Equation Solver

1
Equation Solver

• A Grid solution

Important hint A follow up example demonstrating
the Parameter Study solution for the mass
calculations using the same Equation Solver can
be found in the DocumentParameter Study support
in P-GRADE Portal 2.5, Pinciples Practices.ppt
2
Outline

• Access to the Demo program
• The Mathematic problem
• The Matrix operation package
• The Grid Workflow solution
• ExampleBasic solutionAdvanced solution
• Summary

3
Access to the Demo program

• 1. The demo applications discussed here can be
  uploaded and used directly within the P-PGRADE
  Portals administrated by the MTA Sztaki (Seegrid,
  Voce, Gilda),(Example shows tab Workflow/Upload
  of the Seegrid Portal)

where, Equation solver contains the basic
solution, Equation solver single
input the more advanced one. Before
eventual workflow submission do not forget to 2.
Open and Save the uploaded application with the
Workflow Editor.(The Workflow Editor can be
started in the tab Workflow / Workflow Manager)
3. Define a proxy Certificate within tab
Certificates / Download
4
The mathematical problem

• Let us solve the equation
• Ax B where the coefficients
  ai,j bi  are real
• A-1Ax  A-1B
• A-1A E
• x Ex
• x A-1B

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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 )

6
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".
• 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 ltOP_codegt ltExtensiongt
  Verbose
• OP Extension Explanation ShortName
• A  I1I2 -gt O Add
• S  I1I2 -gt O Subtract
• M  I1I2 -gt O Multiply
• R  I2I1 -gt O Reverse
  Multiply
• T  transpose of I1 -gt O Transpose
• I  invert of I1 -gt O Invert
• c floting value I1-gt O constant
  multiply
• L integer I1value,-gt O Line of
• C integer I1,value-gt 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
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The Grid Workflow solutionPart 1 basic algorithm

• Two additional jobs (Copy_A, Copy_B) simplify
  the work of the user. They copy their inputs to
  their outputs, with the consequence that the user
  may to define each input file just at a single
  Port. If these jobs would have be omitted it
  were the responsibility of the user to define
  files with the same content at the proper
  placesport 0 of Invert_A should be equal with
  port 0 of A_Mull_X and port 1 of Multip_B
  should be equal with port 1 of A_Mull_X
• The job Invert_A performs the inversion of
  matrtix A,
• The jobs Multip_B, A_mul_X perform matrix
  multiplications,
• The job Subtr_B compares the results by
  performing subtraction operation

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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 the AxB
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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
5 5 10.0 9.0 8.0 7.0 6.0 30.0 8.0 7.0 5.0 9.0
40.0 0.0 11.0 5.0 71.0 1.0 6.0 5.0 0.0 4.0 21.0
7.0 4.0 8.0 0.0
5 1 110.0 132.0 448.0 48.0 79.0
A
A
B
B
A(A-1B)-B
This value should be zero
A-1
A-1B
A(A-1B)
Result x reached at this point, control follows
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The Grid Workflow solution (6)Workflow result
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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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The Grid Workflow solutionPart 2 advanced
algorithm

• The jobs Copy_A, Copy_B will be
  substituted by the single one, by the
  Separator. By convention it receives just one
  file containing the values of the matrices A and
  B. The values are represented in a text form and
  separated by a character. The jobs algorithm
  finds this character and yields the files
  containing A and B an separate output ports.
  Listing the content of the input file of the
  separator job is the following
• 5 5 10.0 9.0 8.0 7.0 6.0 30.0 8.0 7.0 5.0 9.0
  40.0 0.0 11.0 5.0 71.0 1.0 6.0 5.0 0.0 4.0 21.0
  7.0 4.0 8.0 0.05 1 110.0 132.0 448.0 48.0 79.0

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The Grid Workflow solutionPart 2 advanced
algorithm view
5 5 10.0 9.0 8.0 7.0 6.0 30.0 8.0 7.0 5.0 9.0
40.0 0.0 11.0 5.0 71.0 1.0 6.0 5.0 0.0 4.0 21.0
7.0 4.0 8.0 0.05 1 110.0 132.0 448.0 48.0 79.0
5 1 110.0 132.0 448.0 48.0 79.0
AB
5 5 10.0 9.0 8.0 7.0 6.0 30.0 8.0 7.0 5.0 9.0
40.0 0.0 11.0 5.0 71.0 1.0 6.0 5.0 0.0 4.0 21.0
7.0 4.0 8.0 0.0
A
B
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Summary

• Simple way of calculation
• Extendibility
• Graphical usage
• Immediate access