Chapter 6 Graphs

6.1 Figure Components

6.1.1 Matlab Graph Safe Colors for Web, Presentation and Publications Examples

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6.1.1.1 Good Colors to Use Darker

Nice darker light colors to use in matlab.

close all

blue = [57 106 177]./255;
red = [204 37 41]./255;
black = [83 81 84]./255;
green = [62 150 81]./255;
brown = [146 36 40]./255;
purple = [107 76 154]./255;
cl_colors = {blue, red, black, ...
             green, brown, purple};
cl_str_clr_names = ["blue", "red", "black", "green", "brown", "purple"];

for it_color=1:length(cl_colors)
    
    figure();
    x = [0 1 1 0];
    y = [0 0 1 1];
    fill(x, y, cl_colors{it_color});
    st_text = [cl_str_clr_names(it_color) num2str(round(cl_colors{it_color}*255))];
    hText = text(.10,.55, st_text);
    hText.Color = 'white';
    hText.FontSize = 30; 
    snapnow;
    
end

6.1.1.2 Good Colors to Use Lighter

Nice ligher colors to use in matlab.

close all

blue = [114 147 203]./255;
red = [211 94 96]./255;
black = [128 133 133]./255;
green = [132 186 91]./255;
brown = [171 104 87]./255;
purple = [144 103 167]./255;
cl_colors = {blue, red, black, ...
             green, brown, purple};
cl_str_clr_names = ["blue", "red", "black", "green", "brown", "purple"];

for it_color=1:length(cl_colors)
    
    figure();
    x = [0 1 1 0];
    y = [0 0 1 1];
    fill(x, y, cl_colors{it_color});
    
    st_text = [cl_str_clr_names(it_color) num2str(round(cl_colors{it_color}*255))];
    hText = text(.10,.55, st_text);
    hText.Color = 'white';
    hText.FontSize = 30; 
    snapnow;
    
end

6.1.1.3 Matlab has a graphical tool for picking color

Enter uisetcolor pick color from new window and color values will appear uisetcolor

% Color Pickers
% uisetcolor

Picked Color use

figure();
hold on;

x = rand([10,1]);
y = rand([10,1]);

% Then can use for plot
plot(x,y,'Color',[.61 .51 .74]);

% Can use for Scatter
scatter(x, y, 10, ...
    'MarkerEdgeColor', [.61 .51 .74], 'MarkerFaceAlpha', 0.1, ...
    'MarkerFaceColor', [.61 .51 .74], 'MarkerEdgeAlpha', 0.1);

6.1.2 Matlab Graph Titling, Labels and Legends Examples

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6.1.2.1 Draw A figure Label Title, X and Y Axises with Latex Equations

clear all;
close all;
figure();

% draw some lines
xline0 = xline(0);
xline0.HandleVisibility = 'off';
yline0 = yline(0);
yline0.HandleVisibility = 'off';
hline = refline([1 0]);
hline.Color = 'k';
hline.LineStyle = ':';
hline.HandleVisibility = 'off';

% Titling with multiple lines
title({'Cash-on-Hand given w(k+b),k,z' '$\alpha + \beta = \zeta$'},'Interpreter','latex');
ylabel({'Cash-on-Hand' 'line 2 $\frac{1}{2}$'},'Interpreter','latex');
xlabel({'Index of Cash-on-Hand Discrete Point'...
        ' $\frac{1}{2} + \alpha + \max + \sum_1^{B}$ Each Segment is a w=k+b; within segment increasing k'...
        'For each w and z, coh maximizing k is different'},'Interpreter','latex');
grid on;
grid minor;

6.1.2.2 Matlab Graph Specify Legends Manually

Specify labels manually, note we can use HandleVisibility to control what part of figure show up in legends.

