Introduction to programmingwith Matlab/Python

— Lecture 1

Brian Thorsbro

Department of Astronomyand Theoretical Physics,Lund University, Sweden.

Monday, October 30, 2017

Courses

These lectures are a mini-series companion to:

ASTM13 Dynamical Astronomy

ASTM21 Statistical tools in Astrophysics

Matlab installed in the lab (Lyra). Personal laptops are OK!Install Matlab from: http://program.ddg.lth.se/Install Python3 from: https://www.anaconda.com/download/

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Outline

Content in this lecture:

I Matlab

I Python/Spyder

I The Hertzsprung-Russell diagram(example computational task)

I Basic machine architecture

I Data representation

I Data manipulation

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Matlab

Install from: http://program.ddg.lth.se/

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Python/Spyder

Install version 3 from: https://www.anaconda.com/download/

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The HR diagram

(from http://www.astronomynotes.com)

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The task at hand

The task at hand:

I Load the Hipparcos database(about 120000 stars)

I Plot the stars in a HR diagram

But first: Machine architecture

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Basic Machine Architecture

(from http://en.wikibooks.org)

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The Hipparcos Database

The Hipparcos database:

I HIP - primary key / identifier

I l - Star longitude (deg)

I b - Star latitude (deg)

I p - Parallax (mas)

I ul - Proper motion, ’l’ direction (mas/yr)

I ub - Proper motion, ’b’ direction (mas/yr)

I ep - Standard Error in parallax (mas)

I el - Standard Error in proper motion, ’l’ direction (mas/yr)

I eb - Standard Error in proper motion, ’b’ direction (mas/yr)

I V - Visual magnitude (mag)

I col - Colour index, B-V (mag)

I mult - Stellar multiplicity, i.e. binaries etc.

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Data representation

Computers work with on or off, i.e. bits: 1 or 0.

However, there are different conventions for how data can bestored using combinations of these ones and zeroes.

The number 10 can be represented in multiple ways:

I Integer (10): 0 0000000000000000000000000001010

I Double (1.0 · 101): 0 100000000100100000000000000000000000000000000000000000000000000

I ASCII String (”10”): 00110001 00110000

In science you normally want to work with doubles. In Matlab thisis automatic, in Python and many other programming languagesalways include at least one decimal, i.e. type 10.0 — good idea tomake this a habit.

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Advanced data structures

We like to work on big data sets with many numbers Toaccommodate that Matlab and Python lets us group up thenumbers in multidimensional arrays.

Matlab:

myMatrix = [ 17 15 ; 13 11 ];

val = myMatrix(1,2);

row = myMatrix(1,:);

col = myMatrix(:,2);

Python (with numpy library):

myMatrix = array([[17.0,15.0],[13.0,11.0]])

val = myMatrix[0,1]

row = myMatrix[0,...]

col = myMatrix[...,1]

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The database file

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File to memory

Data in the file is in text format (like ASCII string) with a spacebetween the numbers. Matlab and Python provides methods to doautomatic conversion for you.

Matlab:

data = dlmread(’hipparcos.txt’);

Python (with numpy library):

data = loadtxt(’hipparcos.txt’)

In both cases “data” is then a matrix of 116812x12 doubles(rows x columns — really cool).

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Data refinement

With data loaded we can start refining it. First extract the usefuldata from the big loaded data matrix:

Matlab:

p = data(:, 4); % (mas) Parallax.

V = data(:,10); % (mag) Visual magnitude.

col = data(:,11); % (mag) Colour index, B-V.

Python (with numpy library):

p = data[..., 3] # (mas) Parallax.

V = data[..., 9] # (mag) Visual magnitude.

col = data[...,10] # (mag) Colour index, B-V.

However, the absolute magnitude is not stored in the database. Ithas to be calculated.

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Absolute magnitude

Absolute magnitude is the magnitude a star would have were itplaced at a distance of 10 pc. Thus by definition of astronomicalmagnitudes for stars:

Mv − V = −5 · log10

(d

10pc

),

with the distance determined by using the parallax:

d =1000pc

p,

thus

Mv = V + 5 · log10

( p

100

).

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Data refinement

Even though our visual apparent magnitude and parallaxes are inarrays, the actual calculation is quite simple:

Matlab:

Mv = V + 5 * log10(p / 100);

Python (with numpy library):

Mv = V + 5 * log10(p / 100)

The resulting “Mv” variable is thus also an array with the samedimensions.

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Plotting Mv vs B-V

Python plotting is actually based on Matlab plotting.

Matlab:

figure(1);

plot(col,Mv,’k.’);

axis([-0.5 2 -5 15]);

xlabel(’B-V [mag]’);

ylabel(’M_v [mag]’);

set(gca, ’Ydir’, ’reverse’);

Python (with matplotlib.pyplot library):

figure(1)

plot(col,Mv,’k.’)

xlim(-0.5,2.0)

ylim(-5,15)

xlabel(’B-V [mag]’)

ylabel(’M_v [mag]’)

gca().invert_yaxis()

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Plotting Mv vs B-V

Only plotting stars with small parallax error (max 5% error).

Matlab:

figure(2);

plot(col(p>20*ep),Mv(p>20*ep),’k.’);

axis([-0.5 2 -5 15]);

xlabel(’B-V [mag]’);

ylabel(’M_v [mag]’);

set(gca, ’Ydir’, ’reverse’);

Python (with matplotlib.pyplot library):

figure(2)

plot(col[p>20*ep],Mv[p>20*ep],’k.’);

xlim(-0.5,2.0)

ylim(-5,15)

xlabel(’B-V [mag]’)

ylabel(’M_v [mag]’)

gca().invert_yaxis()

Note: Parallax error maps non-linearly to distance due tod = 1000/p [pc]!

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Plotting Mv vs B-V

Possible to build up selection masks.

Matlab:

hrMask = (p>20*ep) & (mult==0);

figure(3);

plot(col(hrMask),Mv(hrMask),’k.’);

axis([-0.5 2 -5 15]);

xlabel(’B-V [mag]’);

ylabel(’M_v [mag]’);

set(gca, ’Ydir’, ’reverse’);

Python (with matplotlib.pyplot library):

hrMask = (p>20*ep) & (mult==0)

figure(3)

plot(col[hrMask],Mv[hrMask],’k.’)

xlim(-0.5,2.0)

ylim(-5,15)

xlabel(’B-V [mag]’)

ylabel(’M_v [mag]’)

gca().invert_yaxis()

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The End

Questions?

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