|
|
NAG[f08nuc] NAG[nag_zunmhr] - Apply unitary transformation matrix from reduction to Hessenberg form determined by f08nsc (nag_zgehrd)
|
|
Calling Sequence
f08nuc(side, trans, ilo, ihi, a, tau, c, 'm'=m, 'n'=n, 'fail'=fail)
nag_zunmhr(. . .)
Parameters
|
|
side - String;
|
|
|
|
Constraint:   "Nag_LeftSide" or "Nag_RightSide". .
|
|
|
|
trans - String;
|
|
|
|
Constraint:   "Nag_NoTrans" or "Nag_ConjTrans". .
|
|
|
|
ilo - integer;
ihi - integer;
|
|
|
|
On entry: these must be the same arguments ilo and ihi, respectively, as supplied to f08nsc (nag_zgehrd).
|
|
|
|
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.
|
|
|
On entry: details of the vectors which define the elementary reflectors, as returned by f08nsc (nag_zgehrd).
|
|
|
|
tau - Vector(1..dim, datatype=complex[8]);
|
|
|
|
Note: the dimension, dim, of the array tau must be at least
|
|
|
 when  ;
|
|
|
 when  .
|
|
|
|
c - 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.
|
|
|
|
'm'=m - integer; (optional)
|
|
|
|
Default value: the first dimension of the array c.
|
|
|
Constraint:  . .
|
|
|
|
'n'=n - integer; (optional)
|
|
|
|
Default value: the second dimension of the array c.
|
|
|
Constraint:  . .
|
|
|
|
'fail'=fail - table; (optional)
|
|
|
|
The NAG error argument, see the documentation for NagError.
|
|
|
|
|
Description
|
|
|
|
Purpose
|
|
nag_zunmhr (f08nuc) multiplies an arbitrary complex matrix  by the complex unitary matrix  which was determined by f08nsc (nag_zgehrd) when reducing a complex general matrix to Hessenberg form.
|
|
|
Error Indicators and Warnings
|
|
"NE_ALLOC_FAIL"
Dynamic memory allocation failed.
"NE_BAD_PARAM"
On entry, argument  had an illegal value.
"NE_ENUM_INT_4"
On entry,  ,  ,  ,  ,  . Constraint: if  and  ,  and  .
On entry,  ,  ,  ,  ,  . Constraint: if  and  ,  .
On entry,  ,  ,  ,  ,  . Constraint: if  and  ,  and  .
On entry,  ,  ,  ,  ,  . Constraint: if  and  ,  .
"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 result differs from the exact result by a matrix  such that
 = O(epsilon)*LinearAlgebra[Norm](C, 2)](/support/helpjp/helpview.aspx?si=10454/file08281/math483.png)
where  is the machine precision.
|
|
|
|
Examples
|
|
|
>
|
side := "Nag_LeftSide":
trans := "Nag_NoTrans":
m := 4:
n := 2:
ilo := 1:
ihi := 4:
a := Matrix([[-3.97 -5.04*I , -1.131805187339771 -2.56930489882744*I , -4.602742437533554 -0.142631904083292*I , -1.424912289366528 +1.732983703342187*I ], [-5.479653273702635 +0*I , 1.858472820765587 -1.55018070644029*I , 4.414465526917013 -0.7638237115550982*I , -0.4805261336990153 -1.197599997332747*I ], [0.6932222118146283 -0.4828752762602551*I , 6.267276818064224 +0*I , -0.4503809403345019 -0.02898183259817936*I , -1.346684450078735 +1.65792489538873*I ], [-0.2112946907920694 +0.0864412259893682*I , 0.1242146188766495 -0.2289276049796828*I , -3.499985837393259 +0*I , 2.561908119568915 -3.370837460961531*I ]], datatype=complex[8]):
tau := Vector([1.062047721455606 -0.2737399475982613*I, 1.805921371640585 +0.3479067029848286*I, 1.181823471041003 +0.9833311880432766*I], datatype=complex[8]):
c := Matrix([[0.9999999999999999 -3.857661933036875e-17*I , 0.2613040867512704 +0.5283875825457144*I ], [0.333896237376093 -0.3906135999457946*I , -0.6020569110082327 +0.2903496482826593*I ], [0.08840188787511424 +0.3310704781636436*I , 1 +9.855836951550319e-18*I ], [0.07925597470461819 +0.1017388061223025*I , 0.3074174862711926 +0.2185870109734626*I ]], datatype=complex[8]):
NAG:-f08nuc(side, trans, ilo, ihi, a, tau, c, 'm' = m, 'n' = n):
|
|
|
