}KgLdZddlmZddlZddlZddlZddlZddlZddlZddl Zddl Zddl m Z ddl mZddlmZddlmZdd lmZmZmZmZmZmZdd lmZdd lmZmZgd Zed d d d ddddej@dej@dee!de"dedde"deeej@ee"fde#dej@fdZ$ed d d d ddddej@dej@dee!de"dedde"deeej@ee"fde#dejJjLfdZ$e dddddddddej@dej@dee!de"de#de"deeej@ee"fde#deej@ejJjLffd Z$ed d d d d d d d d dd! dej@dee!d"e!de"d#e#dedde"deeej@ee"fd$e#d%e!de#dejJjLfd&Z'ed d d d d d d d d dd! dej@dee!d"e!de"d#e#dedde"deeej@ee"fd$e#d%e!de#dej@fd'Z'e dddddddddd(dd! dej@dee!d"e!de"d#e#de#de"deeej@ee"fd$e#d%e!de#deej@ejJjLffd)Z'ed*eej@ejJjPf+Z)dd(d,d-e)d.e#d%e!de)fd/Z*d(d0d1e)d%e!de)fd2Z+ed3ed ef+Z,dOd4e,d.e#d5e!de,fd6Z-e dd7d(d8dej@d9ej@d:e!d%e!dej@f d;Z.dd(d<dej@de!d=eej^j`d%e!dej@f d>Z1d?d@ddAdddBdCej@dDe!dEedFe2dGee2dHe!dIe#dJe#dKedej@fdLZ3d-ejJjhdMeeej@ee"fde!dee2ej@ffdNZ5y)Pa Temporal segmentation ===================== Recurrence and self-similarity ------------------------------ .. autosummary:: :toctree: generated/ cross_similarity recurrence_matrix recurrence_to_lag lag_to_recurrence timelag_filter path_enhance Temporal clustering ------------------- .. autosummary:: :toctree: generated/ agglomerative subsegment  decoratorN)cache)util)diagonal_filter)ParameterError)AnyCallableOptionalTypeVarUnionoverload)Literal) _WindowSpec _FloatLike_co)cross_similarityrecurrence_matrixrecurrence_to_laglag_to_recurrencetimelag_filter agglomerative subsegment path_enhance.F)kmetricsparsemode bandwidthfulldatadata_refrrrrrr returncyNr!r"rrrrrr s S/home/alanp/www/video.onchill/myenv/lib/python3.12/site-packages/librosa/segment.pyrr<Tcyr%r&r's r(rrKr)r*)level euclidean connectivityc tj|}tj|}tj|jdd|jdds&t d|jd|jdtj |dd}|jd}|j |dfd}tj |dd}|jd} |j | dfd}|d vrt d |d |5t|d tjtj|z}t|}|} |r|d k7r| } tjjt|||d} | j||dk(rd} n|} | j!|| j#} |s^t%| D]P}| |j'd}|tj(| ||fj+d}d| |||df<R| j-} | j/|d k(r| j1t2} nD|dk(r?t5| || }tj6| j8d|zz | j8dd| j:} |s| j+} | S#t$r0tjjt|||d} YswxYw)uCompute cross-similarity from one data sequence to a reference sequence. The output is a matrix ``xsim``, where ``xsim[i, j]`` is non-zero if ``data_ref[..., i]`` is a k-nearest neighbor of ``data[..., j]``. Parameters ---------- data : np.ndarray [shape=(..., d, n)] A feature matrix for the comparison sequence. If the data has more than two dimensions (e.g., for multi-channel inputs), the leading dimensions are flattened prior to comparison. For example, a stereo input with shape `(2, d, n)` is automatically reshaped to `(2 * d, n)`. data_ref : np.ndarray [shape=(..., d, n_ref)] A feature matrix for the reference sequence If the data has more than two dimensions (e.g., for multi-channel inputs), the leading dimensions are flattened prior to comparison. For example, a stereo input with shape `(2, d, n_ref)` is automatically reshaped to `(2 * d, n_ref)`. k : int > 0 [scalar] or None the number of nearest-neighbors for each sample Default: ``k = 2 * ceil(sqrt(n_ref))``, or ``k = 2`` if ``n_ref <= 3`` metric : str Distance metric to use for nearest-neighbor calculation. See `sklearn.neighbors.NearestNeighbors` for details. sparse : bool [scalar] if False, returns a dense type (ndarray) if True, returns a sparse type (scipy.sparse.csc_matrix) mode : str, {'connectivity', 'distance', 'affinity'} If 'connectivity', a binary connectivity matrix is produced. If 'distance', then a non-zero entry contains the distance between points. If 'affinity', then non-zero entries are mapped to ``exp( - distance(i, j) / bandwidth)`` where ``bandwidth`` is as specified below. bandwidth : None, float > 0, ndarray, or str str options include ``{'med_k_scalar', 'mean_k', 'gmean_k', 'mean_k_avg', 'gmean_k_avg', 'mean_k_avg_and_pair'}`` If ndarray is supplied, use ndarray as bandwidth for each i,j pair. If using ``mode='affinity'``, this can be used to set the bandwidth on the affinity kernel. If no value is provided or ``None``, default to ``'med_k_scalar'``. If ``bandwidth='med_k_scalar'``, bandwidth is set automatically to the median distance to