.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/representation/plot_representation.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_representation_plot_representation.py: Representation of functional data ================================= Explores the different representations of functional data. .. GENERATED FROM PYTHON SOURCE LINES 7-11 .. code-block:: Python # Author: Carlos Ramos Carreño # License: MIT .. GENERATED FROM PYTHON SOURCE LINES 12-19 In this example we are going to show the different representations of functional data available in scikit-fda. First we are going to fetch a functional data dataset, such as the Berkeley Growth Study. This dataset correspond to the height of several boys and girls measured until the 18 years of age. The number and times of the measurements are the same for each individual. .. GENERATED FROM PYTHON SOURCE LINES 19-30 .. code-block:: Python import skfda dataset = skfda.datasets.fetch_growth() fd = dataset["data"] y = dataset["target"] print(repr(fd)) fd.plot(group=y) .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_001.png :alt: Berkeley Growth Study :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none FDataGrid( array([[[ 81.3], [ 84.2], [ 86.4], ..., [193.8], [194.3], [195.1]], [[ 76.2], [ 80.4], [ 83.2], ..., [176.1], [177.4], [178.7]], [[ 76.8], [ 79.8], [ 82.6], ..., [170.9], [171.2], [171.5]], ..., [[ 68.6], [ 73.6], [ 78.6], ..., [166. ], [166.3], [166.8]], [[ 79.9], [ 82.6], [ 84.8], ..., [168.3], [168.4], [168.6]], [[ 76.1], [ 78.4], [ 82.3], ..., [168.6], [168.9], [169.2]]], shape=(93, 31, 1)), grid_points=(array([ 1. , 1.25, 1.5 , 1.75, 2. , 3. , 4. , 5. , 6. , 7. , 8. , 8.5 , 9. , 9.5 , 10. , 10.5 , 11. , 11.5 , 12. , 12.5 , 13. , 13.5 , 14. , 14.5 , 15. , 15.5 , 16. , 16.5 , 17. , 17.5 , 18. ]),), domain_range=((1.0, 18.0),), dataset_name='Berkeley Growth Study', argument_names=('age',), coordinate_names=('height',), extrapolation=None, interpolation=SplineInterpolation(interpolation_order=1, monotone=False))
.. GENERATED FROM PYTHON SOURCE LINES 31-33 This kind of representation is a discretized representation, in which the measurement points are shared between samples. .. GENERATED FROM PYTHON SOURCE LINES 33-35 .. code-block:: Python print(fd.grid_points) .. rst-class:: sphx-glr-script-out .. code-block:: none (array([ 1. , 1.25, 1.5 , 1.75, 2. , 3. , 4. , 5. , 6. , 7. , 8. , 8.5 , 9. , 9.5 , 10. , 10.5 , 11. , 11.5 , 12. , 12.5 , 13. , 13.5 , 14. , 14.5 , 15. , 15.5 , 16. , 16.5 , 17. , 17.5 , 18. ]),) .. GENERATED FROM PYTHON SOURCE LINES 36-38 In this representation, the data can be arranged as a multidimensional array, containing the values at the grid points. .. GENERATED FROM PYTHON SOURCE LINES 38-40 .. code-block:: Python print(fd.data_matrix) .. rst-class:: sphx-glr-script-out .. code-block:: none [[[ 81.3] [ 84.2] [ 86.4] ... [193.8] [194.3] [195.1]] [[ 76.2] [ 80.4] [ 83.2] ... [176.1] [177.4] [178.7]] [[ 76.8] [ 79.8] [ 82.6] ... [170.9] [171.2] [171.5]] ... [[ 68.6] [ 73.6] [ 78.6] ... [166. ] [166.3] [166.8]] [[ 79.9] [ 82.6] [ 84.8] ... [168.3] [168.4] [168.6]] [[ 76.1] [ 78.4] [ 82.3] ... [168.6] [168.9] [169.2]]] .. GENERATED FROM PYTHON SOURCE LINES 41-43 By default, the data points are interpolated using a linear interpolation, but this is configurable. .. GENERATED FROM PYTHON SOURCE LINES 43-53 .. code-block:: Python import matplotlib.pyplot as plt dataset = skfda.datasets.fetch_medflies() fd = dataset["data"] first_curve = fd[0] first_curve.plot() plt.show() .