I am trying to solve the following coupled pde's in fipy. I tried the following
eq1 = (DiffusionTerm(coeff=1, var=f)-f*DiffusionTerm(coeff=1, var=phi)
+f-f**3 == 0)
eq2 = (2*DiffusionTerm(coeff=f, var=phi)+f*DiffusionTerm(coeff=1, var=phi)
== 0)
eq = eq1 & eq2
eq.solve()
but it does not like "f*DiffusionTerm(coeff=1, var=phi)" and I get the error.
"TermMultiplyError: Must multiply terms by int or float." Is there a way that I can implement a cell variable times a diffusion term?
Neither of the following will work in FiPy,
from fipy import CellVariable, DiffusionTerm, Grid1D
mesh = Grid1D(nx=10)
var = CellVariable(mesh=mesh)
# eqn = var * DiffusionTerm(coeff=1)
eqn = ImplicitSourceTerm(coeff=DiffusionTerm(coeff=1))
eqn.solve(var)
They both simply don't make sense with respect to the discretization in the finite volume method. Regardless, you can use the following identity to rewrite the term of interest
Basically, instead of using
var * DiffusionTerm(coeff=1)
you can use
DiffusionTerm(coeff=var) - var.grad.mag**2
Giving a regular diffusion term and an extra explicit source term.
Related
I am trying to find the optimal parameter of a Lasso regression:
alpha_tune = {'alpha': np.linspace(start=0.000005, stop=0.02, num=200)}
model_tuner = Lasso(fit_intercept=True)
cross_validation = RepeatedKFold(n_splits=5, n_repeats=3, random_state=1)
model = GridSearchCV(estimator=model_tuner, param_grid=alpha_tune, cv=cross_validation, scoring='neg_mean_squared_error', n_jobs=-1).fit(features_train_std, labels_train)
print(model.best_params_['alpha'])
My variables are demeaned and standardized. But I get the following error:
ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 1.279e+02, tolerance: 6.395e-01
I know this error has been reported several times, but none of the previous posts answer how to solve it. In my case, the error is generated by the fact that the lowerbound 0.000005 is very small, but this is a reasonable value as indicated by solving the tuning problem via the information criteria:
lasso_aic = LassoLarsIC(criterion='aic', fit_intercept=True, eps=1e-16, normalize=False)
lasso_aic.fit(X_train_std, y_train)
print('Lambda: {:.8f}'.format(lasso_aic.alpha_))
lasso_bic = LassoLarsIC(criterion='bic', fit_intercept=True, eps=1e-16, normalize=False)
lasso_bic.fit(X_train_std, y_train)
print('Lambda: {:.8f}'.format(lasso_bic.alpha_))
AIC and BIC give values of around 0.000008. How can this warning be solved?
Increasing the default parameter max_iter=1000 in Lasso will do the job:
alpha_tune = {'alpha': np.linspace(start=0.000005, stop=0.02, num=200)}
model_tuner = Lasso(fit_intercept=True, max_iter=5000)
cross_validation = RepeatedKFold(n_splits=5, n_repeats=3, random_state=1)
model = GridSearchCV(estimator=model_tuner, param_grid=alpha_tune, cv=cross_validation, scoring='neg_mean_squared_error', n_jobs=-1).fit(features_train_std, labels_train)
print(model.best_params_['alpha'])
I feel I must be missing something obvious, in struggling to get a positive control for logistic regression going in tensorflow probability.
I've modified the example for logistic regression here, and created a positive control features and labels data. I struggle to achieve accuracy over 60%, however this is an easy problem for a 'vanilla' Keras model (accuracy 100%). What am I missing? I tried different layers, activations, etc.. With this method of setting up the model, is posterior updating actually being performed? Do I need to specify an interceptor object? Many thanks..
### Added positive control
nSamples = 80
features1 = np.float32(np.hstack((np.reshape(np.ones(40), (40, 1)),
np.reshape(np.random.randn(nSamples), (40, 2)))))
features2 = np.float32(np.hstack((np.reshape(np.zeros(40), (40, 1)),
np.reshape(np.random.randn(nSamples), (40, 2)))))
features = np.vstack((features1, features2))
labels = np.concatenate((np.zeros(40), np.ones(40)))
featuresInt, labelsInt = build_input_pipeline(features, labels, 10)
###
#w_true, b_true, features, labels = toy_logistic_data(FLAGS.num_examples, 2)
#featuresInt, labelsInt = build_input_pipeline(features, labels, FLAGS.batch_size)
with tf.name_scope("logistic_regression", values=[featuresInt]):
layer = tfp.layers.DenseFlipout(
units=1,
activation=None,
kernel_posterior_fn=tfp.layers.default_mean_field_normal_fn(),
bias_posterior_fn=tfp.layers.default_mean_field_normal_fn())
logits = layer(featuresInt)
labels_distribution = tfd.Bernoulli(logits=logits)
neg_log_likelihood = -tf.reduce_mean(labels_distribution.log_prob(labelsInt))
kl = sum(layer.losses)
elbo_loss = neg_log_likelihood + kl
predictions = tf.cast(logits > 0, dtype=tf.int32)
accuracy, accuracy_update_op = tf.metrics.accuracy(
labels=labelsInt, predictions=predictions)
with tf.name_scope("train"):
optimizer = tf.train.AdamOptimizer(learning_rate=FLAGS.learning_rate)
train_op = optimizer.minimize(elbo_loss)
init_op = tf.group(tf.global_variables_initializer(),
tf.local_variables_initializer())
with tf.Session() as sess:
sess.run(init_op)
