I am struggling to understand the behaviour of dsolve for this simple ODE:
Y''(t) = b*Y'(t) + f(t)
For some reason, dsolve throws an error if I use f(t)=exp(t-a), but for general f(t) or f(t)=exp(a*t) or if I put a value for a, dsolve succeeds. The complete error message:
File "~/.local/lib/python3.7/site-packages/sympy/solvers/ode.py",
line 679, in dsolve
return _helper_simplify(eq, hint, hints, simplify, ics=ics)
File "~/.local/lib/python3.7/site-packages/sympy/solvers/ode.py",
line 704, in _helper_simplify
sols = solvefunc(eq, func, order, match)
File "~/.local/lib/python3.7/site-packages/sympy/solvers/ode.py",
line 5674, in ode_nth_linear_constant_coeff_undetermined_coefficients
return _solve_undetermined_coefficients(eq, func, order, match)
File "~/.local/lib/python3.7/site-packages/sympy/solvers/ode.py",
line 5766, in _solve_undetermined_coefficients
coeffsdict[s[x]] += s['coeff']
KeyError: exp(t)
I am using this code:
from sympy import symbols, Function, dsolve, exp, Eq
a, b, t = symbols('a b t')
Y = Function('Y')(t)
#f = Function('f')(t) # works
#f = exp(a*t) # works
f = exp(t-a) # KeyError: exp(t)
#f = exp(t-2) # works
odeY = Eq( Y.diff(t,t), b*Y.diff(t) + f )
dsolve(odeY,Y)
I am using sympy version 1.5.1 with python3.7
Many thanks!
Related
I have my function:
function [result] = my_func(x,y)
result = y^2*(1-3*x)-3*y;
endfunction
Also, my vector with Ts, my function address and my initial variable x_0
load file_with_ts
# Add my limits as I also want to calculate those
# (all values in file_with_ts are within those limits.)
t_points = [-1, file_with_ts, 2]
myfunc = str2func("my_func")
x_0 = 0.9142
I am trying to execute the following line:
lsode_d1 = lsode(myfunc, x_0, t_points)
And expecting a result, but getting the following error:
INTDY-- T (=R1) ILLEGAL
In above message, R1 = 0.7987082301475D+00
T NOT IN INTERVAL TCUR - HU (= R1) TO TCUR (=R2)
In above, R1 = 0.8091168896311D+00 R2 = 0.8280400838323D+00
LSODE-- TROUBLE FROM INTDY. ITASK = I1, TOUT = R1
In above message, I1 = 1
In above message, R1 = 0.7987082301475D+00
error: lsode: invalid input detected (see printed message)
error: called from
main at line 20 column 10
Also, the variable sizes are:
x_0 -> 1x1
t_points -> 1x153
myfunc -> 1x1
I tried transposing the t_points vector
using #my_func instead of the str2func function
I tried adding multiple variables as the starting point (instead of x_0 I entered [x_0; x_1])
Tried changing my function header from my_func(x, y) to my_func(y, x)
Read the documentation and confirmed that my_func allows x to be a vector and returns a vector (whenever x is a vector).
