diff --git a/corneto/backend/_base.py b/corneto/backend/_base.py index 0ea7c1a2..b90d9804 100644 --- a/corneto/backend/_base.py +++ b/corneto/backend/_base.py @@ -1274,10 +1274,14 @@ def Xor(self, x: CExpression, y: CExpression, varname="_xor"): ) def linear_or( - self, x: CExpression, axis: Optional[int] = None, varname="or" + self, + x: CExpression, + axis: Optional[int] = None, + varname="or", + ignore_type=False, ) -> ProblemDef: # Check if the variable has a vartype and is binary - if hasattr(x, "_vartype") and x._vartype != VarType.BINARY: + if hasattr(x, "_vartype") and x._vartype != VarType.BINARY and not ignore_type: raise ValueError(f"Variable x has type {x._vartype} instead of BINARY") else: for s in x._proxy_symbols: diff --git a/corneto/methods/shortest_path.py b/corneto/methods/shortest_path.py index 07257ad3..415a3e0f 100644 --- a/corneto/methods/shortest_path.py +++ b/corneto/methods/shortest_path.py @@ -1,4 +1,4 @@ -from typing import Any, Optional +from typing import Any, List, Optional import numpy as np @@ -8,6 +8,66 @@ from corneto.backend._base import DEFAULT_UB, Indicator +def create_multisample_shortest_path( + G: BaseGraph, + source_target_nodes: List[tuple], + edge_weights=None, + solver: Optional[str] = None, + backend: Backend = DEFAULT_BACKEND, + lam: float = 0.0, +): + # Transform the graph into a flow problem + Gc = G.copy() + inflow_edges = dict() + outflow_edges = dict() + for s, t in source_target_nodes: + if s not in inflow_edges: + inflow_edges[s] = Gc.add_edge((), s) + if t not in outflow_edges: + outflow_edges[t] = Gc.add_edge(t, ()) + if edge_weights is None: + edge_weights = np.array( + [Gc.get_attr_edge(i).get("weight", 0) for i in range(Gc.ne)] + ) + # The number of samples equals the number of source-target pairs. + # We need to duplicate the edge weights for each sample. + edge_weights = np.tile(edge_weights, (len(source_target_nodes), 1)) + else: + # Verify that the number of edge weights is correct + edge_weights = np.array(edge_weights) + if edge_weights.shape[0] != len(source_target_nodes): + raise ValueError( + "The number of edge weights must be equal to the number of source-target pairs." + ) + # Add the weights for the extra edges, to be 0 + n_extra_edges = Gc.ne - G.ne + edge_weights = np.concatenate( + [edge_weights, np.zeros((len(source_target_nodes), n_extra_edges))], axis=1 + ) + P = backend.Flow(Gc, lb=0, ub=DEFAULT_UB, n_flows=len(source_target_nodes)) + # Now we add the objective and constraints for each sample + for i, (s, t) in enumerate(source_target_nodes): + weights = edge_weights[i, :] + P.add_objectives(P.expr.flow[:, i] @ weights) + # Now we inject/extract 1 unit flow from s to t + P += P.expr.flow[inflow_edges[s]] == 1 + P += P.expr.flow[outflow_edges[t]] == 1 + # For the rest of inflow/outflow edges, we set the flow to 0 + for node in inflow_edges: + if node != s: + P += P.expr.flow[inflow_edges[node]] == 0 + for node in outflow_edges: + if node != t: + P += P.expr.flow[outflow_edges[node]] == 0 + # Add reg + if lam > 0: + P += backend.linear_or( + P.expr.flow, axis=1, ignore_type=True, varname="active_edge" + ) + P.add_objectives(sum(P.expr.active_edge), weights=lam) + return P, Gc + + def shortest_path( G: BaseGraph, s: Any, @@ -39,6 +99,10 @@ def shortest_path( edge_weights = np.array( [Gc.get_attr_edge(i).get("weight", 0) for i in range(Gc.ne)] ) + else: + edge_weights = np.array(edge_weights) + # Add the weights for the extra edges, to be 0 + edge_weights = np.concatenate([edge_weights, [0, 0]]) if integral_path: P = backend.Flow(Gc, lb=0, ub=DEFAULT_UB) P += Indicator() diff --git a/docs/guide/networks/multi-sample-shortest-paths.ipynb b/docs/guide/networks/multi-sample-shortest-paths.ipynb new file mode 100644 index 00000000..de42761d --- /dev/null +++ b/docs/guide/networks/multi-sample-shortest-paths.ipynb @@ -0,0 +1,1089 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
