% Laboratory in Oceanography - Data and Methods
% SMAST, UMass Dartmouth
%
% Code for generating plot of example of system of equations - this case
% stage vs. flow rating curve, with observations at different times.
%
% Written by Miles A. Sundermeyer, 1/27/09

% set the variables
time = [0 14 28 42 56 70];
stage = [0.6120 0.6470 0.5800 0.6290 0.6880 0.5830];
flow = [0.330 0.395 0.241 0.338 0.531 0.279];

% create a figure window, figure number 1
figure(1)
clf
plot(stage,flow,'b*')
xlabel('stage(m)')
ylabel('flow (m^3s)')
title('Stage vs. Discharge Rating Curve')

% fit line to data
% create X matrix for linear fit
X = [stage' ones(size(time'))];
B = X\flow';    % left divide y = Xb by X to solve for B=[m b]'
                        % (need to transpose stage to column vector first)

% now B contains both the slope, m, and intercept, b
stagefit = [min(stage) max(stage)];
hold on
plot(stagefit,[stagefit' ones(size(stagefit'))]*B,'r-');

% print the figure to a postscript file
print -deps2c stage_example_1    % replace ‘-deps2c’ with ‘-djpeg’ for jpeg file