[ncl-talk] Need a solution for calculate Determinant of a (rather) large matrix

[Lam Hoang]

Please find the attachment for my "x" matrix
I run determinant(x) and still waiting for the result after 2mins

On Tue, Jul 10, 2018 at 9:13 PM, Lam Hoang <lamhpvn at gmail.com> wrote:

> Dear Dennis,
> uname -a gives:
>
> Darwin MACBooks-MBP 16.7.0 Darwin Kernel Version 16.7.0: Thu Jan 11
> 22:59:40 PST 2018; root:xnu-3789.73.8~1/RELEASE_X86_64 x86_64
>
> and gcc --version gives:
>
>
> Configured with: --prefix=/Applications/Xcode.app/Contents/Developer/usr
> --with-gxx-include-dir=/usr/include/c++/4.2.1
>
> Apple LLVM version 8.1.0 (clang-802.0.42)
>
> Target: x86_64-apple-darwin16.7.0
>
> Thread model: posix
>
> InstalledDir: /Applications/Xcode.app/Contents/Developer/Toolchains/
> XcodeDefault.xctoolchain/usr/bin
>
>
> anything looks suspicious?
> Regards,
>
>
> On Tue, Jul 10, 2018 at 8:59 PM, Dennis Shea <shea at ucar.edu> wrote:
>
>> Normally, NCL would use an LAPACK code to compute a mathematical
>> quantity. However, LAPACK contains no such subroutine due to issues with
>> accuracy and stability:
>>
>>        http://www.netlib.org/lapack/faq.html#_are_there_routines_in
>> _lapack_to_compute_determinants
>>
>> Really, 'they' (applied mathematicians) do not want people calculating
>> the determinant.
>> ===
>>
>> NCL uses a computer program from:
>>
>>     An Introduction to  Computational Physics, Tao Pang (Cambridge
>> University Press,1997).
>> ===
>>
>> The use of integer or float values as input should have no effect. All
>> non-double input is promoted to double prior to input to the fortran code
>> used to perform the calculations.
>>
>> I have no idea why you are encountering extremely long execution times.
>> My 6.3.0 [MAC] returns a result more or less immediately. What version of
>> gcc do you have installed? Please send the output from the following:
>>
>> %> uname -a
>>
>> %> gcc --version
>>
>> ====
>> That said:  I have tried to calculate the determinant with N=41
>>
>>    N = 41
>>    x = random_uniform(0,5,(/N,N/))
>>    d = determinant(x)                          ; VERY fast;
>> instantaneous return value
>>    print(d)
>>
>> Variable: d
>> Type: float
>> Total Size: 4 bytes
>>             1 values
>> Number of Dimensions: 1
>> Dimensions and sizes:   [1]
>> Coordinates:
>> (0)
>>
>> *1.767279e+31       <====  ????  I have no idea what the correct answer
>> is*
>> Ummm, rather large number!!!
>>
>> ====
>> I will open a JIRA trouble ticket and ask the core NCL developers if
>> everything looks good.
>>
>> ====
>> Again, echoing LAPACK, calculating a determinant has issues.
>>
>> Regards
>>
>> On Tue, Jul 10, 2018 at 6:34 AM, Lam Hoang <lamhpvn at gmail.com> wrote:
>>
>>> Dear all,
>>> I want to calculate determinant of a 41x41 real (float) matrix. I used
>>> determinant() function
>>> https://www.ncl.ucar.edu/Document/Functions/Built-in/determinant.shtml
>>>
>>> However it is very slow.
>>>
>>> I try to run the sample in the above page, it's quick. Even if I replace
>>> integer values by float values (i.e replace 1 by 1.0, 0 by 0.0 and so on)
>>> I try to create a 4x4 real matrix, give all members a value of 1.0
>>> It seems that the determinant() function runs forever and does not
>>> return any value
>>>
>>> In the following illustration, a is sample matrix after replacing
>>> integer by float values. It takes NCL few seconds to return the value d = 30
>>>
>>> x is new 4x4 matrix created by my new() function, it never gives me any
>>> result.
>>>
>>> *Variable: a*
>>>
>>> *Type: float*
>>>
>>> *Total Size: 64 bytes*
>>>
>>> *            16 values*
>>>
>>> *Number of Dimensions: 2*
>>>
>>> *Dimensions and sizes: [4] x [4]*
>>>
>>> *Coordinates: *
>>>
>>> *(0) d = 30*
>>>
>>>
>>> *Variable: x*
>>>
>>> *Type: float*
>>>
>>> *Total Size: 64 bytes*
>>>
>>> *            16 values*
>>>
>>> *Number of Dimensions: 2*
>>>
>>> *Dimensions and sizes: [4] x [4]*
>>>
>>> *Coordinates: *
>>>
>>>
>>>
>>> Any suggestion or solution for this?
>>>
>>> Regards,
>>>
>>>
>>> p/s: I am using NCL v6.3.0
>>>
>>> --
>>> Lam Hoang, PhD
>>> Chief of Climate Prediction Division,
>>> Viet Nam National Center of Hydro-Meteorology Forecasting
>>> National Hydro-Meteorological Services of Vietnam
>>> 8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam
>>> <https://maps.google.com/?q=8+Phao+Dai+Lang+street,+Lang+Thuong,+Dong+Da,+Ha+Noi,+Vietnam&entry=gmail&source=g>
>>> Mob: +84 9 682 34 682
>>>
>>> Associate Researcher,
>>> School of Earth, Atmosphere and Environment
>>> Monash University, VIC 3800
>>> Email: lam.hoang at monash.edu
>>>
>>> _______________________________________________
>>> ncl-talk mailing list
>>> ncl-talk at ucar.edu
>>> List instructions, subscriber options, unsubscribe:
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>>>
>>>
>>
>
>
> --
> Lam Hoang, PhD
> Chief of Climate Prediction Division,
> Viet Nam National Center of Hydro-Meteorology Forecasting
> National Hydro-Meteorological Services of Vietnam
> 8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam
> Mob: +84 9 682 34 682
>
> Associate Researcher,
> School of Earth, Atmosphere and Environment
> Monash University, VIC 3800
> Email: lam.hoang at monash.edu
>



-- 
Lam Hoang, PhD
Chief of Climate Prediction Division,
Viet Nam National Center of Hydro-Meteorology Forecasting
National Hydro-Meteorological Services of Vietnam
8 Phao Dai Lang street, Lang Thuong, Dong Da, Ha Noi, Vietnam
Mob: +84 9 682 34 682

Associate Researcher,
School of Earth, Atmosphere and Environment
Monash University, VIC 3800
Email: lam.hoang at monash.edu
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