Basically I wanted to get some fun and solve for a temperature in thermodynamics where I must get 'T_f' which appear in a transcendental equation: ##Aln left ( frac{T_f^2}{T_1T_2} right )+2B[2T_f-(T_1T_2)]=0##.
Where T_1 is worth 100, T_2 is worth 200, A=2 and B=0.005.
Here is my code: that I compile along with The problem is that for the values I said above, I get the message 'There's an even number of root(s) in that interval'. Thus apparently the condition f(a)*f(b)>0 is satisfied. However when I enter the numbers in my pocket calculator I get f(a)=-2.3862.. and f(b)=2.3862.. where I truncated both values. Thus the condition is not satisfied.
I really don't see what's wrong. Any idea?
Edit: I tried with many different values for a and b. I even changed t_1 and t_2, same message.
Edit2: I've just tested the values of fa and fb. It thinks they are worth infinity. Going to check this out.
Edit3: No idea why it thinks they are worth infinity. o_0.
Edit4: ok it does not plug in t_1 and t_2 inside my function.
I'm trying to implement Bisection Method with Fortran 90 to get solution, accurate to within 10^-5 for 3x - e^x = 0 for 1 <= x <= 2
This is the code that I came up with, but when I run the code it just list .1.5000000000000000 100 times.
How should I fix this code so that I can keep applying bisection method correctly until I get to a number around 10^-5?
1 Answer
The problem is actually not with your algorithm, but rather in how you calculate f
. Because you have not specified implicit none
in the function, the compiler allowed e**x
to slip through, even though Fortran doesn't define e
as you would have liked.
When you correct the function as follows, the program works fine:
This is a good lesson to use implicit none everywhere.
Not the answer you're looking for? Browse other questions tagged fortranbisection or ask your own question.
BISECTION_RC is a FORTRAN90 library which demonstrates the simple bisection method for solving a scalar nonlinear equation in a change of sign interval, using reverse communication (RC).
The routine assumes that an interval [a,b] is known, over which the function f(x) is continuous, and for which f(a) and f(b) are of opposite sign. By repeatedly computing and testing the midpoint, the halving change of sign interval may be reduced, so that either the uncertainty interval or the magnitude of the function value becomes small enough to satisfy the user as an approximation to the location of a root of the function.
This routine is in part a demonstration of the idea of reverse communication. Many zero finders require that the user define f(x) by writing a function with a very specific set of input and output arguments, and sometimes with a specific name, so that the user can call the zero finder, which in turn can call the function. This is sometimes an awkward formulation to follow. Reverse communication instead allows the user's calling program to retain control of the function evaluation.
To use the reverse communication zero finder, the user defines the values of A and B, and sets a parameter JOB to zero to indicate that this is the first call. From then on, the zero finder repeatedly returns a value X, asking the user to evaluate the function there. Once the user has evaluated FX = f(X), the user may accept this approximation to the root, or else call the zero finder again, passing the just-computed value of FX so that it can take another bisection step.
Licensing:
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
Languages:
BISECTION_RC is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.
Related Data and Programs:
BACKTRACK_BINARY_RC, a FORTRAN90 library which carries out a backtrack search for a set of binary decisions, using reverse communication.
BISECTION_INTEGER, a FORTRAN90 library which seeks an integer solution to the equation F(X)=0, using bisection within a user-supplied change of sign interval [A,B].
BRENT, a FORTRAN90 library which contains Richard Brent's routines for finding the zero, local minimizer, or global minimizer of a scalar function of a scalar argument, without the use of derivative information.
CG_RC, a FORTRAN90 library which implements the conjugate gradient (CG) method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).
LOCAL_MIN_RC, a FORTRAN90 library which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, using reverse communication (RC), by Richard Brent.
NMS, a FORTRAN90 library which includes a wide variety of numerical software, including solvers for linear systems of equations, interpolation of data, numerical quadrature, linear least squares data fitting, the solution of nonlinear equations, ordinary differential equations, optimization and nonlinear least squares, simulation and random numbers, trigonometric approximation and Fast Fourier Transforms (FFT).
ROOT_RC, a FORTRAN90 library which seeks a solution of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC), by Gaston Gonnet.
