Introduction to 2D functions plots#

Simple plot of (well-behaved) functions in 2D#

This is a (slightly modified) example from the Matplotlib tutorials.

See https://matplotlib.org/stable/gallery/lines_bars_and_markers/simple_plot.html

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D01_Simpleplot.py, and the XML code in the file D01_Simpleplot.2D.xml.

Simpleplot

Function plots on different scales#

This is an example from the Matplotlib tutorials.

See https://matplotlib.org/stable/gallery/subplots_axes_and_figures/two_scales.html

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D02_PlotDiffScales.py, and the XML code in the file D02_PlotDiffScales.2D.xml.

picDiffScales

Stepplot#

This is an example from the Matplotlib tutorials.

See https://matplotlib.org/stable/gallery/lines_bars_and_markers/step_demo.html

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D03_Stepplot.py, and the XML code in the file D03_Stepplot.2D.xml.

Stepplot

Stemplot#

This is an example from the Matplotlib tutorials.

See https://matplotlib.org/stable/gallery/lines_bars_and_markers/stem_plot.html#sphx-glr-gallery-lines-bars-and-markers-stem-plot-py

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D04_Stemplot.py, and the XML code in the file D04_Stemplot.2D.xml.

Stemplot

Histograms and densities#

This is an example from the Matplotlib tutorials.

See https://matplotlib.org/stable/gallery/statistics/histogram_normalization.html#

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D05_HistogramsAndDensities.py, and the XML code in the file D05_HistogramsAndDensities.2D.xml.

Pdf3

Cumulative histogram and CDF#

This is an example from the Matplotlib tutorials.

# see https://matplotlib.org/stable/gallery/statistics/histogram_cumulative.html#

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D06_CumulativeHistogramAndCDF.py, and the XML code in the file D06_CumulativeHistogramAndCDF.2D.xml.

picCdf

Plots of continuous distribution functions#

Some text

Probability density function (pdf)#

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D07_DistPlotContinuous.py, and the XML code in the file D07_DistPlotContinuous.2D.xml.

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None
        target = 'pdf' # pdf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'

        Title = 'Beta distribution'
        a = [5, 10.0, 20.5]
        b = [20.5, 10.0, 5]
        xlim = [0, 0.999]
        if target=='hf': ylim=[0, 100]

        dlist = []
        ltext = []
        for j in range(len(a)):
            dlist.append(dreal.dist_beta(a[j], b[j]))
            ltext.append('a=' + str(a[j]) + ', b=' + str(b[j]))

        DistPlotContinuous(Title = Title, dlist=dlist, xlim = xlim,
            ylim = ylim, target = target, ltext = ltext, marker='o',
            markersize=0)

picBeta_distribution_pdf

Cumulative distribution function (cdf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None
        target = 'cdf' # pdf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'

        Title = 'Beta distribution'
        a = [5, 10.0, 20.5]
        b = [20.5, 10.0, 5]
        xlim = [0, 0.999]
        if target=='hf': ylim=[0, 100]

        dlist = []
        ltext = []
        for j in range(len(a)):
            dlist.append(dreal.dist_beta(a[j], b[j]))
            ltext.append('a=' + str(a[j]) + ', b=' + str(b[j]))

        DistPlotContinuous(Title = Title, dlist=dlist, xlim = xlim,
            ylim = ylim, target = target, ltext = ltext, marker='o',
            markersize=0)

picBeta_distribution_cdf

Survival function (sf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None
        target = 'sf' # pdf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'

        Title = 'Beta distribution'
        a = [5, 10.0, 20.5]
        b = [20.5, 10.0, 5]
        xlim = [0, 0.999]
        if target=='hf': ylim=[0, 100]

        dlist = []
        ltext = []
        for j in range(len(a)):
            dlist.append(dreal.dist_beta(a[j], b[j]))
            ltext.append('a=' + str(a[j]) + ', b=' + str(b[j]))

        DistPlotContinuous(Title = Title, dlist=dlist, xlim = xlim,
            ylim = ylim, target = target, ltext = ltext, marker='o',
            markersize=0)

picBeta_distribution_sf

Hazard function (hf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None
        target = 'hf' # pdf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'

