diff --git a/.cproject b/.cproject index ed2d41ca6..d0c9e6d01 100644 --- a/.cproject +++ b/.cproject @@ -5,47 +5,46 @@ - - - - - - - - - - - + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + @@ -299,589 +298,605 @@ - - - make - -j2 - install - true - true - true - - - make - -j2 - check - true - true - true - - - make - - clean - true - true - true - - - make - -k - check - true - false - true - - - make - -j2 - testSimpleCamera.run - true - true - true - - - make - -f local.mk - testCal3_S2.run - true - true - true - - - make - -j2 - testVSLAMFactor.run - true - true - true - - - make - -j2 - testCalibratedCamera.run - true - true - true - - - make - -j2 - testGaussianConditional.run - true - true - true - - - make - -j2 - testPose2.run - true - true - true - - - make - -j2 - testRot3.run - true - true - true - - - make - -j2 - testNonlinearOptimizer.run - true - true - true - - - make - -j2 - testGaussianFactor.run - true - true - true - - - make - -j2 - testGaussianFactorGraph.run - true - true - true - - - make - -j2 - testNonlinearFactorGraph.run - true - true - true - - - make - -j2 - testPose3.run - true - true - true - - - make - -j2 - testVectorMap.run - true - true - true - - - make - -j2 - testPoint2.run - true - true - true - - - make - -j2 - testNonlinearFactor.run - true - true - true - - - make - -j2 - timeGaussianFactor.run - true - true - true - - - make - -j2 - timeGaussianFactorGraph.run - true - true - true - - - make - -j2 - testGaussianBayesNet.run - true - true - true - - - make - testBayesTree.run - true - false - true - - - make - - testSymbolicBayesNet.run - true - false - true - - - make - testSymbolicFactorGraph.run - true - false - true - - - make - -j2 - testVector.run - true - true - true - - - make - -j2 - testMatrix.run - true - true - true - - - make - -j2 - testVSLAMGraph.run - true - true - true - - - make - -j2 - testNonlinearEquality.run - true - true - true - - - make - -j2 - testSQP.run - true - true - true - - - make - -j2 - testNonlinearConstraint.run - true - true - true - - - make - -j2 - testVSLAMConfig.run - true - true - true - - - make - -j2 - testOrdering.run - true - true - true - - - make - -j2 - testRot2.run - true - true - true - - - make - -j2 - testGaussianBayesTree.run - true - true - true - - - make - -j2 - testPose3Config.run - true - true - true - - - make - -j2 - testUrbanMeasurement.run - true - true - true - - - make - -j2 - testUrbanOdometry.run - true - true - true - - - make - -j2 - testIterative.run - true - true - true - - - make - -j2 - testGaussianISAM2.run - true - true - true - - - make - -j2 - testSubgraphPreconditioner.run - true - true - true - - - make - -j2 - testBayesNetPreconditioner.run - true - true - true - - - make - -j2 - testPose2Factor.run - true - true - true - - - make - -j2 - timeRot3.run - true - true - true - - - make - -j2 - testPose2SLAM.run - true - true - true - - - make - -j2 - testPose2Config.run - true - true - true - - - make - -j2 - testLieConfig.run - true - true - true - - - make - -j2 - testPlanarSLAM.run - true - true - true - - - make - testGraph.run - true - false - true - - - make - -j2 - testPose3SLAM.run - true - true - true - - - make - -j2 - testTupleConfig.run - true - true - true - - - make - -j2 - testPose2Prior.run - true - true - true - - - make - -j2 - testNoiseModel.run - true - true - true - - - make - -j2 - testISAM.run - true - true - true - - - make - -j2 - testGaussianISAM.run - true - true - true - - - make - - testSimulated2D.run - true - false - true - - - make - -j2 - timeMatrix.run - true - true - true - - - make - -j2 - testKey.run - true - true - true - - - make - -j2 - timeVectorConfig.run - true - true - true - - - make - -j2 - testHomography2.run - true - true - true - - - make - -j2 - testVectorBTree.run - true - true - true - - - make - testErrors.run - true - false - true - - - make - testDSF.run - true - true - true - - - make - -j2 - testFactorGraph.run - true - true - true - - - make - testConstraintOptimizer.run - true - true - true - - - make - - testBTree.run - true - true - true - - - make - testSimulated2DOriented.run - true - false - true - - - make - - testDSFVector.run - true - true - true - - - make - - testSPQRUtil.run - true - true - true - - - make - - testInference.run - true - true - true - - - make - -j2 - install - true - true - true - - - make - -j2 - clean - true - true - true - - - make - -j2 - check - true - true - true - - - - + + +make + +all +true +true +true + + +make + +clean +true +true +true + + +make +-j2 +install +true +true +true + + +make +-j2 +check +true +true +true + + +make +clean +true +true +true + + +make +-k +check +true +false +true + + +make +-j2 +testSimpleCamera.run +true +true +true + + +make +-f local.mk +testCal3_S2.run +true +true +true + + +make +-j2 +testVSLAMFactor.run +true +true +true + + +make +-j2 +testCalibratedCamera.run +true +true +true + + +make +-j2 +testGaussianConditional.run +true +true +true + + +make +-j2 +testPose2.run +true +true +true + + +make +-j2 +testRot3.run +true +true +true + + +make +-j2 +testNonlinearOptimizer.run +true +true +true + + +make +-j2 +testGaussianFactor.run +true +true +true + + +make +-j2 +testGaussianFactorGraph.run +true +true +true + + +make +-j2 +testNonlinearFactorGraph.run +true +true +true + + +make +-j2 +testPose3.run +true +true +true + + +make +-j2 +testVectorMap.run +true +true +true + + +make +-j2 +testPoint2.run +true +true +true + + +make +-j2 +testNonlinearFactor.run +true +true +true + + +make +-j2 +timeGaussianFactor.run +true +true +true + + +make +-j2 +timeGaussianFactorGraph.run +true +true +true + + +make +-j2 +testGaussianBayesNet.run +true +true +true + + +make + +testBayesTree.run +true +false +true + + +make +testSymbolicBayesNet.run +true +false +true + + +make + +testSymbolicFactorGraph.run +true +false +true + + +make +-j2 +testVector.run +true +true +true + + +make +-j2 +testMatrix.run +true +true +true + + +make +-j2 +testVSLAMGraph.run +true +true +true + + +make +-j2 +testNonlinearEquality.run +true +true +true + + +make +-j2 +testSQP.run +true +true +true + + +make +-j2 +testNonlinearConstraint.run +true +true +true + + +make +-j2 +testVSLAMConfig.run +true +true +true + + +make +-j2 +testOrdering.run +true +true +true + + +make +-j2 +testRot2.run +true +true +true + + +make +-j2 +testGaussianBayesTree.run +true +true +true + + +make +-j2 +testPose3Config.run +true +true +true + + +make +-j2 +testUrbanMeasurement.run +true +true +true + + +make +-j2 +testUrbanOdometry.run +true +true +true + + +make +-j2 +testIterative.run +true +true +true + + +make +-j2 +testGaussianISAM2.run +true +true +true + + +make +-j2 +testSubgraphPreconditioner.run +true +true +true + + +make +-j2 +testBayesNetPreconditioner.run +true +true +true + + +make +-j2 +testPose2Factor.run +true +true +true + + +make +-j2 +timeRot3.run +true +true +true + + +make +-j2 +testPose2SLAM.run +true +true +true + + +make +-j2 +testPose2Config.run +true +true +true + + +make +-j2 +testLieConfig.run +true +true +true + + +make +-j2 +testPlanarSLAM.run +true +true +true + + +make + +testGraph.run +true +false +true + + +make +-j2 +testPose3SLAM.run +true +true +true + + +make +-j2 +testTupleConfig.run +true +true +true + + +make +-j2 +testPose2Prior.run +true +true +true + + +make +-j2 +testNoiseModel.run +true +true +true + + +make +-j2 +testISAM.run +true +true +true + + +make +-j2 +testGaussianISAM.run +true +true +true + + +make +testSimulated2D.run +true +false +true + + +make +-j2 +timeMatrix.run +true +true +true + + +make +-j2 +testKey.run +true +true +true + + +make +-j2 +timeVectorConfig.run +true +true +true + + +make +-j2 +testHomography2.run +true +true +true + + +make +-j2 +testVectorBTree.run +true +true +true + + +make + +testErrors.run +true +false +true + + +make + +testDSF.run +true +true +true + + +make +-j2 +testFactorGraph.run +true +true +true + + +make + +testConstraintOptimizer.run +true +true +true + + +make +testBTree.run +true +true +true + + +make + +testSimulated2DOriented.run +true +false +true + + +make +testDSFVector.run +true +true +true + + +make +testSPQRUtil.run +true +true +true + + +make +testInference.run +true +true +true + + +make +-j2 +install +true +true +true + + +make +-j2 +clean +true +true +true + + +make +-j2 +check +true +true +true + + + + - - + + diff --git a/colamd/Makefile b/colamd/Makefile index 85b1a2243..936880863 100755 --- a/colamd/Makefile +++ b/colamd/Makefile @@ -5,9 +5,8 @@ all: libcolamd.a CC ?= gcc -CXX ?= g++ -CXXFLAGS += -O2 -CXXFLAGS += -fPIC +CFLAGS += -O2 +CFLAGS += -fPIC sources = $(shell ls *.c) @@ -17,11 +16,9 @@ library = libcolamd.a #Note: hack was added to ensure that flags are acutally used for compilation # This should probably be fixed, but will work for 64 bit machines now -$(library): - $(CXX) $(CXXFLAGS) -c -o colamd.o colamd.c - $(CXX) $(CXXFLAGS) -c -DDLONG -o colamd_l.o colamd.c - $(CXX) $(CXXFLAGS) -c -o colamd_global.o colamd_global.c - ar crsv $@ colamd.o colamd_l.o colamd_global.o +$(library): colamd.o colamd_global.o ccolamd.o ccolamd_global.o + $(CC) $(CFLAGS) -c -DDLONG -o colamd_l.o colamd.c + ar crsv $@ $^ colamd_l.o ranlib $(library) clean: diff --git a/colamd/ccolamd.c b/colamd/ccolamd.c new file mode 100644 index 000000000..924747126 --- /dev/null +++ b/colamd/ccolamd.c @@ -0,0 +1,4620 @@ +/* ========================================================================== */ +/* === CCOLAMD/CSYMAMD - a constrained column ordering algorithm ============ */ +/* ========================================================================== */ + +/* ---------------------------------------------------------------------------- + * CCOLAMD, Copyright (C) Univ. of Florida. Authors: Timothy A. Davis, + * Sivasankaran Rajamanickam, and Stefan Larimore + * See License.txt for the Version 2.1 of the GNU Lesser General Public License + * http://www.cise.ufl.edu/research/sparse + * -------------------------------------------------------------------------- */ + +/* + * ccolamd: a constrained approximate minimum degree column ordering + * algorithm, LU factorization of symmetric or unsymmetric matrices, + * QR factorization, least squares, interior point methods for + * linear programming problems, and other related problems. + * + * csymamd: a constrained approximate minimum degree ordering algorithm for + * Cholesky factorization of symmetric matrices. + * + * Purpose: + * + * CCOLAMD computes a permutation Q such that the Cholesky factorization of + * (AQ)'(AQ) has less fill-in and requires fewer floating point operations + * than A'A. This also provides a good ordering for sparse partial + * pivoting methods, P(AQ) = LU, where Q is computed prior to numerical + * factorization, and P is computed during numerical factorization via + * conventional partial pivoting with row interchanges. CCOLAMD is an + * extension of COLAMD, available as built-in function in MATLAB Version 6, + * available from MathWorks, Inc. (http://www.mathworks.com). This + * routine can be used in place of COLAMD in MATLAB. + * + * CSYMAMD computes a permutation P of a symmetric matrix A such that the + * Cholesky factorization of PAP' has less fill-in and requires fewer + * floating point operations than A. CSYMAMD constructs a matrix M such + * that M'M has the same nonzero pattern of A, and then orders the columns + * of M using colmmd. The column ordering of M is then returned as the + * row and column ordering P of A. CSYMAMD is an extension of SYMAMD. + * + * Authors: + * + * Timothy A. Davis and S. Rajamanickam wrote CCOLAMD, based directly on + * COLAMD by Stefan I. Larimore and Timothy A. Davis, University of + * Florida. The algorithm was developed in collaboration with John + * Gilbert, (UCSB, then at Xerox PARC), and Esmond Ng, (Lawrence Berkeley + * National Lab, then at Oak Ridge National Laboratory). + * + * Acknowledgements: + * + * This work was supported by the National Science Foundation, under + * grants DMS-9504974 and DMS-9803599, CCR-0203270, and a grant from the + * Sandia National Laboratory (Dept. of Energy). + * + * Copyright and License: + * + * Copyright (c) 1998-2005 by the University of Florida. + * All Rights Reserved. + * COLAMD is also available under alternate licenses, contact T. Davis + * for