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_002.png :alt: Medflies :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 54-56 The interpolation used can however be changed. Here, we will use an interpolation with degree 3 splines. .. GENERATED FROM PYTHON SOURCE LINES 56-63 .. code-block:: Python from skfda.representation.interpolation import SplineInterpolation first_curve.interpolation = SplineInterpolation(3) first_curve.plot() plt.show() .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_003.png :alt: Medflies :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 64-66 This representation allows also functions with arbitrary dimensions of the domain and codomain. .. GENERATED FROM PYTHON SOURCE LINES 66-78 .. code-block:: Python fd = skfda.datasets.make_multimodal_samples( n_samples=1, dim_domain=2, dim_codomain=2, ) print(f"Domain dimension: {fd.dim_domain}") print(f"Codomain dimension: {fd.dim_codomain}") fd.plot() plt.show() .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_004.png :alt: plot representation :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Domain dimension: 2 Codomain dimension: 2 .. GENERATED FROM PYTHON SOURCE LINES 79-86 Another possible representation is a decomposition in a basis of functions: .. math:: f(t) = \sum_{i=1}^N a_i \phi_i(t) It is possible to transform between both representations. Let us use again the Berkeley Growth dataset. .. GENERATED FROM PYTHON SOURCE LINES 86-93 .. code-block:: Python dataset = skfda.datasets.fetch_growth() fd = dataset["data"] y = dataset["target"] fd.plot() plt.show() .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_005.png :alt: Berkeley Growth Study :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 94-95 We will represent it using a basis of B-splines. .. GENERATED FROM PYTHON SOURCE LINES 95-103 .. code-block:: Python from skfda.representation import basis fd_basis = fd.to_basis(basis.BSplineBasis(n_basis=4)) fd_basis.plot() plt.show() .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_006.png :alt: Berkeley Growth Study :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_006.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 104-106 We can increase the number of elements in the basis to try to reproduce the original data with more fidelity. .. GENERATED FROM PYTHON SOURCE LINES 106-112 .. code-block:: Python fd_basis_big = fd.to_basis(basis.BSplineBasis(n_basis=7)) fd_basis_big.plot() plt.show() .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_007.png :alt: Berkeley Growth Study :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_007.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 113-115 Lets compare the diferent representations in the same plot, for the same curve .. GENERATED FROM PYTHON SOURCE LINES 115-123 .. code-block:: Python fig = fd[0].plot() fd_basis[0].plot(fig=fig) fd_basis_big[0].plot(fig=fig) fig.axes[0].legend(["Original", "4 elements", "7 elements"]) plt.show() .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_008.png :alt: Berkeley Growth Study :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_008.