LPDS MTA SZTAKI 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 a i, j b i 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 (M input1, M input2,M output) operation is controlled by command line arguments: M output = OP (M input1 ) M output = OP (M input1,scalarArg) M output = OP (M input1,M input2 )

LPDS MTA SZTAKI The Matrix Operation Package(2) Detailed I/O conventions OP INPUT1 INPUT2 OUTPUT 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: represents the following matrix:

LPDS MTA SZTAKI The Matrix Operation Package(3) Operations Syntax: [ ] [V[erbose]] OP Extension Explanation ShortName A I1+I2 -> O Add S I1–I2 -> O Subtract M I1*I2 -> O Multiply R I2*I1 -> O Reverse Multiply T transpose of I1 -> O Transpose I invert of I1 -> O Invert c floting value * I1-> O constant multiply L integer I1[value,*]-> O Line of C integer I1[*,value]-> O Column of Example: L 3 V Operation and I/0 files will be printed on standard output Eventual extension values 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 AA B B A -1 A -1 *BA*A -1 *B A*A -1 *B-B Result reached at this point, control followes

LPDS MTA SZTAKI 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