这可能是电脑里的窃听器吗scipy.sparse.linalg公司.eigs在Anaconda 2.5.0环境中的功能？

import numpy as np from scipy import fftpack as fft from scipy.sparse import lil_matrix, csc_matrix from scipy.sparse.linalg import eigs, inv nz = 100 zin = np.arange(nz+1, dtype=np.float64)/nz N2 = np.full(nz, 1.) f0 = 1. beta = 0. Nx = int(1e2) Ny = int(1e2) dx = 1e-1 dy = 1e-1 vbar = np.zeros(nz+1) ubar = zin etax = np.zeros(2) etay = np.zeros(2) k = fft.fftfreq(Nx, dx)[:Nx/2] l = fft.fftfreq(Ny, dy)[:Ny/2] zc = np.hstack(0.5*(zin[1:] + zin[:-1])) dzc = np.hstack(np.diff(zc)) depth = 1. dztop = zc[0] dzbot = depth - zc[-1] zf = zin dzf = np.diff(zf) j = 0 for i in range(len(k)): L = lil_matrix((nz+1, nz+1), dtype=np.float64) G = L.copy() ################ # n = 0 (surface) ################ R = k[i] * .5*(ubar[0]+ubar[1]) + l[j] * .5*(vbar[0]+vbar[1]) D = dzf[0]**-1 S = .5 * ( k[i] * ( (ubar[0]-ubar[1])*D - N2[0]/f0 * etay[0] ) + l[j] * ( (vbar[0]-vbar[1])*D + N2[0]/f0 * etax[0] ) ) L[0, 0] = R * D - S L[0, 1] = R * (-D) - S G[0, 0] = D G[0, 1] = - D ################ # n = nz (bottom) ################ R = k[i] * .5*(ubar[nz-1]+ubar[nz]) + l[j] * .5*(vbar[nz-1]+vbar[nz]) D = dzf[nz-1]**-1 S = .5 * ( k[i] * ( (ubar[nz-1]-ubar[nz])*D - N2[nz-1]/f0 * etay[1] ) + l[j] * ( (vbar[nz-1]-vbar[nz])*D + N2[nz-1]/f0 * etax[1] ) ) L[nz, nz-1] = R * D - S L[nz, nz] = R * (-D) - S G[nz, nz-1] = D G[nz, nz] = - D ################ # 0 < n < nz (interior) ################ for n in range(1,nz): R = k[i] * ubar[n] + l[j] * vbar[n] K2 = k[i]**2 + l[j]**2 bf = f0**2 * dzc[n-1]**-1 b_1 = N2[n-1] * dzf[n-1] b = N2[n] * dzf[n] B_1 = bf * b_1**-1 B = - (bf * ( b**-1 + b_1**-1 ) + K2) Bt1 = bf * b**-1 N2Z = (N2[n]*dzf[n])**-1 N2Z_1 = (N2[n-1]*dzf[n-1])**-1 P = ( k[i] * ( beta - bf * ( ubar[n+1] * N2Z - (N2Z + N2Z_1) * ubar[n] + N2Z_1 * ubar[n-1] ) ) - l[j] * bf * ( vbar[n+1] * N2Z - (N2Z + N2Z_1) * vbar[n] + N2Z_1 * vbar[n-1] ) ) L[n, n-1] = R * B_1 L[n, n] = R * B + P L[n, n+1] = R * Bt1 G[n, n-1] = B_1 G[n, n] = B G[n, n+1] = Bt1 val, func = eigs( csc_matrix(inv(csc_matrix(G)).dot(csc_matrix(L))), k=2, which='LI', ncv=100, maxiter=1000 ) # default returns 6 eigenvectors if i == 0 and j == 0: omega = np.zeros( (len(val), len(k)), dtype=complex ) psi = np.zeros( (nz+1, len(val), len(k)), dtype=complex ) omega[:, i] = val psi[:, :, i] = func # Each column is the eigenfunction omega_imag = omega.imag.max(axis=1) p = np.argsort(omega_imag)[::-1] omega = omega[p] psi = psi[:, p] print(omega_imag[p])

