# [ncl-talk] inverse_matrix problem

Will Hobbs Will.Hobbs at utas.edu.au
Mon Nov 10 16:17:29 MST 2014

```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.

===

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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