details. + * + * This library is free software; you can redistribute it and/or + * modify it under the terms of the GNU Lesser General Public + * License as published by the Free Software Foundation; either + * version 2.1 of the License, or (at your option) any later version. + * + * This library is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * Lesser General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public + * License along with this library; if not, write to the Free Software + * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 + * USA + * + * Permission is hereby granted to use or copy this program under the + * terms of the GNU LGPL, provided that the Copyright, this License, + * and the Availability of the original version is retained on all copies. + * User documentation of any code that uses this code or any modified + * version of this code must cite the Copyright, this License, the + * Availability note, and "Used by permission." Permission to modify + * the code and to distribute modified code is granted, provided the + * Copyright, this License, and the Availability note are retained, + * and a notice that the code was modified is included. + * + * Availability: + * + * The CCOLAMD/CSYMAMD library is available at + * + * http://www.cise.ufl.edu/research/sparse/ccolamd/ + * + * This is the http://www.cise.ufl.edu/research/sparse/ccolamd/ccolamd.c + * file. + * + * See the ChangeLog file for changes since Version 1.0. + */ + +/* ========================================================================== */ +/* === Description of user-callable routines ================================ */ +/* ========================================================================== */ + +/* CCOLAMD includes both int and UF_long versions of all its routines. The + * description below is for the int version. For UF_long, all int arguments + * become UF_long integers. UF_long is normally defined as long, except for + * WIN64 */ + +/* ---------------------------------------------------------------------------- + * ccolamd_recommended: + * ---------------------------------------------------------------------------- + * + * C syntax: + * + * #include "ccolamd.h" + * size_t ccolamd_recommended (int nnz, int n_row, int n_col) ; + * size_t ccolamd_l_recommended (UF_long nnz, UF_long n_row, + * UF_long n_col) ; + * + * Purpose: + * + * Returns recommended value of Alen for use by ccolamd. Returns 0 + * if any input argument is negative. The use of this routine + * is optional. Not needed for csymamd, which dynamically allocates + * its own memory. + * + * Arguments (all input arguments): + * + * int nnz ; Number of nonzeros in the matrix A. This must + * be the same value as p [n_col] in the call to + * ccolamd - otherwise you will get a wrong value + * of the recommended memory to use. + * + * int n_row ; Number of rows in the matrix A. + * + * int n_col ; Number of columns in the matrix A. + * + * ---------------------------------------------------------------------------- + * ccolamd_set_defaults: + * ---------------------------------------------------------------------------- + * + * C syntax: + * + * #include "ccolamd.h" + * ccolamd_set_defaults (double knobs [CCOLAMD_KNOBS]) ; + * ccolamd_l_set_defaults (double knobs [CCOLAMD_KNOBS]) ; + * + * Purpose: + * + * Sets the default parameters. The use of this routine is optional. + * Passing a (double *) NULL pointer for the knobs results in the + * default parameter settings. + * + * Arguments: + * + * double knobs [CCOLAMD_KNOBS] ; Output only. + * + * knobs [0] and knobs [1] behave differently than they did in COLAMD. + * The other knobs are new to CCOLAMD. + * + * knobs [0]: dense row control + * + * For CCOLAMD, rows with more than + * max (16, knobs [CCOLAMD_DENSE_ROW] * sqrt (n_col)) + * entries are removed prior to ordering. + * + * For CSYMAMD, rows and columns with more than + * max (16, knobs [CCOLAMD_DENSE_ROW] * sqrt (n)) + * entries are removed prior to ordering, and placed last in the + * output ordering (subject to the constraints). + * + * If negative, only completely dense rows are removed. If you + * intend to use CCOLAMD for a Cholesky factorization of A*A', set + * knobs [CCOLAMD_DENSE_ROW] to -1, which is more appropriate for + * that case. + * + * Default: 10. + * + * knobs [1]: dense column control + * + * For CCOLAMD, columns with more than + * max (16, knobs [CCOLAMD_DENSE_COL] * sqrt (MIN (n_row,n_col))) + * entries are removed prior to ordering, and placed last in the + * output column ordering (subject to the constraints). + * Not used by CSYMAMD. If negative, only completely dense + * columns are removed. Default: 10. + * + * knobs [2]: aggressive absorption + * + * knobs [CCOLAMD_AGGRESSIVE] controls whether or not to do + * aggressive absorption during the ordering. Default is TRUE + * (nonzero). If zero, no aggressive absorption is performed. + * + * knobs [3]: optimize ordering for LU or Cholesky + * + * knobs [CCOLAMD_LU] controls an option that optimizes the + * ordering for the LU of A or the Cholesky factorization of A'A. + * If TRUE (nonzero), an ordering optimized for LU is performed. + * If FALSE (zero), an ordering for Cholesky is performed. + * Default is FALSE. CSYMAMD ignores this parameter; it always + * orders for Cholesky. + * + * ---------------------------------------------------------------------------- + * ccolamd: + * ---------------------------------------------------------------------------- + * + * C syntax: + * + * #include "ccolamd.h" + * int ccolamd (int n_row, int n_col, int Alen, int *A, int *p, + * double knobs [CCOLAMD_KNOBS], int stats [CCOLAMD_STATS], + * int *cmember) ; + * + * UF_long ccolamd_l (UF_long n_row, UF_long n_col, UF_long Alen, + * UF_long *A, UF_long *p, double knobs [CCOLAMD_KNOBS], + * UF_long stats [CCOLAMD_STATS], UF_long *cmember) ; + * + * Purpose: + * + * Computes a column ordering (Q) of A such that P(AQ)=LU or + * (AQ)'AQ=LL' have less fill-in and require fewer floating point + * operations than factorizing the unpermuted matrix A or A'A, + * respectively. + * + * Returns: + * + * TRUE (1) if successful, FALSE (0) otherwise. + * + * Arguments (for int version): + * + * int n_row ; Input argument. + * + * Number of rows in the matrix A. + * Restriction: n_row >= 0. + * ccolamd returns FALSE if n_row is negative. + * + * int n_col ; Input argument. + * + * Number of columns in the matrix A. + * Restriction: n_col >= 0. + * ccolamd returns FALSE if n_col is negative. + * + * int Alen ; Input argument. + * + * Restriction (see note): + * Alen >= MAX (2*nnz, 4*n_col) + 17*n_col + 7*n_row + 7, where + * nnz = p [n_col]. ccolamd returns FALSE if this condition is + * not met. We recommend about nnz/5 more space for better + * efficiency. This restriction makes an modest assumption + * regarding the size of two typedef'd structures in ccolamd.h. + * We do, however, guarantee that + * + * Alen >= ccolamd_recommended (nnz, n_row, n_col) + * + * will work efficiently. + * + * int A [Alen] ; Input argument, undefined on output. + * + * A is an integer array of size Alen. Alen must be at least as + * large as the bare minimum value given above, but this is very + * low, and can result in excessive run time. For best + * performance, we recommend that Alen be greater than or equal to + * ccolamd_recommended (nnz, n_row, n_col), which adds + * nnz/5 to the bare minimum value given above. + * + * On input, the row indices of the entries in column c of the + * matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices + * in a given column c need not be in ascending order, and + * duplicate row indices may be be present. However, ccolamd will + * work a little faster if both of these conditions are met + * (ccolamd puts the matrix into this format, if it finds that the + * the conditions are not met). + * + * The matrix is 0-based. That is, rows are in the range 0 to + * n_row-1, and columns are in the range 0 to n_col-1. ccolamd + * returns FALSE if any row index is out of range. + * + * The contents of A are modified during ordering, and are + * undefined on output. + * + * int p [n_col+1] ; Both input and output argument. + * + * p is an integer array of size n_col+1. On input, it holds the + * "pointers" for the column form of the matrix A. Column c of + * the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first + * entry, p [0], must be zero, and p [c] <= p [c+1] must hold + * for all c in the range 0 to n_col-1. The value nnz = p [n_col] + * is thus the total number of entries in the pattern of the + * matrix A. ccolamd returns FALSE if these conditions are not + * met. + * + * On output, if ccolamd returns TRUE, the array p holds the column + * permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is + * the first column index in the new ordering, and p [n_col-1] is + * the last. That is, p [k] = j means that column j of A is the + * kth pivot column, in AQ, where k is in the range 0 to n_col-1 + * (p [0] = j means that column j of A is the first column in AQ). + * + * If ccolamd returns FALSE, then no permutation is returned, and + * p is undefined on output. + * + * double knobs [CCOLAMD_KNOBS] ; Input argument. + * + * See ccolamd_set_defaults for a description. + * + * int stats [CCOLAMD_STATS] ; Output argument. + * + * Statistics on the ordering, and error status. + * See ccolamd.h for related definitions. + * ccolamd returns FALSE if stats is not present. + * + * stats [0]: number of dense or empty rows ignored. + * + * stats [1]: number of dense or empty columns ignored (and + * ordered last in the output permutation p, subject to the + * constraints). Note that a row can become "empty" if it + * contains only "dense" and/or "empty" columns, and similarly + * a column can become "empty" if it only contains "dense" + * and/or "empty" rows. + * + * stats [2]: number of garbage collections performed. This can + * be excessively high if Alen is close to the minimum + * required value. + * + * stats [3]: status code. < 0 is an error code. + * > 1 is a warning or notice. + * + * 0 OK. Each column of the input matrix contained row + * indices in increasing order, with no duplicates. + * + * 1 OK, but columns of input matrix were jumbled (unsorted + * columns or duplicate entries). CCOLAMD had to do some + * extra work to sort the matrix first and remove + * duplicate entries, but it still was able to return a + * valid permutation (return value of ccolamd was TRUE). + * + * stats [4]: highest column index of jumbled columns + * stats [5]: last seen duplicate or unsorted row index + * stats [6]: number of duplicate or unsorted row indices + * + * -1 A is a null pointer + * + * -2 p is a null pointer + * + * -3 n_row is negative. stats [4]: n_row + * + * -4 n_col is negative. stats [4]: n_col + * + * -5 number of nonzeros in matrix is negative + * + * stats [4]: number of nonzeros, p [n_col] + * + * -6 p [0] is nonzero + * + * stats [4]: p [0] + * + * -7 A is too small + * + * stats [4]: required size + * stats [5]: actual size (Alen) + * + * -8 a column has a negative number of entries + * + * stats [4]: column with < 0 entries + * stats [5]: number of entries in col + * + * -9 a row index is out of bounds + * + * stats [4]: column with bad row index + * stats [5]: bad row index + * stats [6]: n_row, # of rows of matrx + * + * -10 (unused; see csymamd) + * + * int cmember [n_col] ; Input argument. + * + * cmember is new to CCOLAMD. It did not appear in COLAMD. + * It places contraints on the output ordering. s = cmember [j] + * gives the constraint set s that contains the column j + * (Restriction: 0 <= s < n_col). In the output column + * permutation, all columns in set 0 appear first, followed by + * all columns in set 1, and so on. If NULL, all columns are + * treated as if they were in a single constraint set, and you + * will obtain the same ordering as COLAMD (with one exception: + * the dense row/column threshold and other default knobs in + * CCOLAMD and COLAMD are different). + * + * Example: + * + * See + * http://www.cise.ufl.edu/research/sparse/ccolamd/ccolamd_example.c + * for a complete example. + * + * To order the columns of a 5-by-4 matrix with 11 nonzero entries in + * the following nonzero pattern + * + * x 0 x 0 + * x 0 x x + * 0 x x 0 + * 0 0 x x + * x