|
|
NAG[f08asc] NAG[nag_zgeqrf] -  factorization of complex general rectangular matrix
|
|
Calling Sequence
f08asc(a, tau, 'm'=m, 'n'=n, 'fail'=fail)
nag_zgeqrf(. . .)
Parameters
|
|
a - Matrix(1..dim1, 1..dim2, datatype=complex[8], order=order);
|
|
|
|
Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
|
|
|
The diagonal elements of  are real.
|
|
|
|
tau - Vector(1..dim, datatype=complex[8]);
|
|
|
|
Note: the dimension, dim, of the array tau must be at least  .
|
|
|
On exit: further details of the unitary matrix  .
|
|
|
|
'm'=m - integer; (optional)
|
|
|
|
Default value: the first dimension of the array a.
|
|
|
On entry:  , the number of rows of the matrix  .
|
|
|
Constraint:  . .
|
|
|
|
'n'=n - integer; (optional)
|
|
|
|
Default value: the second dimension of the array a.
|
|
|
On entry:  , the number of columns of the matrix  .
|
|
|
Constraint:  . .
|
|
|
|
'fail'=fail - table; (optional)
|
|
|
|
The NAG error argument, see the documentation for NagError.
|
|
|
|
|
Description
|
|
|
|
Purpose
|
|
nag_zgeqrf (f08asc) computes the  factorization of a complex  by  matrix.
|
|
|
Error Indicators and Warnings
|
|
"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.
|
|
|
Accuracy
|
|
The computed factorization is the exact factorization of a nearby matrix  , where
 = O(epsilon)*LinearAlgebra[Norm](A, 2)](/support/helpjp/helpview.aspx?si=9847/file08227/math284.png)
and  is the machine precision.
|
|
|
Further Comments
|
|
The total number of real floating-point operations is approximately  if  or  if  .
To form the unitary matrix  nag_zgeqrf (f08asc) 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_zgeqrf (f08asc).
When  , it is often only the first  columns of  that are required, and they may be formed by the call:
nag_zungqr (m,n,n,a,tau,'m'=m,'n'=n)
To apply  to an arbitrary complex rectangular matrix  , nag_zgeqrf (f08asc) 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 with column pivoting, use f08bsc (nag_zgeqpf).
The real analogue of this function is f08aec (nag_dgeqrf).
|
|
|
|
Examples
|
|
|
>
|
m := 6:
n := 4:
a := Matrix([[0.96 -0.8100000000000001*I , -0.03 +0.96*I , -0.91 +2.06*I , -0.05 +0.41*I ], [-0.98 +1.98*I , -1.2 +0.19*I , -0.66 +0.42*I , -0.8100000000000001 +0.5600000000000001*I ], [0.62 -0.46*I , 1.01 +0.02*I , 0.63 -0.17*I , -1.11 +0.6*I ], [-0.37 +0.38*I , 0.19 -0.54*I , -0.98 -0.36*I , 0.22 -0.2*I ], [0.83 +0.51*I , 0.2 +0.01*I , -0.17 -0.46*I , 1.47 +1.59*I ], [1.08 -0.28*I , 0.2 -0.12*I , -0.07000000000000001 +1.23*I , 0.26 +0.26*I ]], datatype=complex[8]):
tau := Vector(4, datatype=complex[8]):
NAG:-f08asc(a, tau, 'm' = m, 'n' = n):
|
|
|
