[ncl-talk] inverse_matrix problem
Will Hobbs
Will.Hobbs at utas.edu.au
Mon Nov 10 16:38:08 MST 2014
Walter/Dennis
I just had another look at your post, and the inverse_matrix() documentation. It looks like inverse_matrix() gives the same error codes as solve_linsys(), and you'd actually reported them. Sorry for leading you up the garden path.
Anyway, it does like like you have a singular (non-invertible) matrix.
If you have a dig through some of the linear algebra literature there are a number of ways that you can alter a matrix, but that's definitely beyond the remit of ncl-talk.
Will
From: Walter Hannah <whannah at atmos.colostate.edu<mailto:whannah at atmos.colostate.edu>>
Date: Tuesday, 11 November 2014 10:25 AM
To: Will Hobbs <will.hobbs at utas.edu.au<mailto:will.hobbs at utas.edu.au>>, Dennis Shea <shea at ucar.edu<mailto:shea at ucar.edu>>
Cc: "ncl-talk at ucar.edu<mailto:ncl-talk at ucar.edu>" <ncl-talk at ucar.edu<mailto:ncl-talk at ucar.edu>>
Subject: Re: [ncl-talk] inverse_matrix problem
Will,
I tried your suggestion, but all I got back was missing values.
After Dennis's suggestion, I tried replacing the zeros with tiny random numbers, using this code:
R = random_normal( 0.,1e-12, (/nlev*2,nlev*2/))
M = where(M.eq.0,R,M)
iM = inverse_matrix(M)
Interestingly, this worked perfectly, and I got what I expected.
I also tried using this approach to trying Will's suggestion, and that also worked with the random numbers!
I can't figure out a mathematical explanation, but this seems like a pretty nice fix. Might be good to add this to the online documentation.
Thanks,
Walter
On 11/10/14 6:17 PM, Will Hobbs wrote:
Walter
Instead of using the inverse matrix() function, try using solve_linsys(A, B) instead, for A = your matrix and B = I (the identity matrix). Since A * inv(A) = I, the output will be the inverse.
Mathematically this is no different to inverse_matrix(), but the code is a little different. In particular, if the matrix is singular (i.e. the determinant = 0, and it cannot be inverted) then it will return an error code.
https://www.ncl.ucar.edu/Document/Functions/Built-in/solve_linsys.shtml
This might help you figure out if the matrix itself is the problem (I suspect, as Dennis has suggested, that may be the issue).
Will
From: Walter Hannah <whannah at atmos.colostate.edu<mailto:whannah at atmos.colostate.edu>>
Date: Tuesday, 11 November 2014 9:52 AM
To: Dennis Shea <shea at ucar.edu<mailto:shea at ucar.edu>>
Cc: "ncl-talk at ucar.edu<mailto:ncl-talk at ucar.edu>" <ncl-talk at ucar.edu<mailto:ncl-talk at ucar.edu>>
Subject: Re: [ncl-talk] inverse_matrix problem
Dennis,
Wow! Thanks for going above and beyond! This helps a lot. I'll try to look for a way to get a modified matrix that doesn't have all those zeros.
Walter
On 11/10/14 5:50 PM, Dennis Shea wrote:
You have rows of 0.0 ... I think that is causing issues. I'm sure some 'math-whiz' could answer but I attached a simple test code that reads your data (thx for providing). It calculates the inverse and the identity matrix. Note that NCL is using a direct call to the documented LAPACK routines.
===
TEST1: duplicates your findings
TEST 2: create a bogus 20x20 array of random numbers. No row consists of all constants. Identity matrix is successfully calculated.
TEST 3: wherever the original array had a row of all 0.0, substitute random numbers. The identity matrix is successfully calculated.
