Procedures

ProcedureLocationProcedure TypeDescription
Bisection non_linear_solvers Function

Solves the scalar non-linear equation: using the bisection method on the interval

df test_non_linear_solvers Function
eigen_inv eigenvectors Subroutine

Given the matrix A, computes the eigenvector v associated to the eivenvalue lambda closer to the value p using the inverse power method.
eigen_max eigenvectors Subroutine

Given the matrix A, computes the eigenvector v associated to the eivenvalue of maximum modulus lambda using the power method.
f test_integrals Function
f test_non_linear_solvers Function
f_vec test_non_linear_solvers Function
factor_LU linear_solvers Subroutine

Computes de LU factorization of a non-singular matrix A

forward_euler ode Function

function for integrating vector first order ODEs of the form: using the forward (explicit) euler method.
g test_integrals Function
gauss_solve linear_solvers Function

Computes the solution of the system: where A is a non-singular matrix.
GaussSeidel linear_solvers Function

Computes the solution to the system using the Gauss-Seidel iterative method.
J test_non_linear_solvers Function
Jacobi linear_solvers Function

Computes the solution to the system using the Jacobi iterative method.
lorenz test_ode Function

function for defining derivative in the Lorenz system written as: where: and

make_U linear_solvers Subroutine

Makes the matrix M upper triangular
Newton non_linear_solvers Function

Solves the scalar non-linear equation: using Newton's method.
print_matrix utilities Subroutine

Prints a real matrix in a tabular form (can be improved)
quad integrals Function

Approximates the integral: using some integration method on a linearly spaced set of points.
quad_simpson integrals Function

Approximates the integral: using Simpson's rule on a linearly spaced set of points.
quad_trapz integrals Function

Approximates the integral: using the trapezoidal rule on a linearly spaced set of points.
read_2_columns_csv utilities Subroutine

Reads a two-column csv from file filename and stores it in D
Runge_Kutta2 ode Function

function for integrating vector first order ODEs of the form: using the Runke-Kutta (2) method.
Secant non_linear_solvers Function

Solves the scalar non-linear equation: using the secant method.
solve linear_solvers Function

Computes the solution to the system: using LU factorization.
solve_L linear_solvers Function

Computes the solution of a lower triangular system:

solve_LU linear_solvers Function

Computes the solution to the system: where L and U are the matrices obtained from a LU factorization.
solve_U linear_solvers Function

Computes the solution of an upper triangular system:

to_csv utilities Subroutine

saves two-dimensional array D to csv file filename
trapz integrals Function

Aproximates the integral of the function given a set of points: using the trapezoidal rule. The points do not need to be linearly spaced along the integration domain.
VectorNewton non_linear_solvers Function

Solves the vector non-linear equation: using Newton's method.
call~~graph~~CallGraph proc~bisection Bisection proc~df df proc~eigen_inv eigen_inv proc~factor_lu factor_LU proc~eigen_inv->proc~factor_lu proc~solve_lu solve_LU proc~eigen_inv->proc~solve_lu proc~eigen_max eigen_max proc~f f proc~f_vec f_vec proc~forward_euler forward_euler proc~f~2 f proc~g g proc~gauss_solve gauss_solve proc~make_u make_U proc~gauss_solve->proc~make_u proc~solve_u solve_U proc~gauss_solve->proc~solve_u proc~gaussseidel GaussSeidel proc~solve_l solve_L proc~gaussseidel->proc~solve_l proc~j J proc~jacobi Jacobi proc~lorenz lorenz proc~newton Newton proc~print_matrix print_matrix proc~quad quad proc~quad_simpson quad_simpson proc~quad->proc~quad_simpson proc~quad_trapz quad_trapz proc~quad->proc~quad_trapz proc~read_2_columns_csv read_2_columns_csv proc~runge_kutta2 Runge_Kutta2 proc~secant Secant proc~solve solve proc~solve->proc~factor_lu proc~solve->proc~solve_lu proc~solve_lu->proc~solve_l proc~solve_lu->proc~solve_u proc~to_csv to_csv proc~trapz trapz proc~vectornewton VectorNewton proc~vectornewton->proc~solve program~test_eigenvectors test_eigenvectors program~test_eigenvectors->proc~eigen_inv program~test_eigenvectors->proc~eigen_max program~test_integrals test_integrals program~test_integrals->proc~quad program~test_linear_solvers test_linear_solvers program~test_linear_solvers->proc~gauss_solve program~test_linear_solvers->proc~gaussseidel program~test_linear_solvers->proc~jacobi program~test_linear_solvers->proc~solve program~test_non_linear_solvers test_non_linear_solvers program~test_non_linear_solvers->proc~bisection program~test_non_linear_solvers->proc~newton program~test_non_linear_solvers->proc~secant program~test_non_linear_solvers->proc~vectornewton program~test_ode test_ode program~test_ode->proc~forward_euler program~test_utilities test_utilities program~test_utilities->proc~print_matrix
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