ROOTS_RC, a FORTRAN90 library which seeks a solution of a system of nonlinear equations f(x) = 0, using reverse communication (RC), by Gaston Gonnet.
SORT_RC, a FORTRAN90 library which can sort a list of any kind of objects, using reverse communication (RC).
TEST_ZERO, a FORTRAN90 library which implements test problems for the solution of a single nonlinear equation in one variable.
ZERO_RC, a FORTRAN90 library which seeks a solution of a scalar nonlinear equation f(x) = 0, using reverse communication (RC), by Richard Brent.
ZOOMIN, a FORTRAN90 library which includes various zero finder routines.
Reference:
- Werner Rheinboldt,
Algorithms for finding zeros of a function,
UMAP Journal,
Volume 2, Number 1, 1981, pages 43-72. - Werner Rheinboldt,
Methods for Solving Systems of Nonlinear Equations,
SIAM, 1998,
ISBN: 089871415X,
LC: QA214.R44.
Source Code:
- bisection_rc.f90, the source code.
Examples and Tests:
- bisection_rc_prb.f90, a sample calling program.
- bisection_rc_prb_output.txt, the output file.
List of Routines:
- BISECTION_RC seeks a zero of f(x) in a change of sign interval.
- R8_SIGN returns the sign of an R8.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to the FORTRAN90 source codes.
Last revised on 13 January 2013.In this tutorial you will get program for bisection method in C and C++.
To find a root very accurately Bisection Method is used in Mathematics. Bisection method algorithm is very easy to program and it always converges which means it always finds root.
Bisection Method repeatedly bisects an interval and then selects a subinterval in which root lies. It is a very simple and robust method but slower than other methods.
It is also called Interval halving, binary search method and dichotomy method. Registry mechanic patch download.
Bisection Method calculates the root by first calculating the mid point of the given interval end points.
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Bisection Method Procedure
The input for the method is a continuous function f, an interval [a, b], and the function values f(a) and f(b). The function values are of opposite sign (there is at least one zero crossing within the interval). Each iteration performs these steps:
1. Calculate the midpoint c = (a + b)/2
C Program For Bisection Method
2. Calculate the function value at the midpoint, function(c).
3. If convergence is satisfactory (that is, a – c is sufficiently small, or f(c) is sufficiently small), return c and stop iterating.
4. Examine the sign of f(c) and replace either (a, f(a)) or (b, f(b)) with (c, f(c)) so that there is a zero crossing within the new interval.
Pros and Cons
Advantage of the bisection method is that it is guaranteed to be converged and very easy to implement.
Disadvantage of bisection method is that it cannot detect multiple roots and is slower compared to other methods of calculating the roots.
Program for Bisection Method in C
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 | doublefunc(doublex) returnx*x*x-2*x*x+3; doublec; voidbisection(doublea,doubleb) if(func(a)*func(b)>=0) printf('Incorrect a and b'); } c=a; while((b-a)>=e) c=(a+b)/2; printf('Root = %lfn',c); } printf('Root = %lfn',c); } printf('Root = %lfn',c); } } intmain() doublea,b; b=20; printf('The function used is x^3-2x^2+3n'); printf('b = %lfn',b); printf('n'); } |
Output
a = -10.000000
b = 20.000000
Root = 5.000000
Root = -2.500000
Root = 1.250000
Root = -0.625000
Root = -1.562500
Root = -1.093750
Root = -0.859375
Root = -0.976563
Root = -1.035156
Root = -1.005859
Root = -0.991211
Root = -0.998535
Accurate Root calculated is = -0.998535
Program for Bisection Method in C++
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 | doublefunc(doublex) returnx*x*x-2*x*x+3; doublec; voidbisection(doublea,doubleb) if(func(a)*func(b)>=0) cout<<'Incorrect a and b'; } c=a; while((b-a)>=e) c=(a+b)/2; cout<<'Root = '<<c<<endl; } cout<<'Root = '<<c<<endl; } cout<<'Root = '<<c<<endl; } } intmain() doublea,b; b=20; cout<<'The function used is x^3-2x^2+3n'; cout<<'b = '<<b<<endl; cout<<'n'; } |
This article is submitted by Rahul Maheshwari. You can connect with him on facebook.
