Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage

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      - f07adc (nag_dgetrf)
      - f07aec (nag_dgetrs)
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      - f07ahc (nag_dgerfs)
      - f07ajc (nag_dgetri)
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      - f07ugc (nag_dtpcon)
      - f07uhc (nag_dtprfs)
      - f07ujc (nag_dtptri)
      - f07usc (nag_ztptrs)
      - f07uuc (nag_ztpcon)
      - f07uvc (nag_ztprfs)
      - f07uwc (nag_ztptri)
      - f07vec (nag_dtbtrs)
      - f07vgc (nag_dtbcon)
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NAG[f07usc] NAG[nag_ztptrs] - Solution of complex triangular system of linear equations, multiple right-hand sides, packed storage

Calling Sequence

f07usc(uplo, trans, diag, ap, b, 'n'=n, 'nrhs'=nrhs, 'fail'=fail)

nag_ztptrs(. . .)

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 .

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.

is a unit triangular matrix; the diagonal elements are not referenced and are assumed to be .

Constraint: "Nag_NonUnitDiag" or "Nag_UnitDiag". .

ap - Vector(1..dim, datatype=complex[8]);

Note: the dimension, dim, of the array ap must be at least .

On entry: the by triangular matrix , packed by rows or columns. The storage of elements depends on the storage order and uplo arguments as follows:

if and , is stored in , for ;

if and , is stored in , for .

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.

On entry: the by right-hand side matrix .

On exit: the by solution matrix .

'n'=n - integer; (optional)

Default value: the dimension of the array ap.

On entry: , the order of the matrix .

Constraint: . .

'nrhs'=nrhs - integer; (optional)

Default value: the second dimension of the array b.

On entry: , the number of right-hand sides.

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_ztptrs (f07usc) solves a complex triangular system of linear equations with multiple right-hand sides, , or , using packed storage.

	Description
	nag_ztptrs (f07usc) solves a complex triangular system of linear equations , or using packed storage.

	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. "NE_SINGULAR" The matrix is singular.

Accuracy

The solutions of triangular systems of equations are usually computed to high accuracy. See Higham (1989).

For each right-hand side vector , the computed solution is the exact solution of a perturbed system of equations , where

is a modest linear function of , and is the machine precision.

If is the true solution, then the computed solution satisfies a forward error bound of the form

where .

Note that ; can be much smaller than and it is also possible for , which is the same as , to be much larger (or smaller) than .

Forward and backward error bounds can be computed by calling f07uvc (nag_ztprfs), and an estimate for can be obtained by calling f07uuc (nag_ztpcon) with .

	Further Comments
	The total number of real floating-point operations is approximately . The real analogue of this function is f07uec (nag_dtptrs).

Examples

uplo := "Nag_Lower":
trans := "Nag_NoTrans":
diag := "Nag_NonUnitDiag":
n := 4:
nrhs := 2:
ap := Vector([4.78 +4.56*I, 2 -0.3*I, -4.11 +1.25*I, 2.89 -1.34*I, 2.36 -4.25*I, 4.15 +0.8*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'):
NAG:-f07usc(uplo, trans, diag, ap, b, 'n' = n, 'nrhs' = nrhs):

	See Also
	Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore Higham N J (1989) The accuracy of solutions to triangular systems SIAM J. Numer. Anal. 26 1252–1265 f07 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.