Equation Solver Light
A Grid solution
LPDS MTA SZTAKI
Outline
•
•
•
•
•
The Mathematic problem
The Matrix operation package
The Grid Workflow solution
Example
Summary
LPDS MTA SZTAKI
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
LPDS MTA SZTAKI
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 )
LPDS MTA SZTAKI
The Matrix Operation Package(2)
Detailed I/O conventions
• 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". INPUT1
OUTPUT
INPUT2
OP
• 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
2.1
1.2
2.2
1.3
2.3
LPDS MTA SZTAKI
The Matrix Operation Package(3)
Operations
Syntax:
<OP_code> [<Extension>] [V[erbose]]
OP Extension
A
S
M
R
T
I
c floting
L integer
C integer
Example:
Explanation
ShortName
I1+I2 -> O
Add
I1–I2 -> O
Subtract
I1*I2 -> O
Multiply
I2*I1 -> O
Reverse Multiply
transpose of I1 -> O Transpose
invert of I1 -> O
Invert
value * I1-> O
constant multiply
I1[value,*]-> O
Line of
I1[*,value]-> O
Column of
L 3 V
Operation and I/0 files will be
Eventual extension values
printed on standard output
are defined as command line
values
LPDS MTA SZTAKI
The Grid Workflow solution(1)
LPDS MTA SZTAKI
The Grid Workflow solution (2)
Input Matrix association
Location of file
representing “B” in
the
A*x=B
LPDS MTA SZTAKI
The Grid Workflow solution (3)
Matrix Operation Input Definition
Expected file names
are INPUT1 and
INPUT2
LPDS MTA SZTAKI
The Grid Workflow solution (4)
Matrix operation definition
Matrix
Operation
Package
Op Code
LPDS MTA SZTAKI
The Grid Workflow solution(5)
The progress
A
B
A
B
A*A-1*B-B
A-1
A-1*B
Result reached at
this point, control
followes
LPDS MTA SZTAKI
A*A-1*B
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
LPDS MTA SZTAKI
Summary
•
•
•
•
Simple way of calculation
Extendibility
Graphical usage
Immediate access:
http://www.lpds.sztaki.hu/pgportal/v23/includes/Equation_Solver.html
LPDS MTA SZTAKI