        Title = 'Beta distribution'
        a = [5, 10.0, 20.5]
        b = [20.5, 10.0, 5]
        xlim = [0, 0.999]
        if target=='hf': ylim=[0, 100]

        dlist = []
        ltext = []
        for j in range(len(a)):
            dlist.append(dreal.dist_beta(a[j], b[j]))
            ltext.append('a=' + str(a[j]) + ', b=' + str(b[j]))

        DistPlotContinuous(Title = Title, dlist=dlist, xlim = xlim,
            ylim = ylim, target = target, ltext = ltext, marker='o',
            markersize=0)

picBeta_distribution_hf

Cumulative hazard function (chf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None
        target = 'chf' # pdf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'

        Title = 'Beta distribution'
        a = [5, 10.0, 20.5]
        b = [20.5, 10.0, 5]
        xlim = [0, 0.999]
        if target=='hf': ylim=[0, 100]

        dlist = []
        ltext = []
        for j in range(len(a)):
            dlist.append(dreal.dist_beta(a[j], b[j]))
            ltext.append('a=' + str(a[j]) + ', b=' + str(b[j]))

        DistPlotContinuous(Title = Title, dlist=dlist, xlim = xlim,
            ylim = ylim, target = target, ltext = ltext, marker='o',
            markersize=0)

picBeta_distribution_chf

Quantile function (qtf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None
        target = 'qtf' # pdf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'

        Title = 'Beta distribution'
        a = [5, 10.0, 20.5]
        b = [20.5, 10.0, 5]
        xlim = [0, 0.999]
        if target=='hf': ylim=[0, 100]

        dlist = []
        ltext = []
        for j in range(len(a)):
            dlist.append(dreal.dist_beta(a[j], b[j]))
            ltext.append('a=' + str(a[j]) + ', b=' + str(b[j]))

        DistPlotContinuous(Title = Title, dlist=dlist, xlim = xlim,
            ylim = ylim, target = target, ltext = ltext, marker='o',
            markersize=0)

picBeta_distribution_qtf

Inverse survival function (isf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None
        target = 'qtf' # pdf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'

        Title = 'Beta distribution'
        a = [5, 10.0, 20.5]
        b = [20.5, 10.0, 5]
        xlim = [0, 0.999]
        if target=='hf': ylim=[0, 100]

        dlist = []
        ltext = []
        for j in range(len(a)):
            dlist.append(dreal.dist_beta(a[j], b[j]))
            ltext.append('a=' + str(a[j]) + ', b=' + str(b[j]))

        DistPlotContinuous(Title = Title, dlist=dlist, xlim = xlim,
            ylim = ylim, target = target, ltext = ltext, marker='o',
            markersize=0)

picBeta_distribution_isf

Plots of discrete distribution functions#

Probability mass function (pmf)#

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D08_DistPlotDiscrete.py, and the XML code in the file D08_DistPlotDiscrete.2D.xml.

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None

        Title = 'Poisson distribution'
        target = 'pmf' # pmf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'
        mu = [1, 4, 10]
        xlim = [0.0, 20.0]
        ylim = None
        if target=='qtf': ylim=[0, 20]

        dlist = []
        ltext = []
        for j in range(len(mu)):
            dlist.append(dreal.dist_poisson(mu[j]))
            ltext.append('mu=' + str(mu[j]))
        DistPlotDiscrete(Title = Title, dlist=dlist, xlim = xlim,  ylim = ylim,
            target = target, ltext = ltext, lattice=True, marker='o',
            markersize=3, vertical_lines=True)

picPoisson_distribution_pmf

Cumulative distribution function (cdf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None