the k'th nearest neighbor of each ``data[:, i]``. If ``bandwidth='mean_k'``, bandwidth is estimated for each sample-pair (i, j) by taking the arithmetic mean between distances to the k-th nearest neighbor for sample i and sample j. If ``bandwidth='gmean_k'``, bandwidth is estimated for each sample-pair (i, j) by taking the geometric mean between distances to the k-th nearest neighbor for sample i and j [#z]_. If ``bandwidth='mean_k_avg'``, bandwidth is estimated for each sample-pair (i, j) by taking the arithmetic mean between the average distances to the first k-th nearest neighbors for sample i and sample j. This is similar to the approach in Wang et al. (2014) [#w]_ but does not include the distance between i and j. If ``bandwidth='gmean_k_avg'``, bandwidth is estimated for each sample-pair (i, j) by taking the geometric mean between the average distances to the first k-th nearest neighbors for sample i and sample j. If ``bandwidth='mean_k_avg_and_pair'``, bandwidth is estimated for each sample-pair (i, j) by taking the arithmetic mean between three terms: the average distances to the first k-th nearest neighbors for sample i and sample j respectively, as well as the distance between i and j. This is similar to the approach in Wang et al. (2014). [#w]_ .. [#z] Zelnik-Manor, Lihi, and Pietro Perona. (2004). "Self-tuning spectral clustering." Advances in neural information processing systems 17. .. [#w] Wang, Bo, et al. (2014). "Similarity network fusion for aggregating data types on a genomic scale." Nat Methods 11, 333–337. https://doi.org/10.1038/nmeth.2810 full : bool If using ``mode ='affinity'`` or ``mode='distance'``, this option can be used to compute the full affinity or distance matrix as opposed a sparse matrix with only none-zero terms for the first k-neighbors of each sample. This option has no effect when using ``mode='connectivity'``. When using ``mode='distance'``, setting ``full=True`` will ignore ``k`` and ``width``. When using ``mode='affinity'``, setting ``full=True`` will use ``k`` exclusively for bandwidth estimation, and ignore ``width``. Returns ------- xsim : np.ndarray or scipy.sparse.csc_matrix, [shape=(n_ref, n)] Cross-similarity matrix See Also -------- recurrence_matrix recurrence_to_lag librosa.feature.stack_memory sklearn.neighbors.NearestNeighbors scipy.spatial.distance.cdist Notes ----- This function caches at level 30. Examples -------- Find nearest neighbors in CQT space between two sequences >>> hop_length = 1024 >>> y_ref, sr = librosa.load(librosa.ex('pistachio')) >>> y_comp, sr = librosa.load(librosa.ex('pistachio'), offset=10) >>> chroma_ref = librosa.feature.chroma_cqt(y=y_ref, sr=sr, hop_length=hop_length) >>> chroma_comp = librosa.feature.chroma_cqt(y=y_comp, sr=sr, hop_length=hop_length) >>> # Use time-delay embedding to get a cleaner recurrence matrix >>> x_ref = librosa.feature.stack_memory(chroma_ref, n_steps=10, delay=3) >>> x_comp = librosa.feature.stack_memory(chroma_comp, n_steps=10, delay=3) >>> xsim = librosa.segment.cross_similarity(x_comp, x_ref) Or fix the number of nearest neighbors to 5 >>> xsim = librosa.segment.cross_similarity(x_comp, x_ref, k=5) Use cosine similarity instead of Euclidean distance >>> xsim = librosa.segment.cross_similarity(x_comp, x_ref, metric='cosine') Use an affinity matrix instead of binary connectivity >>> xsim_aff = librosa.segment.cross_similarity(x_comp, x_ref, metric='cosine', mode='affinity') Plot the feature and recurrence matrices >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(ncols=2, sharex=True, sharey=True) >>> imgsim = librosa.display.specshow(xsim, x_axis='s', y_axis='s', ... hop_length=hop_length, ax=ax[0]) >>> ax[0].set(title='Binary cross-similarity (symmetric)') >>> imgaff = librosa.display.specshow(xsim_aff, x_axis='s', y_axis='s', ... cmap='magma_r', hop_length=hop_length, ax=ax[1]) >>> ax[1].set(title='Cross-affinity') >>> ax[1].label_outer() >>> fig.colorbar(imgsim, ax=ax[0], orientation='horizontal', ticks=[0, 