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1 Data Structures

1.1 Matrices and Arrays

  1. Array Reshape, Repeat and Expand: mlx | m | pdf | html
    • Reshape and flatten arrays.
    • m: reshape()
  2. Array Index Slicing and Subsetting to Replace and Expand: mlx | m | pdf | html
    • Index based column and row expansions.
    • Anonymous function to slice array subsets.
    • m: sub2ind() + @(it_subset_n, it_ar_n) unique(round(((0:1:(it_subset_n-1))/(it_subset_n-1)) times (it_ar_n-1)+1))
  3. Find the Maximum Value and Index in Matrix Over Columns and Overall: mlx | m | pdf | html
    • Given 2D array, find the maximum value and index for each column.
    • Find the maximum value in a 2D array's row and column indexes.
    • m: max() + ind2sub() + maxk()
  4. Array Broadcasting Examples: mlx | m | pdf | html
    • broadcast means: array + array’ + matrix = matrix.
  5. Grid States, Choices and Optimal Choices Example: mlx | m | pdf | html
    • States, choices, and find max.
  6. Accumarray Examples: mlx | m | pdf | html
    • Accumarray to sum up probabilities/values for discrete elements of arrays.
    • m: unique() + reshape() + accumarray()
  7. Matlab Miscellaneous Array and Numeric Operations: mlx | m | pdf | html
    • Divide an array into sub-segments.
    • Loop over numbers, find modulus (remainder) and quotient given divisor.
    • Check data and parameter types.
    • Compare approximately similar values.
    • m: imag() + isfloat() + iscell() + isnan() + isnumeric()

1.2 ND Dimensional Arrays

  1. All Possible Combinations of Arrays as Table or Random Subset Mesh: mlx | m | pdf | html
    • Generate a Table based on all possible combinations of several arrays.
    • Draw randomly from array, permutate arrays.
    • m: ndgrid() + cell2mat(cellfun(@(m) m(:), cl_mt_all, 'uni', 0))
  2. 3D, 4D, ND Arrays Reshape and Summarize: mlx | m | pdf | html
    • Slice 2D matrixes out of ND matrixes. The 2D matrix is contiguous, but can be intermediate dimensions.
    • Summarize a nd dimensional matrix along one or two dimensions group by various other dimensions.
    • m: permute(mn, [3,1,2,4]) + squeeze(num2cell(mn, [1,2])) + celldisp() + ndgrid()
  3. ND Array Wide to Long Reshape to Table Dataframe with Variable Values for Each Dimension: mlx | m | pdf | html
    • Given 2D policy function f(a,z), generate table/dataframe with a, z, and f(a,z) columns.
    • There is a ND Array where each dimension is a different attribute, generate 2D dataframe with columns for attribute values and ND Array values stored as a single column.
    • There might be many NaN values in the ND array, drop NaN values in the ND array for 2D dataframe. Find the non-NaN values along each index dimension.
    • m: cell() + NaN() + isnan() + ind2sub() + find()

1.3 Cells

  1. Combine Cells: mlx | m | pdf | html
    • Combine string cell arrays and string.
    • m: [{st_param}, ls_st_param_key, cl_st_param_keys]
  2. List Comprehension with Cells: mlx | m | pdf | html
    • Cell2mat, cellfun, anonymous function list comprehension over cells.
    • Find min and max of all arrays in cells.
    • Find length of all arrays in cells; find index of elements of one array in another cell array.
    • Trim and concatenate floats to single string.
    • m: cell2mat() + cellfun() + strcmp() + strtrim() + find() + cell2mat(cellfun(@(m) find(strcmp(ls_st_param_key, m)), cl_st_param_keys, ‘UniformOutput’, false)) + cellfun(@(x) strtrim(x), cellstr(st_fl_rand), 'UniformOutput', false)
  3. Permutate Cells: mlx | m | pdf | html
    • Generate all possible combinations of various arrays contained in cell array.
    • m: ndgrid() + cell2mat() + array2table() + cell2mat(cellfun(@(m) m(:), cl_mt_all, ‘uni’, 0))
  4. Nested Cells: mlx | m | pdf | html
    • Cell of cells with inner cell having multiple types.
    • m: linspace() + cell([4,1]) + clns_parm_tstar{1} = {‘fl_crra’, ‘CRRA’, linspace(1, 2, it_simu_vec_len)} + disp(clns_parm_tstar(1)) + disp(clns_parm_tstar{1}{1})

