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NAG[f07vhc] NAG[nag_dtbrfs] - Error bounds for solution of real band triangular system of linear equations, multiple right-hand sides
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Calling Sequence
f07vhc(uplo, trans, diag, kd, nrhs, ab, b, x, ferr, berr, 'n'=n, 'fail'=fail)
nag_dtbrfs(. . .)
Parameters
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uplo - String;
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On entry: indicates whether is upper or lower triangular.
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is upper triangular.
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is lower triangular.
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Constraint: "Nag_Upper" or "Nag_Lower". .
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trans - String;
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On entry: indicates the form of the equations.
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The equations are of the form .
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Constraint: "Nag_NoTrans", "Nag_Trans" or "Nag_ConjTrans". .
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diag - String;
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On entry: indicates whether is a non-unit or unit triangular matrix.
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is a non-unit triangular matrix.
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Constraint: "Nag_NonUnitDiag" or "Nag_UnitDiag". .
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kd - integer;
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Constraint: . .
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nrhs - integer;
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On entry: , the number of right-hand sides.
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Constraint: . .
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ab - Matrix(1..dim1, 1..dim2, datatype=float[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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b - Matrix(1..dim1, 1..dim2, datatype=float[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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x - Matrix(1..dim1, 1..dim2, datatype=float[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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ferr - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array ferr must be at least .
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berr - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array berr must be at least .
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'n'=n - integer; (optional)
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Default value: the second dimension of the array ab.
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On entry: , the order 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_dtbrfs (f07vhc) returns error bounds for the solution of a real triangular band system of linear equations with multiple right-hand sides, or .
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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: .
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 bounds returned in ferr are not rigorous, because they are estimated, not computed exactly; but in practice they almost always overestimate the actual error.
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Further Comments
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A call to nag_dtbrfs (f07vhc), for each right-hand side, involves solving a number of systems of linear equations of the form or ; the number is usually 4 or 5 and never more than 11. Each solution involves approximately floating-point operations (assuming ).
The complex analogue of this function is f07vvc (nag_ztbrfs).
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Examples
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>
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uplo := "Nag_Lower":
trans := "Nag_NoTrans":
diag := "Nag_NonUnitDiag":
n := 4:
kd := 1:
nrhs := 2:
ab := Matrix([[0, -4.16, -2.25, 4.78], [5.86, 6.32, -4.82, 0.16]], datatype=float[8], order='C_order'):
b := Matrix([[-16.64, -4.16], [-13.78, -16.59], [13.1, -4.94], [-14.14, -9.960000000000001]], datatype=float[8], order='C_order'):
x := Matrix([[4, 1], [-0.9999999999999998, -3], [3, 2], [1.999999999999988, -2.000000000000002]], datatype=float[8], order='C_order'):
ferr := Vector(2, datatype=float[8]):
berr := Vector(2, datatype=float[8]):
NAG:-f07vhc(uplo, trans, diag, kd, nrhs, ab, b, x, ferr, berr, 'n' = n):
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