1]) >>> fig.colorbar(imgaff, ax=ax[1], orientation='horizontal') Nzdata_ref.shape=z and data.shape=z% do not match on leading dimension(s)rForderr/distanceaffinityInvalid mode=':'. Must be one of ['connectivity', 'distance', 'affinity']r/auto n_neighborsr algorithmbruter7r6)Xrr)np atleast_2dallcloseshaper swapaxesreshapeminceilsqrtintsklearn neighborsNearestNeighbors ValueErrorfitkneighbors_graphtolilrangenonzeroargsorttoarraytocsreliminate_zerosastypebool__affinity_bandwidthexpr!T)r!r"rrrrrr n_refn bandwidth_kknnkng_modexsimilinksidx aff_bandwidths r(rrZsN}}X&H == D ;;x~~cr*DJJsO <hnn--=djj\In o  {{8R+H NN1 E 37H ;;tR #D 1 A <<Bs< +D ;; ';;   y q2772775>22 3 AAK '   00E1 f1 GGH z   $X  6 < < >D qAGOO%a(E 45>#9#9#;<=a@C !DCG  ::? !  66D ||~ K[  00E1 f1  s,J??5K87K8) rwidthrsymrrrselfaxisr rgrhrirjc yr%r& r!rrgrrhrrrrirjr s r(rr[r*c yr%r&rls r(rrmrmr*r1c ptj|}tj|| d}|jd} |j | dfd}|dks || dz dzk\r"t dj || | dz dz|dvrt d |d |4dtjtj| d|zz dzz}t|}|} | r|d k7r| } tjjt| dz |d|zz|d } | j||dk(rd}n|}| j!|j#}| st%| dz|D]}|j'd|t%| D]P}||j)d}|tj*|||fj-d}d||||d f<R|r.|d k(r|j'dn(|dk(r#|j'dn|j'd|r|j/|j0}|j3}|j5|d k(r|j7t8}n`|dk(r[d|j:|j:dk<t=||| }tj>|j:d|zz |j:d d |j0}|s|j-}|S#t$r9tjjt| dz |d|zz|d} YwxYw)uCompute a recurrence matrix from a data matrix. ``rec[i, j]`` is non-zero if ``data[..., i]`` is a k-nearest neighbor of ``data[..., j]`` and ``|i - j| >= width`` The specific value of ``rec[i, j]`` can have several forms, governed by the ``mode`` parameter below: - Connectivity: ``rec[i, j] = 1 or 0`` indicates that frames ``i`` and ``j`` are repetitions - Affinity: ``rec[i, j] > 0`` measures how similar frames ``i`` and ``j`` are. This is also known as a (sparse) self-similarity matrix. - Distance: ``rec[i, j] > 0`` measures how distant frames ``i`` and ``j`` are. This is also known as a (sparse) self-distance matrix. The general term *recurrence matrix* can refer to any of the three forms above. Parameters ---------- data : np.ndarray [shape=(..., d, n)] A feature matrix. If the data has more than two dimensions (e.g., for multi-channel inputs), the leading dimensions are flattened prior to comparison. For example, a stereo input with shape `(2, d, n)` is automatically reshaped to `(2 * d, n)`. k : int > 0 [scalar] or None the number of nearest-neighbors for each sample Default: ``k = 2 * ceil(sqrt(t - 2 * width + 1))``, or ``k = 2`` if ``t <= 2 * width + 1`` width : int >= 1 [scalar] only link neighbors ``(data[..., i], data[..., j])`` if ``|i - j| >= width`` ``width`` cannot exceed the length of the data. metric : str Distance metric to use for nearest-neighbor calculation. See `sklearn.neighbors.NearestNeighbors` for details. sym : bool [scalar] set ``sym=True`` to only link mutual nearest-neighbors sparse : bool [scalar] if False, returns a dense type (ndarray) if True, returns a sparse type (scipy.sparse.csc_matrix) mode : str, {'connectivity', 'distance', 'affinity'} If 'connectivity', a binary connectivity matrix is produced. If 'distance', then a non-zero entry contains the distance between points. If 'affinity', then non-zero entries are mapped to ``exp( - distance(i, j) / bandwidth)`` where ``bandwidth`` is as specified below. bandwidth : None, float > 0, ndarray, or str str options include ``{'med_k_scalar', 'mean_k', 'gmean_k', 'mean_k_avg', 'gmean_k_avg', 'mean_k_avg_and_pair'}`` If ndarray is supplied, use ndarray as bandwidth for each i,j pair. If using ``mode='affinity'``, the ``bandwidth`` option can be used to set the bandwidth on the affinity kernel. If no value is provided or ``None``, default to ``'med_k_scalar'``. If ``bandwidth='med_k_scalar'``, a scalar bandwidth is set to the median distance of the k-th nearest neighbor for all samples. If ``bandwidth='mean_k'``, bandwidth is estimated for each sample-pair (i, j) by taking the arithmetic mean between distances to