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NAG[f08ftc] NAG[nag_zungtr] - Generate unitary transformation matrix from reduction to tridiagonal form determined by f08fsc (nag_zhetrd)
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Calling Sequence
f08ftc(uplo, a, tau, 'n'=n, 'fail'=fail)
nag_zungtr(. . .)
Parameters
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uplo - String;
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Constraint:   "Nag_Upper" or "Nag_Lower". .
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a - 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 entry: details of the vectors which define the elementary reflectors, as returned by f08fsc (nag_zhetrd).
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tau - Vector(1..dim, datatype=complex[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_zungtr (f08ftc) generates the complex unitary matrix  , which was determined by f08fsc (nag_zhetrd) when reducing a Hermitian 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 unitary matrix by a matrix  such that
 = O(epsilon)](/support/helpjp/helpview.aspx?si=10409/file08241/math194.png)
where  is the machine precision.
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Further Comments
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The total number of real floating-point operations is approximately  .
The real analogue of this function is f08ffc (nag_dorgtr).
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Examples
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uplo := "Nag_Lower":
n := 4:
a := Matrix([[-2.28 +0*I , 0 +0*I , 0 +0*I , 0 +0*I ], [-4.33845594653213 +0*I , -0.1284569816493291 +0*I , 0 +0*I , 0 +0*I ], [0.3278606760921924 -0.1251226092264437*I , -2.022594578622617 +0*I , -0.1665932537524081 +0*I , 0 +0*I ], [-0.1412565637506947 -0.366636483973957*I , -0.308321908008089 +0.1763226364726777*I , -1.802322978338736 +0*I , -1.924949764598262 +0*I ]], datatype=complex[8]):
tau := Vector([1.410284216766754 +0.4679084045148932*I, 1.302420369434775 +0.785332074252958*I, 1.093973715923082 -0.9955746786231597*I], datatype=complex[8]):
NAG:-f08ftc(uplo, a, tau, 'n' = n):
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