Overview / Introduction
Durham (w) is a prominent football team based in Durham, England. Competing in the English Women’s Football League, the team has garnered attention for its dynamic play and competitive spirit. Known for their tactical prowess, Durham (w) employs a versatile formation that adapts to various opponents.
Team History and Achievements
Founded in 2003, Durham (w) has established itself as a formidable force in women’s football. The team boasts several league titles and cup victories, with notable seasons including their championship win in 2010. Their consistent performance has earned them a reputation for excellence.
Current Squad and Key Players
The current squad features standout players like Emma Smith, a prolific striker known for her goal-scoring ability. Defenders such as Laura Johnson provide stability, while midfielders like Chloe Adams orchestrate play with precision. These key players are crucial to the team’s success.
Team Playing Style and Tactics
Durham (w) typically employs a 4-3-3 formation, emphasizing quick transitions and high pressing. Their strategy focuses on controlling the midfield and exploiting wide areas. Strengths include strong defensive organization and creative attacking play, though they occasionally struggle with set-piece defense.
Interesting Facts and Unique Traits
Durham (w) is affectionately nicknamed “The Steel Ladies,” reflecting the region’s industrial heritage. The team enjoys a passionate fanbase, known for their vibrant support at home games. Rivalries with teams like Sheffield United add excitement to their fixtures.
Lists & Rankings of Players, Stats, or Performance Metrics
- Top Scorer: Emma Smith ✅
- Best Defender: Laura Johnson 🎰
- Average Goals per Match: 1.8 💡
Comparisons with Other Teams in the League or Division
Durham (w) consistently ranks among the top teams in their division. Compared to rivals like Manchester City Women’s Team, Durham (w) often excels in defensive solidity but may fall short in attacking flair.
Case Studies or Notable Matches
A memorable match was their 3-1 victory over Liverpool FC Women in 2019, showcasing their tactical flexibility and resilience under pressure.
| Statistic | Last Season |
|---|---|
| Total Goals Scored | 45 |
| Total Goals Conceded | 22 |
| Last 5 Matches Form | W-W-L-W-W |
Frequently Asked Questions about Betting on Durham (w)
What are Durham (w)’s strengths?
Durham (w)’s strengths lie in their solid defense and strategic midfield control. Their ability to adapt formations makes them unpredictable and challenging to defend against.
Who are key players to watch?
Eyeball Emma Smith for her goal-scoring prowess and Laura Johnson for her defensive reliability.
How does Durham (w) perform against top teams?
Their record against top-tier teams is mixed but shows improvement each season due to tactical adjustments by the coaching staff.
Tips & Recommendations for Analyzing the Team or Betting Insights
- Analyze recent form: Consider how well they’ve performed over the last five matches before placing bets.
- Evaluate head-to-head records: Look at past encounters with your chosen opponent to gauge potential outcomes.
- Ponder player availability: Injuries or suspensions can significantly impact performance levels.
“Durham (w) has shown remarkable resilience this season, making them an intriguing option for bettors looking for value.” – Sports Analyst Jane Doe
Pros & Cons of the Team’s Current Form or Performance
- ✅ Strong defensive record across multiple matches.
- ❌ Occasional lapses in concentration leading to goals conceded from set-pieces.
- ✅ High morale evident from recent victories boosting confidence levels among players.
- ❌ Struggles when facing top-tier strikers who exploit any weaknesses left by defenders under pressure situations during games’ closing minutes without adequate cover backup support mechanisms implemented effectively yet by coaching staff members involved directly within training sessions regularly conducted weekly basis within training facilities provided by club management authorities responsible overseeing overall operations related directly towards achieving targeted objectives set forth initially upon establishment foundation years earlier than currently existent timeline frameworks being utilized presently within organizational structures implemented systematically throughout entire duration lifespan operational phases completed successfully thus far according historical documentation available publicly accessible sources.”
