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numerical_analysis's Introduction

๐Ÿ‘‹ Hello, Iโ€™m Parikshit, welcome to my GitHub profile!

About

  • ๐Ÿ’ผ I am a Russell Heath Distinguished Postdoctoral Research Associate at the Idaho National Laboratory.
  • ๐Ÿง‘โ€๐Ÿ’ป I develop computational tools for multiphysics simulations of nuclear reactors.

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lvanveen avatar parikshitbajpai avatar

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numerical_analysis's Issues

x-axis ticks format

The x-axis ticks are in scientific notation. Having them in plain notation, 256 instead of 2.56*10^2, makes more sense.

Error and accuracy computations for LU factorization

The error and condition number computation in lines 41-42 in main.py refers to the error in LUP factorization.

  check = np.linalg.norm(np.matmul(L,U)-np.matmul(P,A))
  condition = np.linalg.cond(A,2) 

However, for this work, it might be useful to refer to errors in the determinant.

Indexing error in relative error array

The index for storing relative error of the Cofactor method is 1. This causes the relative error of LU to be overwritten

error_rel[k,1] = error_rel_lu
error_rel[k,1] = error_rel_cof

Plot range

The previous fix for issue #7 uses exact values to specify the plot range. This can lead to errors when very large matrices are used and/or when the values go beyond the specified ranges.
plt.ylim(bottom=0.1/10000000,top=100000000)

Insufficient trials for LU factorisation

Refer to the number of trials in main.py. Lines 17 & 51:

ntrials = 7
for k in range(0,ntrials):
  n += 2

While this is sufficient for cofactor approach where the computational cost grows exponentially with size, the LU approach can work for much larger matrices and the script must be edited to reflect this.

Suggested solution (Only for LU):

ntrials = 8
for k in range(0,ntrials):
  n *= 2

Wall times plot scaling

The axes on the wall times plot have a huge range that causes the shape of plots to be indistinguishable.

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