# packages in environment at /home/takaya/.conda/envs/oceanmodes: # backports 1.0 py27_0 defaults backports-abc 0.4 <pip> backports.shutil-get-terminal-size 1.0.0 <pip> backports.ssl-match-hostname 3.4.0.2 <pip> backports_abc 0.4 py27_0 defaults cairo 1.12.18 6 defaults configparser 3.5.0b2 py27_1 defaults cycler 0.10.0 py27_0 defaults decorator 4.0.9 py27_0 defaults entrypoints 0.2 py27_1 defaults fontconfig 2.11.1 5 defaults freetype 2.5.5 0 defaults functools32 3.2.3.2 py27_0 defaults get_terminal_size 1.0.0 py27_0 defaults ipykernel 4.3.1 py27_0 defaults ipython 4.2.0 py27_0 defaults ipython-genutils 0.1.0 <pip> ipython_genutils 0.1.0 py27_0 defaults ipywidgets 4.1.1 py27_0 defaults jinja2 2.8 py27_0 defaults jsonschema 2.5.1 py27_0 defaults jupyter 1.0.0 py27_2 defaults jupyter-client 4.2.2 <pip> jupyter-console 4.1.1 <pip> jupyter-core 4.1.0 <pip> jupyter_client 4.2.2 py27_0 defaults jupyter_console 4.1.1 py27_0 defaults jupyter_core 4.1.0 py27_0 defaults libgcc 5.2.0 0 defaults libgfortran 3.0.0 1 defaults libpng 1.6.17 0 defaults libsodium 1.0.3 0 defaults libxml2 2.9.2 0 defaults markupsafe 0.23 py27_0 <unknown> matplotlib 1.5.1 np111py27_0 defaults mistune 0.7.2 py27_0 defaults mkl 11.3.1 0 defaults nbconvert 4.2.0 py27_0 defaults nbformat 4.0.1 py27_0 defaults notebook 4.2.0 py27_0 defaults numpy 1.11.0 py27_0 defaults openssl 1.0.2h 0 defaults path.py 8.2.1 py27_0 defaults pexpect 4.0.1 py27_0 defaults pickleshare 0.5 py27_0 defaults pip 8.1.1 py27_1 defaults pixman 0.32.6 0 defaults ptyprocess 0.5 py27_0 defaults pycairo 1.10.0 py27_0 defaults pygments 2.1.3 py27_0 defaults pyparsing 2.1.1 py27_0 defaults pyqt 4.11.4 py27_1 defaults python 2.7.11 0 defaults python-dateutil 2.5.2 py27_0 defaults pytz 2016.3 py27_0 defaults pyzmq 15.2.0 py27_0 defaults qt 4.8.7 1 defaults qtconsole 4.2.1 py27_0 defaults readline 6.2 2 <unknown> scipy 0.17.0 np111py27_3 defaults setuptools 20.7.0 py27_0 defaults simplegeneric 0.8.1 py27_0 defaults singledispatch 3.4.0.3 py27_0 defaults sip 4.16.9 py27_0 defaults six 1.10.0 py27_0 defaults sqlite 3.9.2 0 defaults ssl_match_hostname 3.4.0.2 py27_1 defaults terminado 0.5 py27_1 defaults tk 8.5.18 0 http://repo.continuum.io/pkgs/free/linux-64/tk-8.5.18-0.tar.bz2 tornado 4.3 py27_0 defaults traitlets 4.2.1 py27_0 defaults wheel 0.29.0 py27_0 defaults zeromq 4.1.3 0 defaults zlib 1.2.8 0 http://repo.continuum.io/pkgs/free/linux-64/zlib-1.2.8-0.tar.bz2

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1楼 · 发布于 2024-06-02 09:08:34

ARPACK中的起始向量（如果没有指定）是随机的。您可以尝试指定v0参数以使用固定参数。你知道吗

此外，如果计算对初始值敏感（病态），则可能在不同的运行中得到不同的结果，因为浮点舍入误差可能会受到外部因素的影响，这些因素可能会发生变化（内存对齐、BLAS中的线程等）。你知道吗

换句话说，现在确保确定性结果需要的不仅仅是编写程序并运行它——您可能需要使用额外的C/Fortran编译器选项编译所有内容（Numpy、scipy等），这些选项可以生成更严格的确定性浮点算术机码。您可能还需要在优化的线性代数库（MKL、Openblas）中控制线程等的使用。最简单的选择通常是确保计算不是病态的，这样小的扰动就不重要了——但是在ARPACK的情况下，它可能不直接在你的控制之下，除非在某种意义上，它可能以这样一种变化不重要的方式来构造你正试图做的计算（或者你自己）根本不计算特征值）。你知道吗

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