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293 lines (238 loc) · 9.53 KB
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/*
* Copyright (c) 2006-Present, Redis Ltd.
* All rights reserved.
*
* Licensed under your choice of the Redis Source Available License 2.0
* (RSALv2); or (b) the Server Side Public License v1 (SSPLv1); or (c) the
* GNU Affero General Public License v3 (AGPLv3).
*/
//------------------------------------------------------------------------------
// LAGraph_pagerank: pagerank using a real semiring
//------------------------------------------------------------------------------
/*
LAGraph: graph algorithms based on GraphBLAS
Copyright 2019 LAGraph Contributors.
(see Contributors.txt for a full list of Contributors; see
ContributionInstructions.txt for information on how you can Contribute to
this project).
All Rights Reserved.
NO WARRANTY. THIS MATERIAL IS FURNISHED ON AN "AS-IS" BASIS. THE LAGRAPH
CONTRIBUTORS MAKE NO WARRANTIES OF ANY KIND, EITHER EXPRESSED OR IMPLIED,
AS TO ANY MATTER INCLUDING, BUT NOT LIMITED TO, WARRANTY OF FITNESS FOR
PURPOSE OR MERCHANTABILITY, EXCLUSIVITY, OR RESULTS OBTAINED FROM USE OF
THE MATERIAL. THE CONTRIBUTORS DO NOT MAKE ANY WARRANTY OF ANY KIND WITH
RESPECT TO FREEDOM FROM PATENT, TRADEMARK, OR COPYRIGHT INFRINGEMENT.
Released under a BSD license, please see the LICENSE file distributed with
this Software or contact permission@sei.cmu.edu for full terms.
Created, in part, with funding and support from the United States
Government. (see Acknowledgments.txt file).
This program includes and/or can make use of certain third party source
code, object code, documentation and other files ("Third Party Software").
See LICENSE file for more details.
*/
#include "pagerank.h"
#include "util/rmalloc.h"
#include <assert.h>
//------------------------------------------------------------------------------
// scalar operators
//------------------------------------------------------------------------------
#define DAMPING 0.85
void fdiff(void *z, const void *x, const void *y) {
float delta = (* ((float *) x)) - (* ((float *) y)) ;
(*((float *) z)) = delta * delta ;
}
//------------------------------------------------------------------------------
// comparison function for qsort
//------------------------------------------------------------------------------
int compar(const void *x, const void *y) {
LAGraph_PageRank *a = (LAGraph_PageRank *) x ;
LAGraph_PageRank *b = (LAGraph_PageRank *) y ;
// sort by pagerank in descending order
if(a->pagerank > b->pagerank) {
return (-1) ;
} else if(a->pagerank == b->pagerank) {
return (0) ;
} else {
return (1) ;
}
}
//------------------------------------------------------------------------------
// LAGraph_pagerank: compute the pagerank of all nodes in a graph
//------------------------------------------------------------------------------
GrB_Info Pagerank // GrB_SUCCESS or error condition
(
LAGraph_PageRank **Phandle, // output: array of LAGraph_PageRank structs
GrB_Matrix A, // binary input graph, not modified
int itermax, // max number of iterations
double tol, // stop when norm (r-rnew,2) < tol