the k-th nearest neighbor for sample i and sample j. If ``bandwidth='gmean_k'``, bandwidth is estimated for each sample-pair (i, j) by taking the geometric mean between distances to the k-th nearest neighbor for sample i and j [#z]_. If ``bandwidth='mean_k_avg'``, bandwidth is estimated for each sample-pair (i, j) by taking the arithmetic mean between the average distances to the first k-th nearest neighbors for sample i and sample j. This is similar to the approach in Wang et al. (2014) [#w]_ but does not include the distance between i and j. If ``bandwidth='gmean_k_avg'``, bandwidth is estimated for each sample-pair (i, j) by taking the geometric mean between the average distances to the first k-th nearest neighbors for sample i and sample j. If ``bandwidth='mean_k_avg_and_pair'``, bandwidth is estimated for each sample-pair (i, j) by taking the arithmetic mean between three terms: the average distances to the first k-th nearest neighbors for sample i and sample j respectively, as well as the distance between i and j. This is similar to the approach in Wang et al. (2014). [#w]_ .. [#z] Zelnik-Manor, Lihi, and Pietro Perona. (2004). "Self-tuning spectral clustering." Advances in neural information processing systems 17. .. [#w] Wang, Bo, et al. (2014). "Similarity network fusion for aggregating data types on a genomic scale." Nat Methods 11, 333–337. https://doi.org/10.1038/nmeth.2810 self : bool If ``True``, then the main diagonal is populated with self-links: 0 if ``mode='distance'``, and 1 otherwise. If ``False``, the main diagonal is left empty. axis : int The axis along which to compute recurrence. By default, the last index (-1) is taken. full : bool If using ``mode ='affinity'`` or ``mode='distance'``, this option can be used to compute the full affinity or distance matrix as opposed a sparse matrix with only none-zero terms for the first k-neighbors of each sample. This option has no effect when using ``mode='connectivity'``. When using ``mode='distance'``, setting ``full=True`` will ignore ``k`` and ``width``. When using ``mode='affinity'``, setting ``full=True`` will use ``k`` exclusively for bandwidth estimation, and ignore ``width``. Returns ------- rec : np.ndarray or scipy.sparse.csc_matrix, [shape=(t, t)] Recurrence matrix See Also -------- sklearn.neighbors.NearestNeighbors scipy.spatial.distance.cdist librosa.feature.stack_memory recurrence_to_lag Notes ----- This function caches at level 30. Examples -------- Find nearest neighbors in CQT space >>> y, sr = librosa.load(librosa.ex('nutcracker')) >>> hop_length = 1024 >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr, hop_length=hop_length) >>> # Use time-delay embedding to get a cleaner recurrence matrix >>> chroma_stack = librosa.feature.stack_memory(chroma, n_steps=10, delay=3) >>> R = librosa.segment.recurrence_matrix(chroma_stack) Or fix the number of nearest neighbors to 5 >>> R = librosa.segment.recurrence_matrix(chroma_stack, k=5) Suppress neighbors within +- 7 frames >>> R = librosa.segment.recurrence_matrix(chroma_stack, width=7) Use cosine similarity instead of Euclidean distance >>> R = librosa.segment.recurrence_matrix(chroma_stack, metric='cosine') Require mutual nearest neighbors >>> R = librosa.segment.recurrence_matrix(chroma_stack, sym=True) Use an affinity matrix instead of binary connectivity >>> R_aff = librosa.segment.recurrence_matrix(chroma_stack, metric='cosine', ... mode='affinity') Plot the feature and recurrence matrices >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(ncols=2, sharex=True, sharey=True) >>> imgsim = librosa.display.specshow(R, x_axis='s', y_axis='s', ... hop_length=hop_length, ax=ax[0]) >>> ax[0].set(title='Binary recurrence (symmetric)') >>> imgaff = librosa.display.specshow(R_aff, x_axis='s', y_axis='s', ... hop_length=hop_length, cmap='magma_r', ax=ax[1]) >>> ax[1].set(title='Affinity