A smaller dx,dy plot
"see lecture 15 for multiple precision"
[CMSC 455] | [Syllabus] | [Lecture Notes] | [Homework] | [Projects] | [Files] | [Notes, all]
Do not talk to other students about the project.
You may use gmp, BigDecimal, apfloat, mpmath, MatLab, Maple,
Mathematica or other existing software, and any software from
the course WEB site. (Slightly different from previous semesters.)
Given the equation:
z = exp(sin(50.0*x)) + sin(60.0*exp(y)) +
sin(70.0*sin(x)) + sin(sin(80.0*y)) -
sin(20.0*(x+y)) + (x*x+y*y)/4.0
Find the global minimum z in -1 < x < 1 , -1 < y < 1
Print x, y, z at end of file. Your z should be < -3.31
Use just normal programming, too slow to do this in multiple precision.
OK to submit global search and code to minimize as seperate files.
Then put best global minimum into multiple precision in some language.
From my download directory, sample code:
for C, mpf_math.h mpf_sin_cos.c mpf_exp.c and supporting code
Also, for Java, Big_math.java and test_Big_math.java.
and test_apfloat.java
Also, for Python, test_mpmath.py3 need python 3 on linux.gl
There are many local minima, do not get stuck in one of them.
A global search with dx and dy <= 0.001 should be in the
global minimum.
From the global search starting point, use optimization.
See lecture 17, optmn samples and spiral examples.
Or:
Optimization for finding x,y of smallest z(x,y)
X
| x-dx,y+dy x,y+dy x+dx,y+dy
| o o o
|
| x-dx,y x,y x+dx,y
| o o o
|
| x-dx,y-dy x,y-dy x+dx,y-dy
| o o o
|
--------+------------------------------------------------ Y
|
| You are at minimum, from global search, z(x,y)
| Check z at 8 points shown above, around x,y
| If any z(point) < z(x,y) move x,y to minimum point
| Else move to ((x,y) + (minimum point))/2 decrease dx,dy, or both
| Keep repeating until no progress, you are at smallest dx,dy
Do not allow dx, dy to get too small, roundoff error if less than
1.0E-16 in 64 bit floating point
1.0E-100 in multiple precision
Print your x and y and z.
I would expect, all to the same number of digits accuracy. (not just %f)
Your points are based on the accuracy of your computed
"x", "y", "z".
Your largest error in x, y, or z rounded to significant digits:
2 digits 50 points
3 digits 70 points
4 digits 75 points
5 digits 80 points
6 digits 81 points
7 digits 82 points
8 digits 83 points
9 digits 84 points
10 digits 85 points
11 digits 86 points
12 digits 87 points
13 digits 88 points
14 digits 89 points
15 digits 90 points
16 digits 91 points
20 digits 92 points
30 digits 93 points
40 digits 95 points
50 digits 96 points
60 digits 97 points
70 digits 98 points
90 digits 99 points
100 digits 100 points
The project source and output is to be submitted on GL as submit cs455 proj list-of-source-files text_output-file one file should be your text output file The list-of-files should include source code and output and other files that were used. Do not submit executable file(s). Use a language of your choice on an operating system of your choice, unless otherwise stated. Talk to the instructor if your language choice is not one of: Ada 95, C, C++, Fortran 95, Java, Python, Scala, SML, MATLAB, Maple, Mathematica, or similar available language or product. The goal of the project is to give you a useful numeric code that you can apply as needed to future tasks. This includes converting a working numeric code to your language of choice or being able to interface some working numeric code with your language of choice. Copying of a project results is zero points for everyone involved in copying. Be sure to check your own answers by using several languages or several implementations. You may want to do the global search in a language that is fast, submit that code, and then start the multiple precision at the x,y found in the global search with a small dx,dy. A crude plot of similar equation z vs x,y is
Last updated 12/1/2019