int *iters // number of iterations taken
) {
//--------------------------------------------------------------------------
// initializations
//--------------------------------------------------------------------------
GrB_Info info ;
float rsum ;
float *X = NULL ;
LAGraph_PageRank *P = NULL ;
GrB_BinaryOp op_diff = NULL ;
GrB_Index n, nvals, *I = NULL ;
GrB_Vector r = NULL, t = NULL, d = NULL ;
GrB_Matrix C = NULL, D = NULL, T = NULL ;
GrB_Info rc;
assert(Phandle);
(*Phandle) = NULL ;
// n = size (A,1) ; // number of nodes
rc = GrB_Matrix_nrows(&n, A) ;
assert(rc == GrB_SUCCESS) ;
if(n == 0) return (GrB_SUCCESS) ;
// teleport = (1 - 0.85) / n
float one = 1.0 ;
float teleport = (one - DAMPING) / ((float) n) ;
// r (i) = 1/n for all nodes i
float x = 1.0 / ((float) n) ;
rc = GrB_Vector_new(&r, GrB_FP32, n) ;
assert(rc == GrB_SUCCESS) ;
rc = GrB_assign(r, NULL, NULL, x, GrB_ALL, n, NULL) ;
assert(rc == GrB_SUCCESS) ;
// d (i) = out deg of node i
rc = GrB_Vector_new(&d, GrB_FP32, n) ;
assert(rc == GrB_SUCCESS) ;
rc = GrB_reduce(d, NULL, NULL, GrB_PLUS_FP32, A, NULL) ;
assert(rc == GrB_SUCCESS) ;
// GxB_print (d, 3) ;
// D = (1/diag (d)) * DAMPING
bool iso ;
bool jumbled ;
GrB_Type type ;
GrB_Index vi_size;
GrB_Index vx_size;
rc = GxB_Vector_export_CSC(&d, &type, &n, &I, (void **)(&X), &vi_size,
&vx_size, &iso, &nvals, &jumbled, NULL) ;
assert(rc == GrB_SUCCESS) ;
for(int64_t k = 0 ; k < nvals ; k++) X [k] = DAMPING / X [k] ;
rc = GrB_Matrix_new(&D, GrB_FP32, n, n) ;
assert(rc == GrB_SUCCESS) ;
rc = GrB_Matrix_build(D, I, I, X, nvals, GrB_PLUS_FP32) ;
assert(rc == GrB_SUCCESS) ;
rm_free(I) ;
rm_free(X) ;
// C = diagonal matrix with all zeros on the diagonal. This ensures that
// the vectors r and t remain dense, which is faster, and is required
// for the t += teleport_scalar step.
rc = GrB_Matrix_new(&C, GrB_FP32, n, n) ;
assert(rc == GrB_SUCCESS) ;
// GxB_set (C, GxB_HYPER, GxB_ALWAYS_HYPER) ;
for(int64_t k = 0 ; k < n ; k++) {
// C(k,k) = 0
rc = GrB_Matrix_setElement(C, (float) 0, k, k) ;
assert(rc == GrB_SUCCESS) ;
}
// make sure D is diagonal
rc = GrB_eWiseAdd(D, NULL, NULL, GrB_PLUS_FP32, D, C, NULL) ;
assert(rc == GrB_SUCCESS) ;
// use GrB_mxv for t=C*r below
// C = C+(D*A)' = C+A'*D' : using the transpose of C, and C*r below
// T = D*A
rc = GrB_Matrix_new(&T, GrB_FP32, n, n) ;
assert(rc == GrB_SUCCESS) ;
rc = GrB_mxm(T, NULL, NULL, GxB_PLUS_TIMES_FP32, D, A, NULL) ;
assert(rc == GrB_SUCCESS) ;
// C = C+T'
rc = GrB_transpose(C, NULL, GrB_PLUS_FP32, T, NULL) ;
assert(rc == GrB_SUCCESS) ;
rc = GrB_free(&T) ;
assert(rc == GrB_SUCCESS) ;
rc = GrB_free(&D) ;
assert(rc == GrB_SUCCESS) ;
// create operator
rc = GrB_BinaryOp_new(&op_diff, fdiff, GrB_FP32, GrB_FP32, GrB_FP32) ;
assert(rc == GrB_SUCCESS) ;
float ftol = tol * tol ; // use tol^2 so sqrt(rdiff) not needed
float rdiff = 1 ; // so first iteration is always done
rc = GrB_Vector_new(&t, GrB_FP32, n) ;
assert(rc == GrB_SUCCESS) ;
//--------------------------------------------------------------------------
// iterate to compute the pagerank of each node
//--------------------------------------------------------------------------
