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NAG[f08axc] NAG[nag_zunmlq] - Apply unitary transformation determined by f08avc (nag_zgelqf)
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Calling Sequence
f08axc(side, trans, k, a, tau, c, 'm'=m, 'n'=n, 'fail'=fail)
nag_zunmlq(. . .)
Parameters
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side - String;
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Constraint:   "Nag_LeftSide" or "Nag_RightSide". .
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trans - String;
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Constraint:   "Nag_NoTrans" or "Nag_ConjTrans". .
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k - integer;
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On entry:  , the number of elementary reflectors whose product defines the matrix  .
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if  ,  ;
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if  ,  .
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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 f08avc (nag_zgelqf).
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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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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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On entry:  , the number of rows of the matrix  .
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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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On entry:  , the number of columns 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_zunmlq (f08axc) multiplies an arbitrary complex matrix  by the complex unitary matrix  from an  factorization computed by f08avc (nag_zgelqf).
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Description
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nag_zunmlq (f08axc) is intended to be used after a call to f08avc (nag_zgelqf), which performs an  factorization of a complex matrix  . The unitary matrix  is represented as a product of elementary reflectors.
This function may be used to form one of the matrix products
overwriting the result on  (which may be any complex rectangular matrix).
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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_ENUM_INT_3"
On entry,  ,  ,  ,  . Constraint: if  ,  .
On entry,  ,  ,  ,  . Constraint: if  ,  .
"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=10058/file08232/math360.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 f08akc (nag_dormlq).
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Examples
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side := "Nag_LeftSide":
trans := "Nag_ConjTrans":
m := 4:
n := 2:
k := 3:
a := Matrix([[-2.225511177235469 -0*I , 0.2438442594612761 -0.3082069932914802*I , -0.2741364985191491 -0.230966496866882*I , 0.5807709514701289 +0.3468663602164287*I ], [0.8207552577961005 +1.238457046719376*I , 1.688100989346069 -0*I , -0.1936415258449461 +0.5429517855236941*I , 0.2789084851242076 -0.2203175797458332*I ], [0.001033470433007241 -0.6822252862760427*I , 0.774751330164006 -0.6154727158531147*I , -1.590258250459319 -0*I , -0.1267668516113225 +0.1109845202357172*I ]], datatype=complex[8]):
tau := Vector([1.12581379184436 +0.1617605895141772*I, 1.099053669168954 +0.5468590598466785*I, 1.132925657311579 -0.9590540478961487*I], datatype=complex[8]):
c := Matrix([[0.6066022106781647 -0.08537364446581577*I , -2.170287909315211 +1.199724372230148*I ], [5.216747404439202 -2.512397031673043*I , -2.377178681793995 +2.987456497043376*I ], [6.293162138826466 -7.861098176652018*I , 0.121499129356357 +0.4587240367613852*I ], [0 +0*I , 0 +0*I ]], datatype=complex[8]):
NAG:-f08axc(side, trans, k, a, tau, c, 'm' = m, 'n' = n):
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