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<div>Walter/Dennis</div>
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<div>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.</div>
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<div>Anyway, it does like like you have a singular (non-invertible) matrix.</div>
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<div>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.</div>
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<div>Will</div>
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<span style="font-weight:bold">From: </span>Walter Hannah <<a href="mailto:whannah@atmos.colostate.edu">whannah@atmos.colostate.edu</a>><br>
<span style="font-weight:bold">Date: </span>Tuesday, 11 November 2014 10:25 AM<br>
<span style="font-weight:bold">To: </span>Will Hobbs <<a href="mailto:will.hobbs@utas.edu.au">will.hobbs@utas.edu.au</a>>, Dennis Shea <<a href="mailto:shea@ucar.edu">shea@ucar.edu</a>><br>
<span style="font-weight:bold">Cc: </span>"<a href="mailto:ncl-talk@ucar.edu">ncl-talk@ucar.edu</a>" <<a href="mailto:ncl-talk@ucar.edu">ncl-talk@ucar.edu</a>><br>
<span style="font-weight:bold">Subject: </span>Re: [ncl-talk] inverse_matrix problem<br>
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<div bgcolor="#FFFFFF" text="#000000">Will,<br>
<br>
I tried your suggestion, but all I got back was missing values.<br>
<br>
After Dennis's suggestion, I tried replacing the zeros with tiny random numbers, using this code:<br>
<blockquote><tt>R = random_normal( 0.,1e-12, (/nlev*2,nlev*2/))</tt><tt><br>
</tt><tt>M = where(M.eq.0,R,M)</tt><tt><br>
</tt><tt>iM = inverse_matrix(M)</tt><br>
</blockquote>
Interestingly, this worked perfectly, and I got what I expected.<br>
I also tried using this approach to trying Will's suggestion, and that also worked with the random numbers!<br>
<br>
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.<br>
<br>
Thanks,<br>
Walter<br>
<br>
<div class="moz-cite-prefix">On 11/10/14 6:17 PM, Will Hobbs wrote:<br>
</div>
<blockquote cite="mid:D0879173.90CA%25will.hobbs@utas.edu.au" type="cite">
<div>Walter</div>
<div><br>
</div>
<div>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.</div>
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<div>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.</div>
<div><a moz-do-not-send="true" href="https://www.ncl.ucar.edu/Document/Functions/Built-in/solve_linsys.shtml">https://www.ncl.ucar.edu/Document/Functions/Built-in/solve_linsys.shtml</a></div>
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<div>This might help you figure out if the matrix itself is the problem (I suspect, as Dennis has suggested, that may be the issue).</div>
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<div>Will</div>
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<span style="font-weight:bold">From: </span>Walter Hannah <<a moz-do-not-send="true" href="mailto:whannah@atmos.colostate.edu">whannah@atmos.colostate.edu</a>><br>
<span style="font-weight:bold">Date: </span>Tuesday, 11 November 2014 9:52 AM<br>
<span style="font-weight:bold">To: </span>Dennis Shea <<a moz-do-not-send="true" href="mailto:shea@ucar.edu">shea@ucar.edu</a>><br>
<span style="font-weight:bold">Cc: </span>"<a moz-do-not-send="true" href="mailto:ncl-talk@ucar.edu">ncl-talk@ucar.edu</a>" <<a moz-do-not-send="true" href="mailto:ncl-talk@ucar.edu">ncl-talk@ucar.edu</a>><br>
<span style="font-weight:bold">Subject: </span>Re: [ncl-talk] inverse_matrix problem<br>
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<div bgcolor="#FFFFFF" text="#000000">Dennis,<br>
<br>
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.<br>
<br>
Walter<br>
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<div class="moz-cite-prefix">On 11/10/14 5:50 PM, Dennis Shea wrote:<br>
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<blockquote cite="mid:CAOF1d_7VTz2TU8BRDMqZFrD4r=w0_E+gbnXHWbUC2YNvQuA3hQ@mail.gmail.com" type="cite">
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<div>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.<br>
<br>
===<br>
</div>
TEST1: duplicates your findings<br>
<br>
</div>
TEST 2: create a bogus 20x20 array of random numbers. No row consists of all constants. Identity matrix is successfully calculated.<br>
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</div>
TEST 3: wherever the original array had a row of all 0.0, substitute random numbers. The identity matrix is successfully calculated.</div>
<div class="gmail_extra"><br>
<div class="gmail_quote">On Mon, Nov 10, 2014 at 1:57 PM, Walter Hannah <span dir="ltr">
<<a moz-do-not-send="true" href="mailto:whannah@atmos.colostate.edu" target="_blank">whannah@atmos.colostate.edu</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000">Hi,<br>
<br>
I'm trying to use the "inverse_matrix" function. The matrix doesn't have any missing values, but I still get this error message:<br>
<blockquote><tt>Variable: M</tt><tt><br>
</tt><tt>Type: float</tt><tt><br>
</tt><tt>Total Size: 1600 bytes</tt><tt><br>
</tt><tt> 400 values</tt><tt><br>
</tt><tt>Number of Dimensions: 2</tt><tt><br>
</tt><tt>Dimensions and sizes: [pertlev | 20] x [tendlev | 20]</tt><tt><br>
</tt><tt>Coordinates:</tt><tt><br>
</tt><tt> pertlev: [50..1950]</tt><tt><br>
</tt><tt> tendlev: [50..1950]</tt><tt><br>
</tt><tt>Number Of Attributes: 2</tt><tt><br>
</tt><tt> missing_value : 9.96921e+36</tt><tt><br>
</tt><tt> _FillValue : 9.96921e+36</tt><tt><br>
</tt><tt>(0) ----------------------------------------------------------------------------</tt><tt><br>
</tt><tt><br>
</tt><tt> 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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
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<br>
<br>
(0) ----------------------------------------------------------------------------<br>
(0) # missing values: 0<br>
(0) # values = 0.0 : 111</tt><tt><br>
</tt><tt>warning:inverse_matrix: info = 1; missing values not allowed</tt><br>
</blockquote>
<br>
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:<br>
<blockquote><tt>...<br>
(0) ----------------------------------------------------------------------------</tt><tt><br>
</tt><tt>(0) # missing values: 0</tt><tt><br>
</tt><tt>(0) # values = 0.0 : 0</tt><tt><br>
</tt><tt>warning:inverse_matrix: info = 20; missing values not allowed</tt><br>
</blockquote>
<br>
<br>
Thanks,<br>
Walter </div>
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