|
|
NAG[f07vvc] NAG[nag_ztbrfs] - Error bounds for solution of complex band triangular system of linear equations, multiple right-hand sides
|
|
Calling Sequence
f07vvc(uplo, trans, diag, kd, nrhs, ab, b, x, ferr, berr, 'n'=n, 'fail'=fail)
nag_ztbrfs(. . .)
Parameters
|
|
uplo - String;
|
|
|
|
On entry: indicates whether  is upper or lower triangular.
|
|
|
  is upper triangular.
|
|
|
  is lower triangular.
|
|
|
Constraint:   "Nag_Upper" or "Nag_Lower". .
|
|
|
|
trans - String;
|
|
|
|
On entry: indicates the form of the equations
|
|
|
 The equations are of the form  .
|
|
|
 The equations are of the form  .
|
|
|
 The equations are of the form  .
|
|
|
Constraint:   "Nag_NoTrans", "Nag_Trans" or "Nag_ConjTrans". .
|
|
|
|
diag - String;
|
|
|
|
On entry: indicates whether  is a non-unit or unit triangular matrix.
|
|
|
  is a non-unit triangular matrix.
|
|
|
Constraint:   "Nag_NonUnitDiag" or "Nag_UnitDiag". .
|
|
|
|
kd - integer;
|
|
|
|
Constraint:  . .
|
|
|
|
nrhs - integer;
|
|
|
|
On entry:  , the number of right-hand sides.
|
|
|
Constraint:  . .
|
|
|
|
ab - 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.
|
|
|
|
b - 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.
|
|
|
|
x - 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.
|
|
|
|
ferr - Vector(1..dim, datatype=float[8]);
|
|
|
|
Note: the dimension, dim, of the array ferr must be at least  .
|
|
|
|
berr - Vector(1..dim, datatype=float[8]);
|
|
|
|
Note: the dimension, dim, of the array berr must be at least  .
|
|
|
|
'n'=n - integer; (optional)
|
|
|
|
Default value: the second dimension of the array ab.
|
|
|
On entry:  , the order of the matrix  .
|
|
|
Constraint:  . .
|
|
|
|
'fail'=fail - table; (optional)
|
|
|
|
The NAG error argument, see the documentation for NagError.
|
|
|
|
|
Description
|
|
|
|
Purpose
|
|
nag_ztbrfs (f07vvc) returns error bounds for the solution of a complex triangular band system of linear equations with multiple right-hand sides,  ,  or  .
|
|
|
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:  .
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 bounds returned in ferr are not rigorous, because they are estimated, not computed exactly; but in practice they almost always overestimate the actual error.
|
|
|
Further Comments
|
|
A call to nag_ztbrfs (f07vvc), for each right-hand side, involves solving a number of systems of linear equations of the form  or  ; the number is usually 5 and never more than 11. Each solution involves approximately  real floating-point operations (assuming  ).
The real analogue of this function is f07vhc (nag_dtbrfs).
|
|
|
|
Examples
|
|
|
>
|
uplo := "Nag_Lower":
trans := "Nag_NoTrans":
diag := "Nag_NonUnitDiag":
n := 4:
kd := 2:
nrhs := 2:
ab := Matrix([[0 +0*I , 0 +0*I , -1.94 +4.43*I , 0 +0*I ], [-3.39 +3.44*I , 4.12 -4.27*I , 1.62 +3.68*I , -1.84 +5.53*I ], [0.43 -2.66*I , -2.77 -1.93*I , 1.74 -0.04*I , 0.44 +0.1*I ]], datatype=complex[8], order='C_order'):
b := Matrix([[-8.859999999999999 -3.88*I , -24.09 -5.27*I ], [-15.57 -23.41*I , -57.97 +8.140000000000001*I ], [-7.63 +22.78*I , 19.09 -29.51*I ], [-14.74 -2.4*I , 19.17 +21.33*I ]], datatype=complex[8], order='C_order'):
x := Matrix([[3.232334947666749e-17 +2*I , 1 +5*I ], [0.9999999999999999 -3*I , -7 -1.999999999999999*I ], [-4 -5*I , 3 +4.000000000000001*I ], [1.999999999999998 -1*I , -6 -9*I ]], datatype=complex[8], order='C_order'):
ferr := Vector(2, datatype=float[8]):
berr := Vector(2, datatype=float[8]):
NAG:-f07vvc(uplo, trans, diag, kd, nrhs, ab, b, x, ferr, berr, 'n' = n):
|
|
|