% Generate Random Data
rng(123);
it_x_n = 10;
it_x_groups_n = 3;
mat_y = rand([it_x_n, it_x_groups_n]);
mat_y = mat_y + sqrt(1:it_x_groups_n);
mat_y = mat_y + log(1:it_x_n)';
ar_x = 1:1:it_x_n;

% Start Figure
figure('PaperPosition', [0 0 10 10]);

hold on;

g1 = scatter(ar_x,  mat_y(:,1), 30, 'filled');
g2 = scatter(ar_x,  mat_y(:,2), 30, 'filled');
g3 = scatter(ar_x,  mat_y(:,3), 30, 'filled');

legend([g1, g2, g3], {'near','linear','spline'}, 'Location','best',...
        'NumColumns',1,'FontSize',12,'TextColor','black');

% PLot this line, but this line will not show up in legend
hline = refline([1 0]);
hline.Color = 'k';
hline.LineStyle = ':';
% not to show up in legend
hline.HandleVisibility = 'off';
grid on;
grid minor;

title(sprintf('griddedInterpolant comparison, crra utility approximation, interp grid n=%d', it_x_n))
ylabel('Actual Utility Evaluated at c')
xlabel('Approximated Util based on  Interpolation')

snapnow;

6.1.2.3 Given Graph, Graph Subset of Lines and Add Extra Line with Legend

Same plot as before, except we plot only 2 of the three lines and add another line with associated legend entry.

legendCell = cellstr(num2str(ar_x', 'shock=%3.2f'));
xlinemax = xline(min(mat_y, [], 'all'));
xlinemax.Color = 'b';
xlinemax.LineWidth = 1.5;

legendCell{length(legendCell) + 1} = 'max-agg-save';
legend([g1, g3, xlinemax], legendCell([1,3,length(legendCell)]), 'Location', 'best');

snapnow;

6.1.3 Matlab Graph Matrix with Jet Spectrum Color, Label a Subset Examples

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6.1.3.1 Plot a Subset of Data Matrix with Appropriate Legends

Sometimes we solve a model across many states, but we can only plot at a subset of states, or perhaps we plot at all states, but only show legends/labels for a subset.

In the example below, many lines are plotted, however, only a subset of lines are labeled in the legend.

clear all;
close all;

% Generate Random Data
rng(123);
it_x_n = 10;
it_y_groups_n = 100;
ar_y = linspace(1,2,it_y_groups_n);
mat_y = rand([it_x_n, it_y_groups_n]);
mat_y = mat_y + sqrt(1:it_y_groups_n);
mat_y = mat_y + log(1:it_x_n)' + ar_y;
ar_x = 1:1:it_x_n;

% Jet color Graph All
figure('PaperPosition', [0 0 7 4]);
chart = plot(mat_y);
clr = jet(numel(chart));
for m = 1:numel(chart)
    set(chart(m),'Color',clr(m,:))
end

% zero lines
xline(0);
yline(0);

% invalid points separating lines
yline_borrbound = yline(3);
yline_borrbound.HandleVisibility = 'on';
yline_borrbound.LineStyle = ':';
yline_borrbound.Color = 'black';
yline_borrbound.LineWidth = 3;

% Titling
title('Cash-on-Hand given w(k+b),k,z');
ylabel('Cash-on-Hand');
xlabel({'Index of Cash-on-Hand Discrete Point'...
    'Each Segment is a w=k+b; within segment increasing k'...
    'For each w and z, coh maximizing k is different'});

% Xlim controls
xlim([min(ar_x), max(ar_x)]);

% Grid ons
grid on;
grid minor;
% Legends
legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4)  numel(chart)]);
legendCell = cellstr(num2str(ar_y', 'shock=%3.2f'));

legendCell{length(legendCell) + 1} = 'borrow-constraint';
chart(length(chart)+1) = yline_borrbound;
legend(chart([legend2plot length(legendCell)]), ...
       legendCell([legend2plot length(legendCell)]), ...
       'Location', 'best');

6.2 Basic Figure Types

6.2.1 Matlab Graph Scatter Plot Examples

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6.2.1.1 Scatter Plot Example

The plot below as square scatter points, each one with think border. Can set transparency of border/edge and inside separately.

close all;
figure();
size = 100;
s = scatter(1:10,1:10,size);

s.Marker = 's';
% color picked by using: uisetcolor
s.MarkerEdgeColor = [0    0.4471    0.7412];
s.MarkerEdgeAlpha = 0.5;
s.MarkerFaceColor = [.61 .51 .74];
s.MarkerFaceAlpha = 1.0;
s.LineWidth = 10;
grid on;
grid minor;

% 'o'   Circle
% '+'   Plus sign
% '*'   Asterisk
% '.'   Point
% 'x'   Cross
% 'square' or 's'   Square
% 'diamond' or 'd'  Diamond
% '^'   Upward-pointing triangle
% 'v'   Downward-pointing triangle
% '>'   Right-pointing triangle
% '<'   Left-pointing triangle
% 'pentagram' or 'p'    Five-pointed star (pentagram)
% 'hexagram' or 'h' Six-pointed star (hexagram)
% 'none'    No markers

6.2.1.2 Scatter with Edge and Face Color and Transparency

Here is another way to Set Scatter Edge and Fac Colors and Transparencies.