for((*iters) = 0 ; (*iters) < itermax && rdiff > ftol ; (*iters)++) {
//----------------------------------------------------------------------
// t = (r*C or C*r) + (teleport * sum (r)) ;
//----------------------------------------------------------------------
// GxB_print (r, 2) ;
rc = GrB_reduce(&rsum, NULL, GxB_PLUS_FP32_MONOID, r, NULL) ;
assert(rc == GrB_SUCCESS) ;
// t = C*r
// using the transpose of A, scaled (dot product)
rc = GrB_mxv(t, NULL, NULL, GxB_PLUS_TIMES_FP32, C, r, NULL) ;
assert(rc == GrB_SUCCESS) ;
// t += teleport_scalar ;
float teleport_scalar = teleport * rsum ;
rc = GrB_assign(t, NULL, GrB_PLUS_FP32, teleport_scalar, GrB_ALL, n, NULL) ;
assert(rc == GrB_SUCCESS) ;
//----------------------------------------------------------------------
// rdiff = sum ((r-t).^2)
//----------------------------------------------------------------------
rc = GrB_eWiseAdd(r, NULL, NULL, op_diff, r, t, NULL) ;
assert(rc == GrB_SUCCESS) ;
rc = GrB_reduce(&rdiff, NULL, GxB_PLUS_FP32_MONOID, r, NULL) ;
assert(rc == GrB_SUCCESS) ;
//----------------------------------------------------------------------
// swap r and t
//----------------------------------------------------------------------
GrB_Vector temp = r ;
r = t ;
t = temp ;
}
rc = GrB_free(&C) ;
assert(rc == GrB_SUCCESS) ;
rc = GrB_free(&t) ;
assert(rc == GrB_SUCCESS) ;
//--------------------------------------------------------------------------
// scale the result
//--------------------------------------------------------------------------
// rsum = sum (r)
rc = GrB_reduce(&rsum, NULL, GxB_PLUS_FP32_MONOID, r, NULL) ;
assert(rc == GrB_SUCCESS) ;
// r = r / rsum
rc = GrB_Vector_assign_FP32(r, NULL, GrB_TIMES_FP32, 1 / rsum, GrB_ALL, n, NULL) ;
assert(rc == GrB_SUCCESS) ;
//--------------------------------------------------------------------------
// sort the nodes by pagerank
//--------------------------------------------------------------------------
// [r,irank] = sort (r, 'descend') ;
// extract the contents of r
rc = GxB_Vector_export_CSC(&r, &type, &n, &I, (void **)(&X), &vi_size,
&vx_size, &iso, &nvals, &jumbled, NULL) ;
assert(rc == GrB_SUCCESS) ;
// this will always be true since r is dense, but check anyway:
if(nvals != n) return (GrB_PANIC) ;
// P = struct (X,I)
P = rm_malloc(n * sizeof(LAGraph_PageRank)) ;
assert(P != NULL);
for(int64_t k = 0 ; k < nvals ; k++) {
// The kth ranked page is P[k].page (with k=0 being the highest rank),
// and its pagerank is P[k].pagerank.
P [k].pagerank = X [k] ;
// I [k] == k will be true for SuiteSparse:GraphBLAS but in general I
// can be returned in any order, so use I [k] instead of k, for other
// GraphBLAS implementations.
P [k].page = k ;
}
// qsort (P) in descending order
qsort(P, n, sizeof(LAGraph_PageRank), compar) ;
//--------------------------------------------------------------------------
// return result
//--------------------------------------------------------------------------
(*Phandle) = P ;
// Clean up.
rm_free(I) ;
rm_free(X) ;
GrB_free(&T) ;
GrB_free(&D) ;
GrB_free(&C) ;
GrB_free(&r) ;
GrB_free(&t) ;
GrB_free(&d) ;
GrB_free(&op_diff) ;
return (GrB_SUCCESS) ;
}
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