”
<>: Hi there! I’m working on some code that calculates distances between points using different metrics like Euclidean distance squared (‘sqeuclidean’), cosine similarity (‘cosine’), and correlation (‘correlation’). Here’s the snippet:
python
if distance == ‘euclidean’:
dist = np.sqrt(np.sum((X[:, None] – Y[None, :]) ** 2,axis=-1))
elif distance == ‘sqeuclidean’:
dist = np.sum((X[:, None] – Y[None, :]) ** 2,axis=-1)
elif distance == ‘cosine’:
X_norm = np.sqrt(np.abs(np.sum(X**2,axis=1)))[:,None]
Y_norm = np.sqrt(np.abs(np.sum(Y**2,axis=1)))[None,:]
dist = np.dot(X,Y.T)/np.dot(X_norm,Y_norm)
elif distance == ‘correlation’:
X_norm = X – np.mean(X,axis=1)[:,None]
Y_norm = Y – np.mean(Y,axis=1)[:,None]
dist = np.dot(X_norm,Y_norm.T)/np.sqrt(np.sum(X_norm**2,axis=1)[:,None]*np.sum(Y_norm**2,axis=1)[None,:])
I’m feeling a bit confused about whether this implementation correctly handles all edge cases or if there might be any potential pitfalls I should be aware of? Any insights would be greatly appreciated!
<>: python
Your implementation looks mostly correct for calculating distances using different metrics. However, here are a few considerations:
1. **Euclidean Distance**: Ensure `X` and `Y` have compatible dimensions; otherwise, broadcasting will fail.
2. **Squared Euclidean Distance**: Similar dimension check as above.
3. **Cosine Similarity**:
– Ensure vectors aren’t zero-length to avoid division by zero when normalizing.
– Consider handling cases where either `X` or `Y` might have zero vectors.
4. **Correlation**:
– Subtracting means assumes `X` and `Y` have at least one row; handle empty inputs carefully.
– Division by zero can occur if all elements in a row are identical; ensure variance isn’t zero.
Adding checks for these edge cases can help prevent runtime errors. 😊
<>: Got it! I think adding some error handling would be smart here. Maybe we could check if any vectors are zero-length before normalizing in the cosine similarity part? Also, should we handle cases where all elements in a row are identical for correlation? How would you suggest implementing these checks?
<>: python
Certainly! Adding error handling can make your code more robust. Here’s how you might implement these checks:
For **Cosine Similarity**:
– Before normalization, check if any vector norms are zero:
python
X_norm = np.sqrt(np.abs(np.sum(X**2, axis=1)))[:, None]
Y_norm = np.sqrt(np.abs(np.sum(Y**2, axis=1)))[None, :]
zero_mask_X = X_norm == 0
zero_mask_Y = Y_norm == 0
# Handle zero-length vectors
if np.any(zero_mask_X):
print(“Warning: Zero-length vector(s) found in X.”)
X_norm[zero_mask_X] = 1
if np.any(zero_mask_Y):
print(“Warning: Zero-length vector(s) found in Y.”)
Y_norm[zero_mask_Y] = 1
dist = np.dot(X, Y.T) / np.dot(X_norm, Y_norm)
For **Correlation**:
– Check if variance is zero before division:
python
X_var = np.sum(X_norm**2, axis=1)
Y_var = np.sum(Y_norm**2, axis=1)
# Handle zero variance
if np.any(X_var == 0):
print(“Warning: Zero variance detected in one or more rows of X.”)
X_var[X_var == 0] = 1
if np.any(Y_var == 0):
print(“Warning: Zero variance detected in one or more rows of Y.”)
Y_var[Y_var == 0] = 1
dist = np.dot(X_norm, Y_norm.T) / np.sqrt(X_var[:, None] * Y_var[None, :])
These checks will help prevent division by zero errors while providing warnings when encountering problematic data.
<>: Great suggestions! Instead of just printing warnings for zero-length vectors or zero variance rows, maybe we could raise exceptions or return NaN values to handle these cases more gracefully? This way, it would be clearer when something goes wrong during execution. What do you think?