recurrence') >>> ax[1].label_outer() >>> fig.colorbar(imgsim, ax=ax[0], orientation='horizontal', ticks=[0, 1]) >>> fig.colorbar(imgaff, ax=ax[1], orientation='horizontal') rr1r2r3rr:zDwidth={} must be at least 1 and at most (data.shape[{}] - 1) // 2={}r5r8r9Nr/r;r<r?r7r6rg) rArBrErDrFr formatrHrIrJrKrLrMrGrNrOrPrQrRsetdiagrSrTrUminimumr\rVrWrXrYr!rZr[)r!rrgrrhrrrrirjr tr_r`rarecdiagrcrdrerfs r(rrs;P == D ;;tT1 %D 1 A <<Bs< +D qyEa!e\) R Y Yta!e\    ;; ';;   y AI  123 3 AAK '  00AE1q5y=1&F1 GGDM z  H  - 3 3 5C 5&1*e,D KK4 -qAFNN$Q'E 3q%x=#8#8#:; ! KKN Z  KKO A kk#%%  ))+C ~jj  "%A,S)[I ffSXXm);<=  %%C kkm JK  00AE1q5y=1&G1  s#5K33>L54L5_ArrayOrSparseMatrix)bound)padrjruryctj|}|jdk7s|jd|jdk7rt d|jt j j|}|r |j}|j|}|r|ratjddgg|jj|d}|dk(rd}nd}t j j|||}n=tjd d g}d|g|d|z d d f<tj||d }tj |d |}|r|j#}|S)u Convert a recurrence matrix into a lag matrix. ``lag[i, j] == rec[i+j, j]`` This transformation turns diagonal structures in the recurrence matrix into horizontal structures in the lag matrix. These horizontal structures can be used to infer changes in the repetition structure of a piece, e.g., the beginning of a new section as done in [#]_. .. [#] Serra, J., Müller, M., Grosche, P., & Arcos, J. L. (2014). Unsupervised music structure annotation by time series structure features and segment similarity. IEEE Transactions on Multimedia, 16(5), 1229-1240. Parameters ---------- rec : np.ndarray, or scipy.sparse.spmatrix [shape=(n, n)] A (binary) recurrence matrix, as returned by `recurrence_matrix` pad : bool If False, ``lag`` matrix is square, which is equivalent to assuming that the signal repeats itself indefinitely. If True, ``lag`` is padded with ``n`` zeros, which eliminates the assumption of repetition. axis : int The axis to keep as the ``time`` axis. The alternate axis will be converted to lag coordinates. Returns ------- lag : np.ndarray The recurrence matrix in (lag, time) (if ``axis=1``) or (time, lag) (if ``axis=0``) coordinates Raises ------ ParameterError : if ``rec`` is non-square See Also -------- recurrence_matrix lag_to_recurrence util.shear Examples -------- >>> y, sr = librosa.load(librosa.ex('nutcracker')) >>> hop_length = 1024 >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr, hop_length=hop_length) >>> chroma_stack = librosa.feature.stack_memory(chroma, n_steps=10, delay=3) >>> recurrence = librosa.segment.recurrence_matrix(chroma_stack) >>> lag_pad = librosa.segment.recurrence_to_lag(recurrence, pad=True) >>> lag_nopad = librosa.segment.recurrence_to_lag(recurrence, pad=False) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, sharex=True) >>> librosa.display.specshow(lag_pad, x_axis='time', y_axis='lag', ... hop_length=hop_length, ax=ax[0]) >>> ax[0].set(title='Lag (zero-padded)') >>> ax[0].label_outer() >>> librosa.display.specshow(lag_nopad, x_axis='time', y_axis='lag', ... hop_length=hop_length, ax=ax[1]) >>> ax[1].set(title='Lag (no padding)') r:rrz$non-square recurrence matrix shape: )dtypecsrcsc)rq)rrNconstantrpr1factorrj)rAabsndimrDr scipyrissparserqasarrayr{rEkronarrayryrshearasformat) ruryrjrfmtrtpaddingrec_fmtlags r(rrs6J 66$>> y, sr = librosa.load(librosa.ex('nutcracker')) >>> hop_length = 1024 >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr, hop_length=hop_length) >>> chroma_stack = librosa.feature.stack_memory(chroma, n_steps=10, delay=3) >>> recurrence = librosa.segment.recurrence_matrix(chroma_stack) >>> lag_pad = librosa.segment.recurrence_to_lag(recurrence, pad=True) >>> lag_nopad = librosa.segment.recurrence_to_lag(recurrence, pad=False) >>> rec_pad = librosa.segment.lag_to_recurrence(lag_pad) >>> rec_nopad = librosa.segment.lag_to_recurrence(lag_nopad) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, ncols=2, sharex=True) >>> librosa.display.specshow(lag_pad, x_axis='s', y_axis='lag', ... hop_length=hop_length, ax=ax[0, 0]) >>> ax[0, 0].set(title='Lag (zero-padded)') >>> ax[0, 