# Copyright (c) 2009-2016, Jack Poulson
# All rights reserved.
#
# This file is part of Elemental and is under the BSD 2-Clause License,
# which can be found in the LICENSE file in the root directory, or at
# http://opensource.org/licenses/BSD-2-Clause
#
import math, El
n = 100 # matrix size
realRes = imagRes = 100 # grid resolution
# Display an instance of the Fox-Li/Landau matrix
A = El.DistMatrix(El.zTag)
El.FoxLi(A,n)
El.Display(A,"Fox-Li/Landau matrix")
# Display its spectral portrait
portrait, box = El.SpectralPortrait(A,realRes,imagRes)
El.DisplayPortrait(portrait,box,"spectral portrait of Fox-Li/Landau matrix")
# Display its singular values
s = El.SingularValues(A)
El.EntrywiseMap(s,math.log10)
El.Display(s,"log10(svd(A))")
# Require the user to press a button before the figures are closed
worldSize = El.mpi.WorldSize()
El.Finalize()
if worldSize == 1:
raw_input('Press Enter to exit')
# Copyright (c) 2009-2015, Jack Poulson
# All rights reserved.
#
# This file is part of Elemental and is under the BSD 2-Clause License,
# which can be found in the LICENSE file in the root directory, or at
# http://opensource.org/licenses/BSD-2-Clause
#
import El
n = 200 # matrix size
realRes = imagRes = 100 # grid resolution
# Display an instance of the Fourier matrix
A = El.DistMatrix(El.zTag)
El.Fourier(A, n)
El.Display(A, "Fourier matrix")
# Display a submatrix and subvector of the Fourier matrix
El.Display(A[(n / 4):(3 * n / 4), (n / 4):(3 * n / 4)], "Middle submatrix")
El.Display(A[1, 0:n], "Second row")
# Display the spectral portrait
portrait, box = El.SpectralPortrait(A, realRes, imagRes)
El.DisplayPortrait(portrait, box, "spectral portrait of Fourier matrix")
# Require the user to press a button before the figures are closed
commSize = El.mpi.Size(El.mpi.COMM_WORLD())
El.Finalize()
if commSize == 1:
raw_input('Press Enter to exit')
#
# This file is part of Elemental and is under the BSD 2-Clause License,
# which can be found in the LICENSE file in the root directory, or at
# http://opensource.org/licenses/BSD-2-Clause
#
import El, time, math
n=100
realRes = imagRes = 50 # grid resolution
A = El.DistMatrix()
El.JordanCholesky( A, n )
El.Display( A, "A" )
El.Cholesky( El.UPPER, A )
El.MakeTrapezoidal( El.UPPER, A )
El.Display( A, "U" )
portrait = El.SpectralWindow(A,0,6,4,realRes,imagRes)
box = El.SpectralBox_d()
box.center = El.TagToType(El.Complexify(A.tag))(0)
box.realWidth = 6
box.imagWidth = 4
El.DisplayPortrait(portrait,box,"spectral portrait of 2*J_{1/2}(n)")
# Require the user to press a button before the figures are closed
worldSize = El.mpi.WorldSize()
El.Finalize()
if worldSize == 1:
raw_input('Press Enter to exit')
#
# This file is part of Elemental and is under the BSD 2-Clause License,
# which can be found in the LICENSE file in the root directory, or at
# http://opensource.org/licenses/BSD-2-Clause
#
import math, El
n = 100 # matrix size
realRes = imagRes = 100 # grid resolution
# Display an instance of the pathological example
A = El.DistMatrix()
El.GEPPGrowth(A,n)
El.Display(A,"GEPP growth matrix")
# Display the spectral portrait
portrait, box = El.SpectralPortrait(A,realRes,imagRes)
El.DisplayPortrait(portrait,box,"spectral portrait of GEPP growth matrix")
# Display the relevant pieces of pivoted LU factorization
p = El.LU(A)
El.Display(p,"LU permutation")
El.EntrywiseMap(A,lambda x:math.log10(max(abs(x),1)))
El.Display(A,"Logarithmically-scaled LU factors")
El.Display(A[0:n,n-1],"Last column of logarithmic U")
# Require the user to press a button before the figures are closed
worldSize = El.mpi.WorldSize()
El.Finalize()
if worldSize == 1:
raw_input('Press Enter to exit')
El.RealPart(A, AReal)
El.Display(AReal, 'Real part of Fox-Li matrix (n={})'.format(n))
# Compute the Schur decomposition (overwriting A with the Schur factor)
schurStart = time.time()
w = El.Schur(A)
schurStop = time.time()
if A.Grid().Rank() is 0:
print('Schur decomp for n={}: {} [sec]'.format(
n,
schurStop - schurStart,
))
# Compute the spectral portrait of the Schur factor
portraitStart = time.time()
portrait, box = El.TriangularSpectralPortrait(A, realRes, imagRes)
portraitStop = time.time()
if A.Grid().Rank() is 0:
print('Portrait for n={}: {} [sec]'.format(
n,
portraitStop - portraitStart,
))
# Display the eigenvalues on top of log10 plot of portrait
El.DisplayPortrait(portrait,
box,
title='Fox-Li portrait (n={})'.format(n),
eigvals=w)
El.Finalize()