1.4 Characters and Strings

  1. Basic String Operations, DisplayDisplay, Search, Join and Split: mlx | m | pdf | html
    • Generating a string for file suffix based on date and time.
    • Print info segment of multiple numeric and string parameters, scalar and array.
    • Compose string and rounded numeric array.
    • Cut string suffix and append new suffix.
    • m: datestr(now, 'mm-dd-yyyy-HH-MM') + char() + compose() + strjoin() + contains() + matches() + str_sub = split(string, ".") + strcat(str_sub{1}, '_m.m')
  2. String Arrays Operations, Join, Find, Replace and the Alphabet: mlx | m | pdf | html
    • Generate string arrays and cell strings.
    • String array from single and double quoted strings.
    • Duplicate strings, concatenate string, and paste strings jointly with separator.
    • Find string element positions, replace substrings.
    • m: repmat() + num2str() + string() + strcat() + strjoin() + fprintf() + strcmp() + strrep() + cel2mat(cellfun(@(m) find(strcmp()))) + cellstr() + 'a':'z'
  3. Convert and Cancatenate String and Numeric Array Concatenations: mlx | m | pdf | html
    • Generate rounded string array matrix with leading zero, leading space, decimal round from numeric matrix.
    • Generate a string from a numeric array and join with positional counter.
    • Create a title string by joining rounded parameter and parameter names, with decimal formatting.
    • Concatenate multiple numeric arrays together with strings and format.
    • m: num2str() + compose() + cellstr() + strcat() + strjoin() + %.2f

1.5 Map Containers

  1. Container Map Basics: mlx | m | pdf | html
    • Numeric container map, dynamically filled container map.
    • Numeric scalar, string, matrix as values for map container.
    • String and stringed numeric arrays as keys for map container.
    • Get values for multiple keys in map.
    • m: isKey() + strjoin() + num2str() + containers.Map('KeyType', 'char', 'ValueType', 'any') + map.keys() + map.values() + values(param_map, {'share_unbanked_j', 'equi_r_j'})
  2. Container Map Display Swtich Key and Values and Subseting: mlx | m | pdf | html
    • Loop over map, display keys and values.
    • Select Container map subset by keys.
    • Generate new container map by switching the values to keys and keys to values.
    • m: strjoin() + keys(map) + values(map) + containers.Map(keys, values) + cellfun(@(x) num2str(x(:)), num_cell, 'uni', 0);
  3. Cell Override: mlx | m | pdf | html
    • Override default map with externally fed map, update existing and add new keys.
    • m: param_map_updated = [param_map_old; param_map_updates_new]

1.6 Map Structure Array

  1. Struct of Map Container for Nested Value Retrieval: mlx | m | pdf | html
    • There is a list of parameters, use several container maps to store information about parameters, and combine them in a struct.
    • Use struct to in effect make single-line nested container map calls.
    • m: struct

2 Functions and Programming

2.1 Development and Debugging

  1. Matlab Errors and Warnings: mlx | m | pdf | html
    • Turn off warning messages.
    • m: lastwarn + warning('off', st_warn_id);
  2. Matlab tic toc timeit Timers and Profiler Save to HTML, Testing to Improve Code Speed: mlx | m | pdf | html
    • timeit for testing anonymous functions, and tic toc for testing code segment speed.
    • Profile code segment and save profiling results to HTML folder in the current directory.
    • m: tic + toc + timeit + profile on + profile off + profsave(profile('info'), spn) + matlab.desktop.editor.getActiveFilename + fileparts() + fullfile()

2.2 varargin Default Parameters

  1. Use varargin as a Function Parameter: mlx | m | pdf | html
    • Default parameters allow for maintaining code testability.
    • Use varargin for functions with limited parameters.
    • m: varargin + cell2mat() + function [out_put] = func_name(varargin)
  2. Container Default Parameter with varargin and Input Type Check: mlx | m | pdf | html
    • The varargin structure could lead to excessive code lines. Container Map works well with large parameter structure.
    • Core model functions with potentially many parameters, possibly override default generation to save time.
    • m: varargin + function [out_put] = func_name(varargin) + cm_defaults = {cm_a, cm_b} + [cm_defaults{1:optional_params_len}] = varargin{:} + cm_c = [cm_a;cm_b]