x 0 0 + * + * with default knobs, no output statistics, and no ordering + * constraints, do the following: + * + * #include "ccolamd.h" + * #define ALEN 144 + * int A [ALEN] = {0, 1, 4, 2, 4, 0, 1, 2, 3, 1, 3} ; + * int p [ ] = {0, 3, 5, 9, 11} ; + * int stats [CCOLAMD_STATS] ; + * ccolamd (5, 4, ALEN, A, p, (double *) NULL, stats, NULL) ; + * + * The permutation is returned in the array p, and A is destroyed. + * + * ---------------------------------------------------------------------------- + * csymamd: + * ---------------------------------------------------------------------------- + * + * C syntax: + * + * #include "ccolamd.h" + * + * int csymamd (int n, int *A, int *p, int *perm, + * double knobs [CCOLAMD_KNOBS], int stats [CCOLAMD_STATS], + * void (*allocate) (size_t, size_t), void (*release) (void *), + * int *cmember, int stype) ; + * + * UF_long csymamd_l (UF_long n, UF_long *A, UF_long *p, UF_long *perm, + * double knobs [CCOLAMD_KNOBS], UF_long stats [CCOLAMD_STATS], + * void (*allocate) (size_t, size_t), void (*release) (void *), + * UF_long *cmember, UF_long stype) ; + * + * Purpose: + * + * The csymamd routine computes an ordering P of a symmetric sparse + * matrix A such that the Cholesky factorization PAP' = LL' remains + * sparse. It is based on a column ordering of a matrix M constructed + * so that the nonzero pattern of M'M is the same as A. Either the + * lower or upper triangular part of A can be used, or the pattern + * A+A' can be used. You must pass your selected memory allocator + * (usually calloc/free or mxCalloc/mxFree) to csymamd, for it to + * allocate memory for the temporary matrix M. + * + * Returns: + * + * TRUE (1) if successful, FALSE (0) otherwise. + * + * Arguments: + * + * int n ; Input argument. + * + * Number of rows and columns in the symmetrix matrix A. + * Restriction: n >= 0. + * csymamd returns FALSE if n is negative. + * + * int A [nnz] ; Input argument. + * + * A is an integer array of size nnz, where nnz = p [n]. + * + * The row indices of the entries in column c of the matrix are + * held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a + * given column c need not be in ascending order, and duplicate + * row indices may be present. However, csymamd will run faster + * if the columns are in sorted order with no duplicate entries. + * + * The matrix is 0-based. That is, rows are in the range 0 to + * n-1, and columns are in the range 0 to n-1. csymamd + * returns FALSE if any row index is out of range. + * + * The contents of A are not modified. + * + * int p [n+1] ; Input argument. + * + * p is an integer array of size n+1. On input, it holds the + * "pointers" for the column form of the matrix A. Column c of + * the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first + * entry, p [0], must be zero, and p [c] <= p [c+1] must hold + * for all c in the range 0 to n-1. The value p [n] is + * thus the total number of entries in the pattern of the matrix A. + * csymamd returns FALSE if these conditions are not met. + * + * The contents of p are not modified. + * + * int perm [n+1] ; Output argument. + * + * On output, if csymamd returns TRUE, the array perm holds the + * permutation P, where perm [0] is the first index in the new + * ordering, and perm [n-1] is the last. That is, perm [k] = j + * means that row and column j of A is the kth column in PAP', + * where k is in the range 0 to n-1 (perm [0] = j means + * that row and column j of A are the first row and column in + * PAP'). The array is used as a workspace during the ordering, + * which is why it must be of length n+1, not just n. + * + * double knobs [CCOLAMD_KNOBS] ; Input argument. + * + * See colamd_set_defaults for a description. + * + * int stats [CCOLAMD_STATS] ; Output argument. + * + * Statistics on the ordering, and error status. + * See ccolamd.h for related definitions. + * csymand returns FALSE if stats is not present. + * + * stats [0]: number of dense or empty row and columns ignored + * (and ordered last in the output permutation perm, subject + * to the constraints). Note that a row/column can become + * "empty" if it contains only "dense" and/or "empty" + * columns/rows. + * + * stats [1]: (same as stats [0]) + * + * stats [2]: number of garbage collections performed. + * + * stats [3]: status code. < 0 is an error code. + * > 1 is a warning or notice. + * + * 0 to -9: same as ccolamd, with n replacing n_col and n_row, + * and -3 and -7 are unused. + * + * -10 out of memory (unable to allocate temporary workspace + * for M or count arrays using the "allocate" routine + * passed into csymamd). + * + * void * (*allocate) (size_t, size_t) + * + * A pointer to a function providing memory allocation. The + * allocated memory must be returned initialized to zero. For a + * C application, this argument should normally be a pointer to + * calloc. For a MATLAB mexFunction, the routine mxCalloc is + * passed instead. + * + * void (*release) (size_t, size_t) + * + * A pointer to a function that frees memory allocated by the + * memory allocation routine above. For a C application, this + * argument should normally be a pointer to free. For a MATLAB + * mexFunction, the routine mxFree is passed instead. + * + * int cmember [n] ; Input argument. + * + * Same as ccolamd, except that cmember is of size n, and it places + * contraints symmetrically, on both the row and column ordering. + * Entries in cmember must be in the range 0 to n-1. + * + * int stype ; Input argument. + * + * If stype < 0, then only the strictly lower triangular part of + * A is accessed. The upper triangular part is assumed to be the + * transpose of the lower triangular part. This is the same as + * SYMAMD, which did not have an stype parameter. + * + * If stype > 0, only the strictly upper triangular part of A is + * accessed. The lower triangular part is assumed to be the + * transpose of the upper triangular part. + * + * If stype == 0, then the nonzero pattern of A+A' is ordered. + * + * ---------------------------------------------------------------------------- + * ccolamd_report: + * ---------------------------------------------------------------------------- + * + * C