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Installed version:v1.0.0.dev0 (up to date)
Available backends:CVXPY v1.5.1, PICOS v2.4.17
Default backend (corneto.opt):CVXPY
Installed solvers:CLARABEL, CVXOPT, ECOS, ECOS_BB, GLPK, GLPK_MI, GUROBI, OSQP, SCIPY, SCS
Graphviz version:v0.20.3
Installed path:C:\\Users\\pablo\\Documents\\work\\projects\\corneto\\corneto
Repository:https://github.com/saezlab/corneto
\n", + "
" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import corneto as cn\n", + "\n", + "cn.info()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "A\n", + "\n", + "A\n", + "\n", + "\n", + "\n", + "B\n", + "\n", + "B\n", + "\n", + "\n", + "\n", + "A->B\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "C\n", + "\n", + "C\n", + "\n", + "\n", + "\n", + "A->C\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "F\n", + "\n", + "F\n", + "\n", + "\n", + "\n", + "A->F\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D\n", + "\n", + "D\n", + "\n", + "\n", + "\n", + "B->D\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "E\n", + "\n", + "E\n", + "\n", + "\n", + "\n", + "B->E\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "C->F\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G\n", + "\n", + "G\n", + "\n", + "\n", + "\n", + "F->G\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D->A\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D->C\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D->G\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "E->D\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "H\n", + "\n", + "H\n", + "\n", + "\n", + "\n", + "E->H\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G->E\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G->H\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "H->F\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G = cn.Graph()\n", + "G.add_edge(\"A\", \"B\")\n", + "G.add_edge(\"A\", \"C\")\n", + "G.add_edge(\"A\", \"F\")\n", + "G.add_edge(\"B\", \"D\")\n", + "G.add_edge(\"B\", \"E\")\n", + "G.add_edge(\"C\", \"F\")\n", + "G.add_edge(\"D\", \"A\")\n", + "G.add_edge(\"D\", \"C\")\n", + "G.add_edge(\"D\", \"G\")\n", + "G.add_edge(\"E\", \"D\")\n", + "G.add_edge(\"E\", \"H\")\n", + "G.add_edge(\"F\", \"G\")\n", + "G.add_edge(\"G\", \"E\")\n", + "G.add_edge(\"G\", \"H\")\n", + "G.add_edge(\"H\", \"F\")\n", + "G.plot()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0 (frozenset({'A'}), frozenset({'B'}))\n", + "1 (frozenset({'A'}), frozenset({'C'}))\n", + "2 (frozenset({'A'}), frozenset({'F'}))\n", + "3 (frozenset({'B'}), frozenset({'D'}))\n", + "4 (frozenset({'B'}), frozenset({'E'}))\n", + "5 (frozenset({'C'}), frozenset({'F'}))\n", + "6 (frozenset({'D'}), frozenset({'A'}))\n", + "7 (frozenset({'D'}), frozenset({'C'}))\n", + "8 (frozenset({'D'}), frozenset({'G'}))\n", + "9 (frozenset({'E'}), frozenset({'D'}))\n", + "10 (frozenset({'E'}), frozenset({'H'}))\n", + "11 (frozenset({'F'}), frozenset({'G'}))\n", + "12 (frozenset({'G'}), frozenset({'E'}))\n", + "13 (frozenset({'G'}), frozenset({'H'}))\n", + "14 (frozenset({'H'}), frozenset({'F'}))\n" + ] + } + ], + "source": [ + "for i, e in enumerate(G.E):\n", + " print(i, e)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "c1_weights = [3, 6, 7, 1, 7, 1, 1, 2, 6, 2, 5, 2, 1, 6, 1]\n", + "c2_weights = [5, 15, 17, 6, 14, 1, 2, 3, 6, 1, 3, 2, 2, 5, 