% Generate Data
rng(123);
it_x_n = 10;
it_x_groups_n = 3;
mat_y = rand([it_x_n, it_x_groups_n]);
mat_y = mat_y + sqrt(1:it_x_groups_n);
mat_y = mat_y + log(1:it_x_n)';
ar_x = 1:1:it_x_n;

% Colors
blue = [57 106 177]./255;
red = [204 37 41]./255;
black = [83 81 84]./255;
green = [62 150 81]./255;
brown = [146 36 40]./255;
purple = [107 76 154]./255;
cl_colors = {blue, red, black, ...
             green, brown, purple};

% Scatter Shapes
cl_scatter_shapes = {'s','x','o','d','p','*'};
% Scatter Sizes
cl_scatter_sizes = {100,100,50,50,50,50};
% Legend Keys
cl_legend = {'For Borr', 'Inf Borr', 'For+Inf Br'};

% Plot
figure();
hold on;
for it_m = 1:it_x_groups_n
    scatter(ar_x, mat_y(:,it_m), cl_scatter_sizes{it_m}, ...
        'Marker', cl_scatter_shapes{it_m}, ...
        'MarkerEdgeColor', cl_colors{it_m}, 'MarkerFaceAlpha', 0.8, ...
        'MarkerFaceColor', cl_colors{it_m}, 'MarkerEdgeAlpha', 0.8);
    cl_legend{it_m} = cl_legend{it_m};
end
legend(cl_legend, 'Location', 'best');
grid on; 
grid minor;

6.2.2 Matlab Line and Scatter Plot with Multiple Lines and Axis Lines

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6.2.2.1 Six lines Plot

Colors from optimal colors. Generate A line plot with multiple lines using safe colors, with differening shapes. Figures include lines as well as scatter overlayed jointly.

close all
figure();
hold on;

blue = [57 106 177]./255;
red = [204 37 41]./255;
black = [83 81 84]./255;
green = [62 150 81]./255;
brown = [146 36 40]./255;
purple = [107 76 154]./255;
cl_colors = {blue, red, black, ...
             green, brown, purple};
cl_legend = {'For Borr', 'Inf Borr', 'For+Inf Br', 'For+Br+Save', 'Bridge Loan', 'For Save'};
cl_scatter_shapes = {'s','x','o','d','p','*'};
cl_linestyle = {'--','-',':','-.','--','-'};
it_sca_bs = 20;
cl_scatter_csizes = {10*it_sca_bs, 20*it_sca_bs, 10*it_sca_bs, 10*it_sca_bs, 5*it_sca_bs, 8*it_sca_bs};
it_line_bs = 2;
cl_line_csizes = {1*it_line_bs, 2*it_line_bs, 1*it_line_bs, 1*it_line_bs, 1*it_line_bs, 2*it_line_bs};

it_x_groups_n = length(cl_scatter_csizes);
it_x_n = 10;

% Generate Random Data
rng(123);
mat_y = rand([it_x_n, it_x_groups_n]);
mat_y = mat_y + sqrt(1:it_x_groups_n);
mat_y = mat_y + log(1:it_x_n)';
ar_x = 1:1:it_x_n;

ar_it_graphs_run = 1:6;
it_graph_counter = 0;
ls_chart = [];
for it_fig = ar_it_graphs_run

    % Counter
    it_graph_counter = it_graph_counter + 1;

    % Y Outcome
    ar_y = mat_y(:, it_fig)';

    % Color and Size etc
    it_csize = cl_scatter_csizes{it_fig};
    ar_color = cl_colors{it_fig};
    st_shape = cl_scatter_shapes{it_fig};
    st_lnsty = cl_linestyle{it_fig};
    st_lnwth = cl_line_csizes{it_fig};
    
    % plot scatter and include in legend
    ls_chart(it_graph_counter) = scatter(ar_x, ar_y, it_csize, ar_color, st_shape);

