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NAG[f08fgc] NAG[nag_dormtr] - Apply orthogonal transformation determined by f08fec (nag_dsytrd)
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Calling Sequence
f08fgc(side, uplo, trans, a, tau, c, 'm'=m, 'n'=n, 'fail'=fail)
nag_dormtr(. . .)
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_Trans". .
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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 f08fec (nag_dsytrd).
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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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 when  ;
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 when  .
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c - 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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'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_dormtr (f08fgc) multiplies an arbitrary real matrix  by the real orthogonal matrix  which was determined by f08fec (nag_dsytrd) when reducing a real 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:  .
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=10407/file08238/math356.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  if  and  if  .
The complex analogue of this function is f08fuc (nag_zunmtr).
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Examples
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side := "Nag_LeftSide":
uplo := "Nag_Lower":
trans := "Nag_NoTrans":
m := 4:
n := 2:
a := Matrix([[2.07, 0, 0, 0], [-5.825753170191817, 1.474093708197552, 0, 0], [0.4331793442217867, 2.624045178795587, -0.6491595075457839, 0], [-0.1186086299654892, 0.806288153277579, 0.9162727563219193, -1.694934200651768]], datatype=float[8]):
tau := Vector([1.664291789738249, 1.212047324162142, 0], datatype=float[8]):
c := Matrix([[0.5657591788223872, -0.2328424308031573], [0.6869179572505917, -0.1626170961491636], [-0.4395889372131648, -0.3017273343882723], [0.1217449705930083, 0.9101102670229791]], datatype=float[8]):
NAG:-f08fgc(side, uplo, trans, a, tau, c, 'm' = m, 'n' = n):
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