2.3 Dynamic Functions

  1. Anonymous Function Examples: mlx | m | pdf | html
    • Define a wage equation where individuals working part time earn a fraction of the full time earnings.
    • m: gamrnd() + f_x = @(x) x
  2. Dynamically Generate M File: mlx | m | pdf | html
    • Get current working file file name and path.
    • Generate a m file from strings, add file to path, can call that m file.
    • m: matlab.desktop.editor.getActiveFilename + fileparts() + fullfile() + addpath() + fopen() + fprintf() + fclose()

3 Distributional Processes

3.1 Time Series

  1. Autoregressive Process AR(1): mlx | m | pdf | html
    • The Mean and standard deviation of an AR(1) process.
    • Simulate and graph an AR(1) persistent process.
    • Simulate log income process with parameters estimated from Indian income data.
    • Given a monthly persistent AR(1) process, estimate the persistence of the process when data is aggregated at the annual and quadrennial levels, persistence weakens with aggregation.
    • m: normrnd() + for it_t=1:1:length(ar_shk) + plot(ar_t, ar_y) + polyfit(x, y, 1)
    • stats: fitlm(table, 'y ~ x1 + x2')
  2. Moving Average of Neighboring Values: mlx | m | pdf | html
    • Compute moving average of surrounding values with different windows.
    • Visualize moving averages compare actual to smoothed average to fully flat moving average.
    • m: movmean()
    • MEconTools: ff_graph_grid()

3.2 Cross-sectional Data

  1. Mincer Wage Earnings Equation with Experience, Education and Gamma Shocks: mlx | m | pdf | html
    • Define a wage equation where individuals working part time earn a fraction of the full time earnings.
    • Wage at different education and experience levels.
    • Simluate wage with an array of gamma distribution shocks.
    • m: gamrnd() + f_x = @(x) x + histogram()
    • MEconTools: ff_graph_grid + ff_simu_stats

4 Simulation

4.1 Normal Distribution

  1. Compute CDF for Normal and Bivariate Normal Distributions: mlx | m | pdf | html
    • CDF for normal random variable through simulation and with NORMCDF function.
    • CDF for bivariate normal random variables through simulation and with NORMCDF function, using cholesky deomposition to model correlation from uniform random draws.
    • m: mvncdf + norminv
  2. Cholesky Decomposition Correlated Two Dimensional Normal Shock: mlx | m | pdf | html
    • Draw two correlated normal shocks using the MVNRND function.
    • Draw two correlated normal shocks from uniform random variables using Cholesky Decomposition.
    • m: mvnrnd + corrcoef + norminv
  3. Cholesky Decomposition Correlated Five Dimensional Normal Shock: mlx | m | pdf | html
    • Generate variance-covariance matrix from correlation and standard deviation.
    • Draw five correlated normal shocks using the MVNRND function.
    • Draw five correlated normal shocks from uniform random variables using Cholesky Decomposition.
    • m: mvnrnd + corrcoef + norminv + subplot

5 Estimation

5.1 Linear Estimation

  1. Estimate and Solve for Parameters in Linear System of Equation and OLS Regression: mlx | m | pdf | html
    • Fit a line through the origin with two points of data.
    • Solve/estimate an exactly identified system of linear equations.
    • m: fitlm() + fc_ols_lin = @(y, x) (x'x)^(-1)(x'y);

5.2 Nonlinear Estimation

  1. Matlab Simple Nonlinear Estimation: mlx | m | pdf | html
    • Nonlinear estimation using fminunc.
    • m: optimset() + fminunc()

6 Graphs

6.1 Figure Components

  1. Image Pick Safe Colors: mlx | m | pdf | html
    • Display safe colors.
    • m: blue = [57 106 177]./255 + fill(x, y, cl_colors{it_color})
  2. Figure Titling and Legend: mlx | m | pdf | html
    • Multi-line titles, add legend lines.
    • Add to legend, select legend to show.
    • m: title({'Cash-on-Hand' '$\alpha + \beta = \zeta$'},'Interpreter','latex') + legend([g1, g2, g3], {'near','linear','spline'}, 'Location', 'best', 'NumColumns', 1, 'FontSize', 12, 'TextColor', 'black');
  3. Graph Many Lines Legend for Subset: mlx | m | pdf | html
    • State-space plots with color spectrum: can not show all states in legend, show subset, add additional line to plot and legend.
    • m: jet() + numel() + fliplr() + jet(numel(chart)), set(chart(m), 'Color', clr(m,:))

