1997, MATLAB 5: Object oriented (OO) programming. 2008, MATLAB R2008a: enhanced ... Blog post comments: majority in favo
Exploiting Recent Developments Research Matters in MATLAB February 25, 2009 Nick Higham Nick Higham School of Mathematics Director of Research The University of Manchester
School of Mathematics
http://www.maths.manchester.ac.uk/~higham @nhigham, nickhigham.wordpress.com 2017 Joint Mathematics Meetings, Atlanta MAA Session on Innovative and Effective Ways to Teach Linear Algebra, I 1/6
MATLAB and Me Used for research starting with 1984 “Gatlinburg” Fortran version. Used for teaching from around 1986. Still my language of choice for research and teaching. The 6-monthly release cycle has made it hard to keep up with what’s new. For a period in the 2000s there wasn’t much new as regards core math. These slides available at http://bit.ly/2je4nJI.
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MATLAB Guide 3rd Edition, 2017
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New Classes 1997, MATLAB 5: Object oriented (OO) programming. 2008, MATLAB R2008a: enhanced OO programming. Building on the new OO system in last four years: updated graphics system (R2014b), graph and digraph classes (R2015b), table data type and categorical arrays (R2013b), datastores (R2014b), tall arrays (R2016b).
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Scalar Expansion >> A = spiral(2), B = A - 1 A = 1 2 4 3 B = 0 1 3 2
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Scalar Expansion >> A = spiral(2), B = A - 1 A = 1 2 4 3 B = 0 1 3 2 Implicit expansion takes this idea further . . .
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Implicit Expansion (R2016b) >> A = ones(2), B = A + [1 5] A = 1 1 1 1 B = 2 6 2 6 >> A = ones(2) + [1 5]’ A = 2 2 6 6
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Subtracting the Mean R2016b Release Notes mention A - mean(A). >> A = [1 4; 3 2], A - mean(A) A = 1 4 3 2 ans = -1 1 1 -1 Using bsxfun (from R2007a): >> bsxfun(@minus,A,mean(A)) ans = -1 1 1 -1
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Linear Algebra Rules “Matrix plus vector” and “row vector plus column vector” are now legal operations! >> [1 2] + [3 4]’ ans = 4 5 5 6 Concerns: Students may “learn” incorrect linear algebra rules from MATLAB. Codes with bugs may run and be hard to debug.
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Maybe It’s OK? Cleve Moler first proposed it 14 years ago. MathWorks trialled it in internal development builds and in R2016a Prereleases (but not R2016a itself). NumPy had it for > 16 years, and calls it “broadcasting”. GNU Octave has had “broadcasting” since version 3.6.0 (2012). R has it.
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Reaction One blog post by me
, two at Mathworks
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Blog post comments: majority in favor; some wanted different syntax. No reports of broken code, except with try/catch. Little feedback yet from those teaching linear algebra.
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Min Manipulations Form matrix with aij = min(i, j): >> d = 1:4; A = min(d,d’) A = 1 1 1 1 1 2 2 2 1 2 3 3 1 2 3 4
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Multiplication by a Diagonal Matrix(1) >> A = ones(3); d = [1 1e-4 1e-8]; >> A.*d % A*diag(d) ans = 1.0000e+00 1.0000e-04 1.0000e-08 1.0000e+00 1.0000e-04 1.0000e-08 1.0000e+00 1.0000e-04 1.0000e-08 >> A.*d’ % diag(d)*A ans = 1.0000e+00 1.0000e+00 1.0000e-04 1.0000e-04 1.0000e-08 1.0000e-08
Nick Higham
1.0000e+00 1.0000e-04 1.0000e-08
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Multiplication by a Diagonal Matrix(2) >> A./d ans =
% A/diag(d) or A*inv(diag(d)) 1 1 1
10000 10000 10000
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100000000 100000000 100000000
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Conclusions Implicit expansion allows elegant code and brings improved efficiency without the need for calling bsxfun. No compatibility issues with existing codes. Can it cause problems in linear algebra teaching? Time will tell: no reports of it doing so yet.
Join MathWorks and SIAM to celebrate publication of MATLAB Guide 3ed: SIAM booth (#139), 11am today.
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