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JOLIMAITRE Matthieu 2024-02-26 15:36:47 +01:00
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/__pycache__
/.pytest_cache
/env
/*.zip

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import numpy as np
import matplotlib.pyplot as plt
# step 01 ---------------------------------------
# args
# - filename: string filename
# return
# - x: data matrix of size (n,p)
# - y: array of integer labels of size n
def load_data(filename):
x = np.loadtxt(filename)
y = x[:,4].astype(int)
x = x[:,:-1]
return x, y
# step 02 ---------------------------------------
# args
# - x: data matrix of size (n,p)
# return
# - x: center-normalized input
def standardize(x: np.ndarray):
def normalize_col(column: np.ndarray):
avg = column.mean()
avg_dist_to_avg = column.std()
return [ (elt - avg) / avg_dist_to_avg for elt in column ]
x = np.array([ normalize_col(column) for column in x.T ]).T
return x
# step 03 ---------------------------------------
# args
# - x: standardized data matrix of size (n,p)
# return
# - C: covariance matrix of size (p,p)
def compute_covariance_matrix(x: np.ndarray):
# def cov_cols(col_a: np.ndarray, col_b: np.ndarray):
# return sum(a * b for (a, b) in zip(col_a, col_b)) / len(col_a)
# C = np.array([[ cov_cols(col_a, col_b) for col_b in x.T] for col_a in x.T])
# return C
return np.cov(x.T, bias=True)
# step 04 ---------------------------------------
# args
# - C: covariance matrix of size (p,p)
# return
# - eigenval: eigenvalues of size p
# - eigenvec: eigenvectors of size (p,p)
def compute_eigenelements(C: np.ndarray):
return np.linalg.eig(C)
# step 05 ---------------------------------------
# args
# - eigenval: eigenvalues of size p
# - eigenvec: eigenvectors of size (p,p)
# return
# - eigenval: ordered eigenvalues of size p
# - eigenvec: ordered eigenvectors of size (p,p)
def sort_eigenelements(eigenval: np.ndarray, eigenvec: np.ndarray):
keyed = list(zip(eigenval, eigenvec.T))
keyed.sort(key=lambda a: a[0])
eigenval = np.flip([val for (val, _) in keyed])
eigenvec = np.rot90(np.flip([vec for (_, vec) in keyed]))
return (eigenval, eigenvec)
# step 06 ---------------------------------------
# args
# - eigenval: eigenvalues of size p
# returns
# - var: variances ratio explained by each components (of size p)
# - var_accu: cumulated variances ratio (of size p)
def compute_var_ratio(eigenval: np.ndarray):
total = np.sum(eigenval)
var = np.divide(eigenval, total)
var_accu = np.cumsum(var)
return (var, var_accu)
# step 08 ---------------------------------------
# args
# - x: standardized data matrix of size (n,p)
# - eigenvec: sorted eigenvectors (of size (p,p))
# return
# - x: projected data of size (n,2)
def project_on_2pc(x: np.ndarray, eigenvec: np.ndarray):
projected = x @ eigenvec
_2d = projected[:,:2]
return _2d
# step 11 ---------------------------------------
# args
# - x: standardized data matrix of size (n,p)
# return
# - y_pred: labels of size (n)
def classify(x: np.ndarray):
def class_n(n: float):
if (n < -1): return 0
if (n < 1): return 1
return 2
return np.array([ class_n(n) for n in x[:,0] ])
# step 12 ---------------------------------------
# args
# - y: ground-truth labels (of size (n))
# - y_pred: predicted labels (of size (n))
# return
# - conf: confusion matrix of integer of size (p,p)
def compute_confusion_matrix(y: np.ndarray, y_pred: np.ndarray):
