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Thisprogram will solve the system of linear equations, A*X=B, where A is a symmetric, positive definite matrix as is commonly used in structural analysis. Since the matrix is symmetric, only the upper triangular potion is input using columns. So, given a 4x4 matrix, for example, only the following elements are input::
A11 A12 A13 A14
- A22 A23 A24
- - A33 A34
- - - A41
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Test case:
Linear Equations - Compact Crout
to solve multiple symmetric equations of the form
A1*x1+A2*x2+...+An*xn=B
data is input by columns using the upper triangle of matrix A
enter 'q' at any prompt to quit
Enter A matrix dimension: 4
Enter A matrix upper triangle
upper part of column 1
A(1,1)= 1
data correct (y/n)? y
upper part of column 2
A(1,2)= .5
A(2,2)= .33333
data correct (y/n)? y
upper part of column 3
A(1,3)= .33333
A(2,3)= .25
A(3,3)= .2
data correct (y/n)? y
upper part of column 4
A(1,4)= .25
A(2,4)= .2
A(3,4)= .16667
A(4,4)= .14286
data correct (y/n)? y
Determinant of A
Det = 0.16111108e-6
input vector B (constants)
B(1)= .58333
B(2)= .21667
B(3)= .11666
B(4)= .07381
Solution
X(1)= 1.0
X(2)= -1.0
X(3)= 1.0
X(4)= -1.0
Do you want to input another vector B (y/n)? n
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