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http://spoken-tutorial.org/watch/Scilab/Linear%2Bequations%2BGaussian%2BMethods/English/

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In this tutorial the first loop in the code makes an UT array. Or, at least it's supposed to.

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Looking at this code using the debugger with breaks set at 32 and 34 I get the following results for the loop indexes: k=1, j=2, i=2 for the first iteration of the code.

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Line 32 shows the factor, line 34 shows the code to zero out the following columns below the index element.

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At line 32: factor = A(2,1)/A(1,1) is evaluated at the given index values which is OK. A(1,1) to normalize the row and A(2,1) to get rid of the first col in the following row. That's OK.

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At line 34 we get A(i,j)=A(i,j)-factor*A(k,j) which resolves to

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A(2,2)=A(2,2)-factor*A(1,2) using the i, j, k values. Not good!

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This code should resolve to

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A(2,1)=A(2,1) - factor * A(1,1)

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to set A(2,1) to zero, the rest of the loop changes the other elements in this row by the same factor. So this loop is screwed up. If I change the code so A(2,1) is used where it should, the element is now zero, but the code shows an index error when I run it. So I'll have to monkey around with the code to make the UT array, but there is definitely a problem with this example!

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And the last loop back substitutes to get the solution: I hope the last loop works as I have not tried it yet!

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I modified the original code to make debugging simpler: I hard wired in the A and b arrays, and deleted the back substitution section, so I can focus only on the UT matrix code.

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