritten by the updated matrix  .
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q - 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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On exit: if  , q contains the updated matrix of Schur vectors.
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If  , q is not referenced.
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ifst - integer;
ilst - integer;
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On entry: ifst and ilst must specify the reordering of the diagonal elements of  . The element with row index ifst is moved to row ilst by a sequence of exchanges between adjacent elements.
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Constraint:  and  . .
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'n'=n - integer; (optional)
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Default value: the dimension of the array t.
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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_ztrexc (f08qtc) reorders the Schur factorization of a complex general matrix.
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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_INT_3"
On entry,  ,  ,  . Constraint:  and  .
"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.
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Accuracy
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The computed matrix  is exactly similar to a matrix  , where
 = O(epsilon)*LinearAlgebra[Norm](T, 2)](/support/helpjp/helpview.aspx?si=10466/file08293/math259.png)
and  is the machine precision.
The values of the eigenvalues are never changed by the reordering.
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Examples
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compq := "Nag_NotQ":
n := 4:
ifst := 1:
ilst := 4:
t := Matrix([[-6 -7*I , 0.36 -0.36*I , -0.19 +0.48*I , 0.88 -0.25*I ], [0 +0*I , -5 +2*I , -0.03 -0.72*I , -0.23 +0.13*I ], [0 +0*I , 0 +0*I , 8 -1*I , 0.9399999999999999 +0.53*I ], [0 +0*I , 0 +0*I , 0 +0*I , 3 -4*I ]], datatype=complex[8]):
q := Matrix([[0 +0*I ]], datatype=complex[8]):
NAG:-f08qtc(compq, t, q, ifst, ilst, 'n' = n):
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