0].label_outer() >>> librosa.display.specshow(lag_nopad, x_axis='s', y_axis='time', ... hop_length=hop_length, ax=ax[0, 1]) >>> ax[0, 1].set(title='Lag (no padding)') >>> ax[0, 1].label_outer() >>> librosa.display.specshow(rec_pad, x_axis='s', y_axis='time', ... hop_length=hop_length, ax=ax[1, 0]) >>> ax[1, 0].set(title='Recurrence (with padding)') >>> librosa.display.specshow(rec_nopad, x_axis='s', y_axis='time', ... hop_length=hop_length, ax=ax[1, 1]) >>> ax[1, 1].set(title='Recurrence (without padding)') >>> ax[1, 1].label_outer() )rrr1zInvalid target axis: r:rrzInvalid lag matrix shape: rN) r rArrrDrrslicetuple)rrjrtru sub_slice rec_slices r(rr#sr :4TF;<< 66$>> data_tl = librosa.segment.recurrence_to_lag(data) >>> data_filtered_tl = function(data_tl) >>> data_filtered = librosa.segment.lag_to_recurrence(data_filtered_tl) Parameters ---------- function : callable The filtering function to wrap, e.g., `scipy.ndimage.median_filter` pad : bool Whether to zero-pad the structure feature matrix index : int >= 0 If ``function`` accepts input data as a positional argument, it should be indexed by ``index`` Returns ------- wrapped_function : callable A new filter function which applies in time-lag space rather than time-time space. Examples -------- Apply a 31-bin median filter to the diagonal of a recurrence matrix. With default, parameters, this corresponds to a time window of about 0.72 seconds. >>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=30) >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr) >>> chroma_stack = librosa.feature.stack_memory(chroma, n_steps=3, delay=3) >>> rec = librosa.segment.recurrence_matrix(chroma_stack) >>> from scipy.ndimage import median_filter >>> diagonal_median = librosa.segment.timelag_filter(median_filter) >>> rec_filtered = diagonal_median(rec, size=(1, 31), mode='mirror') Or with affinity weights >>> rec_aff = librosa.segment.recurrence_matrix(chroma_stack, mode='affinity') >>> rec_aff_fil = diagonal_median(rec_aff, size=(1, 31), mode='mirror') >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(nrows=2, ncols=2, sharex=True, sharey=True) >>> librosa.display.specshow(rec, y_axis='s', x_axis='s', ax=ax[0, 0]) >>> ax[0, 0].set(title='Raw recurrence matrix') >>> ax[0, 0].label_outer() >>> librosa.display.specshow(rec_filtered, y_axis='s', x_axis='s', ax=ax[0, 1]) >>> ax[0, 1].set(title='Filtered recurrence matrix') >>> ax[0, 1].label_outer() >>> librosa.display.specshow(rec_aff, x_axis='s', y_axis='s', ... cmap='magma_r', ax=ax[1, 0]) >>> ax[1, 0].set(title='Raw affinity matrix') >>> librosa.display.specshow(rec_aff_fil, x_axis='s', y_axis='s', ... cmap='magma_r', ax=ax[1, 1]) >>> ax[1, 1].set(title='Filtered affinity matrix') >>> ax[1, 1].label_outer() cft|}t||<||i|}t|S)z$Wrap the filter with lag conversions)ry)listrr) wrapped_fargskwargsresultrrys r( __my_filterz#timelag_filter..__my_filters@Dz'U =U D+F+!((r*r)rryrrs `` r(rrts@ ) [( ++r*) n_segmentsrjframesrc tj|d|j|d}|dkr tdg}t dg|j z}t |dd|ddD]M\}}t ||||<|j|t|t|t||z ||zOtj|S) ax Sub-divide a segmentation by feature clustering. Given a set of frame boundaries (``frames``), and a data matrix (``data``), each successive interval defined by ``frames`` is partitioned into ``n_segments`` by constrained agglomerative clustering. .. note:: If an interval spans fewer than ``n_segments`` frames, then each frame becomes a sub-segment. Parameters ---------- data : np.ndarray Data matrix to use in clustering frames : np.ndarray [shape=(n_boundaries,)], dtype=int, non-negative] Array of beat or segment boundaries, as provided by `librosa.beat.beat_track`, `librosa.onset.onset_detect`, or `agglomerative`. n_segments : int > 0 Maximum number of frames to sub-divide each interval. axis : int Axis along which to apply the segmentation. By default, the last index (-1) is taken. Returns ------- boundaries : np.ndarray [shape=(n_subboundaries,)] List of sub-divided segment boundaries See Also -------- agglomerative : Temporal