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NAG[f08gfc] NAG[nag_dopgtr] - Generate orthogonal transformation matrix from reduction to tridiagonal form determined by f08gec (nag_dsptrd)
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Calling Sequence
f08gfc(uplo, ap, tau, q, 'n'=n, 'fail'=fail)
nag_dopgtr(. . .)
Parameters
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uplo - String;
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Constraint:   "Nag_Upper" or "Nag_Lower". .
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ap - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array ap must be at least  .
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On entry: details of the vectors which define the elementary reflectors, as returned by f08gec (nag_dsptrd).
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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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q - 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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'n'=n - integer; (optional)
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Default value: the dimension of the array ap.
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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_dopgtr (f08gfc) generates the real orthogonal matrix  , which was determined by f08gec (nag_dsptrd) when reducing a symmetric matrix to tridiagonal 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_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=10415/file08245/math207.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  .
The complex analogue of this function is f08gtc (nag_zupgtr).
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Examples
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uplo := "Nag_Lower":
n := 4:
ap := Vector([-0.8719237738479123, 3.065514671071713, 6.082006282652207, 0.9717705782198055, 2.871665463430541, -2.200082508804293, -0.2554462546564815, 0.1399401221161594, -2.441925469788134, -1.81], datatype=float[8], order='C_order'):
tau := Vector([0, 1.028627708599706, 1.843596590267241], datatype=float[8]):
q := Matrix(4, 4, datatype=float[8], order='C_order'):
NAG:-f08gfc(uplo, ap, tau, q, 'n' = n):
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