EDIT: T points is the following 1x153 matrix (with -1 and 2 added to the beggining and the end respectively):
-4.9451e-01
-4.9139e-01
-4.7649e-01
-4.8026e-01
-4.6177e-01
-4.5412e-01
-4.4789e-01
-4.2746e-01
-4.1859e-01
-4.0983e-01
-4.0667e-01
-3.8436e-01
-3.7825e-01
-3.7150e-01
-3.5989e-01
-3.5131e-01
-3.4875e-01
-3.3143e-01
-3.2416e-01
-3.1490e-01
-3.0578e-01
-2.9267e-01
-2.9001e-01
-2.6518e-01
-2.5740e-01
-2.5010e-01
-2.4017e-01
-2.3399e-01
-2.1491e-01
-2.1067e-01
-2.0357e-01
-1.8324e-01
-1.8112e-01
-1.7295e-01
-1.6147e-01
-1.5424e-01
-1.4560e-01
-1.1737e-01
-1.1172e-01
-1.0846e-01
-1.0629e-01
-9.4327e-02
-8.0883e-02
-6.6043e-02
-6.6660e-02
-6.1649e-02
-4.7245e-02
-2.8332e-02
-1.8043e-02
-7.7416e-03
-6.5142e-04
1.0918e-02
1.7619e-02
3.4310e-02
3.3192e-02
5.2275e-02
5.5756e-02
6.8326e-02
8.2764e-02
9.5195e-02
9.4412e-02
1.1630e-01
1.2330e-01
1.2966e-01
1.3902e-01
1.4891e-01
1.5848e-01
1.7012e-01
1.8026e-01
1.9413e-01
2.0763e-01
2.1233e-01
2.1895e-01
2.3313e-01
2.4092e-01
2.4485e-01
2.6475e-01
2.7154e-01
2.8068e-01
2.9258e-01
3.0131e-01
3.0529e-01
3.1919e-01
3.2927e-01
3.3734e-01
3.5841e-01
3.5562e-01
3.6758e-01
3.7644e-01
3.8413e-01
3.9904e-01
4.0863e-01
4.2765e-01
4.2875e-01
4.3468e-01
4.5802e-01
4.6617e-01
4.6885e-01
4.7247e-01
4.8778e-01
4.9922e-01
5.1138e-01
5.1869e-01
5.3222e-01
5.4196e-01
5.4375e-01
5.5526e-01
5.6629e-01
5.7746e-01
5.8840e-01
6.0006e-01
5.9485e-01
6.1771e-01
6.3621e-01
6.3467e-01
6.5467e-01
6.6175e-01
6.6985e-01
6.8091e-01
6.8217e-01
6.9958e-01
7.1802e-01
7.2049e-01
7.3021e-01
7.3633e-01
7.4985e-01
7.6116e-01
7.7213e-01
7.7814e-01
7.8882e-01
8.1012e-01
7.9871e-01
8.3115e-01
8.3169e-01
8.4500e-01
8.4168e-01
8.5705e-01
8.6861e-01
8.8211e-01
8.8165e-01
9.0236e-01
9.0394e-01
9.2033e-01
9.3326e-01
9.4164e-01
9.5541e-01
9.6503e-01
9.6675e-01
9.8129e-01
9.8528e-01
9.9339e-01
Credits to Lutz Lehmann and PierU.
The problem lied in the array t_points not being a monotonous array. Adding a sort(t_points) before doing any calculations fixed the error.
I am having a weird "ValueError: mean must be 1 dimensional" when I am trying to build a Hierarchical GL-LVM model. Basically I'm trying to reproduce this paper: Hierarchical Gaussian Process Latent Variable Models using GPflow.
Therefore I implemented my own new model as follow:
class myGPLVM(gpflow.models.BayesianModel):
def __init__(self, data, latent_data, x_data_mean, kernel):
super().__init__()
print("GPLVM")
self.kernel0 = kernel[0]
self.kernel1 = kernel[1]
self.mean_function = Zero()
self.likelihood0 = gpflow.likelihoods.Gaussian(1.0)
self.likelihood1 = gpflow.likelihoods.Gaussian(1.0)
# make some parameters
self.data = (gpflow.Parameter(x_data_mean), gpflow.Parameter(latent_data), data)
def hierarchy_ll(self):
x, h, y = self.data
K = self.kernel0(x)
num_data = x.shape[0]
k_diag = tf.linalg.diag_part(K)
s_diag = tf.fill([num_data], self.likelihood0.variance)
ks = tf.linalg.set_diag(K, k_diag + s_diag)
L = tf.linalg.cholesky(ks)
m = self.mean_function(x)
return multivariate_normal(h, m, L)
def log_likelihood(self):
"""
Computes the log likelihood.
.. math::
\log p(Y | \theta).
"""
x, h, y = self.data
K = self.kernel1(h)
num_data = h.shape[0]
k_diag = tf.linalg.diag_part(K)
s_diag = tf.fill([num_data], self.likelihood1.variance)
ks = tf.linalg.set_diag(K, k_diag + s_diag)
L = tf.linalg.cholesky(ks)
m = self.mean_function(h)
# [R,] log-likelihoods for each independent dimension of Y
log_prob = multivariate_normal(y, m, L). # <- trows the error!
log_prob_h = self.hierarchy_ll()
log_likelihood = tf.reduce_sum(log_prob) + tf.reduce_sum(log_prob_h)
return log_likelihood
The model seems to work with a toy example:
from sklearn.datasets.samples_generator import make_blobs
X, y = make_blobs(n_samples=40, centers=3, n_features=12, random_state=2)
Y = tf.convert_to_tensor(X, dtype=default_float())
but fails and trough me the error when I am trying with a bvh file (the one from the paper actually). I also used Lawrence's code to read my bvh from mocap which I modified to fit python3
Anyway, it's been few a days and I am out of ideas. I tried multiple way to force my mean array "m" to be of one dimensional but nothing worked. I also tried with the "three_phase_oil_flow" dataset from the first GPLVM paper which works as well.