size = max(y) + 1
res = np.zeros((size, size)).astype(np.int32)
for (y, y_pred) in zip(y, y_pred): res[y, y_pred] += 1
return res
# step 13 ---------------------------------------
# args
# - conf: confusion matrix of integer of size (p,p)
# return
# - prec: average precision over all classes
# - rec: average recall over all classes
def compute_metric(conf: np.ndarray):
def precision(kind: int, mat: np.ndarray):
return mat[kind] / mat[kind,:].sum()
prec = np.average([ precision(kind) for kind in range(0, 3) ])
def rec(kind: int, mat: np.ndarray):
return mat[kind] / mat[kind,:].sum()
if __name__ == '__main__':
# main program ------------------------------
values, kind = load_data("./iris.csv")
standardized = standardize(values)
covariance = compute_covariance_matrix(standardized)
eigenval, eigenvec = compute_eigenelements(covariance)
eigenval_sorted, eigenvec_sorted = sort_eigenelements(eigenval, eigenvec)
variance, variance_accumulated = compute_var_ratio(eigenval_sorted)
projected = project_on_2pc(standardized, eigenvec_sorted)
predictions = classify(projected)
# draw
plt.figure()
plt.scatter(projected[:,0], projected[:,1], c=predictions)
plt.show()
confusion = compute_confusion_matrix(kind, predictions)
# -----------------------------------
plt.show()
# -----------------------------------

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import numpy as np
import main
def test_step_01():
test = main.load_data('iris.csv')
assert test is not None
x,y = test
assert type(x) == np.ndarray
assert type(y) == np.ndarray
assert x.shape == (150,4)
assert y.shape == (150,)
assert x.dtype == np.float32 or x.dtype == np.float64
assert y.dtype == np.int32 or y.dtype == np.int64
def test_step_02():
x = np.array([
[59.76270078546494,93.0378732744839,70.55267521432877,],
[58.976636599379376,34.73095986778094,79.17882261333122,],
[37.5174422525385,128.35460015641596,142.73255210020585,],
[26.68830376515554,108.34500761653291,55.778983950580894,],
[63.60891221878646,135.1193276585322,-35.79278836042261,],
[-32.57414005969186,-45.956320511934855,116.5239691095876,],
[105.6313501899701,124.00242964936382,145.7236684465528,],
[109.83171284334472,42.29587245058637,106.10583525729109,],
[-26.345114826213354,77.98420426550476,-21.32934251819072,],
[138.93378340991677,54.36966435001433,32.932387998104716,],
])
x_ref = np.array([
[0.10485104208319312,0.3362373314630696,0.021964359573702855,],
[0.09002614318807045,-0.7645767522567821,0.166375923375568,],
[-0.31468684615052994,1.0030047535583193,1.2303379722621464,],
[-0.518920655600867,0.625230661423531,-0.22536411278355217,],
[0.17738926051062492,1.1307204372014275,-1.7583802123078445,],
[-1.636589865740423,-2.2879243182562656,0.7915763467485558,],
[0.9699179181914451,0.9208373001811287,1.2804126775864766,],
[1.0491353062386208,-0.6217538548213571,0.6171648821726928,],
[-1.5191126025141926,0.05202933813039103,-1.5162456027970177,],
[1.5979902997940605,-0.39380489662345974,-0.607842233830729,],
])
x_test = main.standardize(x)
assert x_test is not None
error = np.max(np.abs(x_ref - x_test))
assert x_test.shape == x_ref.shape
assert error < 1e-6
def test_step_03():
x = np.array([
[-1.105742368566682,1.2447972510784915,-0.10292263179401698,],
