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#Problem 1 | |
The function 'least_squares' inputs a matrix Z and a scalar y and outputs best-dit constants, best-fit function as well as the coefficients of determination. | |
For each one of the proposed cases, the following set of values is obtained: | |
a) y=0.3745+0.98644x+0.84564/x | |
| a | fx | r2 | | |
|---------|--------|--------| | |
| 0.3745 | 2.2066 | 0.9996 | | |
| 0.9864 | 2.7702 | | | |
| 0.8456 | 3.6157 | | | |
| | 4.5317 | | | |
| | 5.4758 | | | |
b) y=-11.4887+7.143817x-1.04121 x^2+0.046676 x^3 | |
| a | fx | r2 | | |
|---------|--------|--------| | |
|-11.4887 | 1.8321 | 0.8290 | | |
| 7.1438 | 3.4145 | | | |
| -1.0412 | 4.0347 | | | |
| 0.0467 | 2.9227 | | | |
| | 2.4947 | | | |
| | 3.2330 | | | |
| | 4.9595 | | | |
c) y=4.0046e^(-1.5x)+2.9213e^(-0.3x)+1.5647e^(-0.05x) | |
| a | fx | r2 | | |
|---------|--------|--------| | |
| 4.0046 | 5.9321 | 0.9971 | | |
| 2.9213 | 4.5461 | | | |
| 1.5647 | 3.2184 | | | |
| | 2.5789 | | | |
| | 2.1709 | | | |
| | 1.8726 | | | |
| | 1.6425 | | | |
| | 1.4605 | | | |
| | 1.1940 | | | |
#Problem 2 | |
For this problem, we look at the case where the independent variable is temperature and the dependent variable is failure (1=fail, 0=pass). A function called cost_logistic.m takes the vector a, independent variable x and dependent variable y so that the output is [J,grad] or [cost, gradient]. Also, we solved for a0 and a1 on part b and plotted the data in part c. | |
a) | |
[J, grad] = cost_logistic(a, x, y) | |
J = 115.5085 | |
grad = 5.0130 | |
b) The result for a0 and a1 generated through cost_logistic | |
#Problem 3 | |
The function boussinesq_lookup.m is writtent so that when you enter a force , q, dimensions of rectangular area a, b, and depth, z, it uses a third-order polynomial interpolation of the four closest values of m to determine the stress in the vertical direction as shown in the file in the repository. | |
b) The boussinesq_lookup.m code is copied to a file called boussinesq_spline.m using a cubic spline to interpolate in two dimensions, both m and n, that returns sigma_z. | |