def eigenv_calccomb(self, matrix_hessian, jobid, verbose):
'''Calculates eigenvectors and eigenvalues of a matrix.'''
if verbose == True:
print 'calculating eigenvalues and eigenvectors of the '+str(len(matrix_hessian))+'x'+str(len(matrix_hessian))+' Hessian matrix'
import LinearAlgebra
## diagonalize hessian matrix
eigen_tuple = LinearAlgebra.Heigenvectors(matrix_hessian)
## parse eigenvalues and eigenvectors
eigenvalues = list(eigen_tuple[0])
eigenvectors = list(eigen_tuple[1])
## organize eigenvalues and eigenvectors in list
eigen_list = zip(eigenvalues, eigenvectors)
## sort list
eigen_list.sort()
## parse sorted eigenvalues and eigenvectors
eigenvalues = [eigen_list[eigen][0] for eigen in range(len(eigen_list))]
eigenvectors = [eigen_list[eigen][1] for eigen in range(len(eigen_list))]
if verbose == True:
lines = ['rows=modes, cols=coordinates\n']
for mode in range(6,len(eigenvectors)):
lines += [str(eigenvectors[mode])+'\n']
fd = open('%s_eigenvectors.txt' %(jobid),'w')
fd.writelines(lines)
fd.close()
import math, Numeric
## calculate length of mode 7 (equals 1 when using module linearalgebra)
len7 = math.sqrt(sum(Numeric.array(eigenvectors[6])*Numeric.array(eigenvectors[6])))
## ## loop over modes
## for i in range(7,len(eigenvalues)-1):
##
## ## calculate length of mode i
## leni = math.sqrt(sum(Numeric.array(eigenvectors[i])*Numeric.array(eigenvectors[i])))
##
## ## scale length of mode i relative to length of mode 7
## lenfactor = (len7/leni)/(eigenvalues[i]/eigenvalues[6])
## for j in range(len(eigenvectors[i])):
## eigenvectors[i][j] *= lenfactor
## copy lists of eigenvectors to eigenvectors_combined
eigenvectors_combined = []
for mode in range(len(eigenvalues)):
eigenvectors_combined.append(list(eigenvectors[mode]))
## change mode i to be the sum of modes 7 to i
for mode in range(7,len(eigenvalues)):
for coordinate in range(len(eigenvalues)):
eigenvectors_combined[mode][coordinate] += eigenvectors_combined[mode-1][coordinate]
## print 'calculated eigenvalues and eigenvectors of the '+str(len(matrix_hessian))+'x'+str(len(matrix_hessian))+' Hessian matrix'
return eigenvectors, eigenvalues, eigenvectors_combined
def diagonalization(matrix):
import LinearAlgebra
eigen_tuple = LinearAlgebra.Heigenvectors(matrix)
## parse eigenvalues and eigenvectors
eigenvalues = list(eigen_tuple[0])
eigenvectors = list(eigen_tuple[1])
## organize eigenvalues and eigenvectors in list
eigen_list = zip(eigenvalues, eigenvectors)
## sort list
eigen_list.sort()
## parse sorted eigenvalues and eigenvectors
eigenvalues = [eigen_list[eigen][0] for eigen in range(len(eigen_list))]
eigenvectors = [eigen_list[eigen][1] for eigen in range(len(eigen_list))]
return eigenvalues, eigenvectors
def calculate_eigenvectors(matrix_hessian):
import LinearAlgebra
## diagonalize hessian matrix
eigen_tuple = LinearAlgebra.Heigenvectors(matrix_hessian)
## parse eigenvalues and eigenvectors
eigenvalues = list(eigen_tuple[0])
eigenvectors = list(eigen_tuple[1])
## organize eigenvalues and eigenvectors in list
eigen_list = zip(eigenvalues, eigenvectors)
## sort list
eigen_list.sort()
## parse sorted eigenvalues and eigenvectors
eigenvalues = [eigen_list[eigen][0] for eigen in range(len(eigen_list))]
eigenvectors = [eigen_list[eigen][1] for eigen in range(len(eigen_list))]
return eigenvectors
row_sub] = value #upper super off-diagonal; yixj, zixj, ziyj
matrix_hessian[
3 * col_sup + row_sub, 3 * row_sup +
col_sub] = value #lower super off-diagonal; xjyi, xjzi, yjzi
matrix_hessian[
3 * row_sup + col_sub, 3 * row_sup +
row_sub] -= value ##super diagonal; yixi, zixi, ziyi
matrix_hessian[
3 * col_sup + row_sub, 3 * col_sup +
col_sub] -= value ##super diagonal; yjxj, zjxj, zjyj
##
## calculate eigenvectors
##
## diagonalize hessian matrix
eigen_tuple = LinearAlgebra.Heigenvectors(matrix_hessian)
## parse eigenvalues and eigenvectors
eigenvalues = list(eigen_tuple[0])
eigenvectors = list(eigen_tuple[1])
## organize eigenvalues and eigenvectors in list
eigen_list = zip(eigenvalues, eigenvectors)
## sort list
eigen_list.sort()
## parse sorted eigenvalues and eigenvectors
eigenvalues = [eigen_list[eigen][0] for eigen in range(len(eigen_list))]
eigenvectors = [eigen_list[eigen][1] for eigen in range(len(eigen_list))]
print eigenvalues
for i in range(6, 9):
print eigenvectors[i]
print matrix_hessian