6.2 Basic Figure Types

  1. Scatter Plot Examples: mlx | m | pdf | html
    • Scatter multiple lines different colors, shapes and sizes.
    • m: scatter(x, y, size) + Marker + MarkerEdgeColor + MarkerEdgeAlpha + MarkerFaceColor + MarkerFaceAlpha
  2. Scatter Plot Examples: mlx | m | pdf | html
    • Scatter and lines multiple lines different colors, shapes and sizes.
    • X axis, Y axis, and 45 degree line.
    • m: xline(0) + yline(0) + refline([1 0]) + plot(x,y) + HandleVisibility + Color + LineStyle + LineWidth
  3. Three variables Scatter and Lines with Color Spectrum: mlx | m | pdf | html
    • Two dimensional matrix for x and y, a third variable with color spectrum set via loop.
    • m: plot(2d, 2d) + jet + set(chart(m), 'Color', clr)

6.3 Graph Functions

  1. Matlab Plot Polynomials, Budget and Indifference Functions: mlx | m | pdf | html
    • Use fplot to plot a one variable function.
    • Plot budget constraint and indifference curve.
    • m: fplot() + xline() + yline() + title([char(f_x)],'Interpreter',"none");

6.4 Write and Read Plots

  1. Graph Generate EPS Postscript Figures: mlx | m | pdf | html
    • EPS vector graphics, avoid bitmap (jpg, png), use vector graphics.
    • m: figure('Renderer', 'Painters')

7 Tables

7.1 Basic Table Generation

  1. Table Generate Table And Fill Data Row by Row or Cell by Cell: mlx | m | pdf | html
    • Generate an empty table and fill with data row by row.
    • Replace or fill table cell value with tb.col{it_row} = rand() is faster than tb{it_row, st_col} = rand().
    • Convert a random matrix to a table with column and row names defined with arrays.
    • m: table() + array2table() + tb{it_row, st_col} = rand() + tb.col{it_row} = rand() + strcat() + addvars() + matlab.lang.makeValidName() + timeit + tic + toc
  2. Order, Sort and Rename Columns: mlx | m | pdf | html
    • Convert a matrix to table with mean and sd columns. Rearrange and rename columns.
    • m: array2table() + rng() + addvars() + movevars() + removevars() + matlab.lang.makeValidName() + tb.Properties.VariableNames + tb.Properties.RowNames
  3. Array Based Row and Column Names: mlx | m | pdf | html
    • Generate a column and row named table. Convert row names to a column as strings. Remove Row Names.
    • Generate string-keys based on column names and values for a subset of columns.
    • m: array2table() + string() + strcat('rowA=', string((1:size(mt, 1)))) + tb_test_a.Properties.VariableNames + tb_test_a.Properties.RowNames + addvars(tb, rownames, 'Before', 1) + strcat() + strjoin() + cellfun(@(x) f(x), ar_x)
  4. Select Subset of Rows and Columns: mlx | m | pdf | html
    • Conditional selection based on cell values and column and row names.
    • Select if row value matches any value from an arry of values.
    • Load a excel file and select based on column name string conditions.
    • m: tb(strcmp(tb.v1, "b"),:) + tb(tb.va==0.4,:) + readtable() + startsWith() + endsWith() + contains() + matches()

7.2 Table Joining

  1. Join Table by Keys: mlx | m | pdf | html
    • Left join larger table with smaller table with common keys.
    • m: join() + table()
  2. Stack Matlab Tables: mlx | m | pdf | html
    • Append columns to existing table. Stack tables vertically and horizontally.
    • m: array2table() + [tb_a tb_b] + [tb_a; tb_b] + tb.Properties.VariableNames + tb.Properties.RowNames
  3. Stack and Join Estimation and Simulation Results: mlx | m | pdf | html
    • Stack different tables together with varying columns via outerjoin, store with parallel parfor.
    • Stack different estiamtion results together into a common table where columns show parameter names and other strings.
    • Simulate a model, column combine simulation parameters with multi-row simulation results. Then row stack results from multiple simulations together.
    • m: array2table() + outerjoin() + addvars()
    • parallel: parfor

7.3 Summarize

  1. Table Summarize and Aggregate by Groups: mlx | m | pdf | html
    • Group table by one or several group variables, and aggregate over another numerical variable within group.
    • m: groupsummary() + table() + movevars()