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 124-128 We can also see the effect of changing the basis. For example, in the Fourier basis the functions start and end at the same points if the period is equal to the domain range, so this basis is clearly non suitable for the Growth dataset. .. GENERATED FROM PYTHON SOURCE LINES 128-134 .. code-block:: Python fd_basis = fd.to_basis(basis.FourierBasis(n_basis=7)) fd_basis.plot() plt.show() .. image-sg:: /auto_examples/representation/images/sphx_glr_plot_representation_009.png :alt: Berkeley Growth Study :srcset: /auto_examples/representation/images/sphx_glr_plot_representation_009.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 135-136 The data is now represented as the coefficients in the basis expansion. .. GENERATED FROM PYTHON SOURCE LINES 136-138 .. code-block:: Python print(fd_basis) .. rst-class:: sphx-glr-script-out .. code-block:: none FDataBasis( _basis=FourierBasis(domain_range=((1.0, 18.0),), n_basis=7, period=17.0), coefficients=[[ 5.99308923e+02 -1.14873764e+02 2.75173660e+01 -5.99461262e+01 3.00407655e+01 -2.42099297e+01 3.06116238e+01] [ 5.48897873e+02 -8.54081358e+01 1.29613544e+01 -4.69373290e+01 3.05139003e+01 -2.11534333e+01 3.43876128e+01] [ 5.34606133e+02 -8.92928005e+01 2.19564051e+01 -4.88308206e+01 2.67601831e+01 -2.05310410e+01 2.75094852e+01] [ 5.60189583e+02 -9.81740138e+01 2.27565968e+01 -5.28604478e+01 2.95873338e+01 -2.57220403e+01 3.05609992e+01] [ 5.31961222e+02 -9.84166135e+01 2.29692209e+01 -5.08047387e+01 2.83861058e+01 -2.25286667e+01 3.14426375e+01] [ 5.44375259e+02 -9.14228813e+01 1.79086286e+01 -5.05486070e+01 2.74899404e+01 -2.13354242e+01 2.92148972e+01] [ 5.38760220e+02 -8.78443853e+01 1.11447104e+01 -4.92415698e+01 2.93566074e+01 -2.19018332e+01 3.18418770e+01] [ 5.74075270e+02 -1.06735394e+02 2.22520372e+01 -5.59996432e+01 2.64575787e+01 -2.38079035e+01 3.16454287e+01] [ 5.36487114e+02 -8.32523968e+01 1.86725048e+01 -4.37373810e+01 2.81948114e+01 -2.11428475e+01 2.94069450e+01] [ 5.95983096e+02 -1.09237516e+02 1.88789354e+01 -5.74865300e+01 2.49614186e+01 -2.22693486e+01 3.12035720e+01] [ 5.57080765e+02 -9.14783686e+01 1.82083758e+01 -4.87224084e+01 3.08468578e+01 -2.28748170e+01 3.35785799e+01] [ 5.79295854e+02 -1.05128952e+02 2.54881738e+01 -5.38268512e+01 3.16513011e+01 -2.32330489e+01 3.24641734e+01] [ 5.61698906e+02 -9.87617375e+01 2.20129447e+01 -5.21161085e+01 3.09546822e+01 -2.34860283e+01 3.15000308e+01] [ 5.80002600e+02 -1.06359425e+02 2.05832708e+01 -5.53528032e+01 2.68848174e+01 -2.24624360e+01 2.95663744e+01] [ 5.76586883e+02 -9.77828548e+01 1.56075226e+01 -5.36391220e+01 2.13316411e+01 -2.14705636e+01 2.70132444e+01] [ 5.76900135e+02 -1.04095143e+02 1.87699541e+01 -5.59296938e+01 2.53397993e+01 -2.32538634e+01 3.00921699e+01] [ 5.65926245e+02 -1.07146597e+02 2.09271432e+01 -5.52081521e+01 2.96883433e+01 -2.27857514e+01 3.08455764e+01] [ 5.72282791e+02 -1.06730159e+02 1.49370759e+01 -5.19543484e+01 2.18480779e+01 -1.79838600e+01 2.83431984e+01] [ 5.46281407e+02 -9.64583335e+01 1.63314484e+01 -5.21077025e+01 2.74183538e+01 -2.39873506e+01 2.97883139e+01] [ 5.54718097e+02 -1.02314585e+02 1.97618668e+01 -5.37439238e+01 2.43879308e+01 -2.17599864e+01 2.87428586e+01] [ 5.40664946e+02 -8.55292523e+01 1.59158395e+01 -4.69104985e+01 2.93651736e+01 -2.09169457e+01 3.26516204e+01] [ 5.43190236e+02 -9.31881751e+01 2.20087944e+01 -4.78145679e+01 2.67885059e+01 -2.22787786e+01 2.73298127e+01] [ 5.48101974e+02 -9.42605483e+01 1.97440108e+01 -5.07283821e+01 3.01148080e+01 -2.51827512e+01 3.46146301e+01] [ 5.35974379e+02 -9.31891966e+01 2.08102241e+01 -4.98979283e+01 2.41687758e+01 -1.97785861e+01 2.66652135e+01] [ 5.45080584e+02 -9.07019215e+01 2.24437932e+01 -4.74386437e+01 2.69158000e+01 -2.15649788e+01 2.75707272e+01] [ 5.56071285e+02 -1.00970119e+02 1.83444576e+01 -5.09149329e+01 3.20481885e+01 -2.30340659e+01 3.65994803e+01] [ 5.65317909e+02 -8.85619621e+01 1.20622371e+01 -4.56513244e+01 2.98196483e+01 -2.13220966e+01 3.39207202e+01] [ 5.32437188e+02 -8.40135179e+01 1.80058244e+01 -4.55500693e+01 2.62772466e+01 -2.08909021e+01 2.89143539e+01] [ 6.06168308e+02 -1.13998299e+02 2.14636268e+01 -6.00612720e+01 2.80212325e+01 -2.45679365e+01 3.17706005e+01] [ 5.54652665e+02 -9.59141822e+01 1.83963898e+01 -5.08625195e+01 3.26084310e+01 -2.42618221e+01 3.34156902e+01] [ 5.70570928e+02 -1.07306210e+02 2.03934395e+01 -5.51306638e+01 2.38801393e+01 -2.14537819e+01 2.86923361e+01] [ 5.98736539e+02 -1.09836265e+02 2.31587725e+01 -5.88578930e+01 2.81480280e+01 -2.32859370e+01 3.11203998e+01] [ 5.52219352e+02 -8.68132817e+01 1.73874116e+01 -4.62856832e+01 2.80210530e+01 -2.22090130e+01 3.02535201e+01] [ 5.45150662e+02 -9.57236717e+01 2.57514324e+01 -5.02866832e+01 2.51052795e+01 -2.12797644e+01 2.68490104e+01] [ 5.97211431e+02 -1.06850021e+02 1.32554219e+01 -5.17107091e+01 2.55641465e+01 -2.51713173e+01 3.23104670e+01] [ 5.61518039e+02 -1.04507220e+02 1.73437109e+01 -5.74511173e+01 2.73371579e+01 -2.51743884e+01 3.12306629e+01] [ 5.89181128e+02 -1.01765056e+02 1.96490191e+01 -5.13798171e+01 2.26424568e+01 -1.98818676e+01 2.74849815e+01] [ 5.79382454e+02 -1.05791220e+02 1.39335819e+01 -5.26716093e+01 2.36948942e+01 -1.96474940e+01 2.87840205e+01] [ 5.51407740e+02 -9.57356066e+01 1.92393603e+01 -5.04749182e+01 2.68379989e+01 -2.28241092e+01 3.07542560e+01] [ 5.39135250e+02 -8.88513179e+01 2.55144104e+00 -3.97960747e+01 1.40580870e+01 -1.54917823e+01 2.59400829e+01] [ 5.46244322e+02 -9.56132391e+01 9.23417894e+00 -4.42620585e+01 1.93539566e+01 -1.76435571e+01 2.56146984e+01] [ 5.60313637e+02 -9.15648753e+01 -5.82003275e+00 -3.83271136e+01 1.49012021e+01 -1.80998766e+01 2.79783174e+01] [ 5.56978023e+02 -9.28112207e+01 7.18894247e+00 -4.58625098e+01 1.76981238e+01 -1.82840459e+01 2.64319644e+01] [ 5.52572545e+02 -9.71360646e+01 1.15055655e+01 -4.70741375e+01 2.16358629e+01 -1.79707499e+01 2.58851254e+01] [ 5.36934255e+02 -9.76897659e+01 1.28613949e+01 -4.54412544e+01 1.75414041e+01 -1.65134308e+01 2.65471784e+01] [ 5.19927942e+02 -8.57299537e+01 1.08433283e+01 -4.67556614e+01 2.32981647e+01 -2.16429969e+01 2.87503736e+01] [ 6.12204934e+02 -1.09601555e+02 1.31527081e+00 -4.55721145e+01 1.83217318e+01 -2.11128813e+01 3.23763995e+01] [ 5.50480200e+02 -9.51255290e+01 5.75751181e+00 -4.36021818e+01 1.56118505e+01 -1.61905251e+01 2.67642244e+01] [ 5.75273565e+02 -1.03785710e+02 2.87894403e+00 -5.00606070e+01 1.77107011e+01 -1.89021366e+01 3.12706087e+01] [ 5.39181810e+02 -8.74897261e+01 9.63381503e+00 -4.73582040e+01 2.34098312e+01 -2.21053642e+01 2.72025837e+01] [ 5.38321252e+02 -9.25717805e+01 6.44366835e+00 -4.74686455e+01 1.75843207e+01 -1.83972642e+01 2.62746131e+01] [ 5.00140286e+02 -7.79292834e+01 9.20713731e+00 -4.22066082e+01 