Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix

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NAG[f16yjc] NAG[nag_dtrsm] - Solves a system of equations with multiple right-hand sides, real triangular coefficient matrix

Calling Sequence

f16yjc(side, uplo, trans, diag, alpha, a, b, 'm'=m, 'n'=n, 'fail'=fail)

nag_dtrsm(. . .)

Parameters

side - String;

On entry: specifies whether is operated on from the left or the right.

is pre-multiplied from the left.

is post-multiplied from the right.

Constraint: "Nag_LeftSide" or "Nag_RightSide". .

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.

"Nag_Trans" or "Nag_ConjTrans" and .

and .

"Nag_Trans" or "Nag_ConjTrans" and .

and .

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". .

alpha - float;

On entry: the scalar .

a - Matrix(1..dim1, 1..dim2, datatype=float[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 or by triangular matrix if .

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.

b - Matrix(1..dim1, 1..dim2, datatype=float[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 matrix .

If , b need not be set.

On exit: the updated matrix .

'm'=m - integer; (optional)

Default value: the first dimension of the array b.

On entry: , the number of rows of the matrix ; the order of if .

Constraint: . .

'n'=n - integer; (optional)

Default value: the second dimension of the array b.

On entry: , the number of columns of the matrix ; the order of if .

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_dtrsm (f16yjc) solves a system of equations given as a real triangular matrix with multiple right-hand sides.

	Description
	nag_dtrsm (f16yjc) performs one of the matrix-matrix operations where is a real triangular matrix, is an by real matrix, and is a real scalar. 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: . "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 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_dtrsm (f16yjc). Such tests must be performed before calling this function.

Examples

side := "Nag_RightSide":
uplo := "Nag_Lower":
transt := "Nag_ConjTrans":
diag := "Nag_NonUnitDiag":
alpha := 0.7:
m := 9:
n := 9:
t := Matrix([[1.146853146853147, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.02297702297702298, 0.9470529470529471, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.4925074925074925, 0.3066933066933067, 0.7472527472527473, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.2627372627372627, -0.4625374625374625, -0.4225774225774226, 0.987012987012987, -10000000000, -10000000000, -10000000000, -10000000000, -10000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.3326673326673327, 0.4665334665334666, 0.1068931068931069, 0, 1.026973026973027, -10000000000, -10000000000, -10000000000, -10000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.3726273726273726, 0.0969030969030969, 0.2667332667332667, 0, 0.05694305694305694, 0.7072927072927073, -10000000000, -10000000000, -10000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.3426573426573427, 0.4265734265734266, -0.1028971028971029, 0, -0.2127872127872128, -0.06293706293706294, 0.8271728271728271, -10000000000, -10000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.3866133866133866, 0.1868131868131868, 0.2267732267732268, 0, 0.2167832167832168, -0.1328671328671329, -0.4125874125874126, 1.146853146853147, -10000000000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.1828171828171828, -0.3826173826173826, 0.2567432567432568, 0, 0.3466533466533466, 0.4965034965034965, 0.01698301698301698, -0.02297702297702298, 0.5074925074925075, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], datatype=float[8], order='C_order'):
b := Matrix([[-0.3326673326673327, 0.4665334665334666, -0.1028971028971029, 0, -0.1428571428571428, 0.3866133866133866, 0.1868131868131868, 0.4165834165834166, 0.3466533466533466, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.2967032967032967, 0.4265734265734266, 0.2267732267732268, 0, -0.4125874125874126, -0.1828171828171828, -0.2527472527472527, -0.4525474525474525, 0.1768231768231768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.3726273726273726, 0.4565434565434565, -0.01298701298701299, 0, 0.01698301698301698, -0.05294705294705294, -0.4225774225774226, -0.09290709290709291, -0.2927072927072927, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.3426573426573427, 0.1868131868131868, 0.4165834165834166, 0.3466533466533466, 0.1468531468531468, -0.2227772227772228, 0.1068931068931069, 0.1368631368631369, -0.1328671328671329, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.3866133866133866, -0.3826173826173826, -0.4525474525474525, 0, -0.4925074925074925, 0.3066933066933067, 0.3366633366633366, 0.06693306693306693, 0.4965034965034965, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.05294705294705294, -0.2527472527472527, 0.3766233766233766, 0, -0.2627372627372627, 0.4665334665334666, 0.2667332667332667, -0.3026973026973027, -0.1728271728271728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.2227772227772228, 0.1068931068931069, -0.09290709290709291, 0, -0.3326673326673327, 0.0969030969030969, 0.2267732267732268, 0.02697302697302697, -0.1428571428571428, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.3066933066933067, 0.3366633366633366, 0.06693306693306693, 0, 0.2967032967032967, 0.4265734265734266, 0.2567432567432568, -0.2127872127872128, -0.4125874125874126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-0.4625374625374625, 0.2667332667332667, -0.3026973026973027, 0, -0.3726273726273726, 0.4565434565434565, -0.01298701298701299, 0.2167832167832168, 0.1468531468531468, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], datatype=float[8], order='C_order'):
NAG:-f16yjc(side, uplo, transt, diag, alpha, t, b, 'm'=m, 'n'=n):