Therefore, I would assume that my model is correct, or at least I got some optimisation going on, and would think that perhaps the bvh reader could be the cause. But the data seems all fine to me... Especially I don't understand why when forcing multivariate function like:
m = np.zeros((np.shape(m)[0], 1))
log_prob = multivariate_normal(y, m, L)
or even with the gpflow Zero function
m = Zero(h)
log_prob = multivariate_normal(y, m, L)
it still trows me the error. Any help will be highly appreciated.
edited thanks to: Artem Artemev
The rest of the code if anyone wants to try to reproduce:
https://github.com/michaelStettler/h-GPLVM
error flow:
(venv) MacBookMichael2:stackOverflow michaelstettler$ python3 HGPLVM.py
(199, 96)
shape Y (199, 3, 38)
2020-01-26 17:00:48.104029: I tensorflow/core/platform/cpu_feature_guard.cc:142] Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX2 FMA
2020-01-26 17:00:48.113609: I tensorflow/compiler/xla/service/service.cc:168] XLA service 0x7f8dd5ff5410 executing computations on platform Host. Devices:
2020-01-26 17:00:48.113627: I tensorflow/compiler/xla/service/service.cc:175] StreamExecutor device (0): Host, Default Version
shape Y (199, 38)
Number of points: 199 and Number of dimensions: 38
shape x_mean_latent (199, 8)
shape x_mean_init (199, 2)
HGPLVM
gpr_data (199, 2) (199, 8) (199, 38)
2020-01-26 17:00:48.139003: W tensorflow/python/util/util.cc:299] Sets are not currently considered sequences, but this may change in the future, so consider avoiding using them.
shape m (199, 1)
Traceback (most recent call last):
File "HGPLVM.py", line 131, in <module>
_ = opt.minimize(closure, method="bfgs", variables=model.trainable_variables, options=dict(maxiter=maxiter))
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/gpflow/optimizers/scipy.py", line 60, in minimize
**scipy_kwargs)
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/scipy/optimize/_minimize.py", line 594, in minimize
return _minimize_bfgs(fun, x0, args, jac, callback, **options)
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/scipy/optimize/optimize.py", line 998, in _minimize_bfgs
gfk = myfprime(x0)
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/scipy/optimize/optimize.py", line 327, in function_wrapper
return function(*(wrapper_args + args))
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/scipy/optimize/optimize.py", line 73, in derivative
self(x, *args)
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/scipy/optimize/optimize.py", line 65, in __call__
fg = self.fun(x, *args)
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/gpflow/optimizers/scipy.py", line 72, in _eval
loss, grads = _compute_loss_and_gradients(closure, variables)
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/gpflow/optimizers/scipy.py", line 116, in _compute_loss_and_gradients
loss = loss_cb()
File "HGPLVM.py", line 127, in closure
return - model.log_marginal_likelihood()
File "/Users/michaelstettler/PycharmProjects/GPflow/venv/lib/python3.6/site-packages/gpflow/models/model.py", line 45, in log_marginal_likelihood
return self.log_likelihood(*args, **kwargs) + self.log_prior()
File "HGPLVM.py", line 62, in log_likelihood
log_prob = multivariate_normal(y, m, L)
File "mtrand.pyx", line 3729, in numpy.random.mtrand.RandomState.multivariate_normal
ValueError: mean must be 1 dimensional
I would recommend posting a working MWE code. I have tried to use your code snippets, but it gives me errors.
I don't have issues with multivariate_normal function. If you have localised the issue correctly you can debug TF2.0 more thoroughly and find the place that causes that exception. Here is the code which I'm running:
In [2]: from sklearn.datasets.samples_generator import make_blobs
...: X, y = make_blobs(n_samples=40, centers=3, n_features=12, random_state=2)
In [10]: m = np.zeros((np.shape(y)[0], 1))
In [11]: m.shape
Out[11]: (40, 1)
In [12]: y.shape
Out[12]: (40,)
In [13]: L = np.eye(m.shape[0])
In [15]: gpflow.logdensities.multivariate_normal(y, m, L)
Out[15]:
<tf.Tensor: shape=(40,), dtype=float64, numpy=
array([ -56.75754133, ...])>
I am writing this F90 program to compute a function in fortran which takes the input from a .mat file and save the results in another .mat file.
