Using MATLAB

Given

function sigma_z=boussinesq_lookup(q,a,b,z)
	% function that determines stress under corner of an a by b rectangular platform
	% z-meters below the platform. The calculated solutions are in the fmn data
	% m=fmn(:,1)
	% in column 2, fmn(:,2), n=1.2
	% in column 3, fmn(:,2), n=1.4
	% in column 4, fmn(:,2), n=1.6
	fmn= [0.1,0.02926,0.03007,0.03058
	0.2,0.05733,0.05894,0.05994
	0.3,0.08323,0.08561,0.08709
	0.4,0.10631,0.10941,0.11135
	0.5,0.12626,0.13003,0.13241
	0.6,0.14309,0.14749,0.15027
	0.7,0.15703,0.16199,0.16515
	0.8,0.16843,0.17389,0.17739];
	m=a/z;
	n=b/z;
	%...
	end

The vertical stress under a corner of a rectangular area subjected to a uniform load of intensity q is given by the solution of the Boussinesq's equation: sigma_z = q/4pi (2mn squareroot m^2+n^2+1 m^2+n^2+2/m^2+n^2+1+m^2n^2 m^2+n^2+1 + sin^-1 (2mn squareroot m^2+n^2+1/m^2+n^2+1+m^2n^2)) Typically, this equation is solved as a table of values where: sigma_z = qf(m, n) where f(m, n) is the influence value, q is the uniform load, m = a/z, n = b/z, a and b are width and length of the rectangular area and z is the depth below the area. Finish the function boussinesq_lookup. m 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, sigma_z = sigma_z. Use a 0th-order, polynomial interpolation for the value of n (i.e. round to the closest value of n) Copy the boussinesq_lookup.m to a file called boussinesq spline m and use a cubic spline to interpolate in two dimensions, both m and n, that returns sigma_z. The vertical stress under a corner of a rectangular area subjected to a uniform load of intensity q is given by the solution of the Boussinesq's equation: sigma_z = q/4pi (2mn squareroot m^2+n^2+1 m^2+n^2+2/m^2+n^2+1+m^2n^2 m^2+n^2+1 + sin^-1 (2mn squareroot m^2+n^2+1/m^2+n^2+1+m^2n^2)) Typically, this equation is solved as a table of values where: sigma_z = qf(m, n) where f(m, n) is the influence value, q is the uniform load, m = a/z, n = b/z, a and b are width and length of the rectangular area and z is the depth below the area. Finish the function boussinesq_lookup. m 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, sigma_z = sigma_z. Use a 0th-order, polynomial interpolation for the value of n (i.e. round to the closest value of n) Copy the boussinesq_lookup.m to a file called boussinesq spline m and use a cubic spline to interpolate in two dimensions, both m and n, that returns sigma_z