        Title = 'Poisson distribution'
        target = 'cdf' # pmf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'
        mu = [1, 4, 10]
        xlim = [0.0, 20.0]
        ylim = None
        if target=='qtf': ylim=[0, 20]

        dlist = []
        ltext = []
        for j in range(len(mu)):
            dlist.append(dreal.dist_poisson(mu[j]))
            ltext.append('mu=' + str(mu[j]))
        DistPlotDiscrete(Title = Title, dlist=dlist, xlim = xlim,  ylim = ylim,
            target = target, ltext = ltext, lattice=True, marker='o',
            markersize=3, vertical_lines=True)

picPoisson_distribution_cdf

Survival function (sf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None

        Title = 'Poisson distribution'
        target = 'sf' # pmf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'
        mu = [1, 4, 10]
        xlim = [0.0, 20.0]
        ylim = None
        if target=='qtf': ylim=[0, 20]

        dlist = []
        ltext = []
        for j in range(len(mu)):
            dlist.append(dreal.dist_poisson(mu[j]))
            ltext.append('mu=' + str(mu[j]))
        DistPlotDiscrete(Title = Title, dlist=dlist, xlim = xlim,  ylim = ylim,
            target = target, ltext = ltext, lattice=True, marker='o',
            markersize=3, vertical_lines=True)

picPoisson_distribution_sf

Hazard function (hf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None

        Title = 'Poisson distribution'
        target = 'hf' # pmf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'
        mu = [1, 4, 10]
        xlim = [0.0, 20.0]
        ylim = None
        if target=='qtf': ylim=[0, 20]

        dlist = []
        ltext = []
        for j in range(len(mu)):
            dlist.append(dreal.dist_poisson(mu[j]))
            ltext.append('mu=' + str(mu[j]))
        DistPlotDiscrete(Title = Title, dlist=dlist, xlim = xlim,  ylim = ylim,
            target = target, ltext = ltext, lattice=True, marker='o',
            markersize=3, vertical_lines=True)

picPoisson_distribution_hf

Cumulative hazard function (chf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None

        Title = 'Poisson distribution'
        target = 'chf' # pmf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'
        mu = [1, 4, 10]
        xlim = [0.0, 20.0]
        ylim = None
        if target=='qtf': ylim=[0, 20]

        dlist = []
        ltext = []
        for j in range(len(mu)):
            dlist.append(dreal.dist_poisson(mu[j]))
            ltext.append('mu=' + str(mu[j]))
        DistPlotDiscrete(Title = Title, dlist=dlist, xlim = xlim,  ylim = ylim,
            target = target, ltext = ltext, lattice=True, marker='o',
            markersize=3, vertical_lines=True)

picPoisson_distribution_chf

Quantile function (qtf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None

        Title = 'Poisson distribution'
        target = 'qtf' # pmf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'
        mu = [1, 4, 10]
        xlim = [0.0, 20.0]
        ylim = None
        if target=='qtf': ylim=[0, 20]

        dlist = []
        ltext = []
        for j in range(len(mu)):
            dlist.append(dreal.dist_poisson(mu[j]))
            ltext.append('mu=' + str(mu[j]))
        DistPlotDiscrete(Title = Title, dlist=dlist, xlim = xlim,  ylim = ylim,
            target = target, ltext = ltext, lattice=True, marker='o',
            markersize=0, vertical_lines=True)

picPoisson_distribution_qtf

Inverse survival function (isf)#

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        ylim = None

        Title = 'Poisson distribution'
        target = 'isf' # pmf, cdf, 'sf', 'hf', 'chf', 'qtf', 'isf'
        mu = [1, 4, 10]
        xlim = [0.0, 20.0]
        ylim = None
        if target=='qtf': ylim=[0, 20]

        dlist = []
        ltext = []
        for j in range(len(mu)):
            dlist.append(dreal.dist_poisson(mu[j]))
            ltext.append('mu=' + str(mu[j]))
        DistPlotDiscrete(Title = Title, dlist=dlist, xlim = xlim,  ylim = ylim,
            target = target, ltext = ltext, lattice=True, marker='o',
            markersize=0, vertical_lines=True)

picPoisson_distribution_isf

Mpmath-inspired functions plots in 2D#

The plots discussed here show some possibilities to deal with not-so-well-behaved plots, i.e plots with real input, but (domain-wise) complex output, plots with singularities, and plots which grow very rapidly. The functions which are used here have been modified from Mpmath (see https://mpmath.readthedocs.io/en/stable/plotting.html).

