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Solving Linear Equations with SAS IML and Matrix Operations

In this tutorial, we explore how to solve a system of linear equations using SAS Interactive Matrix Language (IML). We will learn to formulate equations in matrix form and implement various matrix operations such as addition, subtraction, and multiplication. The example includes creating matrices, generating random data, and using PROC IML to analyze and visualize results. By the end, you'll be proficient in handling linear equations and performing complex matrix computations in SAS.

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Solving Linear Equations with SAS IML and Matrix Operations

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  1. SAS Interactive Matrix Language Computing for Research I Spring 2012 Ramesh

  2. Solve this system of linear equations: • 3x + 2y − 4z = 11 • 5x − 4y = 9 • 3y + 10z = 42 • In matrix form = =

  3. Reading in Data prociml; n = 3; *scalar; b = {11942}; *1 x 3 row vector; A = {32 -4, 5 -40, 0310}; *3 x 3 matrix; print n b a; quit;

  4. Matrix Operators: Arithmetic Addition: + Subtraction: - Division, Elementwise: / Multiplication, Elementwise: # Multiplication, Matrix: * Power, Elementwise: ## Power, Matrix: ** Concatenation, Horizontal: || Concatenation, Vertical: // Number of rows: nrow() Number of columns: ncol()

  5. Subscript Operations [ ] • Addition + • Multiplication # • Mean : • Sum of squares ## • Maximum <> • Minimum >< • Index of maximum <:> • Index of minimum >:< • Transpose: ` (Near number 1 on keyboard) • Determinant: det(matrix) • Inverse: inv(matrix) • Trace: tr(matrix) • Select a single element: i,j • Select a row: i, • Select a column: ,j

  6. Creating special Matrices: • Identity matrix with dimension = size:I(size) • Matrix having # rows = nrow # cols = ncol with all elements = x :j(nrow,ncol,x) • Diagonal matrix: diag(vector) (diag(matrix)) • Block diagonal matrix: block (M1, M2, ...)

  7. Calling SAS PROC’s into IML prociml; callrandseed(9087235); y = j(400,1); callrandgen(y,normal'); z = j(100,1); callrandgen(z,'normal', 2, 2.5); x = y // z; create a var{"x"}; append; close a; submit; procunivariatedata=a; var x; histogram /kernel; run; endsubmit;

  8. Using DO loops prociml; doi=1to3; callrandseed(9087235); mean=i*2; var=0.5*i; y = j(400,1); callrandgen(y, 'normal'); z = j(100,1); callrandgen(z, 'normal',mean, var); x = y // z; createa var {"x"}; append; close a; submit; procunivariatedata=a noprint; varx; histogram/ kernel; run; endsubmit; end;

  9. datamult; • input v1 v2 v3; • datalines; • 0.801 121.41 70.42 • 0.824 127.70 72.47 • 0.841 129.20 78.20 • 0.816 131.80 74.89 • 0.840 135.10 71.21 • 0.842 131.50 78.39 • 0.820 126.70 69.02 • 0.802 115.10 73.10 • 0.828 130.80 79.28 • 0.819 124.60 76.48 • 0.826 118.31 70.25 • 0.802 114.20 72.88 • 0.810 120.30 68.23 • 0.802 115.70 68.12 • ; • prociml; • usemult; • read all into v; • X=v`*v; • print v; • run;

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