Updating element defined as a variable in a matrix for a given range

Hello,

I created a gauss elimination with partial pivoting and back substitution to solve a system of linear equations. What I am having trouble with is creating a matrix that has an element defined as a variable that is updated for a given range of numbers in order to produce a number of solutions based on the range and increments provided. I recieve the following error message:"Error using vertcat: Dimensions of arrays being concatenated are not consistent."

Thank you for your help.

function [x] = FwdElimPPivBckSub(A,b)
tic

R3 = (30.1:.1:100);

A = [1 -1 -1 0 0;
    0 0 1 -1 -1;
    30 0 0 -25 -25;
    -25 0 R3 0 -6;
    0 0 -6 0 21;];

b = [0; 0; 110; 0; -45];
n = length(b);

for k = 1:n-1
    p = k;
    big = abs(A(k,k));
    for ii = k+1:n
        dummy = abs(A(ii,k));
        if dummy > big
            p = ii;
        end
    end
    if p ~= k
        for jj = k:n
            dummy = A(p,jj);
            A(p,jj)= A(k,jj);
            A(k,jj)= dummy;
        end
        dummy = b(p);
        b(p) = b(k);
        b(k) = dummy;
    end
    for i = k+1:n
    factor = A(i,k)/A(k,k);
    for  j = k+1:n
        A(i,j) = A(i,j)-factor *A(k,j);
    end
    b(i) = b(i) - factor*b(k);
    end
end
for i = 1:n
x(i) = b(i)/A(i,i);
end
for i = n-1:-1:1
    sum = b(i);
    for j = i+1:n
        sum = sum - A(i,j)*x(j);
    end
    x(i) = sum/A(i,i);
end
toc

[AbeSal]

Hi Walter,

Thank you for your feedback. What I am trying to define is an array that will in turn produce a list of numbers from 30.1 to 100 in lets say increments of 1 that individually define R3 and create unique solutions when the system of linear equations is solved.

-Abner

[Walter Roberson]

R3_vals = 30.1:.1:100;
num_R3 = length(R3_vals);
results_cell = cell(1, num_R3);
b = [0; 0; 110; 0; -45];

for R3_idx = 1 : num_R3
    R3 = R3_vals(R3_idx);
    A = [1 -1 -1 0 0;
    0 0 1 -1 -1;
    30 0 0 -25 -25;
    -25 0 R3 0 -6;
    0 0 -6 0 21;];
    results_cell{R3_idx} = reshape(FwdElimPPivBckSub(A,b), [], 1);
end
all_results = cell2mat(results_cell);

Answer 1

[Walter Roberson]

R3 = (30.1:.1:100);

R3 is now 1 x 700

A = [1 -1 -1 0 0;
    0 0 1 -1 -1;
    30 0 0 -25 -25;

first row, second row, third are all 1 x 5

    -25 0 R3 0 -6;

There is an R3 in the middle there, and it is 1 x 700, so this line is 1 x (2 + 700 + 2) which is 1 x 704

    0 0 -6 0 21;];

and that line is 1 x 5.

What I am having trouble with is creating a matrix that has an element defined as a variable that is updated for a given range of numbers in order to produce a number of solutions based on the range and increments provided.

You pass in A and b. You should not be defining them inside the function. You should be calling the function in a loop, passing in different variations of A, and doing something appropriate with the results returned by the function.