These plots can use both Python-only contexts like mpm as well as FixedPrec contexts like math53, however, results may differ since the FixedPrec contexts enforce strict typing, whereas the Python-only contexts do not.

Simultaneous plot of sin and cos#

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D09_FuncPlot2d.py, and the XML code in the file D09_FuncPlot2d.2D.xml.

To produce the figure as shown below, using the mpm context, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        FuncPlot2d(ctx=mpm, f=[mpm.cos, mpm.sin], xlim=[-4, 4],
            Title = 'Plot2dCosSin')

To produce the figure as shown below, using the math53 context, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        FuncPlot2d(ctx=math53, f=[ctx.cos, ctx.sin], xlim=[-4, 4],
            Title = 'Plot2dCosSin')

Plot2dCosSin

Simultaneous plots of asin and acos, for mpm and math53#

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D09_FuncPlot2d.py.

To produce the figure as shown below, using the mpm context, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        FuncPlot2d(ctx=mpm, f=[mpm.acos, mpm.asin], xlim=[-2, 2],
            Title = 'Simultaneous plot of asin an acos, using mpm')

Plot2dAcosAsin_mpm

To produce the figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        FuncPlot2d(ctx=math53, f=[ctx.acos, ctx.asin], xlim=[-2, 2],
            Title = 'Simultaneous plot of asin and acos, using math53')

Plot2dAcosAsin_math53

Plot of cotangent without singularities specified#

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D09_FuncPlot2d.py.

If we plot the cotangent without specifying the singularities, we get the results shown below:

To produce the left figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        FuncPlot2d(ctx=mpm, f=mpm.cot, xlim=[-5, 5], ylim=[-5, 5],
            Title = 'Cotangent, singularities not specified, Mpm')

To produce the right figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        FuncPlot2d(ctx=math53, f=ctx.cot, xlim=[-5, 5], ylim=[-5, 5],
            Title = 'Cotangent, singularities not specified, Math53')

Cotangent_singularities_not_specified

Plot of cotangent with singularities specified#

The Python code for the example below can be found online in the DataXlCalcNet repository or in the corresponding local DataXlCalcNet folder in the file D09_FuncPlot2d.py.

If we plot the cotangent and specify the singularities, we get the results shown below:

To produce the left figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        FuncPlot2d(ctx=mpm, f=mpm.cot, xlim=[-5, 5], ylim=[-5, 5],
            singularities=[-mpm.pi, 0, mpm.pi],
            Title = 'Cotangent, singularities specified, mpm')

To produce the right figure as shown below, the try-block at the end of the file should look like this:

try:
    if __name__ == '__main__':
        FuncPlot2d(ctx=math53, f=ctx.cot, xlim=[-5, 5], ylim=[-5, 5],
            singularities=[-ctx.pi(), 0, ctx.pi()],
            Title = 'Cotangent, singularities specified, math53')

Cotangent_singularities_specified

Introduction to 2D functions plots

Contents

Introduction to 2D functions plots#

Simple plot of (well-behaved) functions in 2D#

Function plots on different scales#

Stepplot#

Stemplot#

Histograms and densities#

Cumulative histogram and CDF#

Plots of continuous distribution functions#

Probability density function (pdf)#

Cumulative distribution function (cdf)#

Survival function (sf)#

Hazard function (hf)#

Cumulative hazard function (chf)#

Quantile function (qtf)#

Inverse survival function (isf)#

Plots of discrete distribution functions#

Probability mass function (pmf)#

Cumulative distribution function (cdf)#

Survival function (sf)#

Hazard function (hf)#

Cumulative hazard function (chf)#

Quantile function (qtf)#

Inverse survival function (isf)#

Mpmath-inspired functions plots in 2D#

Simultaneous plot of sin and cos#

Simultaneous plots of asin and acos, for mpm and math53#

Plot of cotangent without singularities specified#

Plot of cotangent with singularities specified#