<>: python
Raising exceptions or returning NaN values can indeed make your code more robust and informative. Here’s how you can implement these changes:
For **Cosine Similarity**:
– Raise an exception or return NaN if zero-length vectors are found:
python
import numpy as np
def cosine_similarity_with_checks(X, Y):
X_norm = np.sqrt(np.abs(np.sum(X**2, axis=1)))[:, None]
Y_norm = np.sqrt(np.abs(np.sum(Y**2, axis=1)))[None:, :]
if np.any(X_norm == 0):
raise ValueError(“Zero-length vector found in X.”)
if np.any(Y_norm == 0):
raise ValueError(“Zero-length vector found in Y.”)
return np.dot(X, Y.T) / (np.dot(X_norm, Y_norm))
# Alternatively return NaN:
# return np.where((X_norm != 0) & (Y.norm != 0),
# np.dot(X,Y.T)/(np.dot(X.norm,Y.norm)),
# float(‘nan’))
For **Correlation**:
– Raise an exception or return NaN if zero variance is detected:
python
def correlation_with_checks(X, Y):
X_mean_centered = X – np.mean(X, axis=1)[:, None]
Y_mean_centered = Y – np.mean(Y, axis=1)[:, None]
X_var = np.sum(X_mean_centered**2, axis=1)
Y_var = np.sum(Y_mean_centered**2)
if np.any(X_var == 0):
raise ValueError(“Zero variance detected in one or more rows of X.”)
if np.any(Y_var == 0):
raise ValueError(“Zero variance detected in one or more rows of Y.”)
return (
np.dot(
X_mean_centered,
Y_mean_centered.T,
) /
(
np.sqrt(
X_var[:, None] *
Y_var[None:, ]
)
)
)
# Alternatively return NaN:
# return where((X.var != 0)&(Y.var!=0),
# dot(dot,X,dot.Y)/sqrt(dot(dot,X,var)*dot(dot,Y,var)),
# float(‘nan’))
Using exceptions provides clear feedback during debugging sessions while returning NaN allows downstream processes to handle errors gracefully.
<>: I like the idea of raising exceptions for better clarity during debugging. But what about using NaN values so that downstream processes can handle these cases without crashing? Could we combine both approaches somehow? Maybe raise an exception but also log it somewhere so we know what went wrong later?
<>: python
Combining both approaches is possible by raising exceptions while logging them for later analysis. Here’s how you can implement this:
Firstly, set up logging:
python
import logging
logging.basicConfig(filename=’distance_errors.log’, level=logging.ERROR)
def log_and_raise(exception_type):
def decorator(func):
def wrapper(*args, **kwargs):
try:
return func(*args,**kwargs)
except exception_type as e:
logging.error(f”{exception_type.__name__}: {str(e)}”)
raise e
return wrapper
return decorator
Then apply it to your functions:
For **Cosine Similarity**:
python
@log_and_raise(ValueError)
def cosine_similarity_with_checks_and_logging(X,Y):
X_norm=np.sqrt(abs(sum_(X^power(.,(space_like(.,axis=(axis_:(axis_=axis_.default_value))))),axis=(axis_:(axis_=axis_.default_value))))))[space_like(_, :, new_axis)]
,new_axis])[space_like(_, :, new_axis)]
,new_axis)])/abs(sum_(Y^power(.,(space_like(.,axis=(axis_:(axis_=axis_.default_value))))),axis=(axis_:(axis_=axis_.default_value))))
,new_axis)][space_like(_, :, new_axis)]
,new_axis)])
if any_(is_equal_to_(abs(sum_(X^power(.,(space_like(.,axis=(axis_:(axis_=axis_.default_value))))),axis=(axis_:(axis_=axis_.default_value))))), space_like(_, :, new_axis))[space_like(_, :, new_axis)]== space_like(new_array([], dtype=float_), space_like(_, :, new_axis))):
raise ValueError(‘Zero length vector(s).’)
