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NAG[f08bsc] NAG[nag_zgeqpf] -  factorization of complex general rectangular matrix with column pivoting
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Calling Sequence
f08bsc(a, jpvt, tau, 'm'=m, 'n'=n, 'fail'=fail)
nag_zgeqpf(. . .)
Parameters
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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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The diagonal elements of  are real.
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jpvt - Vector(1..dim, datatype=integer[kernelopts('wordsize')/8]);
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Note: the dimension, dim, of the array jpvt must be at least  .
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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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On exit: further details of the unitary matrix  .
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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 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 a.
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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_zgeqpf (f08bsc) computes the  factorization, with column pivoting, of a complex  by  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_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 factorization is the exact factorization of a nearby matrix  , where
 = O(epsilon)*LinearAlgebra[Norm](A, 2)](/support/helpjp/helpview.aspx?si=9922/file08234/math356.png)
and  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  or  if  .
To form the unitary matrix  nag_zgeqpf (f08bsc) may be followed by a call to f08atc (nag_zungqr):
nag_zungqr (min(m,n),a,tau,'m'=m,'n'=m)
but note that the second dimension of the array a must be at least m, which may be larger than was required by nag_zgeqpf (f08bsc).
When  , it is often only the first  columns of  that are required, and they may be formed by the call:
nag_zungqr (m,a,tau,'m'=n,'n'=n)
To apply  to an arbitrary complex rectangular matrix  , nag_zgeqpf (f08bsc) may be followed by a call to f08auc (nag_zunmqr). For example,
nag_zunmqr ("Nag_LeftSide","Nag_ConjTrans",min(m,n),a,tau,c,'m'=m,'n'=p)
forms  , where  is  by  .
To compute a  factorization without column pivoting, use f08asc (nag_zgeqrf).
The real analogue of this function is f08bec (nag_dgeqpf).
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Examples
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m := 5:
n := 4:
a := Matrix([[0.47 -0.34*I , -0.4 +0.54*I , 0.6 +0.01*I , 0.8 -1.02*I ], [-0.32 -0.23*I , -0.05 +0.2*I , -0.26 -0.44*I , -0.43 +0.17*I ], [0.35 -0.6*I , -0.52 -0.34*I , 0.87 -0.11*I , -0.34 -0.09*I ], [0.89 +0.71*I , -0.45 -0.45*I , -0.02 -0.57*I , 1.14 -0.78*I ], [-0.19 +0.06*I , 0.11 -0.85*I , 1.44 +0.8*I , 0.07000000000000001 +1.14*I ]], datatype=complex[8]):
jpvt := Vector([0, 0, 0, 0], datatype=integer[kernelopts('wordsize')/8]):
tau := Vector(4, datatype=complex[8]):
NAG:-f08bsc(a, jpvt, tau, 'm' = m, 'n' = n):
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