feat: add piecewise linear cpd (#91)

Author: deepcharles

.gitignore

@@ -83,3 +83,6 @@ docs/build/*
 ehthumbs.db
 Thumbs.db
 site/
+ruptures/utils/_utils/convert_path_matrix.c
+ruptures/detection/_detection/continuous_linear_cpd.c
+ruptures/detection/_detection/ekcpd.c

docs/code-reference/costs/costclinear-reference.md

@@ -0,0 +1,5 @@
+# Continuous linear change (CostCLinear)
+
+::: ruptures.costs.costclinear.CostCLinear
+    rendering:
+        show_root_heading: true

docs/code-reference/detection/greedyar-reference.md

@@ -0,0 +1,56 @@
+# Continuous linear change (`CostCLinear`)
+
+## Description
+
+For a given set of indexes (also called knots) $t_k$ ($k=1,\dots,K$), a linear spline $f$ is such that:
+
+1. $f$ is affine on each interval $t_k..t_{k+1}$, i.e. $f(t)=\alpha_k (t-t_k) + \beta_k$ ($\alpha_k, \beta_k \in \mathbb{R}^d$) for all $t=t_k,t_k+1,\dots,t_{k+1}-1$;
+2. $f$ is continuous.
+
+The cost function [`CostCLinear`][ruptures.costs.costclinear.CostCLinear] measures the error when approximating the signal with a linear spline.
+Formally, it is defined for $0<a<b\leq T$ by
+
+$$
+c(y_{a..b}) := \sum_{t=a}^{b-1} \left\lVert y_t - y_{a-1} - \frac{t-a+1}{b-a}(y_{b-1}-y_{a-1}) \right\rVert^2
+$$
+
+and $c(y_{0..b}):=c(y_{1..b})$ (by convention).
+
+## Usage
+
+Start with the usual imports and create a signal with piecewise linear trends.
+
+```python
+import numpy as np
+import matplotlib.pylab as plt
+import ruptures as rpt
+
+# creation of data
+n_samples, n_dims = 500, 3  # number of samples, dimension
+n_bkps, sigma = 3, 5  # number of change points, noise standard deviation
+signal, bkps = rpt.pw_constant(n_samples, n_dims, n_bkps, noise_std=sigma)
+signal = np.cumsum(signal, axis=1)
+```
+
+Then create a [`CostCLinear`][ruptures.costs.costclinear.CostCLinear] instance and print the cost of the sub-signal `signal[50:150]`.
+
+```python
+c = rpt.costs.CostCLinear().fit(signal)
+print(c.error(50, 150))
+```
+
+You can also compute the sum of costs for a given list of change points.
+
+```python
+print(c.sum_of_costs(bkps))
+print(c.sum_of_costs([10, 100, 200, 250, n]))
+```
+
+In order to use this cost class in a change point detection algorithm (inheriting from [`BaseEstimator`][ruptures.base.BaseEstimator]), either pass a [`CostCLinear`][ruptures.costs.costclinear.CostCLinear] instance (through the argument `custom_cost`) or set `model="clinear"`.
+
+```python
+c = rpt.costs.CostCLinear()
+algo = rpt.Dynp(custom_cost=c)
+# is equivalent to
+algo = rpt.Dynp(model="clinear")
+```

docs/code-reference/detection/greedylinear-reference.md

@@ -55,6 +55,7 @@ nav:
       - 'CostRbf': user-guide/costs/costrbf.md
       - 'CostCosine': user-guide/costs/costcosine.md
       - 'CostLinear': user-guide/costs/costlinear.md
+      - 'CostCLinear': user-guide/costs/costclinear.md
       - 'CostRank': user-guide/costs/costrank.md
       - 'CostMl': user-guide/costs/costml.md
       - 'CostAR': user-guide/costs/costautoregressive.md
@@ -99,6 +100,7 @@ nav:
           - 'CostRbf': code-reference/costs/costrbf-reference.md
           - 'CostCosine': code-reference/costs/costcosine-reference.md
           - 'CostLinear': code-reference/costs/costlinear-reference.md
+          - 'CostCLinear': code-reference/costs/costclinear-reference.md
           - 'CostRank': code-reference/costs/costrank-reference.md
           - 'CostMl': code-reference/costs/costml-reference.md
           - 'CostAR': code-reference/costs/costautoregressive-reference.md

docs/code-reference/detection/omp-reference.md

@@ -10,11 +10,7 @@
     BottomUp,
     Dynp,
     KernelCPD,
-    Omp,
-    OmpK,
     Pelt,
     Window,
-    GreedyAR,
-    GreedyLinear,
 )
 from .show import display

docs/code-reference/detection/ompk-reference.md

@@ -3,6 +3,7 @@
 from .costl1 import CostL1
 from .costl2 import CostL2
 from .costlinear import CostLinear
+from .costclinear import CostCLinear
 from .costrbf import CostRbf
 from .costnormal import CostNormal
 from .costautoregressive import CostAR