System of equations, complex triangular matrix

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NAG[f16sjc] NAG[nag_ztrsv] - System of equations, complex triangular matrix

Calling Sequence

f16sjc(uplo, trans, diag, n, alpha, a, x, incx, 'fail'=fail)

nag_ztrsv(. . .)

Parameters

uplo - String;

On entry: specifies whether is upper or lower triangular.

is upper triangular.

is lower triangular.

Constraint: "Nag_Upper" or "Nag_Lower". .

trans - String;

On entry: specifies the operation to be performed.

Constraint: "Nag_NoTrans", "Nag_Trans" or "Nag_ConjTrans". .

diag - String;

On entry: specifies whether has non-unit or unit diagonal elements.

The diagonal elements are stored explicitly.

The diagonal elements are assumed to be 1 and are not referenced.

Constraint: "Nag_NonUnitDiag" or "Nag_UnitDiag". .

n - integer;

On entry: , the order of the matrix .

Constraint: . .

alpha - complex;

On entry: the scalar .

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: the by triangular matrix .

If , is upper triangular and the elements of the array below the diagonal are not referenced.

If , is lower triangular and the elements of the array above the diagonal are not referenced.

If , the diagonal elements of are not referenced, but are assumed to be 1.

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

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

On entry: the vector .

On exit: the solution vector .

incx - integer;

On entry: the increment in the subscripts of x between successive elements of .

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_ztrsv (f16sjc) solves a system of equations given as a complex triangular matrix.

	Description
	nag_ztrsv (f16sjc) performs one of the matrix-vector operations where is an by complex triangular matrix, is an element complex vector and is a complex scalar. denotes or equivalently ; denotes or equivalently .

	Error Indicators and Warnings
	"NE_BAD_PARAM" On entry, argument had an illegal value. "NE_INT" On entry, . Constraint: . On entry, . Constraint: .

	Accuracy
	The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of The BLAS Technical Forum Standard (2001)).

	Further Comments
	No test for singularity or near-singularity of is included in nag_ztrsv (f16sjc). Such tests must be performed before calling this function.

Examples

uplo := "Nag_Lower":
trans := "Nag_ConjTrans":
diag := "Nag_NonUnitDiag":
n := 9:
incx := -2:
t := Matrix([[1.426573426573427 +0.1068931068931069*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , 0.8671328671328671 +0.3066933066933067*I , -0.2527472527472527 -0.2927072927072927*I , -0.4525474525474525 +0.04295704295704296*I , -0.2127872127872128 -0.1568431568431568*I , -0.1728271728271728 -0.3566433566433567*I , 0.5074925074925075 -0.4925074925074925*I , 0.1068931068931069 +0.2427572427572428*I , 0.3766233766233766 -0.3486513486513487*I , 0.3466533466533466 -0.2927072927072927*I , -0.1428571428571428 -0.1488511488511489*I , -0.2627372627372627 -0.3006993006993007*I ], [0.4565434565434565 -0.1008991008991009*I , 1.226773226773227 -0.3566433566433567*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , 0.06693306693306693 +0.4425574425574426*I , -0.2927072927072927 +0.2427572427572428*I , 0.01698301698301698 +0.4985014985014985*I , 0.2967032967032967 +0.4505494505494506*I , -0.05294705294705294 -0.2927072927072927*I , 0.4665334665334666 +0.3066933066933067*I , 1.426573426573427 -0.3566433566433567*I , -0.1028971028971029 +0.2987012987012987*I , -0.3026973026973027 +0.4505494505494506*I , -0.06293706293706294 +0.05094905094905095*I , 0.1468531468531468 +0.04295704295704296*I ], [0.1868131868131868 -0.1568431568431568*I , -0.01298701298701299 -0.09290709290709291*I , 1.026973026973027 +0.1068931068931069*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I ], [-0.3826173826173826 +0.2507492507492508*I , 0.4165834165834166 +0.4985014985014985*I , 0.05694305694305694 -0.1008991008991009*I , 0.8671328671328671 +0.3066933066933067*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I ], [-0.2527472527472527 -0.2927072927072927*I , -0.4525474525474525 +0.04295704295704296*I , -0.2127872127872128 -0.1568431568431568*I , -0.1728271728271728 -0.3566433566433567*I , 0.5074925074925075 -0.4925074925074925*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I ], [0.1068931068931069 +0.2427572427572428*I , 0.3766233766233766 -0.3486513486513487*I , 0.3466533466533466 -0.2927072927072927*I , -0.1428571428571428 -0.1488511488511489*I , -0.2627372627372627 -0.3006993006993007*I , 1.386613386613387 -0.1568431568431568*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I ], [0.3366633366633366 +0.05094905094905095*I , -0.09290709290709291 -0.4925074925074925*I , 0.1768231768231768 +0.0989010989010989*I , -0.4125874125874126 -0.09290709290709291*I , -0.3326673326673327 +0.4425574425574426*I , -0.1828171828171828 +0.2507492507492508*I , 1.306693306693307 +0.2427572427572428*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I ], [0.2667332667332667 +0.3066933066933067*I , 0.06693306693306693 +0.4425574425574426*I , -0.2927072927072927 +0.2427572427572428*I , 0.01698301698301698 +0.4985014985014985*I , 0.2967032967032967 +0.4505494505494506*I , -0.05294705294705294 -0.2927072927072927*I , 0.4665334665334666 +0.3066933066933067*I , 1.426573426573427 -0.3566433566433567*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I ], [-0.1028971028971029 +0.2987012987012987*I , -0.3026973026973027 +0.4505494505494506*I , -0.06293706293706294 +0.05094905094905095*I , 0.1468531468531468 +0.04295704295704296*I , -0.3726273726273726 +0.1068931068931069*I , -0.2227772227772228 +0.0989010989010989*I , 0.0969030969030969 +0.2987012987012987*I , 0.4565434565434565 -0.1488511488511489*I , 1.186813186813187 -0.09290709290709291*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I , -10000000000 +10000000000*I ]], datatype=complex[8], order='C_order'):
x := Vector([0.007492507492507516 +0.2427572427572428*I, -10000000000 +10000000000*I, 0.2372627372627373 +0.05094905094905095*I, -10000000000 +10000000000*I, 0.1673326673326673 +0.3066933066933067*I, -10000000000 +10000000000*I, 0 +0*I, -10000000000 +10000000000*I, 0.1573426573426573 -0.1488511488511489*I, -10000000000 +10000000000*I, 0.8866133866133866 -0.09290709290709291*I, -10000000000 +10000000000*I, 0.3171828171828172 +0.4985014985014985*I, -10000000000 +10000000000*I, 0.4470529470529471 +0.04295704295704296*I, -10000000000 +10000000000*I, 0.8066933066933066 -0.4925074925074925*I], datatype=complex[8]):
alpha := 1.0:
NAG:-f16sjc(uplo, trans, diag, n, alpha, t, x, incx):