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NAG[f07tvc] NAG[nag_ztrrfs] - Error bounds for solution of complex triangular system of linear equations, multiple right-hand sides
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Calling Sequence
f07tvc(uplo, trans, diag, a, b, x, ferr, berr, 'n'=n, 'nrhs'=nrhs, 'fail'=fail)
nag_ztrrfs(. . .)
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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The equations are of the form .
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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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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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If , is upper triangular and the elements of the array below the diagonal are not referenced.
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If , is lower triangular and the elements of the array above the diagonal are not referenced.
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b - 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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x - 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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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 dimension of the array a.
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On entry: , the order of the matrix .
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Constraint: . .
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'nrhs'=nrhs - integer; (optional)
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Default value: the second dimension of the arrays b, x.
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On entry: , the number of right-hand sides.
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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_ztrrfs (f07tvc) returns error bounds for the solution of a complex triangular 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: .
"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_ztrrfs (f07tvc), 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.
The real analogue of this function is f07thc (nag_dtrrfs).
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Examples
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>
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uplo := "Nag_Lower":
trans := "Nag_NoTrans":
diag := "Nag_NonUnitDiag":
n := 4:
nrhs := 2:
a := Matrix([[4.78 +4.56*I , 0 +0*I , 0 +0*I , 0 +0*I ], [2 -0.3*I , -4.11 +1.25*I , 0 +0*I , 0 +0*I ], [2.89 -1.34*I , 2.36 -4.25*I , 4.15 +0.8*I , 0 +0*I ], [-1.89 +1.15*I , 0.04 -3.69*I , -0.02 +0.46*I , 0.33 -0.26*I ]], datatype=complex[8], order='C_order'):
b := Matrix([[-14.78 -32.36*I , -18.02 +28.46*I ], [2.98 -2.14*I , 14.22 +15.42*I ], [-20.96 +17.06*I , 5.62 +35.89*I ], [9.539999999999999 +9.91*I , -16.46 -1.73*I ]], datatype=complex[8], order='C_order'):
x := Matrix([[-5 -2*I , 0.9999999999999997 +5*I ], [-3 -1*I , -2 -2*I ], [2 +0.9999999999999999*I , 3 +4*I ], [4 +2.999999999999997*I , 3.999999999999993 -3.000000000000003*I ]], datatype=complex[8], order='C_order'):
ferr := Vector(2, datatype=float[8]):
berr := Vector(2, datatype=float[8]):
NAG:-f07tvc(uplo, trans, diag, a, b, x, ferr, berr, 'n' = n, 'nrhs' = nrhs):
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