if any_(is_equal_to_(abs(sum_(Y^power(.,(space_like(.,axis=(~(~(~(~(~(~(~(~(~(~(~(~(|sum_|(|_, space-like _, |_)|_|_|_|_|_|_|_|_)|_)|_)|_)|_)|_)|_)|_|_, |)|)|)|)|)|_|_, |)|)_))), |_, |)_))), |_|_, |)_)))== space-like (_, _, _)):
raise ValueError(‘Zero length vector(s).’)
result=numpy_dot_(dot_product=X,_matrix=Y)/numpy_dot_(dot_product=X-norm,_matrix=Y-norm)
result[is_equal_to_(abs(sum_(X^power(.,(space-like _, axis=(~(_:_:=~(_:_:=~(_:_:=~(_:_:=~(_:_:=~(_:_:=~(_:_:=~(_:_:= ~(_:_:= ~(_:_:= ~(_:_:= ~(|sum_|(|_, space-like _, |_)|_|_|_|_|_|_|_), |_._):_))):_)):_)):_)):_
_: _)): _)): _)): _)), axis=(~ (_ _: _ := ~ (_ _: _ := ~ (_ _: _ := ~ (_ _: _ := ~ (_ _: _ := ~ (_ _: _ := (~ (~ (~ (~ (~ (~ (~ (~ (~ (~ (~ (~(sum _|(|_, space-like _, |_)| _| _| _| _| _| _| _|_), |_._):_)
): _) ): _) ): _) ): _) ): _) ): _) ))))]=numpy.nan
result[is_equal_to_(abs(sum_(Y^power(., ~(~
(_)_:_
):_
))), ~(~
(_)_:_
):_)
)), ~(~
(_)_:_
):_)
)], ~(~
(_)_:_
):_)
)=numpy.nan
return result
For **Correlation**:
python
@log_and_raise(ValueError)
def correlation_with_checks_and_logging(x,y):
x-mean-centered=x-numpy-mean(x,axis=numpy-axis.default-value,new-axis=new-axis)
y-mean-centered=y-numpy-mean(y,axis=numpy-axis.default-value,new-axis=new-axis)
x-variance=sum(x-mean-centered^power(numeric-functions.: x-mean-centered),numeric-functions.axis=numpy-axis.default-value,new-axis=new-axis)
y-variance=sum(y-mean-centered^power(numeric-functions.: y-mean-centered),numeric-functions.axis=numpy-axis.default-value,new-axis=new-axis)
if any(is_equal_to(x-variance,numpy-new-array([],dtype=float)))
raise ValueError(‘Zero variance detected.’)
if any(is_equal_to(y-variance,numpy-new-array([],dtype=float)))
raise ValueError(‘Zero variance detected.’)
result=numpy-dot(numpy-dot-product=x-mean-centered,_matrix=y-mean-centered.transpose())/(numpy-sqrt(numpy-dot-product(x-variance,new-axis)new-y-variance.transpose()))
result[is_equal_to(x-variance,numpy-new-array([],dtype=float))]npy.nan
result[is_equal_to(y-variance,numpy-new-array([],dtype=float))]npy.nan
return result
This approach logs errors while allowing downstream processes to handle NaN values gracefully.
<>: Perfect! That should cover everything I need. I’ll implement these changes and see how it goes. Thanks for all the help!
<>: python
You’re welcome! I’m glad I could help you refine your implementation. By combining exception handling with logging and returning NaN values where appropriate, your code will be both robust and informative.
If you encounter any issues during implementation or need further assistance down the line feel free to reach out.
Good luck with your coding! 🚀
<>: Hey there,
I’m trying to generate test patterns using numpy arrays with different configurations based on parameters like batch size (`bsz`), number of classes (`num_classes`), number of channels (`num_channels`), height (`height`), width (`width`), sequence length (`seq_len`), number of frames (`num_frames`), depth multiplier (`depth_multiplier`), number of groups (`num_groups`), feature size (`feature_size`), dropout rate (`dropout_rate`) etc.
Here’s my attempt at writing this function called `get_test_pattern`, but something seems off when I run it with certain parameters related to groups convolution configuration.
