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NAG[f08guc] NAG[nag_zupmtr] - Apply unitary transformation matrix determined by f08gsc (nag_zhptrd)
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Calling Sequence
f08guc(side, uplo, trans, ap, tau, c, 'm'=m, 'n'=n, 'fail'=fail)
nag_zupmtr(. . .)
Parameters
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side - String;
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Constraint:   "Nag_LeftSide" or "Nag_RightSide". .
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uplo - String;
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Constraint:   "Nag_Upper" or "Nag_Lower". .
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trans - String;
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Constraint:   "Nag_NoTrans" or "Nag_ConjTrans". .
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ap - Vector(1..dim, datatype=complex[8]);
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Note: the dimension, dim, of the array ap must be at least
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 when  ;
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 when  .
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On entry: details of the vectors which define the elementary reflectors, as returned by f08gsc (nag_zhptrd).
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On exit: is used as internal workspace prior to being restored and hence is unchanged.
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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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 when  ;
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 when  .
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c - 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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'm'=m - integer; (optional)
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Default value: the first dimension of the array c.
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Constraint:  . .
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'n'=n - integer; (optional)
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Default value: the second dimension of the array c.
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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_zupmtr (f08guc) multiplies an arbitrary complex matrix  by the complex unitary matrix  which was determined by f08gsc (nag_zhptrd) when reducing a complex 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:  .
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 result differs from the exact result by a matrix  such that
 = O(epsilon)*LinearAlgebra[Norm](C, 2)](/support/helpjp/helpview.aspx?si=10419/file08250/math358.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  if  and  if  .
The real analogue of this function is f08ggc (nag_dopmtr).
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Examples
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side := "Nag_LeftSide":
uplo := "Nag_Upper":
trans := "Nag_NoTrans":
m := 4:
n := 2:
ap := Vector([-2.28 +0*I, -4.33845594653213 +0*I, 0.3278606760921924 +0.1251226092264437*I, -0.1412565637506947 +0.366636483973957*I, -0.1284569816493291 +0*I, -2.022594578622617 +0*I, -0.308321908008089 -0.1763226364726777*I, -0.1665932537524081 +0*I, -1.802322978338736 +0*I, -1.924949764598262 +0*I], datatype=complex[8], order='C_order'):
tau := Vector([1.410284216766754 -0.4679084045148932*I, 1.302420369434775 -0.785332074252958*I, 1.093973715923082 +0.9955746786231597*I], datatype=complex[8]):
c := Matrix([[0.7298945743917051 +0*I , -0.2595449733877609 +0*I ], [0.6258777805557932 +0*I , -0.04325496258655372 +0*I ], [0.2513449473644085 +0*I , 0.4952474101820682 +0*I ], [0.1111603864444915 +0*I , 0.8279465065502339 +0*I ]], datatype=complex[8], order='C_order'):
NAG:-f08guc(side, uplo, trans, ap, tau, c, 'm' = m, 'n' = n):
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