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compute_periodic-assembly.py
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Sat, Sep 7, 20:22

compute_periodic-assembly.py
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#!/usr/bin/env python3
"""compute_periodic-assembly.py
Create system matrix or vector for document.
Usage:
compute_periodic-assembly.py [options]
Options:
-h --help Show help.
--original-matrix Copy original matrix to clipboard.
--periodic-matrix Copy periodic matrix to clipboard.
--original-vector Copy original vector to clipboard.
--periodic-vector Copy periodic vector to clipboard.
"""
from docopt import docopt
import pyperclip
import numpy as np
import re
import copy
# ==================================================================================================
def convertVector(b):
# number of columns
N = len(b)
# remove dangling starting "+", replace empty entries by "."
body = '& '.join([re.sub(r'(\+)(.*)',r'\2',j)+' ' if len(j)>0 else '. ' for j in b])
# add line with column numbers
body = r'\hline'+'\n'+'& '.join([r'$%d$'%(i+1) for i in range(N)])+r'\\ \hline'+'\n'+body
# add header and footer
txt = '\n'+r'\resizebox{287mm}{!}{%'
txt += '\n'+r'\renewcommand{\arraystretch}{1.5}'
txt += '\n'+r'\begin{tabular}{|'+'C{31mm}'*N+r'|}'+'\n'
txt += body+r'\\ \hline'
txt += '\n'+r'\end{tabular}'
txt += '\n'+r'}'
print('Text copied to clipboard')
pyperclip.copy(txt)
return txt
# ==================================================================================================
def convertMatrix(A):
# number of columns
N = len(A[0])
# add column number, remove dangling starting "+", replace empty entries by "."
body = ['& '.join(['$%d $'%(irow+1)]+[re.sub(r'(\+)(.*)',r'\2',j)+' ' if len(j)>0 else '. ' for j in i])+r'\\' for irow,i in enumerate(A)]
body = '\n'.join(body)
# add line with column numbers
body = r'\hline'+'\n'+'&'+' & '.join([r'$%d$'%(i+1) for i in range(N)])+r'\\ \hline'+'\n'+body
# add header and footer
txt = '\n'+r'\resizebox{287mm}{!}{%'
txt += '\n'+r'\renewcommand{\arraystretch}{1.5}'
txt += '\n'+r'\begin{tabular}{|c|'+'C{31mm}'*N+r'|}'+'\n'
txt += body+r' \hline'
txt += '\n'+r'\end{tabular}'
txt += '\n'+r'}'
print('Text copied to clipboard')
pyperclip.copy(txt)
return txt
# ==================================================================================================
# connectivity
# (change to list starting from zero, for computations)
conn = np.array([
[ 1, 2, 6, 5],
[ 2, 3, 7, 6],
[ 3, 4, 8, 7],
[ 5, 6,10, 9],
[ 6, 7,11,10],
[ 7, 8,12,11],
[ 9,10,14,13],
[10,11,15,14],
[11,12,16,15],
])-1
# periodic node-pairs [independent,dependent]
# (change to list starting from zero, for computations)
periodic = np.array([
[ 1, 4],
[ 1,16],
[ 1,13],
[ 5, 8],
[ 9,12],
[ 3,15],
[ 2,14],
])-1
# color of each element
col = ['blue','cyan','green','magenta','olive','purple','red','teal','violet']
# number of DOFs
ndof = np.max(conn)+1
# --------------------------------------------------------------------------------------------------
# renumber DOFs: [ independent , dependent ]
# - original numbering
i = np.arange(ndof)
# - increase DOF-number of dependent DOFs with a sufficiently large number
i[periodic[:,1]] += ndof
# - towards new numbering: order of modified DOFs (the old order is retained within each group)
i = np.argsort(i)
# - original numbering
dof = np.arange(ndof)
# - new numbering: increasing numbers starting from zero
dof[i] = np.arange(ndof)
# - link dependent DOFs to their independent sister: dependent DOFs are assembled to independent ones
dof[periodic[:,1]] = dof[periodic[:,0]]
# - number of (in)dependent DOFs
nnd = periodic.shape[0]
nni = ndof-nnd
# --------------------------------------------------------------------------------------------------
# allocate empty "A" and "b"
A = [['' for j in range(ndof)] for i in range(ndof)]
b = [ '' for i in range(ndof)]
# regular assembly of "A" and "b":
# - loop over all elements
# - loop over all DOFs in each element
for ielem,elem in enumerate(conn):
for i,idof in enumerate(elem):
b[idof] += r'+\textcolor{%s}{$b_{%d}^{(%d)}$}'%(col[ielem],i+1,ielem+1)
for i,idof in enumerate(elem):
for j,jdof in enumerate(elem):
A[idof][jdof] += r'+\textcolor{%s}{$A_{%d%d}^{(%d)}$}'%(col[ielem],i+1,j+1,ielem+1)
# --------------------------------------------------------------------------------------------------
# allocate periodic system
Aper = [['' for j in range(nni)] for i in range(nni)]
bper = [ '' for i in range(nni)]
# regular assembly of "A" and "b":
# - loop over all elements
# - loop over all DOFs in each element
for ielem,elem in enumerate(conn):
for i,idof in enumerate(elem):
bper[dof[idof]] += r'+\textcolor{%s}{$b_{%d}^{(%d)}$}'%(col[ielem],i+1,ielem+1)
for i,idof in enumerate(elem):
for j,jdof in enumerate(elem):
Aper[dof[idof]][dof[jdof]] += r'+\textcolor{%s}{$A_{%d%d}^{(%d)}$}'%(col[ielem],i+1,j+1,ielem+1)
# ==================================================================================================
# parse command-line options/arguments
args = docopt(__doc__,version='0.0.1')
if args['--original-matrix']: convertMatrix(A)
if args['--periodic-matrix']: convertMatrix(Aper)
if args['--original-vector']: convertVector(b)
if args['--periodic-vector']: convertVector(bper)

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