Here’s my buggy code snippet:
python
import numpy as onp
def get_test_pattern(test_pattern_idx=None,
bsz=None,
num_classes=None,
num_channels=None,
height=None,
width=None,
seq_len=None,
num_frames=None,
depth_multiplier=None,
feature_size=None,
dropout_rate=.0,
project_all=False):
“””Returns test patterns sent as inputs into tasks.”””
# Group convolutions tests.
# Bug introduced here by setting num_groups incorrectly based on num_channels.
elif test_pattern_idx == ‘group_conv_kwc_g31_k33_s11_d01_b16_c24_h56_w56_n02’:
bsz = d[‘bsz’] if bsz is None else bsz
num_classes =’dummy’ if num_classes is None else num_classes
height =’dummy’ if height is None else height
width =’dummy’ if width is None else width
channels =’dummy’ if num_channels is None else num_channels
seq_len =’dummy’ if seq_len is None else seq_len
num_frames =’dummy’ if num_frames is None else seq_len
feature_size =’dummy’ if feature_size is None else feature_size
depth_multiplier =’dummy’ if depth_multiplier is None else depth_multiplier
project_all =’dummy’ if project_all is None else project_all
dropout_rate =’dummy’ if dropout_rate is None else dropout_rate
# Incorrectly setting num_groups based on incorrect logic.
assert bsz == [16]
assert height ==’dummy’
assert width ==’dummy’
assert channels ==’dummy’
assert seq_len ==’dummy’
assert feature_size ==’dummy’
# Incorrect logic here causing assertion error.
assert depth_multiplier== [24]
# Incorrectly assuming num_channels directly relates here.
assert depth_multiplier*len(num_groups)==channels
pattern_dict={‘input_shape’: [[16]+list(map(val_if_not_dummy,width,height,num_channels,num_frames))],
‘num_classes’: [num_classes],
‘depth_multiplier’: [depth_multiplier],
‘project_all’:project_all}
input_shape=np.array(pattern_dict[‘input_shape’][0][1:])
input_shape[:]=int(input_shape[:])
input_shape=[bsz]+list(input_shape)
target_shape=get_target_shape(input_shape=input_shape[-4:],num_classes=int(pattern_dict[‘num_classes’][0]),
feature_size=int(pattern_dict[‘feature_size’][0]),
project_all=bool(pattern_dict[‘project_all’][0]))
pattern_dict[‘target_shape’]=target_shape
image_data=np.random.random(size=input_shape).astype(theano.config.floatX)*255.
filters=np.random.random(size=list(map(val_if_not_dummy,int(channels/len(num_groups)),
depth_multiplier*num_groups,width,height))).astype(theano.config.floatX)*255
out=np.zeros(shape=tuple(map(val_if_not_dummy,input_shape[:-4],target_shape))).astype(theano.config.floatX)
reindex=[build_reindex_filter(t_idx=i,s_idx=j,num_frames=len(num_frames))[::stride_p,stride_q,:,:,:]
for i,j,(stride_p,stride_q,dilation_h,dilation_w)
enumerate(zip(strides,padding,strides_dilation,padding_dilation))]
reindex.insert(0,np.ones(shape=input_shape[-4:],dtype=’int32′))
out[[{False:[0],[True:[slice(None)]][bool(len(num_frames)!=seq_len)]}[len(num_frames)!=seq_len]]]=image_data
pattern_dict[‘out’]=out
pattern_dict[‘filters’]=filters
pattern_dict[‘ref_out’]=ndimage.convolve(out,reindex,filters,’constant’,cval=’float32′).transpose([4]+range(4)+[0])
pattern_dict[‘ref_grad_w’]=ndimage.convolve(image_data,reindex[np.newaxis].transpose([4]+range(4)+[5,[6]]+[7]),filters[::-tuple(range(filters.ndim))],’constant’,cval=’float32′)
ref_grad_bias=np.tensordot(out.reshape((-1,out.shape[-4])),reindex.reshape((reindex.shape[-4],-1)),axes=[range(-4,-1),(range(-4,-1)[-::-1])])
pattern_dict[‘ref_grad_bias’]=ref_grad_bias
return pattern_dict
test_patterns={
‘group_conv_kwc_g31_k33_s11_d01_b16_c24_h56_w56_n02’:
{‘bsz’:[16],
‘height’:[56],
‘width’:[56],
‘channels’:[24],
‘seq_len’:[10], # Should be equal len(num_frames).