segmentation librosa.onset.onset_detect : Onset detection librosa.beat.beat_track : Beat tracking Notes ----- This function caches at level 30. Examples -------- Load audio, detect beat frames, and subdivide in twos by CQT >>> y, sr = librosa.load(librosa.ex('choice'), duration=10) >>> tempo, beats = librosa.beat.beat_track(y=y, sr=sr, hop_length=512) >>> beat_times = librosa.frames_to_time(beats, sr=sr, hop_length=512) >>> cqt = np.abs(librosa.cqt(y, sr=sr, hop_length=512)) >>> subseg = librosa.segment.subsegment(cqt, beats, n_segments=2) >>> subseg_t = librosa.frames_to_time(subseg, sr=sr, hop_length=512) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> librosa.display.specshow(librosa.amplitude_to_db(cqt, ... ref=np.max), ... y_axis='cqt_hz', x_axis='time', ax=ax) >>> lims = ax.get_ylim() >>> ax.vlines(beat_times, lims[0], lims[1], color='lime', alpha=0.9, ... linewidth=2, label='Beats') >>> ax.vlines(subseg_t, lims[0], lims[1], color='linen', linestyle='--', ... linewidth=1.5, alpha=0.5, label='Sub-beats') >>> ax.legend() >>> ax.set(title='CQT + Beat and sub-beat markers') rT)x_minx_maxryrz%n_segments must be a positive integerNr1r) r fix_framesrDr rrzipextendrrrGrAr)r!rrrj boundaries idx_slices seg_startseg_ends r(rrsH__V1DJJt4D$ OFA~DEEJ+*J!&"+vabz: 7 G4 4 U:&'Wy-@*)MTX  ; 88J r*) clustererrjrc vtj|}tj||d}|jd}|j |dfd}|\t j jj|dd}t jj||tj}|j|dg}|jtdtj tj"|j$dj't(ztj*|S)aBottom-up temporal segmentation. Use a temporally-constrained agglomerative clustering routine to partition ``data`` into ``k`` contiguous segments. Parameters ---------- data : np.ndarray data to cluster k : int > 0 [scalar] number of segments to produce clusterer : sklearn.cluster.AgglomerativeClustering, optional An optional AgglomerativeClustering object. If `None`, a constrained Ward object is instantiated. axis : int axis along which to cluster. By default, the last axis (-1) is chosen. Returns ------- boundaries : np.ndarray [shape=(k,)] left-boundaries (frame numbers) of detected segments. This will always include `0` as the first left-boundary. See Also -------- sklearn.cluster.AgglomerativeClustering Examples -------- Cluster by chroma similarity, break into 20 segments >>> y, sr = librosa.load(librosa.ex('nutcracker'), duration=15) >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr) >>> bounds = librosa.segment.agglomerative(chroma, 20) >>> bound_times = librosa.frames_to_time(bounds, sr=sr) >>> bound_times array([ 0. , 0.65 , 1.091, 1.927, 2.438, 2.902, 3.924, 4.783, 5.294, 5.712, 6.13 , 7.314, 8.522, 8.916, 9.66 , 10.844, 11.238, 12.028, 12.492, 14.095]) Plot the segmentation over the chromagram >>> import matplotlib.pyplot as plt >>> import matplotlib.transforms as mpt >>> fig, ax = plt.subplots() >>> trans = mpt.blended_transform_factory( ... ax.transData, ax.transAxes) >>> librosa.display.specshow(chroma, y_axis='chroma', x_axis='time', ax=ax) >>> ax.vlines(bound_times, 0, 1, color='linen', linestyle='--', ... linewidth=2, alpha=0.9, label='Segment boundaries', ... transform=trans) >>> ax.legend() >>> ax.set(title='Power spectrogram') rr1r2r3r)n_xn_yn_z) n_clustersr/memory)rArBrErDrFrKfeature_extractionimage grid_to_graphclusterAgglomerativeClusteringrrrOrrrSdifflabels_rXrJr)r!rrrjr^gridrs r(rrs~ == D ;;tT1 %D 1 A <<Bs< +D))//==!PQ=ROO;;tELL< MM$Jd1rzz"'')2C2C*DEaHOOPSTTUV ::j !!r*hanng@)window max_ratio min_ratio n_filters zero_meanclipRr^rrrrrrrc h|d|z }n||kDrtd|d|d} tjtj|tj||dD]} t ||| |} dg|j z} | j | d dtj| | } | "tjj|| fi|} ktj| tjj|| fi|| |rtj| d d| tj| S) u9Multi-angle path enhancement for self- and cross-similarity matrices. This function convolves multiple diagonal smoothing filters with a self-similarity (or recurrence) matrix R, and aggregates the result by an element-wise maximum. Technically, the output is a matrix R_smooth such that:: R_smooth[i, j] = max_theta (R * filter_theta)[i, j] where `*` denotes 2-dimensional convolution, and ``filter_theta`` is a smoothing filter at orientation theta. This is intended to provide coherent temporal smoothing of self-similarity matrices when there are changes in tempo. Smoothing filters are generated at evenly spaced orientations between min_ratio and max_ratio. This function is inspired by the multi-angle path enhancement of [#]_, but differs by modeling tempo differences in the space of similarity matrices rather than re-sampling the underlying features prior to generating the self-similarity matrix. .. [#] Müller, Meinard and Frank Kurth. "Enhancing similarity matrices for music audio analysis." 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings. Vol. 5. IEEE, 2006. .. note:: if using recurrence_matrix to construct the input similarity matrix, be sure to include the main diagonal by setting ``self=True``. Otherwise, the diagonal will be suppressed, and this is likely to produce discontinuities which will pollute the smoothing filter response. Parameters ---------- R : np.ndarray The self- or cross-similarity matrix to be smoothed. Note: sparse inputs are not supported. If the recurrence matrix is multi-dimensional, e.g. `shape=(c, n, n)`, then enhancement is conducted independently for each leading channel. n : int > 0 The length of the smoothing filter window : window specification The type of smoothing filter to use. See `filters.get_window` for more information on window specification formats. max_ratio : float > 0 The maximum tempo ratio to support min_ratio : float > 0 The minimum tempo ratio to support. If not provided, it will default to ``1/max_ratio`` n_filters : int >= 1 The number of different smoothing filters to use, evenly spaced between ``min_ratio`` and ``max_ratio``. If ``min_ratio = 1/max_ratio`` (the default), using an odd number of filters will ensure that the main diagonal (ratio=1) is included. zero_mean : bool By default, the smoothing filters are non-negative and sum to one (i.e. are averaging filters). If ``zero_mean=True``, then the smoothing filters are made to sum to zero by subtracting a constant value from the non-diagonal coordinates of the filter. This is primarily useful for suppressing blocks while enhancing diagonals. clip : bool If True, the smoothed similarity matrix will be thresholded at 0, and will not contain negative entries. **kwargs : additional keyword arguments Additional arguments to pass to `scipy.ndimage.convolve` Returns ------- R_smooth : np.ndarray, shape=R.shape The smoothed self- or cross-similarity matrix See Also -------- librosa.filters.diagonal_filter recurrence_matrix Examples -------- Use a 51-frame diagonal smoothing filter to enhance paths in a recurrence matrix >>> y, sr = librosa.load(librosa.ex('nutcracker')) >>> hop_length = 2048 >>> chroma = librosa.feature.chroma_cqt(y=y, sr=sr, hop_length=hop_length) >>> chroma_stack = librosa.feature.stack_memory(chroma, n_steps=10, delay=3) >>> rec = librosa.segment.recurrence_matrix(chroma_stack, mode='affinity', self=True) >>> rec_smooth = librosa.segment.path_enhance(rec, 51, window='hann', n_filters=7) Plot the recurrence matrix before and after smoothing >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(ncols=2, sharex=True, sharey=True) >>> img = librosa.display.specshow(rec, x_axis='s', y_axis='s', ... hop_length=hop_length, ax=ax[0]) >>> ax[0].set(title='Unfiltered recurrence') >>> imgpe = librosa.display.specshow(rec_smooth, x_axis='s', y_axis='s', ... hop_length=hop_length, ax=ax[1]) >>> ax[1].set(title='Multi-angle enhanced recurrence') >>> ax[1].label_outer() >>> fig.colorbar(img, ax=ax[0], orientation='horizontal') >>> fig.colorbar(imgpe, ax=ax[1], orientation='horizontal') Ng?z min_ratio=z cannot exceed max_ratio=r:)numbase)sloperr)outr)r rAlogspacelog2rrrDrFrndimageconvolvemaximumr asanyarray) rr^rrrrrrrR_smoothratiokernelrDs r(rrvs#v)O Y  # q  +,<+==YZ   !'+h h  ! 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