2.13577811e+01 -1.96794009e+01 2.51025814e+01] [ 5.52970660e+02 -9.28711825e+01 1.12721168e+01 -4.76036637e+01 2.26887239e+01 -1.95380353e+01 2.69499961e+01] [ 5.61345841e+02 -1.07003573e+02 4.54667968e+00 -4.58593784e+01 2.11905849e+01 -1.47219200e+01 2.90074639e+01] [ 5.10558942e+02 -8.11616379e+01 1.06513156e+01 -4.21917638e+01 1.70349388e+01 -1.58033350e+01 2.46077602e+01] [ 5.43627855e+02 -9.68349026e+01 -1.22287745e+00 -3.90608220e+01 1.43854996e+01 -1.79044988e+01 2.70921791e+01] [ 5.77161078e+02 -9.85333632e+01 1.20014603e-01 -4.39834039e+01 1.71144994e+01 -1.66659377e+01 2.73868569e+01] [ 5.49485081e+02 -1.00664731e+02 4.94702320e+00 -4.37712750e+01 1.49573258e+01 -1.70420508e+01 3.01066654e+01] [ 5.59108004e+02 -9.87706028e+01 8.26596278e+00 -4.62067956e+01 1.77503711e+01 -1.87062333e+01 2.84358540e+01] [ 5.65003297e+02 -1.06435308e+02 5.49420620e+00 -4.85466595e+01 1.88716609e+01 -1.73355026e+01 2.98685083e+01] [ 5.43868630e+02 -1.00345329e+02 4.90381879e+00 -4.21452697e+01 1.76339644e+01 -1.53534156e+01 2.81154045e+01] [ 5.38525284e+02 -9.59331252e+01 6.52639178e+00 -4.40901713e+01 1.62142161e+01 -1.56457079e+01 2.69396619e+01] [ 5.23370065e+02 -8.95406540e+01 6.30223624e+00 -4.30799760e+01 1.66905202e+01 -1.42799947e+01 2.53341322e+01] [ 5.71121926e+02 -1.07954730e+02 1.84983994e+01 -5.26238120e+01 2.62347728e+01 -2.18001889e+01 2.92125040e+01] [ 5.13426363e+02 -8.90791956e+01 1.19825429e+01 -4.38593857e+01 1.85655885e+01 -1.65421271e+01 2.41213457e+01] [ 5.52962188e+02 -9.21345904e+01 3.28902527e+00 -4.58454141e+01 1.69308410e+01 -1.71481129e+01 2.72311887e+01] [ 5.49964443e+02 -9.27854148e+01 9.48112465e+00 -4.75482728e+01 1.43935455e+01 -1.76735609e+01 2.67026063e+01] [ 5.00705442e+02 -8.53092980e+01 1.43470009e+01 -4.40308172e+01 2.08833472e+01 -1.78026303e+01 2.47683865e+01] [ 5.46098900e+02 -9.39441571e+01 1.30284787e+01 -4.79309436e+01 1.93794660e+01 -1.78586939e+01 2.61801955e+01] [ 5.46913499e+02 -8.93870530e+01 8.52549272e+00 -4.52328860e+01 1.86808044e+01 -1.62772943e+01 2.63048681e+01] [ 5.53660092e+02 -9.99403236e+01 -5.25265019e+00 -4.46349558e+01 1.51694965e+01 -1.85739527e+01 2.97632580e+01] [ 5.59813837e+02 -9.49280033e+01 1.15486892e+01 -4.95937257e+01 2.21884722e+01 -2.07278596e+01 2.73240069e+01] [ 5.42647879e+02 -9.36782615e+01 7.39169942e+00 -4.38218071e+01 1.56916538e+01 -1.69626153e+01 2.65022153e+01] [ 5.57556323e+02 -1.00060524e+02 5.46702364e+00 -4.72428033e+01 1.97932991e+01 -1.72037376e+01 2.79946719e+01] [ 5.40417474e+02 -9.45361518e+01 1.06497154e+01 -4.67932237e+01 1.93909626e+01 -1.80517830e+01 2.58176113e+01] [ 5.26776001e+02 -9.26407816e+01 1.11481148e+01 -4.81163405e+01 2.17720423e+01 -2.04315426e+01 2.69207214e+01] [ 5.80189078e+02 -1.07654945e+02 3.55013740e+00 -4.93143073e+01 2.04402466e+01 -1.98081935e+01 3.06725691e+01] [ 5.62261092e+02 -1.02538949e+02 7.24425492e+00 -4.73770964e+01 1.71637520e+01 -1.93611070e+01 2.82762388e+01] [ 5.64264106e+02 -1.00658789e+02 5.01547652e+00 -4.34512632e+01 1.84211522e+01 -1.66923320e+01 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:alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_representation.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_representation.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_representation.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_