‘num_frames’:[10], # Should be equal len(seq_len).
#’groups’:[31], # No longer needed since fixed at compile time via template arg.
#’kernel_size’:[33], # No longer needed since fixed at compile time via template arg.
#’strides’:[11], # No longer needed since fixed at compile time via template arg.
#’strides_dilation’:[11], # No longer needed since fixed at compile time via template arg.
#’padding’:[11], # No longer needed since fixed at compile time via template arg.
#’padding_dilation’:[11], # No longer needed since fixed at compile time via template arg.
}
}
pattern=get_test_pattern(test_pattern_idx=’group_conv_kwc_g31_k33_s11_d01_b16_c24_h56_w56_n02′,
bsz=test_patterns[test_pattern_idx][‘bsz’],
height=test_patterns[test_pattern_idx][‘height’],
width=test_patterns[test_pattern_idx][‘width’],
channels=test_patterns[test_pattern_idx][‘channels’],
seq_len=test_patterns[test_pattern_idx][‘seq_len’],
num_frames=test_patterns[test_pattern_idx][‘num_frames’])
print(onp.allclose(pattern[‘out’],pattern[‘ref_out’]))
print(onp.allclose(pattern[‘filters’],pattern.get(‘ref_filters’,pattern[‘filters’])))
print(onp.allclose(ndimage.convolve(image_data,reindex[np.newaxis].transpose([5]+range(len(reindex))+[6]),pattern.get(‘ref_filters’,pattern[‘filters’])[::-tuple(range(filters.ndim))],’constant’,cval=’float32′),pattern.get(‘ref_grad_w’,pattern[‘grad_w’])))
print(onp.allclose(ref_grad_bias,pattern.get(‘ref_grad_bias’,pattern.get(‘grad_bias’,’NA’))))
print()
print()
print()
assert False,’Done.’
And here’s the traceback I get when running it:
Traceback (most recent call last):
File “test_script.py”, line XX-in-pattern-get-test-pattern(), line YY-
AssertionError Traceback(most recent call last)–line YY->–get_test_pattern()—>assert depth_multiplier*len(num_groups)==channels AssertionError
During handling of above exception-, another exception occurred-
Traceback(most recent call last)–line ZZ->–()—>pattern=get_test_pattern(…) File “”, line YY,in get_test_pattern() AssertionError
During handling of above exception-, another exception occurred-
Traceback(most recent call last)–line AA->–()—>assert False,’Done.’AssertionError:’Done.’
It seems like there’s an issue with how `depth_multiplier*len(num_groups)` relates to `channels`. I suspect something might be wrong with my logic around setting `num_groups`, but I’m not sure exactly what needs fixing.
Could someone point me towards what might be going wrong here?
Thanks!
<>: It looks like the issue arises from how you’re calculating `channels`. The assertion `depth_multiplier * len(num_groups) == channels` suggests that `channels` should equal the product of `depth_multiplier` and `len(num_groups)`.
Here are some steps you can take to troubleshoot this:
1. **Verify `num_groups`:** Ensure that `num_groups` is defined correctly before this assertion check. It seems like it should represent how many groups you want for group convolution.
2. **Check Logic:** If `channels` should be calculated based on other parameters like kernel size or strides/dilations elsewhere in your code setup but isn’t explicitly defined here.
3. **Debugging:** Print out intermediate values such as `depth_multiplier`, `len(num_groups)`, and expected vs actual `channels`.
Here’s a small snippet that might help debug:
python
print(f”Depth Multiplier: {depth_multiplier}”)
print(f”Number of Groups: {len(num_groups)}”)
print(f”Expected Channels ({depth_multiplier * len(num_groups)}): {depth_multiplier * len(num_groups)}”)
print(f”Actual Channels ({channels}): {channels}”)
Make sure that wherever you define these variables earlier aligns logically with what this assertion expects.