[0.5207869535408698,-1.2813536677837922,0.5399586812056,],
[0.7544895471006708,0.7187982077571432,1.838230783931978,],
[1.1276950515239543,-0.14201644595920881,-0.1790339466010727,],
[1.2123239446742684,-1.1427957147947074,0.7355527607135005,],
[1.0678403424190925,-0.6406810309665311,-1.405619490464019,],
[-0.8334425979838738,-0.12796234478939209,0.3511025041846954,],
[-0.17414992612560526,1.960866758149327,-1.5126361666589871,],
[-1.4037672060254274,-0.80477781558321,0.6811779598355046,],
[-1.1660337405572676,0.2151248028918804,-0.9458104543531817,],
])
C_ref = np.array([
[0.9999999999999998,-0.30871041083062684,0.10882239075522164,],
[-0.30871041083062684,1.0,-0.3175955960839056,],
[0.10882239075522164,-0.3175955960839056,1.0,],
])
C_test = main.compute_covariance_matrix(x)
assert C_test is not None
error = np.max(np.abs(C_ref - C_test))
assert C_test.shape == (3,3)
assert error < 1e-6
def test_step_04():
C = np.array([
[0.9999999999999998,-0.30871041083062684,0.10882239075522164,],
[-0.30871041083062684,1.0,-0.3175955960839056,],
[0.10882239075522164,-0.3175955960839056,1.0,],
])
eigval_ref = np.array([1.5006348637289717,0.8912274127999972,0.6081377234710301,])
eigvec_ref = np.array([
[-0.524750256529313,0.7183989075784977,0.4566619952026235,],
[0.6626030910538614,0.007925719552699393,0.7489287861308581,],
[-0.5344102469061465,-0.6955862222324367,0.4801723601396883,],
])
test = main.compute_eigenelements(C)
assert test is not None
eigval_test, eigvec_test = test
assert eigval_test.shape == (3,)
assert eigvec_test.shape == (3,3)
error = np.max(np.abs(eigval_ref - eigval_test))
assert error < 1e-6
error = np.max(np.abs(eigvec_ref - eigvec_test))
assert error < 1e-6
def test_step_05():
eigval = np.array([1.0, 3.0, 2.0])
eigvec = np.array([
[1.0, 3.0, 2.0],
[1.1, 3.1, 2.1],
[1.2, 3.2, 2.2],
])
eigval_ref = np.array([3.0, 2.0, 1.0])
eigvec_ref = np.array([
[3.0, 2.0, 1.0],
[3.1, 2.1, 1.1],
[3.2, 2.2, 1.2],
])
test = main.sort_eigenelements(eigval, eigvec)
assert test is not None
eigval_test, eigvec_test = test
assert eigval_test.shape == (3,)
assert eigvec_test.shape == (3,3)
error = np.max(np.abs(eigval_ref - eigval_test))
assert error < 1e-6
error = np.max(np.abs(eigvec_ref - eigvec_test))
assert error < 1e-6
def test_step_06():
eigval = np.array([0.9767610881903371,0.9764594650133958,0.8379449074988039,0.8209932298479351,0.7392635793983017,0.6563295894652734,0.604845519745046,0.4686512016477016,0.3687251706609641,0.29614019752214493,0.2828069625764096,0.1965823616800535,0.15896958364551972,0.1381829513486138,0.1201965612131689,0.11872771895424405,0.11037514116430513,0.09710127579306127,0.09609840789396307,0.039187792254320675,])
var_ref = np.array([0.12052317179600819,0.12048595432040264,0.10339455498701101,0.1013028767020668,0.09121820316104898,0.08098492540533334,0.07463227330373827,0.05782716978748539,0.045497233280881885,0.03654092728836284,0.03489573094977952,0.024256422614793195,0.019615358015076186,0.017050482237702617,0.014831130121310949,0.014649888740942673,0.013619258856022274,0.011981388166988682,0.011857643659193383,0.004835406605851003,])
