Adjusting a do loop for matrix algebra? ----- I am trying to write a program in
ID: 3807040 • Letter: A
Question
Adjusting a do loop for matrix algebra?
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I am trying to write a program in Maple to create a lower-triangular matrix. My professor provided a do loop in class that creates an upper-triangular matrix, but I don't even understand how that works, so I can't change the code to make it create a lower-triangular matrix instead.
Given the matrix A:
I can use the code:
for j to 4 do
for i to 4 do
if i > j then
c := -A[i, j]/A[j, j];
for k to 4 do
A[i, k] := c*A[j, k]+A[i, k]
end do
end if
end do
end do;
... which results in the matrix,
How can I adjust this code to make it do lower-triangular instead? I don't even understand the upper-triangular code. I understand Gaussian elimination, but I don't understand how this code works because of the nested loops.
3 1 0 10 21 1021 421 12 12Explanation / Answer
for i to 4 do
for j to 4 do
C[i,j] := A[i,j]
end do
end do
for i to 4 do
for j to 4 do
A[i,j] := C[j,i]
end do
end do
for j to 4 do
for i to 4 do
if i > j then
c := -A[i, j]/A[j, j];
for k to 4 do
A[i, k] := c*A[j, k]+A[i, k]
end do
end if
end do
end do
for i to 4 do
for j to 4 do
C[i,j] := A[i,j]
end do
end do
for i to 4 do
for j to 4 do
A[i,j] := C[j,i]
end do
end do
Explaination :- we have converted the original matrix into mirror image of that matrix such that A[i,j] = A[j,i]. Now we will use the usual code to convert into upper triangular matrix and then again do the same swap to get back lower triangular matrix.