    % plot line do not include in legend
    line = plot(ar_x, ar_y);
    line.HandleVisibility = 'off';
    line.Color = ar_color;
    line.LineStyle = st_lnsty;
    line.HandleVisibility = 'off';
    line.LineWidth = st_lnwth;

    % Legend to include
    cl_legend{it_graph_counter} = cl_legend{it_fig};
end

% Legend
legend(ls_chart, cl_legend, 'Location', 'southeast');

% labeling
title('Optimal Savings');
ylabel('Savings Levels');
xlabel('Cash-on-Hand Today');
grid on;

snapnow;

6.2.2.2 Horizontal and Vertical Lines and 45 Degree

Draw x and y axis, and draw a 45 degree line.

figure();

xline0 = xline(0);
xline0.HandleVisibility = 'off';
xline0.Color = red;
xline0.LineStyle = '--';
yline0 = yline(0);
yline0.HandleVisibility = 'off';
yline0.LineWidth = 1;

hline = refline([1 0]);
hline.Color = 'k';
hline.LineStyle = ':';
hline.HandleVisibility = 'off';

snapnow;
grid on;
grid minor;

6.2.3 Matlab Graph Scatter and Line Spectrum with Three Variables

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Generate k + b = w, color for each w, vectors of k and b such that k + b = w for each w

There are two N by M matrix, A anb B.

Values in Matrix A correspond to the x-axis, values in Matrix B correspond to the y-axis.

The rows and columns in matrix A and B have some other meanings. In this case, we will give color to the columns.

The columns is represented by vector C, which is another variable.

Each line a different color representing variable 3
Legend labeling a subset of colors
X and Y could be asset choices, color could be utility, consumption etc.

6.2.3.1 Setting Up Data

close all
clear all

% Bounds
fl_b_bd = -10;
% Max and Mins
fl_w_max = 50;
fl_w_min = fl_b_bd;
fl_kp_max = fl_w_max - fl_b_bd;
fl_kp_min = 0;

% Grid Point Counts
it_w_i = 30;
it_kb_j = 30;

% Grids
ar_w = linspace(fl_w_min, fl_w_max, it_w_i);
ar_kp = linspace(fl_kp_min, fl_kp_max, it_kb_j);
mt_bp = ar_w - ar_kp';
mt_kp = ar_w - mt_bp;
mt_bl_constrained = (mt_bp < fl_b_bd);
mt_bp_wth_na = mt_bp;
mt_kp_wth_na = mt_kp;
mt_bp_wth_na(mt_bl_constrained) = nan;
mt_kp_wth_na(mt_bl_constrained) = nan;

% Flatten
ar_bp_mw_wth_na = mt_bp_wth_na(:);
ar_kp_mw_wth_na = mt_kp_wth_na(:);
ar_bp_mw = ar_bp_mw_wth_na(~isnan(ar_bp_mw_wth_na));
ar_kp_mw = ar_kp_mw_wth_na(~isnan(ar_kp_mw_wth_na));

6.2.3.2 Graphing

figure('PaperPosition', [0 0 7 4]);
hold on;

chart = plot(mt_bp_wth_na, mt_kp_wth_na, 'blue');

clr = jet(numel(chart));
for m = 1:numel(chart)
   set(chart(m),'Color',clr(m,:))
end
if (length(ar_w) <= 50) 
    scatter(ar_bp_mw, ar_kp_mw, 5, 'filled');
end
xline(0);
yline(0);

title('Choice Grids Conditional on kp+bp=w')
ylabel('Capital Choice')
xlabel({'Borrowing or Saving'})
legend2plot = fliplr([1 round(numel(chart)/3) round((2*numel(chart))/4)  numel(chart)]);
legendCell = cellstr(num2str(ar_w', 'kp+bp=%3.2f'));
legend(chart(legend2plot), legendCell(legend2plot), 'Location','northeast');

grid on;

6.3 Graph Functions

6.3.1 Matlab Graph One Variable Function

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6.3.1.1 fplot a Function of X

Given a cubic (polynomial) function, graph it using the fplot function, between some values along the domain of the function. This function is defined everywhere along the real-line. Note that fplot automatically resizes the y-scale to show the full plot clearly.