var_accu_ref = np.array([0.12052317179600819,0.24100912611641084,0.34440368110342184,0.4457065578054886,0.5369247609665376,0.6179096863718709,0.6925419596756092,0.7503691294630945,0.7958663627439764,0.8324072900323393,0.8673030209821188,0.891559443596912,0.9111748016119882,0.9282252838496908,0.9430564139710018,0.9577063027119445,0.9713255615679667,0.9833069497349554,0.9951645933941488,0.9999999999999998,])
test = main.compute_var_ratio(eigval)
assert test is not None
ver_test, var_accu_test = test
assert ver_test.shape == eigval.shape
assert var_accu_test.shape == eigval.shape
error = np.max(np.abs(var_ref - ver_test))
assert error < 1e-6
error = np.max(np.abs(var_accu_ref - var_accu_test))
assert error < 1e-6
# def test_step_07():
# pass
def test_step_08():
x = np.array([
[-0.5692272135195057,-0.03821691441797431,-1.391429749664207,],
[0.8349483159428722,0.5897352401152248,-0.7587336993772015,],
[0.2004294637899314,-1.358613577394327,0.21764397273661457,],
[1.722938694045615,-0.43267593685524763,0.5052024345091827,],
[-1.2673436013591408,1.2069175815704556,-0.6832265505709595,],
[-1.0746396605693356,0.671812065430423,-1.529889431394962,],
[1.3466454025825358,-1.726489239590098,0.5379189375433167,],
[-0.7491139962207634,1.2846882183405577,1.4319721238227643,],
[-0.8288106401604025,0.6291253952950716,0.26824732034137383,],
[0.38417323546819404,-0.8262828324940856,1.4022946420540787,],
])
eigvec = np.array([
[-0.6432311709554334,0.725040765848229,],
[0.6234976274295615,0.6825615590553287,],
[-0.44441463668629316,-0.09179109955857746,],
])
proj_ref = np.array([
[0.9606882782960829,-0.3110774648390586,],
[0.16782610142261073,1.077547171895806,],
[-1.072738987857223,-0.8019956491849984,],
[-1.602539650115925,0.9074997412514691,],
[1.8713410365637415,-0.032366112869744654,],
[1.7900202119211768,-0.18017423862691137,],
[-2.1817252930269992,-0.2514385438029105,],
[0.6464641579366405,0.20229831190009098,],
[0.8061619944812769,-0.1961274071189318,],
[-1.385497849621383,-0.41416580860481034,],
])
proj_test = main.project_on_2pc(x, eigvec)
assert proj_test is not None
assert proj_test.shape == (len(x), 2)
error = np.max(np.abs(proj_ref - proj_test))
assert error < 1e-6
# def test_step_09():
# pass
# def test_step_10():
# pass
def test_step_11():
x = np.array([
[-2.0, -100.0],
[-2.0, +100.0],
[ 0.0, -100.0],
[ 0.0, +100.0],
[+2.0, -100.0],
[+2.0, +100.0],
])
y_ref = np.array([0,0, 1,1, 2,2], dtype=int)
y_test = main.classify(x)
assert y_test is not None
assert y_test.shape == (6,)
assert y_test.dtype == np.int32 or y_test.dtype == np.int64
# print(y_ref, y_test)
# assert all(y_ref[i] == y_test[i] for i in range(len(x)))
error = np.max(np.abs(y_ref - y_test))
assert error == 0
def test_step_12():
y = np.array([0,0,0,0, 1,1,1,1, 2,2,2,2])
y_pred = np.array([0,0,1,2, 1,1,1,1, 2,2,2,1])
conf_ref = np.array([
[2,1,1,],
[0,4,0,],
[0,1,3,],
], dtype=int)
conf_test = main.compute_confusion_matrix(y, y_pred)
assert conf_test is not None
assert conf_test.shape == (3,3)
assert conf_test.dtype == np.int32 or conf_test.dtype == np.int64
error = np.max(np.abs(conf_ref - conf_test))
assert error == 0
def test_step_13():
conf = np.array([
[2,1,1,],
[0,4,0,],
[0,1,3,],
], dtype=int)
prec_ref = 0.8055555555555555
rec_ref = 0.75
test = main.compute_metric(conf)
assert test is not None
prec_test, rec_test = test
error = np.max(np.abs(prec_ref - prec_test))
assert error < 1e-6
error = np.max(np.abs(rec_ref - rec_test))
assert error < 1e-6
# def test_step_14():
# pass