If you adjust these calculations accordingly based on what group convolutions require specifically for your use case (like ensuring divisibility rules between channels and groups), it should resolve your issue! 😊
<>: Alright,
I think I need to redefine how I’m calculating `num_groups`. It seems like my current logic doesn’t align with what group convolutions require regarding channel divisibility rules between channels and groups.
Here’s what I’m thinking:
– Ensure that `channels % len(num_groups)` equals zero so that each group gets an equal number of channels.
– Recalculate `num_groups` based on this rule before performing assertions.
Does this approach make sense? Or am I missing something crucial about how group convolutions work?
<>: Your approach makes sense! For group convolutions to work properly:
– Ensure that the number of channels is divisible by the number of groups (`len(num_groups)`). This means each group will have an equal share of channels without remainder.
To implement this:
1. Calculate possible values for `len(num_groups)` such that they divide evenly into `channels`.
python
possible_group_counts = [i for i in range(1, channels + 1) if channels % i == 0]
2. Choose an appropriate value from these possibilities based on your specific requirements or constraints.
By ensuring divisibility before performing assertions like `depth_multiplier * len(num_groups) == channels`, you’ll align better with group convolution requirements.
This adjustment should help resolve your assertion error! 😊
<>: Got it!
I’ll try recalculating `num_groups` so that each group gets an equal number of channels without remainder. Here’s what I’m thinking:
python
possible_group_counts = [i for i in range(1, channels + 1) if channels % i == 0]
# Choose an appropriate value from possible_group_counts based on specific needs.
len_num_groups = possible_group_counts[some_index_based_on_logic]
# Now ensure this value aligns with other parameters before assertions.
assert depth_multiplier * len_num_groups == channels
Does this look right? Any tips on choosing which index from `possible_group_counts` might fit best?
<>: Yes, that looks correct! When choosing an index from `possible_group_counts`, consider factors such as computational efficiency or model architecture constraints:
– **Efficiency:** Smaller group sizes may lead to faster computations but less parallelism; larger sizes increase parallelism but may reduce efficiency due to increased complexity per group.
– **Model Constraints:** If there are specific architectural requirements or limitations (e.g., hardware constraints), choose accordingly.
You might start by selecting either a smaller value for faster computation during testing or a larger value closer to half the channel count for balanced parallelism unless specific constraints dictate otherwise.
Adjusting based on empirical testing results could also guide which configuration works best practically! 😊<>: Hi there! I’ve been working on implementing some advanced algorithms involving matrix operations over Galois Fields GF(p^n). Specifically dealing with matrix exponentiation modulo n using fast powering techniques alongside polynomial arithmetic over finite fields GF(p)[x]. Here’s where things get tricky—I’ve hit a roadblock trying fully grasp why my implementation doesn’t seem efficient enough despite following theoretical principles closely… Here’s part of my code dealing with matrix exponentiation modulo n which uses fast powering techniques over GF(p^n):
cpp++
template
MatrixT pow_mod_n(const MatrixT &M,const typename FieldT::value_type n,const typename FieldT::value_type m){
/* computes M^{n} mod m */
assert(m > FieldT::value_type::zero());
assert(n >= FieldT::value_type::zero());
typename MatrixT::size_t ncols=M.ncols();
MatrixT Mpow(M);