# Fit the model to data.
for step in range(FLAGS.max_steps):
_ = sess.run([train_op, accuracy_update_op])
if step % 100 == 0:
loss_value, accuracy_value = sess.run([elbo_loss, accuracy])
print("Step: {:>3d} Loss: {:.3f} Accuracy: {:.3f}".format(
step, loss_value, accuracy_value))
### Check with basic Keras
kerasModel = tf.keras.models.Sequential([
tf.keras.layers.Dense(1)])
optimizer = tf.train.AdamOptimizer(5e-2)
kerasModel.compile(optimizer = optimizer, loss = 'binary_crossentropy',
metrics = ['accuracy'])
kerasModel.fit(features, labels, epochs = 50) #100% accuracy
Compared to the github example, you forgot to divide by the number of examples when defining the KL divergence:
kl = sum(layer.losses) / FLAGS.num_examples
When I change this to your code, I quickly get to an accuracy of 99.9% on your toy data.
Additionaly, the output layer of your Keras model actually expects a sigmoid activation for this problem (binary classification):
kerasModel = tf.keras.models.Sequential([
tf.keras.layers.Dense(1, activation='sigmoid')])
It's a toy problem, but you will notice that the model gets to 100% accuracy faster with a sigmoid activation.
I have this table named BondData which contains the following:
Settlement Maturity Price Coupon
8/27/2016 1/12/2017 106.901 9.250
8/27/2019 1/27/2017 104.79 7.000
8/28/2016 3/30/2017 106.144 7.500
8/28/2016 4/27/2017 105.847 7.000
8/29/2016 9/4/2017 110.779 9.125
For each day in this table, I am about to perform a certain task which is to assign several values to a variable and perform necessary computations. The logic is like:
do while Settlement is the same
m_settle=current_row_settlement_value
m_maturity=current_row_maturity_value
and so on...
my_computation_here...
end
It's like I wanted to loop through my settlement dates and perform task for as long as the date is the same.
EDIT: Just to clarify my issue, I am implementing Yield Curve fitting using Nelson-Siegel and Svensson models.Here are my codes so far:
function NS_SV_Models()
load bondsdata
BondData=table(Settlement,Maturity,Price,Coupon);
BondData.Settlement = categorical(BondData.Settlement);
Settlements = categories(BondData.Settlement); % get all unique Settlement
for k = 1:numel(Settlements)
rows = BondData.Settlement==Settlements(k);
Bonds.Settle = Settlements(k); % current_row_settlement_value
Bonds.Maturity = BondData.Maturity(rows); % current_row_maturity_value
Bonds.Prices=BondData.Price(rows);
Bonds.Coupon=BondData.Coupon(rows);
Settle = Bonds.Settle;
Maturity = Bonds.Maturity;
CleanPrice = Bonds.Prices;
CouponRate = Bonds.Coupon;
Instruments = [Settle Maturity CleanPrice CouponRate];
Yield = bndyield(CleanPrice,CouponRate,Settle,Maturity);
NSModel = IRFunctionCurve.fitNelsonSiegel('Zero',Settlements(k),Instruments);
SVModel = IRFunctionCurve.fitSvensson('Zero',Settlements(k),Instruments);
NSModel.Parameters
SVModel.Parameters
end
end
Again, my main objective is to get each model's parameters (beta0, beta1, beta2, etc.) on a per day basis. I am getting an error in Instruments = [Settle Maturity CleanPrice CouponRate]; because Settle contains only one record (8/27/2016), it's suppose to have two since there are two rows for this date. Also, I noticed that Maturity, CleanPrice and CouponRate contains all records. They should only contain respective data for each day.
Hope I made my issue clearer now. By the way, I am using MATLAB R2015a.
Use categorical array. Here is your function (without its' headline, and all rows I can't run are commented):
BondData = table(datetime(Settlement),datetime(Maturity),Price,Coupon,...
'VariableNames',{'Settlement','Maturity','Price','Coupon'});
BondData.Settlement = categorical(BondData.Settlement);
Settlements = categories(BondData.Settlement); % get all unique Settlement
for k = 1:numel(Settlements)
rows = BondData.Settlement==Settlements(k);
Settle = BondData.Settlement(rows); % current_row_settlement_value
Mature = BondData.Maturity(rows); % current_row_maturity_value
CleanPrice = BondData.Price(rows);
CouponRate = BondData.Coupon(rows);
Instruments = [datenum(char(Settle)) datenum(char(Mature))...
