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Re: matrix log and exp [message #30289 is a reply to message #30276]

Wed, 17 April 2002 14:52

James Kuyper
Messages: 425
Registered: March 2000

Senior Member

Paul Van Delst wrote:

> G Karas wrote:
>
>> Hi group,
>> one quickie and possibly difficult:
>>
>> IDL does not have a matrix logarithm logm and matrix
>> exponent expm function. I was thinking of calling lapack
>> routines which do it, but have no experience with lapack
>> or FORTRAN. Anyone with any tips on this one?
>
>
> Yes. Use ALOG() and EXP().
>
> paulv

He's talking about matrix logarithm and exponent, not the
element-by-element logarithm and exponent. When you calculate
exp(matrix), it produces a new matrix, each of whos elements is exp() of
the corresponding element of the input matrix.

That's very different from the matrix exponential function of x, which
is defined only for square matrices. It uses the same Taylor series
expansion:

1 + x + x^2/2! + x^3/3! + x^4/4! ...

but interprets '1' as the identity matrix of the appropriate size, and
x^n as the matrix multiplication of x by itself n times.

For instance:

IDL> A = [[0,1],[1,0]]
IDL> print, exp(A)
1.00000 2.71828
2.71828 1.00000

Since, for matrix multiplication, A^n = A if n is odd, and
A^n=[[1,0],[0,1]] if n is even, the diagonal elements pick up the even
terms of the exponential series, and the off-diagonal terms pick up odd
terms. Those series are easily summed analytically, giving a matrix
exponential of A as:

IDL> print, [[cosh(1),sinh(1)],[sinh(1),cosh(1)]]
1.54308 1.17520
1.17520 1.54308

Which is quite a bit different from exp(A).

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[Message index]

		Re: matrix log and exp By: G Karas on Thu, 18 April 2002 06:19
		Re: matrix log and exp By: Paul Van Delst[1] on Thu, 18 April 2002 05:43
		Re: matrix log and exp By: James Kuyper on Wed, 17 April 2002 14:52
		Re: matrix log and exp By: hradilv.nospam on Wed, 17 April 2002 14:34
		Re: matrix log and exp By: Paul Van Delst[1] on Wed, 17 April 2002 12:32

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