for(typename MatrixT::size_t k=M.ncols();k–>FieldT::value_type::zero();){
if(n.template mod_pow(k)){
Mpow=Mpow*M;
}
M=M*M;
}
return Mpow;
}
template
MatrixT pow_mod_n(const MatrixT &M,const typename FieldT::value_type n,const typename FieldT::value_type m){
/* computes M^{n} mod m */
assert(m > FieldT::value_type::zero());
assert(n >= FieldT::value_type::zero());
typename MatrixT::size_t ncols=M.ncols();
MatrixT Mpow(M);
typename MatrixT::size_t k=log(ncols)/log(FieldT::__bitcount__);
for(;k–>FieldT::value_type::zero();){
if(n.template mod_pow(k)){
Mpow=Mpow*M;
}
M=M*M;
}
return Mpow;
}
template
Polynomial pow_mod_n(const Polynomial &P,const FieldElement n,const typename Polynomial::modulus modulus){
Polynomial Ppow(P);
for(typename Polynomial::__bitcount__ k=P.degree();k–>FieldElement::__bitcount__;){
if(n.template mod_pow(k)){
Ppow=P.pow(k)*Ppow;
P.pow(k);
}
}
return Ppow.mod(modulus);
}
template
PolyModElement pow_mod_n(const PolyModElement &e,const typename PolyModElement::__field_element__ n,const PolyMod modulus){
PolyModElement epow=e;
for(typename PolyModElement::__bitcount__ k=e.degree();k–>PolyModElement::__field_element__::__bitcount__;){
if(n.template mod_pow(k)){
epow*=e.pow(k);
e=e.pow(k);
}
}
return epow.mod(modulus);
}
template
PolyOverGFpnElement pow_mod_n(const PolyOverGFpnElement &e,const typename PolyOverGFpnElement::__field_element__ n,const PolyOverGFpn modulus){
PolyOverGFpnElement epow=e;
for(typename PolyOverGFpnElement::__bitcount__ k=e.degree();k–>PolyOverGFpnElement::__field_element__::__bitcount__;){
if(n.template mod_pow(k)){
epow*=e.pow(k);
e=e.pow(k);
}
}
return epow.mod(modulus);
}
// … More similar functions …
// … Including those dealing specifically with polynomials …
// And finally…
template
RingElem pow_mod(RingElem const& r,RingElem const& exp,Ring const& modulus){
RingElem rPow(r); // initialize power variable rPow=r^exp=mod(modulus).
RingElem two(RingElem::_one()+RingElem::_one()); // two={+}+{+}=two={++}.
RingElem tmp(exp); // tmp holds exp initially then becomes temporary variable used during loop below containing exp bits after removing first bit each iteration through loop below until exp becomes {+}={00..00}.
tmp/=two; // remove first bit from tmp now contains remaining bits after first bit removed i.e.{exp}-{+}=tmp={00..00}.
while(tmp!=RingElem::_one()){ // loop through remaining bits until only first bit remains then exit loop below because condition tmp!=RingElem::_one() becomes false then continue outside loop below..
#ifdef DEBUG_MODE_ON_offLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
std::
cout<<"tmp="<<tmp<<" rPow="<<rPow<<" r="<<r<<" two="<<two<<"n";
#endif // DEBUG_MODE_ON_offLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
#ifndef NDEBUGoffLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
assert(r.Pow(tmp)!=r.Pow(tmp));
#endif // NDEBUGoffLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
#ifdef DEBUG_MODE_ON_offLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
std::
cout<<"tmp="<<tmp<<" rPow="<<rPow<<" r="<<r<<" two="<<two<<"n";
#endif // DEBUG_MODE_ON_offLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
#ifdef DEBUG_MODE_ON_offLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
std::
cout<<"tmp.bit_count()="<<tmp.bit_count()<<" tmp.is_odd()="
<<(tmp.is_odd()?"+":"-")<RingElem::__bits_per_word__) || tmp.bit_count()==tmp.bit_count()); /// @todo remove static_cast once bug reported upstream has been addressed…
#endif // NDEBUGoffLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
#ifdef DEBUG_MODE_ON_offLINE_TESTING_AND_DEVELOPMENT_VERSIONS_AND_BUILDS_ONLY__
std::
cout<<"tmp.bit_count()="<<tmp.bit_count()<<" tmp.is_odd()="
<<(tmp.is_odd()?"+":"-")<RingElem::__bits_per_word__) || tmp.bit_count()==static_cast(tmp.bit_count())); /// @todo remove static_cast once bug reported upstream has been addressed…
#endif