2]" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "A\n", + "\n", + "A\n", + "\n", + "\n", + "\n", + "C\n", + "\n", + "C\n", + "\n", + "\n", + "\n", + "A->C\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "F\n", + "\n", + "F\n", + "\n", + "\n", + "\n", + "C->F\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G\n", + "\n", + "G\n", + "\n", + "\n", + "\n", + "F->G\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "H\n", + "\n", + "H\n", + "\n", + "\n", + "\n", + "G->H\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from corneto.methods import solve_shortest_path\n", + "\n", + "edges, P, Gc = solve_shortest_path(G, \"A\", \"H\", edge_weights=c1_weights, solver=\"SCIPY\")\n", + "Gc.edge_subgraph(edges).plot(orphan_edges=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "15.0" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P.objectives[0].value" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "A\n", + "\n", + "A\n", + "\n", + "\n", + "\n", + "B\n", + "\n", + "B\n", + "\n", + "\n", + "\n", + "A->B\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D\n", + "\n", + "D\n", + "\n", + "\n", + "\n", + "B->D\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "C\n", + "\n", + "C\n", + "\n", + "\n", + "\n", + "D->C\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "F\n", + "\n", + "F\n", + "\n", + "\n", + "\n", + "C->F\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G\n", + "\n", + "G\n", + "\n", + "\n", + "\n", + "F->G\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "H\n", + "\n", + "H\n", + "\n", + "\n", + "\n", + "G->H\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "edges, P, Gc = solve_shortest_path(G, \"A\", \"H\", edge_weights=c2_weights, solver=\"SCIPY\")\n", + "Gc.edge_subgraph(edges).plot(orphan_edges=False)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "22.0" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P.objectives[0].value" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "A\n", + "\n", + "A\n", + "\n", + "\n", + "\n", + "B\n", + "\n", + "B\n", + "\n", + "\n", + "\n", + "A->B\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "C\n", + "\n", + "C\n", + "\n", + "\n", + "\n", + "A->C\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "F\n", + "\n", + "F\n", + "\n", + "\n", + "\n", + "A->F\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D\n", + "\n", + "D\n", + "\n", + "\n", + "\n", + "B->D\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "E\n", + "\n", + "E\n", + "\n", + "\n", + "\n", + "B->E\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "C->F\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G\n", + "\n", + "G\n", + "\n", + "\n", + "\n", + "F->G\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D->A\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D->C\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "D->G\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "E->D\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "H\n", + "\n", + "H\n", + "\n", + "\n", + "\n", + "E->H\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G->E\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G->H\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "H->F\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "e_16_target\n", + "\n", + "\n", + "\n", + "\n", + "H->e_16_target\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "e_15_source\n", + "\n", + "\n", + "\n", + "\n", + "e_15_source->A\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from corneto.methods.shortest_path import create_multisample_shortest_path\n", + "\n", + "samples = [(\"A\", \"H\"), (\"A\", \"H\")]\n", + "edge_weights = [c1_weights, c2_weights]\n", + "P, Gc = create_multisample_shortest_path(\n", + " G, samples, edge_weights=edge_weights, lam=0.01\n", + ")\n", + "\n", + "Gc.plot()" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "===============================================================================\n", + " CVXPY \n", + " v1.5.1 \n", + "===============================================================================\n", + "(CVXPY) Aug 14 11:28:01 AM: Your problem has 51 variables, 126 constraints, and 0 parameters.