CleanPrice CouponRate];
% Yield = bndyield(CleanPrice,CouponRate,Settle,Mature);
%
% NSModel = IRFunctionCurve.fitNelsonSiegel('Zero',Settlements(k),Instruments);
% SVModel = IRFunctionCurve.fitSvensson('Zero',Settlements(k),Instruments);
%
% NSModel.Parameters
% SVModel.Parameters
end
Keep in mind the following:
You cannot concat different types of variables as you try to do in: Instruments = [Settle Maturity CleanPrice CouponRate];
There is no need in the structure Bond, you don't use it (e.g. Settle = Bonds.Settle;).
Use the relevant functions to convert between a datetime object and string or numbers. For instance, in the code above: datenum(char(Settle)). I don't know what kind of input you need to pass to the following functions.
I'm trying to follow a document that has some code on text mining clustering analysis.
I'm fairly new to R and the concept of text mining/clustering so please bear with me if i sound illiterate.
I create a simple matrix called dtm and then run kmeans to produce 3 clusters. The code im having issues is where a function has been defined to get "five most common words of the documents in the cluster"
dtm0.75 = as.matrix(dt0.75)
dim(dtm0.75)
kmeans.result = kmeans(dtm0.75, 3)
perClusterCounts = function(df, clusters, n)
{
v = sort(colSums(df[clusters == n, ]),
decreasing = TRUE)
d = data.frame(word = names(v), freq = v)
d[1:5, ]
}
perClusterCounts(dtm0.75, kmeans.result$cluster, 1)
Upon running this code i get the following error:
Error in colSums(df[clusters == n, ]) :
'x' must be an array of at least two dimensions
Could someone help me fix this please?
Thank you.
I can't reproduce your error, it works fine for me. Update your question with a reproducible example and you might get a more useful answer. Perhaps your input data object is empty, what do you get with dim(dtm0.75)?
Here it is working fine on the data that comes with the tm package:
library(tm)
data(crude)
dt0.75 <- DocumentTermMatrix(crude)
dtm0.75 = as.matrix(dt0.75)
dim(dtm0.75)
kmeans.result = kmeans(dtm0.75, 3)
perClusterCounts = function(df, clusters, n)
{
v = sort(colSums(df[clusters == n, ]),
decreasing = TRUE)
d = data.frame(word = names(v), freq = v)
d[1:5, ]
}
perClusterCounts(dtm0.75, kmeans.result$cluster, 1)
word freq
the the 69
and and 25
for for 12
government government 11
oil oil 10
This is my source code and I want to reduce the possible errors. When running this code there is a lot of difference between trained output to target. I have tried different ways but didn't work so please help me reducing it.
a=[31 9333 2000;31 9500 1500;31 9700 2300;31 9700 2320;31 9120 2230;31 9830 2420;31 9300 2900;31 9400 2500]'
g=[35000;23000;3443;2343;1244;9483;4638;4739]'
h=[31 9333 2000]'
inputs =(a);
targets =[g];
% Create a Fitting Network
hiddenLayerSize = 1;
net = fitnet(hiddenLayerSize);
% Choose Input and Output Pre/Post-Processing Functions
% For a list of all processing functions type: help nnprocess
net.inputs{1}.processFcns = {'removeconstantrows','mapminmax'};
net.outputs{2}.processFcns = {'removeconstantrows','mapminmax'};
% Setup Division of Data for Training, Validation, Testing
% For a list of all data division functions type: help nndivide
net.divideFcn = 'dividerand'; % Divide data randomly
net.divideMode = 'sample'; % Divide up every sample
net.divideParam.trainRatio = 70/100;
net.divideParam.valRatio = 15/100;
net.divideParam.testRatio = 15/100;
% For help on training function 'trainlm' type: help trainlm
% For a list of all training functions type: help nntrain
net.trainFcn = 'trainlm'; % Levenberg-Marquardt
% Choose a Performance Function
% For a list of all performance functions type: help nnperformance
net.performFcn = 'mse'; % Mean squared error
% Choose Plot Functions
% For a list of all plot functions type: help nnplot
net.plotFcns = {'plotperform','plottrainstate','ploterrhist', ...
'plotregression','plotconfusion' 'plotfit','plotroc'};
% Train the Network
[net,tr] = train(net,inputs,targets);
plottrainstate(tr)
% Test the Network
outputs = net(inputs)
errors = gsubtract(targets,outputs)
fprintf('errors = %4.3f\t',errors);
performance = perform(net,targets,outputs);
% Recalculate Training, Validation and Test Performance
trainTargets = targets .* tr.trainMask{1};
valTargets = targets .* tr.valMask{1};
testTargets = targets .* tr.testMask{1};
trainPerformance = perform(net,trainTargets,outputs);
valPerformance = perform(net,valTargets,outputs);
testPerformance = perform(net,testTargets,outputs);
% View the Network
view(net);
sc=sim(net,h)
I think you need to be more specific.
What is the performance like on your training set and on your test set?
Have you tried doing any regularization?