I followed this answer to get the code compiled and correctly linked. This is my makefile command:
gfortran -g -fcheck=all binhkorn_mat.F90 -I/usr/local/MATLAB/R2015b/extern/include/ -L/usr/local/MATLAB/R2015b/bin/glnxa64 -cpp -o binhkorn_mat -lmat -lmx -Wl,-rpath /usr/local/MATLAB/R2015b/bin/glnxa64/
The output file is apparently correctly compiled, but then once I run the program the following SF appears (I'm working on LINUX Ubuntu 14.04 LTS):
Program received signal SIGSEGV: Segmentation fault - invalid memory reference.
Backtrace for this error:
#0 0x7FD650063F27
#1 0x7FD6500644F4
#2 0x7FD64FCBCD3F
#3 0x7FD64FDD7AF6
#4 0x400A3F in binhkorn_mat at binhkorn_mat.F90:17 (discriminator 2)
./binhkorn_mat: Segmentation fault
I can't figure out if there's an error with the compiler or if I did something wrong with the pointers/functions definitions. Here's the code (binhkorn_mat.F90):
#include "fintrf.h"
PROGRAM binhkorn_mat
IMPLICIT NONE
mwPointer matOpen, matGetVariable, matPutVariable
mwPointer mpin, mpX, mpout, mpcf
INTEGER :: i,j
REAL*8, DIMENSION(2) :: x
REAL*8, DIMENSION(4) :: cf
!input/output through .mat f
mpin = matOpen('X.mat', 'u')
mpX = matGetVariable(mpin, 'X')
CALL mxCopyPtrToReal8(mpX, x, 2)
CALL matClose(mpin)
!fitness functions
cf(1) = ((x(1)-2)**2 + (x(2)-1)**2 + 2)
cf(2) = (9*x(1) + (x(2)-1)**2)
!constraints
cf(3) = x(1)*x(1) + x(2)*x(2) - 225
cf(4) = x(1) - 3*x(2) + 10
!output file created
CALL mxCopyReal8ToPtr(cf, mpcf, 4)
mpout = matOpen('cf.mat', 'w')
mpcf = matPutVariable(mpout, 'cf', mpcf)
CALL matClose(mpout)
END PROGRAM
The X.mat file is correctly created by an external Matlab script and contains a variable named X which is a 2-element row vector.
I basically misunderstood how to use of many functions. The pointers i supplied as input to some of them were not the correct ones. I post here the working solution:
#include "fintrf.h"
PROGRAM binhkorn_mat
IMPLICIT NONE
mwPointer matOpen, matGetVariable!, matPutVariable
mwPointer mxGetData, mxGetNumberOfElements, mxCreateNumericArray
mwPointer mpin, mpX, mpout, mpcf
mwSize ndim
mwSize dims(2)
INTEGER :: s
INTEGER*4 mxClassIDFromClassName
CHARACTER (LEN = 6) :: classname
REAL*8, DIMENSION(2) :: x
REAL*8, DIMENSION(4) :: cf
!input/output through .mat f
mpin = matOpen('X.mat', 'r')
mpX = matGetVariable(mpin, 'X')
CALL mxCopyPtrToReal8(mxGetData(mpX), x, mxGetNumberOfElements(mpX))
!CALL matClose(mpin)
!fitness functions
cf(1) = ((x(1)-2)**2 + (x(2)-1)**2 + 2)
cf(2) = (9*x(1) + (x(2)-1)**2)
!constraints
cf(3) = x(1)*x(1) + x(2)*x(2) - 225
cf(4) = x(1) - 3*x(2) + 10
!output .mat file created and filled
s = size(cf)
ndim = 2
classname = 'double'
dims(1) = 1
dims(2) = s
mpcf = mxCreateNumericArray(ndim, dims, mxClassIDFromClassName(classname), 0)
CALL mxCopyReal8ToPtr(cf, mxGetData(mpcf), mxGetNumberOfElements(mpcf))
mpout = matOpen('cf.mat', 'w')
CALL matPutVariable(mpout, 'cf', mpcf)
!CALL matClose(mpout)
END PROGRAM
I wrote the following function:
function [output_signal] = AddDirectivityError (bat_loc_index, butter_deg_vector, sound_matrix)
global chirp_initial_freq ;
global chirp_end_freq;
global sampling_rate;
global num_of_mics;
global sound_signal_length;
for (i=1 : num_of_mics)
normalized_co_freq = (chirp_initial_freq + chirp_end_freq)/ (1.6* sampling_rate);
A=sound_matrix ( i, : ) ;
peak_signal=max(A);
B=find(abs(A)>peak_signal/100);
if (butter_deg_vector(i)==0)
butter_deg_vector(i)=2;
end
[num, den] = butter(butter_deg_vector(i), normalized_co_freq, 'low');// HERE!!!
