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Equation Solver Light

A Grid solution

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Outline

• The Mathematic problem

• The Matrix operation package

• The Grid Workflow solution

• Example

• Summary

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The mathematical problem

Let us solve the equation

A*x = B where the coefficients ai,j bi  are real:

A-1*A*x  = A-1*B

A-1*A = E

x = E*x

x = A-1*B

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The Matrix Operation Package(1)Base conventions

• sequential  program written in C (MatrixDemoNew)

• Input(s) and output are matrices represented by files (Minput1 , Minput2 ,Moutput)

• operation is controlled by command line arguments:

• Moutput = OP (Minput1)

• Moutput = OP (Minput1,scalarArg)

• Moutput = OP (Minput1,Minput2 )

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The Matrix Operation Package(2)Detailed I/O conventions

OP

INPUT1

INPUT2OUTPUT

• The input(s)  and the output of the MatrixDemoNew are files containing the representation of the matrices. They are referred i.e. opened  within the executable as  "INPUT1" (,"INPUT2") and "OUTPUT".

• The structures the ASCII files are uniform: a space separated list of the following tokens:

Number of lines, number of columns, floating point elements ordered first along the lines of the matrix.

Example: 2 3 1.1 1.2 1.3 2.1 2.2 2.3

represents the following matrix:

1.1 1.2 1.3 2.1 2.2 2.3

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The Matrix Operation Package(3)Operations

Syntax: <OP_code> [<Extension>] [V[erbose]]

OP Extension Explanation ShortNameA  I1+I2 -> O AddS  I1–I2 -> O SubtractM  I1*I2 -> O MultiplyR  I2*I1 -> O Reverse MultiplyT  transpose of I1 -> O TransposeI  invert of I1 -> O Invertc floting value * I1-> O constant multiply L integer I1[value,*]-> O Line ofC integer I1[*,value]-> O Column ofExample:

L 3 VOperation and I/0 files will be printed on standard outputEventual extension values

are defined as command line values

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The Grid Workflow solution(1)

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The Grid Workflow solution (2)Input Matrix association

Location of file representing “B” in

theA*x=B

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The Grid Workflow solution (3)Matrix Operation Input Definition

Expected file names are INPUT1 and

INPUT2

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The Grid Workflow solution (4)Matrix operation definition

Matrix Operation Package

Op Code

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The Grid Workflow solution(5)The progress

A A BB

A-1 A-1*B A*A-1*B

A*A-1*B-B

Result reached at this point, control

followes

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The Grid Workflow solution (6)Workflow result

Test results 1,2,3,4,5

modified by the numerical

instability, due to the division

operations inside of matrix

inversion

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Summary

• Simple way of calculation

• Extendibility

• Graphical usage