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NAG[f01rec] NAG[nag_complex_form_q] - Form columns of  after factorization by f01rcc (nag_complex_qr)
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Calling Sequence
f01rec(wheret, ncolq, a, 'm'=m, 'n'=n, 'tda'=tda, 'theta'=theta, 'fail'=fail)
nag_complex_form_q(. . .)
Parameters
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wheret - String;
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On entry: the elements of  are to be found as follows:
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Constraint: wheret must be one of "Nag_ElementsIn" or "Nag_ElementsSeparate". .
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ncolq - integer;
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On entry:  , the required number of columns of  .
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When  then an immediate return is effected.
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Constraint:  . .
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a - Matrix(1..m, 1..tda, datatype=complex[8], order=C_order);
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'm'=m - integer; (optional)
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Default value: the first dimension of the array a.
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On entry:  , the number of rows of  .
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Constraint:  . .
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'n'=n - integer; (optional)
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Default value: the first dimension of the array theta.
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On entry:  , the number of columns of  .
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Constraint:  . .
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'tda'=tda - integer; (optional)
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On entry: the second dimension of the array a as declared in the function from which nag_complex_form_q (f01rec) is called.
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Constraint:  . .
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'theta'=theta - Vector(1..n, datatype=complex[8]); (optional)
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When  , the array theta is not referenced and may be set to the null pointer, i.e., (Complex *)0.
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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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Error Indicators and Warnings
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"NE_2_INT_ARG_GT"
On entry,  while  . These arguments must satisfy  .
"NE_2_INT_ARG_LT"
On entry,  while  . These arguments must satisfy  .
"NE_ALLOC_FAIL"
Dynamic memory allocation failed.
"NE_BAD_PARAM"
On entry, argument wheret had an illegal value.
"NE_INT_ARG_LT"
On entry, n must not be less than 0:  .
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Accuracy
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The computed matrix  satisfies the relation
where  is an exactly unitary matrix and
 <= c*epsilon](/support/helpjp/helpview.aspx?si=10066/file08045/math360.png)
 being the machine precision,  is a modest function of  and  denotes the spectral (two) norm. See also Section [Further Comments] of f01rcc (nag_complex_qr).
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Further Comments
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The approximate number of real floating-point operations required is given by
![[[8/3n(3,m,-,n)(2,ncolq,-,n)-n(ncolq-n),ncolq>n],[8/3(ncolq)^2(3,m,-,ncolq),ncolq<=n ]]](/support/helpjp/helpview.aspx?si=10066/file08045/math384.png)
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Examples
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>
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wheret := "Nag_ElementsSeparate":
m := 5:
n := 3:
ncolq := 5:
tda := 5:
a := Matrix([[1 +0*I , 1 +1*I , 1 +1*I , 0 +0*I , 0 +0*I ], [-0.2 -0.4*I , -2 +0*I , -0.9999999999999999 -1*I , 0 +0*I , 0 +0*I ], [-0.3200000000000001 -0.16*I , -0.3505424368033064 +0.2629068276024798*I , -3 +0*I , 0 +0*I , 0 +0*I ], [-0.4 +0.2*I , -4.106415728288848e-18 +0.5477225575051662*I , 1.304276919275117e-17 +3.04997943335419e-17*I , 0 +0*I , 0 +0*I ], [-0.12 +0.24*I , 0.1971801207018598 +0.2629068276024797*I , 1.303205497928506e-17 +0.6324555320336759*I , 0 +0*I , 0 +0*I ]], datatype=complex[8], order='C_order'):
theta := Vector([1 +0.5*I, 1.095445115010332 -0.3333333333333333*I, 1.264911064067352 -4.060111260505613e-18*I], datatype=complex[8]):
NAG:-f01rec(wheret, ncolq, a, 'm' = m, 'n' = n, 'tda' = tda, 'theta' = theta):
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