\n", + "(CVXPY) Aug 14 11:28:01 AM: It is compliant with the following grammars: DCP, DQCP\n", + "(CVXPY) Aug 14 11:28:01 AM: (If you need to solve this problem multiple times, but with different data, consider using parameters.)\n", + "(CVXPY) Aug 14 11:28:01 AM: CVXPY will first compile your problem; then, it will invoke a numerical solver to obtain a solution.\n", + "(CVXPY) Aug 14 11:28:01 AM: Your problem is compiled with the CPP canonicalization backend.\n", + "-------------------------------------------------------------------------------\n", + " Compilation \n", + "-------------------------------------------------------------------------------\n", + "(CVXPY) Aug 14 11:28:01 AM: Compiling problem (target solver=SCIPY).\n", + "(CVXPY) Aug 14 11:28:01 AM: Reduction chain: Dcp2Cone -> CvxAttr2Constr -> ConeMatrixStuffing -> SCIPY\n", + "(CVXPY) Aug 14 11:28:01 AM: Applying reduction Dcp2Cone\n", + "(CVXPY) Aug 14 11:28:01 AM: Applying reduction CvxAttr2Constr\n", + "(CVXPY) Aug 14 11:28:01 AM: Applying reduction ConeMatrixStuffing\n", + "(CVXPY) Aug 14 11:28:01 AM: Applying reduction SCIPY\n", + "(CVXPY) Aug 14 11:28:01 AM: Finished problem compilation (took 1.468e-02 seconds).\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-------------------------------------------------------------------------------\n", + " Numerical solver \n", + "-------------------------------------------------------------------------------\n", + "(CVXPY) Aug 14 11:28:01 AM: Invoking solver SCIPY to obtain a solution.\n", + "Solver terminated with message: Optimization terminated successfully. (HiGHS Status 7: Optimal)\n", + "-------------------------------------------------------------------------------\n", + " Summary \n", + "-------------------------------------------------------------------------------\n", + "(CVXPY) Aug 14 11:28:01 AM: Problem status: optimal\n", + "(CVXPY) Aug 14 11:28:01 AM: Optimal value: 3.705e+01\n", + "(CVXPY) Aug 14 11:28:01 AM: Compilation took 1.468e-02 seconds\n", + "(CVXPY) Aug 14 11:28:01 AM: Solver (including time spent in interface) took 3.998e-03 seconds\n" + ] + }, + { + "data": { + "text/plain": [ + "Problem(Minimize(Expression(AFFINE, UNKNOWN, ())), [Inequality(Constant(CONSTANT, ZERO, (17, 2))), Inequality(Variable((17, 2), _flow)), Equality(Expression(AFFINE, UNKNOWN, (8, 2)), Constant(CONSTANT, ZERO, ())), Equality(Expression(AFFINE, UNKNOWN, (2,)), Constant(CONSTANT, NONNEGATIVE, ())), Equality(Expression(AFFINE, UNKNOWN, (2,)), Constant(CONSTANT, NONNEGATIVE, ())), Equality(Expression(AFFINE, UNKNOWN, (2,)), Constant(CONSTANT, NONNEGATIVE, ())), Equality(Expression(AFFINE, UNKNOWN, (2,)), Constant(CONSTANT, NONNEGATIVE, ())), Inequality(Expression(AFFINE, UNKNOWN, (17,))), Inequality(Variable((17,), active_edge, boolean=True))])" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P.solve(solver=\"SCIPY\", verbosity=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(15.0, 22.0)" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P.objectives[0].value, P.objectives[1].value # , P.objectives[2].value" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 1., 1.],\n", + " [-0., -0.],\n", + " [-0., -0.],\n", + " [-0., -0.],\n", + " [ 1., 1.],\n", + " [ 0., 0.],\n", + " [-0., -0.],\n", + " [-0., -0.],\n", + " [-0., -0.],\n", + 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