On Mon, Nov 10, 2014 at 1:57 PM, Walter Hannah <whannah at atmos.colostate.edu<mailto:whannah at atmos.colostate.edu>> wrote:
Hi,
I'm trying to use the "inverse_matrix" function. The matrix doesn't have any missing values, but I still get this error message:
Variable: M
Type: float
Total Size: 1600 bytes
400 values
Number of Dimensions: 2
Dimensions and sizes: [pertlev | 20] x [tendlev | 20]
Coordinates:
pertlev: [50..1950]
tendlev: [50..1950]
Number Of Attributes: 2
missing_value : 9.96921e+36
_FillValue : 9.96921e+36
(0) ----------------------------------------------------------------------------
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -0.31 -0.06 0.15 -0.27 -0.56 -1.21 -1.38 -1.36 1.49 0.00 0.00 4.65 0.37 0.46 0.47 0.52 0.55 0.77 2.49
0.00 0.26 -0.35 -0.29 -0.65 -1.13 -2.24 -2.45 -2.47 2.91 0.00 0.00 4.07 2.45 0.95 0.87 0.90 1.05 1.55 4.81
0.00 -0.11 1.43 -0.91 -1.69 -1.52 -2.63 -2.81 -2.69 3.17 0.00 0.00 -2.35 2.61 1.49 1.01 1.00 1.18 1.78 5.32
0.00 -0.02 0.55 1.08 -1.74 -2.04 -2.59 -2.71 -2.39 2.63 0.00 0.00 -0.75 -1.10 1.35 1.02 0.89 1.00 1.57 4.87
0.00 -0.06 0.16 0.52 0.72 -1.86 -2.88 -2.74 -2.29 2.31 0.00 0.00 0.31 -1.30 -0.26 0.87 0.75 0.82 1.27 4.50
0.00 -0.13 -0.07 0.20 0.54 0.27 -2.74 -3.10 -2.27 2.04 0.00 0.00 0.08 -0.49 -0.47 0.14 0.72 0.69 1.13 4.24
0.00 -0.15 -0.06 0.20 -0.17 0.02 -0.77 -3.87 -3.13 2.39 0.00 0.00 0.69 -0.08 0.09 0.03 0.36 0.90 1.29 4.59
0.00 -0.14 0.05 0.09 -0.17 -0.29 -0.14 -0.66 -5.36 2.00 0.00 0.00 0.39 0.17 0.14 0.07 -0.01 0.22 1.00 4.05
0.00 0.02 -0.07 -0.01 0.00 0.02 0.43 0.94 0.77 -2.90 0.00 0.00 -0.09 0.09 -0.04 -0.07 -0.17 -0.26 -0.49 0.54
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 -0.01 -0.04 0.12 -0.02 -0.01 -0.03 -0.05 -0.05 0.04 0.00 0.00 -2.17 -0.25 -0.14 0.01 0.02 0.02 0.02 0.12
0.00 0.00 -0.19 0.11 0.28 0.06 0.11 0.06 0.07 -0.13 0.00 0.00 2.75 -1.97 -0.04 -0.12 -0.05 -0.05 -0.08 -0.10
0.00 -0.02 -0.14 -0.08 0.31 0.21 0.13 0.08 0.06 -0.08 0.00 0.00 0.48 1.11 -1.09 -0.13 -0.10 -0.06 -0.09 -0.12
0.00 -0.01 -0.03 -0.11 -0.07 0.32 0.27 0.12 0.18 -0.17 0.00 0.00 0.02 0.63 0.52 -0.94 -0.02 -0.15 -0.08 -0.25
0.00 0.02 0.08 -0.06 -0.24 0.10 0.43 0.26 0.16 -0.17 0.00 0.00 0.07 0.31 0.35 0.40 -1.06 -0.06 -0.20 -0.26
0.00 0.06 0.03 -0.10 0.07 0.11 1.03 1.38 0.53 -1.10 0.00 0.00 -0.44 0.14 -0.03 0.08 0.19 -1.61 -0.76 -1.16
0.00 0.11 -0.03 -0.08 0.07 0.16 0.46 1.28 1.65 -1.21 0.00 0.00 -0.25 0.07 -0.06 0.00 0.14 0.41 -3.04 -0.66
0.00 0.12 -0.30 -0.15 0.80 1.58 2.86 3.62 5.02 -3.15 0.00 0.00 -1.23 -0.91 -0.80 -0.94 -0.85 -0.66 0.21 -10.64
(0) ----------------------------------------------------------------------------
(0) # missing values: 0
(0) # values = 0.0 : 111
warning:inverse_matrix: info = 1; missing values not allowed
I thought it might have something to do with those zero values, but if I replace them with non-zero values I get a similar, but not identical, result:
...
(0) ----------------------------------------------------------------------------
(0) # missing values: 0
(0) # values = 0.0 : 0
warning:inverse_matrix: info = 20; missing values not allowed
Thanks,
Walter
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