filtered_signal=filter(num,den, A );
output_signal(i, :)=filtered_signal;
end
This functions runs many-many times without any error. However, when I reach the line: [num, den] = butter ( butter_deg_vector(i), normalized_co_freq, 'low');
And the local variables are: i=3, butter_deg_vector(i)=1, normalized_co_freq=5.625000e-001
MATLAB prompts an error says:
??? Error using ==> buttap Expected N to be integer-valued.
"Error in ==> buttap at 15 validateattributes(n,{'numeric'},{'scalar','integer','positive'},'buttap','N');
Error in ==> butter at 70 [z,p,k] = buttap(n);"
I don't understand why this problem occurs especially in this iteration. Why does this function prompt an error especially in this case?
Try to change the code line for:
[num, den] = butter (round(butter_deg_vector(i)), normalized_co_freq, 'low');
After importing this data file from Matlab with scipy.io.loadmat, things appeared to work fine until we tried to calculate the conditioning number of one of the matrixes within.
Here's the minimum amount of code that reproduces for us:
import scipy
import numpy
stuff = scipy.io.loadmat("dati-esercizio1.mat")
numpy.linalg.cond(stuff["A"])
Here's the extended stacktrace courtesy of iPython:
In [3]: numpy.linalg.cond(A)
---------------------------------------------------------------------------
LapackError Traceback (most recent call last)
/snip/<ipython-input-3-15d9ef00a605> in <module>()
----> 1 numpy.linalg.cond(A)
/snip/python2.7/site-packages/numpy/linalg/linalg.py in cond(x, p)
1409 x = asarray(x) # in case we have a matrix
1410 if p is None:
-> 1411 s = svd(x,compute_uv=False)
1412 return s[0]/s[-1]
1413 else:
/snip/python2.7/site-packages/numpy/linalg/linalg.py in svd(a, full_matrices, compute_uv)
1313 work = zeros((lwork,), t)
1314 results = lapack_routine(option, m, n, a, m, s, u, m, vt, nvt,
-> 1315 work, -1, iwork, 0)
1316 lwork = int(work[0])
1317 work = zeros((lwork,), t)
LapackError: Parameter a has non-native byte order in lapack_lite.dgesdd
All obvious ideas (like flattening and reshaping the matrix or recreating the matrix from scratch reassigning it element by element) failed. How can I want to massage the data, then, in order to make it more agreeable with numpy?
It's a bug, fixed some time ago: https://github.com/numpy/numpy/pull/235
Workaround:
np.linalg.cond(stuff['A'].newbyteorder('='))
This works for me:
In [33]: stuff = loadmat('dati-esercizio1.mat')
In [34]: a = stuff['A']
In [35]: try: np.linalg.cond(a)
....: except: print "Fail!"
Fail!
In [36]: b = np.array(a, dtype='>d')
In [37]: np.linalg.cond(b)
Out[37]: 62493201976.673141
In [38]: np.all(a == b) # Verify they hold the same data.
Out[38]: True
Apparently it's something wrong with the byte order (endianness?) of each number in the resulting ndarray and not just with the ndarray object itself.
Something like this but more elegant should do the trick:
n, m = A.shape()
B = numpy.empty_like(A)
for i in xrange(n):
for j in xrange(m):
B[i,j] = float(A[i,j])
del A
B = A
print numpy.linalg.cond(A) # 62493210091.354507
(For some reason an in-place replacement still gives that error - so there's something wrong with the byte order of the whole object, too.)