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Components of Scientific Programming

Learn about the components of scientific programming, including problem definition, code development, logic assembly, testing, visualization, optimization, analysis, and synthesis. Focus on sorting a row array and searching a grid. Use MATLAB for implementation.

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Components of Scientific Programming

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  1. Components of Scientific Programming • Definition of problem • Physical/mathematical formulation • Development of computer code (Focus today) • Development of logic (e.g., flowchart) • Assembly of correct lines of code • Testing and troubleshooting • Visualization of results • Optimization of code • Analysis of results • Synthesis

  2. Definition of problem(Sorting a row array) • Sort through row array A of random numbers, and organize them from left to right by increasing numerical value in array B • Example • A = rand(1,4) • A = 0.7621 0.4565 0.0185 0.8214 • B = 0.0185 0.4565 0.7621 0.8214

  3. Searching an Array j=1 j=2 j=3 j=4 j=5 j=6 j=7 j=8 j=9 x1 x2 x3 x4 x5 x6 x7 x8 x9 Here, the column number is “j”

  4. Development of logic (first try) Start Create array A of length n Make copy array B B(j) = C For j = 1:n-1 Stop B(j+1) = B(j) No Is B(j)>B(j+1)? C= B(j+1) Yes

  5. function [A,B] = gg250_lab_06_try(n) % function [A,B] = gg250_lab_try(n) % Partially sorts the elements in a vector array % of n-elements on a single pass through the array. % Input parameters % n = input array % Output parameters % A = Unsorted array % B = Partially sorted array % Example % [A,B] = gg250_lab_06_try(5) Assembly of correct lines of code (a)

  6. % Make copies of the input array A = rand(n,1); B = A; % Find the number of elements in the array n = length(A) % Step through the elements one-by-one, switching % consecutive elements such that the lower element % comes before the higher element for j = 1:(n-1) if B(j) > B(j+1) C = B(j+1); B(j+1) = B(j); B(j) = C; end end Assembly of correct lines of code (b)

  7. Testing and troubleshooting

  8. Visualization of results • Can plot the values of the elements vs. their position in the array by including the command plot B

  9. Optimization of code • See Matlab's sort command

  10. Searching a Grid j=1 j=2 j=3 j=4 j=5j=6 j=7 j=8 j=9 y5 y4 y3 y2 y1 i=5 i=4 i=3 i=2 i=1 (i= 3, j = 2) x1 x2 x3 x4 x5 x6 x7 x8 x9 Here, the row number is “i” and the column number is “j”

  11. Searching a Grid U = rand(5,9); [n,m] = size(U); for i = 1:n for j = 1:m if i==3 & j ==2; U(i,j) = 1;end end end Alternatives U(3,2) = 2; Or search a column vector form of U T = U(:); T((2-1).*n + 3) = 3; T = reshape(T,n,m) j=1 j=2 j=3 j=4 j=5j=6 j=7 j=8 j=9 y5 y4 y3 y2 y1 i=5 i=4 i=3 i=2 i=1 (i= 3, j = 2) x1 x2 x3 x4 x5 x6 x7 x8 x9

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