% close all
figure();
hold on;

% Define a function
syms x
f_x = -7*x^(3);

% Set bounds on the domain
fl_x_lower = -2;
fl_x_higher = 2;

% Graph
fplot(f_x, [fl_x_lower, fl_x_higher])

% Add x-axis and y-axis
xline(0);
yline(0);

% Title and y and y-able
title(['Plot function: ' char(f_x)],'Interpreter',"none");
ylabel('f(x)');
xlabel('x');

% Add grids
grid on;
grid minor;

Plot a rational function, that is a function of polynomials.

% close all
figure();
hold on;

% Define a function
syms x
f_x = (x)/(x^2 + 1);

% Set bounds on the domain
fl_x_lower = -2;
fl_x_higher = 2;

% Graph
fplot(f_x, [fl_x_lower, fl_x_higher])

% Add x-axis and y-axis
xline(0);
yline(0);

% Title and y and y-able
title(['Plot function: ' char(f_x)],'Interpreter',"none");
ylabel('f(x)');
xlabel('x');

% Add grids
grid on;
grid minor;

Plot a function that is not defined at all points along the real line. Note also that the function always returns a positive value. Note the fplot function automatically identifies the part of the x-axis where the function is not defined, and draws dashed lines to demarcate.

% close all
figure();
hold on;

% Define a function
syms x
f_x = 5*(x^5 - 6*x^2 + 3*x)^(2/3);

% Set bounds on the domain
fl_x_lower = -1;
fl_x_higher = 2;

% Graph
fplot(f_x, [fl_x_lower, fl_x_higher])

% Add x-axis and y-axis
xline(0);
yline(0);

% Title and y and y-able
title(['Plot function: ' char(f_x)],'Interpreter',"none");
ylabel('f(x)');
xlabel('x');

% Add grids
grid on;
grid minor;

6.3.1.2 Plot Indifference Curve and Budget Constraint

Indifference curve and two budget lines. From two period consumption and savings problem.

% close all
figure();
hold on;

% Define parameters
e1 = 1.5;
e2 = 1.9;
r = 0.05;

u_star = 1.5;
beta = 0.9;

% Define a function
% x = c1, f_x = c2
syms x
f_x_indiff = exp((u_star - log(x))/beta);

% Formula for optimal choice that minimize expenditure
c2_star_exp_min = exp((u_star + log(beta*(1+r)))/(1+beta));
c1_star_exp_min = (1/(beta*(1+r)))*c2_star_exp_min;
f_optimal_cost = c1_star_exp_min*(1+r)+c2_star_exp_min;

% budget equation
% x = c1, f_x = y
f_x_budget = (e1*(1+r) + e2) + (-1)*(1+r)*x;
f_x_budget_optimal_cost = f_optimal_cost + (-1)*(1+r)*x;

% Set bounds on the domain
fl_x_lower = 0;
fl_x_higher = 6;

% Graph
hold on;
fplot(f_x_indiff, [fl_x_lower, fl_x_higher])
fplot(f_x_budget, [fl_x_lower, fl_x_higher])
fplot(f_x_budget_optimal_cost, [fl_x_lower, fl_x_higher])

% plot a one point scatter plot
scatter(c1_star_exp_min, c2_star_exp_min, 300, 'filled');

% Add x-axis and y-axis
xline(0);
yline(0);

% Title and y and y-able
title(['Plot function: ' char(f_x_indiff)],'Interpreter',"none");
ylabel('c2');
xlabel('c1');

% this sets x and y visual boundaries
ylim([0,6]);
xlim([0,6]);
% Add grids
grid on;
grid minor;

6.4 Write and Read Plots

6.4.1 Matlab Graph Generate EPS postscript figures in matlab

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6.4.1.1 Properly Save EPS with Scatter and Other Graphing Methods: Renderer = Painters

scatter plot saving as eps seems to only work when Renderer is set to Painters

fl_fig_wdt = 3;
fl_fig_hgt = 2.65;

figure('PaperPosition', [0 0 fl_fig_wdt fl_fig_hgt], 'Renderer', 'Painters');
x = rand([10,1]);
y = rand([10,1]);
scatter(x, y, 'filled');
grid on;
grid minor;

st_img_path = 'C:/Users/fan/M4Econ/graph/export/_img/';
st_file_name = 'fs_eps_scatter_test';

% eps figure save with tiff preview
print(strcat(st_img_path, st_file_name), '-depsc', '-tiff');