Rank: 193 based on 278 downloads (last 30 days) and 23 files submitted
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Paul Godfrey

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01 Apr 2007 ccom Canonical transforms Perform control state space canonical transforms Author: Paul Godfrey canonical transform, ctrb, obsv, control 10 0
  • 1.0
1.0 | 1 rating
20 Mar 2007 pzplace.m Calculates the gain vectors required to place the Poles and Zeros of a state space linear system. Author: Paul Godfrey poles, zeros, acker, place 2 0
09 Nov 2006 Dett Computes the determinant of non-square matrices. Author: Paul Godfrey linear algebra, determinant, det, dett, matrix, qe 5 14
  • 2.5
2.5 | 3 ratings
23 Oct 2006 Simple SVD SVD computation using QR decomposition Author: Paul Godfrey svd, singular, linear algebra, values, qr 44 10
  • 3.5
3.5 | 2 ratings
23 Oct 2006 adj.m Finds the adjoint of any rectangular matrix Author: Paul Godfrey adjoint, adjugate, linear algebra, matrix, mathematics 92 7
  • 4.2
4.2 | 10 ratings
Comments and Ratings on Paul's Files View all
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10 Jan 2012 Special Functions math library Collection of Special Functions programs. Author: Paul Godfrey Scott

The package is generally excellent.
My only complaint is that the accuracy of the zeta function deterioriates rapidly for |z|>80.
For example, the script returns
0.541674252238781 - 0.348243845696725i
for the 29-th non-trivial zero, which is approximately 0.5+98.8311i.
 
If you ever have time for an upgrade it would be much appreciated!

04 Jan 2012 Special Functions math library Collection of Special Functions programs. Author: Paul Godfrey Bien

Thanks! Needed a erfz function and this works well for me. This should be in the standard MATLAB function.

04 Jan 2012 Rational Polynomial curve fitting Fits a function to a quotient of polynomials Author: Paul Godfrey John

Great job, and good examples.

A couple of modifications that could be implemented.

Let there be one input, the order of the denominator, and accept an array. Calculate rms error and return that for the array. Could either set the numerator to the denominator, or sweep the numerator from 2 to the order of the denominator.

Incorporate a lag term, including raising the exponent to a power.

In your examples, you may want to include extracting the polynomial from a psd, generating a time history from a filter on rand, and replotting the resulting psd for comparison.

28 Oct 2011 Gamma Compute a very accurate Gamma function over the entire complex plane. Author: Paul Godfrey Burrus, Jacques

Thank you!

18 Sep 2011 Special Functions math library Collection of Special Functions programs. Author: Paul Godfrey Young, David

Very helpful and useful (rating and comments based only on gamma and gammaln functions). Suggestions:

1. The code to allocate storage:

 f = 0.*z; % reserve space in advance

is not needed (indeed is wasteful), as preallocation is only useful ahead of a loop or to set up an array of a specific shape.

2. It might be worth switching to logical indexing rather than linear indexing - this would avoid the use of find() and the reshape at the end.

3. gammaln(z) returns infinities for abs(imag(z)) greater than about 226 and real(z) < 0. This is due to overflow of sin() in the reflection formula, but it is an unnecessary restriction as log(sin(z)) can be computed without overflow over a larger set of values than can sin(z). For example, we can use log(sin(x + iy)) (x and y real) is approximately equal to y + log(0.5i * exp(-1i * x)) for large positive y, and the approximation is good to machine accuracy if y > 18 or thereabouts. (For negative y the approximation is -y + log(-0.5i * exp(1i * x)).) Replacing log(sin()) by a call to a logsin() function that uses these approximations greatly extends the set of valid arguments.

Top Tags Applied by Paul
linear algebra, mathematics, complex, matrix, fourier
Files Tagged by Paul View all
Updated   File Tags Downloads
(last 30 days)
Comments Rating
20 Mar 2007 pzplace.m Calculates the gain vectors required to place the Poles and Zeros of a state space linear system. Author: Paul Godfrey poles, zeros, acker, place 2 0
09 Nov 2006 Dett Computes the determinant of non-square matrices. Author: Paul Godfrey linear algebra, determinant, det, dett, matrix, qe 5 14
  • 2.5
2.5 | 3 ratings
23 Oct 2006 Simple SVD SVD computation using QR decomposition Author: Paul Godfrey svd, singular, linear algebra, values, qr 44 10
  • 3.5
3.5 | 2 ratings
23 Oct 2006 adj.m Finds the adjoint of any rectangular matrix Author: Paul Godfrey adjoint, adjugate, linear algebra, matrix, mathematics 92 7
  • 4.2
4.2 | 10 ratings
17 Oct 2006 Symmetric matrix factoring Factors an nxn matrix into a product of n+1 symmetric matrices Author: Paul Godfrey linear algebra, symmetric factoring h..., symmetric matrices, linear 1 0

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