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NAG[f08nfc] NAG[nag_dorghr] - Generate orthogonal transformation matrix from reduction to Hessenberg form determined by f08nec (nag_dgehrd)
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Calling Sequence
f08nfc(ilo, ihi, a, tau, 'n'=n, 'fail'=fail)
nag_dorghr(. . .)
Parameters
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ilo - integer;
ihi - integer;
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On entry: these must be the same arguments ilo and ihi, respectively, as supplied to f08nec (nag_dgehrd).
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if  ,  ;
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a - Matrix(1..dim1, 1..dim2, datatype=float[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 entry: details of the vectors which define the elementary reflectors, as returned by f08nec (nag_dgehrd).
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tau - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array tau must be at least  .
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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_dorghr (f08nfc) generates the real orthogonal matrix  which was determined by f08nec (nag_dgehrd) when reducing a real general matrix  to Hessenberg form.
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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: if  ,  and  .
On entry,  ,  ,  . Constraint: if  ,  .
"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  differs from an exactly orthogonal matrix by a matrix  such that
 = O(epsilon)](/support/helpjp/helpview.aspx?si=10448/file08275/math261.png)
where  is the machine precision.
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Further Comments
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The total number of floating-point operations is approximately  , where ![q = i[hi]-i[lo]](/support/helpjp/helpview.aspx?si=10448/file08275/math274.png) .
The complex analogue of this function is f08ntc (nag_zunghr).
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Examples
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n := 4:
ilo := 1:
ihi := 4:
a := Matrix([[0.35, -0.1159524296205035, -0.3886010343233214, -0.2941840753473021], [-0.5140038910358559, 0.1224867524602574, 0.1003597896821502, 0.1125618799705319], [-0.728472128292763, 0.644263618527062, -0.1357001717571134, -0.09768162270493334], [0.4139046183481608, -0.1665445794905699, 0.4262443722078448, 0.163213419296856]], datatype=float[8]):
tau := Vector([1.175095950769217, 1.946022972139863, 0], datatype=float[8]):
NAG:-f08nfc(ilo, ihi, a, tau, 'n' = n):
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