Comment below if you have any queries regarding above program for bisection method in C and C++.
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BISECTION_RC is a FORTRAN90 library which demonstrates the simple bisection method for solving a scalar nonlinear equation in a change of sign interval, using reverse communication (RC).
The routine assumes that an interval [a,b] is known, over which the function f(x) is continuous, and for which f(a) and f(b) are of opposite sign. By repeatedly computing and testing the midpoint, the halving change of sign interval may be reduced, so that either the uncertainty interval or the magnitude of the function value becomes small enough to satisfy the user as an approximation to the location of a root of the function.
This routine is in part a demonstration of the idea of reverse communication. Many zero finders require that the user define f(x) by writing a function with a very specific set of input and output arguments, and sometimes with a specific name, so that the user can call the zero finder, which in turn can call the function. This is sometimes an awkward formulation to follow. Reverse communication instead allows the user's calling program to retain control of the function evaluation.
To use the reverse communication zero finder, the user defines the values of A and B, and sets a parameter JOB to zero to indicate that this is the first call. From then on, the zero finder repeatedly returns a value X, asking the user to evaluate the function there. Once the user has evaluated FX = f(X), the user may accept this approximation to the root, or else call the zero finder again, passing the just-computed value of FX so that it can take another bisection step.
Licensing:
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
Languages:
BISECTION_RC is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.
Related Data and Programs:
BACKTRACK_BINARY_RC, a FORTRAN90 library which carries out a backtrack search for a set of binary decisions, using reverse communication.
BISECTION_INTEGER, a FORTRAN90 library which seeks an integer solution to the equation F(X)=0, using bisection within a user-supplied change of sign interval [A,B].
BRENT, a FORTRAN90 library which contains Richard Brent's routines for finding the zero, local minimizer, or global minimizer of a scalar function of a scalar argument, without the use of derivative information.
CG_RC, a FORTRAN90 library which implements the conjugate gradient (CG) method for solving a positive definite sparse linear system A*x=b, using reverse communication (RC).
LOCAL_MIN_RC, a FORTRAN90 library which finds a local minimum of a scalar function of a scalar variable, without the use of derivative information, using reverse communication (RC), by Richard Brent.
NMS, a FORTRAN90 library which includes a wide variety of numerical software, including solvers for linear systems of equations, interpolation of data, numerical quadrature, linear least squares data fitting, the solution of nonlinear equations, ordinary differential equations, optimization and nonlinear least squares, simulation and random numbers, trigonometric approximation and Fast Fourier Transforms (FFT).
ROOT_RC, a FORTRAN90 library which seeks a solution of a scalar nonlinear equation f(x) = 0, or a system of nonlinear equations, using reverse communication (RC), by Gaston Gonnet.
Fortran Programming Language Pdf
ROOTS_RC, a FORTRAN90 library which seeks a solution of a system of nonlinear equations f(x) = 0, using reverse communication (RC), by Gaston Gonnet.
SORT_RC, a FORTRAN90 library which can sort a list of any kind of objects, using reverse communication (RC).
Malena english movie hd free download. TEST_ZERO, a FORTRAN90 library which implements test problems for the solution of a single nonlinear equation in one variable.
ZERO_RC, a FORTRAN90 library which seeks a solution of a scalar nonlinear equation f(x) = 0, using reverse communication (RC), by Richard Brent.
ZOOMIN, a FORTRAN90 library which includes various zero finder routines.
Reference:
- Werner Rheinboldt,
Algorithms for finding zeros of a function,
UMAP Journal,
Volume 2, Number 1, 1981, pages 43-72. - Werner Rheinboldt,
Methods for Solving Systems of Nonlinear Equations,
SIAM, 1998,
ISBN: 089871415X,
LC: QA214.R44.
Source Code:
- bisection_rc.f90, the source code.
Examples and Tests:
- bisection_rc_prb.f90, a sample calling program.
- bisection_rc_prb_output.txt, the output file.
List of Routines:
- BISECTION_RC seeks a zero of f(x) in a change of sign interval.
- R8_SIGN returns the sign of an R8.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to the FORTRAN90 source codes.
Last revised on 13 January 2013.