syntax: + * + * #include "ccolamd.h" + * ccolamd_report (int stats [CCOLAMD_STATS]) ; + * ccolamd_l_report (UF_long stats [CCOLAMD_STATS]) ; + * + * Purpose: + * + * Prints the error status and statistics recorded in the stats + * array on the standard error output (for a standard C routine) + * or on the MATLAB output (for a mexFunction). + * + * Arguments: + * + * int stats [CCOLAMD_STATS] ; Input only. Statistics from ccolamd. + * + * + * ---------------------------------------------------------------------------- + * csymamd_report: + * ---------------------------------------------------------------------------- + * + * C syntax: + * + * #include "ccolamd.h" + * csymamd_report (int stats [CCOLAMD_STATS]) ; + * csymamd_l_report (UF_long stats [CCOLAMD_STATS]) ; + * + * Purpose: + * + * Prints the error status and statistics recorded in the stats + * array on the standard error output (for a standard C routine) + * or on the MATLAB output (for a mexFunction). + * + * Arguments: + * + * int stats [CCOLAMD_STATS] ; Input only. Statistics from csymamd. + * + */ + + +/* ========================================================================== */ +/* === Scaffolding code definitions ======================================== */ +/* ========================================================================== */ + +/* Ensure that debugging is turned off: */ +#ifndef NDEBUG +#define NDEBUG +#endif + +/* turn on debugging by uncommenting the following line + #undef NDEBUG + */ + +/* ========================================================================== */ +/* === Include files ======================================================== */ +/* ========================================================================== */ + +#include "ccolamd.h" + +#include +#include +#include + +#ifdef MATLAB_MEX_FILE +#include "mex.h" +#include "matrix.h" +#endif + +#if !defined (NPRINT) || !defined (NDEBUG) +#include +#endif + +#ifndef NULL +#define NULL ((void *) 0) +#endif + +/* ========================================================================== */ +/* === int or UF_long ======================================================= */ +/* ========================================================================== */ + +/* define UF_long */ +#include "UFconfig.h" + +#ifdef DLONG + +#define Int UF_long +#define ID UF_long_id +#define Int_MAX UF_long_max + +#define CCOLAMD_recommended ccolamd_l_recommended +#define CCOLAMD_set_defaults ccolamd_l_set_defaults +#define CCOLAMD_2 ccolamd2_l +#define CCOLAMD_MAIN ccolamd_l +#define CCOLAMD_apply_order ccolamd_l_apply_order +#define CCOLAMD_postorder ccolamd_l_postorder +#define CCOLAMD_post_tree ccolamd_l_post_tree +#define CCOLAMD_fsize ccolamd_l_fsize +#define CSYMAMD_MAIN csymamd_l +#define CCOLAMD_report ccolamd_l_report +#define CSYMAMD_report csymamd_l_report + +#else + +#define Int int +#define ID "%d" +#define Int_MAX INT_MAX + +#define CCOLAMD_recommended ccolamd_recommended +#define CCOLAMD_set_defaults ccolamd_set_defaults +#define CCOLAMD_2 ccolamd2 +#define CCOLAMD_MAIN ccolamd +#define CCOLAMD_apply_order ccolamd_apply_order +#define CCOLAMD_postorder ccolamd_postorder +#define CCOLAMD_post_tree ccolamd_post_tree +#define CCOLAMD_fsize ccolamd_fsize +#define CSYMAMD_MAIN csymamd +#define CCOLAMD_report ccolamd_report +#define CSYMAMD_report csymamd_report + +#endif + +/* ========================================================================== */ +/* === Row and Column structures ============================================ */ +/* ========================================================================== */ + +typedef struct CColamd_Col_struct +{ + /* size of this struct is 8 integers if no padding occurs */ + + Int start ; /* index for A of first row in this column, or DEAD */ + /* if column is dead */ + Int length ; /* number of rows in this column */ + union + { + Int thickness ; /* number of original columns represented by this */ + /* col, if the column is alive */ + Int parent ; /* parent in parent tree super-column structure, if */ + /* the column is dead */ + } shared1 ; + union + { + Int score ; + Int order ; + } shared2 ; + union + { + Int headhash ; /* head of a hash bucket, if col is at the head of */ + /* a degree list */ + Int hash ; /* hash value, if col is not in a degree list */ + Int prev ; /* previous column in degree list, if col is in a */ + /* degree list (but not at the head of a degree list) */ + } shared3 ; + union + { + Int degree_next ; /* next column, if col is in a degree list */ + Int hash_next ; /* next column, if col is in a hash list */ + } shared4 ; + + Int nextcol ; /* next column in this supercolumn */ + Int lastcol ; /* last column in this supercolumn */ + +} CColamd_Col ; + + +typedef struct CColamd_Row_struct +{ + /* size of this struct is 6 integers if no padding occurs */ + + Int start ; /* index for A of first col in this row */ + Int length ; /* number of principal columns in this row */ + union + { + Int degree ; /* number of principal & non-principal columns in row */ + Int p ; /* used as a row pointer in init_rows_cols () */ + } shared1 ; + union + { + Int mark ; /* for computing set differences and marking dead rows*/ + Int first_column ;/* first column in row (used in garbage collection) */ + } shared2 ; + + Int thickness ; /* number of original rows represented by this row */ + /* that are not yet pivotal */ + Int front ; /* -1 if an original row */ + /* k if this row represents the kth frontal matrix */ + /* where k goes from 0 to at most n_col-1 */ + +} CColamd_Row ; + +/* ========================================================================== */ +/* === basic definitions ==================================================== */ +/* ========================================================================== */ + +#define EMPTY (-1) +#define MAX(a,b) (((a) > (b)) ? (a) : (b)) +#define MIN(a,b) (((a) < (b)) ? (a) : (b)) + +/* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */ +#define GLOBAL +#define PUBLIC +#define PRIVATE static + +#define DENSE_DEGREE(alpha,n) \ + ((Int) MAX (16.0, (alpha) * sqrt ((double) (n)))) + +#define CMEMBER(c) ((cmember == (Int *) NULL) ? (0) : (cmember [c])) + +/* True if x is NaN */ +#define SCALAR_IS_NAN(x) ((x) != (x)) + +/* true if an integer (stored in double x) would overflow (or if x is NaN) */ +#define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) Int_MAX)) \ + || SCALAR_IS_NAN (x)) + +#define ONES_COMPLEMENT(r) (-(r)-1) +#undef TRUE +#undef FALSE +#define TRUE (1) +#define FALSE (0) + +/* Row and column status */ +#define ALIVE (0) +#define DEAD (-1) + +/* Column status */ +#define DEAD_PRINCIPAL (-1) +#define DEAD_NON_PRINCIPAL (-2) + +/* Macros for row and column status update and checking. */ +#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark) +#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE) +#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE) +#define COL_IS_DEAD(c) (Col [c].start < ALIVE) +#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE) +#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL) +#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; } +#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; } +#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; } + + +/* ========================================================================== */ +/* === ccolamd reporting mechanism ========================================== */ +/* ========================================================================== */ + +#if defined (MATLAB_MEX_FILE) || defined (MATHWORKS) +/* In MATLAB, matrices are 1-based to the user, but 0-based internally */ +#define INDEX(i) ((i)+1) +#else +/* In C, matrices are 0-based and indices are reported as such in *_report */ +#define INDEX(i) (i) +#endif + +/* All output goes through the PRINTF macro. */ +#define PRINTF(params) { if (ccolamd_printf != NULL) (void) ccolamd_printf params ; } + + +/* ========================================================================== */ +/* === Debugging prototypes and definitions ================================= */ +/* ========================================================================== */ + +#ifndef NDEBUG + +#include + +/* debug print level, present only when debugging */ +PRIVATE Int ccolamd_debug ; + +/* debug print statements */ +#define DEBUG0(params) { PRINTF (params) ; } +#define DEBUG1(params) { if (ccolamd_debug >= 1) PRINTF (params) ; } +#define DEBUG2(params) { if (ccolamd_debug >= 2) PRINTF (params) ; } +#define DEBUG3(params) { if (ccolamd_debug >= 3) PRINTF (params) ; } +#define DEBUG4(params) { if (ccolamd_debug >= 4) PRINTF (params) ; } + +#ifdef MATLAB_MEX_FILE +#define ASSERT(expression) (mxAssert ((expression), "")) +#else +#define ASSERT(expression) (assert (expression)) +#endif + +PRIVATE void ccolamd_get_debug +( + char *method +) ; + +PRIVATE void debug_mark +( + Int n_row, + CColamd_Row Row [], + Int tag_mark, + Int max_mark +) ; + +PRIVATE void debug_matrix +( + Int n_row, + Int n_col, + CColamd_Row Row [], + CColamd_Col Col [], + Int A [] +) ; + +PRIVATE void debug_structures +( + Int n_row, + Int n_col, + CColamd_Row Row [], + CColamd_Col Col [], + Int A [], + Int in_cset [], + Int cset_start [] +) ; + +PRIVATE void dump_super +( + Int super_c, + CColamd_Col Col [], + Int n_col +) ; + +PRIVATE void debug_deg_lists +( + Int n_row, + Int n_col, + CColamd_Row Row [ ], + CColamd_Col Col [ ], + Int head [ ], + Int min_score, + Int should, + Int max_deg +) ; + +#else + +/* === No debugging ========================================================= */ + +#define DEBUG0(params) ; +#define DEBUG1(params) ; +#define DEBUG2(params) ; +#define DEBUG3(params) ; +#define DEBUG4(params) ; + +#define ASSERT(expression) + +#endif + +/* ========================================================================== */ +/* === Prototypes of PRIVATE routines ======================================= */ +/* ========================================================================== */ + +PRIVATE Int init_rows_cols +( + Int n_row, + Int n_col, + CColamd_Row Row [ ], + CColamd_Col Col [ ], + Int A [ ], + Int p [ ], + Int stats [CCOLAMD_STATS] +) ; + +PRIVATE void init_scoring +( + Int n_row, + Int n_col, + CColamd_Row Row [ ], + CColamd_Col Col [ ], + Int A [ ], + Int head [ ], + double knobs [CCOLAMD_KNOBS], + Int *p_n_row2, + Int *p_n_col2, + Int *p_max_deg, + Int cmember [ ], + Int n_cset, + Int cset_start [ ], + Int dead_cols [ ], + Int *p_ndense_row, /* number of dense rows */ + Int *p_nempty_row, /* number of original empty rows */ + Int *p_nnewlyempty_row, /* number of newly empty rows */ + Int *p_ndense_col, /* number of dense cols (excl "empty" cols) */ + Int *p_nempty_col, /* number of original empty cols */ + Int *p_nnewlyempty_col /* number of newly empty cols */ +) ; + +PRIVATE Int find_ordering +( + Int n_row, + Int n_col, + Int Alen, + CColamd_Row Row [ ], + CColamd_Col Col [ ], + Int A [ ], + Int head [ ], +#ifndef NDEBUG + Int n_col2, +#endif + Int max_deg, + Int pfree, + Int cset [ ], + Int cset_start [ ], +#ifndef NDEBUG + Int n_cset, +#endif + Int cmember [ ], + Int Front_npivcol [ ], + Int Front_nrows [ ], + Int Front_ncols [ ], + Int Front_parent [ ], + Int Front_cols [ ], + Int *p_nfr, + Int aggressive, + Int InFront [ ], + Int order_for_lu +) ; + +PRIVATE void detect_super_cols +( +#ifndef NDEBUG + Int n_col, + CColamd_Row Row [ ], +#endif + CColamd_Col Col [ ], + Int A [ ], + Int head [ ], + Int row_start, + Int row_length, + Int in_set [ ] +) ; + +PRIVATE Int garbage_collection +( + Int n_row, + Int n_col, + CColamd_Row Row [ ], + CColamd_Col Col [ ], + Int A [ ], + Int *pfree +) ; + +PRIVATE Int clear_mark +( + Int tag_mark, + Int max_mark, + Int n_row, + CColamd_Row Row [ ] +) ; + +PRIVATE void print_report +( + char *method, + Int stats [CCOLAMD_STATS] +) ; + + +/* ========================================================================== */ +/* === USER-CALLABLE ROUTINES: ============================================== */ +/* ========================================================================== */ + + +/* ========================================================================== */ +/* === ccolamd_recommended ================================================== */ +/* ========================================================================== */ + +/* + * The ccolamd_recommended routine returns the suggested size for Alen. This + * value has been determined to provide good balance between the number of + * garbage collections and the memory requirements for ccolamd. If any + * argument is negative, or if integer overflow occurs, a 0 is returned as + * an error condition. + * + * 2*nnz space is required for the row and column indices of the matrix + * (or 4*n_col, which ever is larger). + * + * CCOLAMD_C (n_col) + CCOLAMD_R (n_row) space is required for the Col and Row + * arrays, respectively, which are internal to ccolamd. This is equal to + * 8*n_col + 6*n_row if the structures are not padded. + * + * An additional n_col space is the minimal amount of "elbow room", + * and nnz/5 more space is recommended for run time efficiency. + * + * The remaining (((3 * n_col) + 1) + 5 * (n_col + 1) + n_row) space is + * for other workspace used in ccolamd which did not appear in colamd. + */ + +/* add two values of type size_t, and check for integer overflow */ +static size_t t_add (size_t a, size_t b, int *ok) +{ + (*ok) = (*ok) && ((a + b) >= MAX (a,b)) ; + return ((*ok) ? (a + b) : 0) ; +} + +/* compute a*k where k is a small integer, and check for integer overflow */ +static size_t t_mult (size_t a, size_t k, int *ok) +{ + size_t i, s = 0 ; + for (i = 0 ; i < k ; i++) + { + s = t_add (s, a, ok) ; + } + return (s) ; +} + +/* size of the Col and Row structures */ +#define CCOLAMD_C(n_col,ok) \ + ((t_mult (t_add (n_col, 1, ok), sizeof (CColamd_Col), ok) / sizeof (Int))) + +#define CCOLAMD_R(n_row,ok) \ + ((t_mult (t_add (n_row, 1, ok), sizeof (CColamd_Row), ok) / sizeof (Int))) + +/* +#define CCOLAMD_RECOMMENDED(nnz, n_row, n_col) \ + MAX (2 * nnz, 4 * n_col) + \ + CCOLAMD_C (n_col) + CCOLAMD_R (n_row) + n_col + (nnz / 5) \ + + ((3 * n_col) + 1) + 5 * (n_col + 1) + n_row + */ + +static size_t ccolamd_need (Int nnz, Int n_row, Int n_col, int *ok) +{ + + /* ccolamd_need, compute the following, and check for integer overflow: + need = MAX (2*nnz, 4*n_col) + n_col + + Col_size + Row_size + + (3*n_col+1) + (5*(n_col+1)) + n_row ; + */ + size_t s, c, r, t ; + + /* MAX (2*nnz, 4*n_col) */ + s = t_mult (nnz, 2, ok) ; /* 2*nnz */ + t = t_mult (n_col, 4, ok) ; /* 4*n_col */ + s = MAX (s,t) ; + + s = t_add (s, n_col, ok) ; /* bare minimum elbow room */ + + /* Col and Row arrays */ + c = CCOLAMD_C (n_col, ok) ; /* size of column structures */ + r = CCOLAMD_R (n_row, ok) ; /* size of row structures */ + s = t_add (s, c, ok) ; + s = t_add (s, r, ok) ; + + c = t_mult (n_col, 3, ok) ; /* 3*n_col + 1 */ + c = t_add (c, 1, ok) ; + s = t_add (s, c, ok) ; + + c = t_add (n_col, 1, ok) ; /* 5 * (n_col + 1) */ + c = t_mult (c, 5, ok) ; + s = t_add (s, c, ok) ; + + s = t_add (s, n_row, ok) ; /* n_row */ + + return (ok ? s : 0) ; +} + +PUBLIC size_t CCOLAMD_recommended /* returns recommended value of Alen. */ +( + /* === Parameters ======================================================= */ + + Int nnz, /* number of nonzeros in A */ + Int n_row, /* number of rows in A */ + Int n_col /* number of columns in A */ +) +{ + size_t s ; + int ok = TRUE ; + if (nnz < 0 || n_row < 0 || n_col < 0) + { + return (0) ; + } + s = ccolamd_need (nnz, n_row, n_col, &ok) ; /* bare minimum needed */ + s = t_add (s, nnz/5, &ok) ; /* extra elbow room */ + ok = ok && (s < Int_MAX) ; + return (ok ? s : 0) ; +} + + +/* ========================================================================== */ +/* === ccolamd_set_defaults ================================================= */ +/* ========================================================================== */ + +/* + * The ccolamd_set_defaults routine sets the default values of the user- + * controllable parameters for ccolamd. + */ + +PUBLIC void CCOLAMD_set_defaults +( + /* === Parameters ======================================================= */ + + double knobs [CCOLAMD_KNOBS] /* knob array */ +) +{ + /* === Local variables ================================================== */ + + Int i ; + + if (!knobs) + { + return ; /* no knobs to initialize */ + } + for (i = 0 ; i < CCOLAMD_KNOBS ; i++) + { + knobs [i] = 0 ; + } + knobs [CCOLAMD_DENSE_ROW] = 10 ; + knobs [CCOLAMD_DENSE_COL] = 10 ; + knobs [CCOLAMD_AGGRESSIVE] = TRUE ; /* default: do aggressive absorption*/ + knobs [CCOLAMD_LU] = FALSE ; /* default: order for Cholesky */ +} + + +/* ========================================================================== */ +/* === symamd =============================================================== */ +/* ========================================================================== */ + +PUBLIC Int CSYMAMD_MAIN /* return TRUE if OK, FALSE otherwise */ +( + /* === Parameters ======================================================= */ + + Int n, /* number of rows and columns of A */ + Int A [ ], /* row indices of A */ + Int p [ ], /* column pointers of A */ + Int perm [ ], /* output permutation, size n+1 */ + double knobs [CCOLAMD_KNOBS], /* parameters (uses defaults if NULL) */ + Int stats [CCOLAMD_STATS], /* output statistics and error codes */ + void * (*allocate) (size_t, size_t),/* pointer to calloc (ANSI C) or */ + /* mxCalloc (for MATLAB mexFunction) */ + void (*release) (void *), /* pointer to free (ANSI C) or */ + /* mxFree (for MATLAB mexFunction) */ + Int cmember [ ], /* constraint set */ + Int stype /* stype of A */ +) +{ + /* === Local variables ================================================== */ + + double cknobs [CCOLAMD_KNOBS] ; + double default_knobs [CCOLAMD_KNOBS] ; + + Int *count ; /* length of each column of M, and col pointer*/ + Int *mark ; /* mark array for finding duplicate entries */ + Int *M ; /* row indices of matrix M */ + size_t Mlen ; /* length of M */ + Int n_row ; /* number of rows in M */ + Int nnz ; /* number of entries in A */ + Int i ; /* row index of A */ + Int j ; /* column index of A */ + Int k ; /* row index of M */ + Int mnz ; /* number of nonzeros in M */ + Int pp ; /* index into a column of A */ + Int last_row ; /* last row seen in the current column */ + Int length ; /* number of nonzeros in a column */ + Int both ; /* TRUE if ordering A+A' */ + Int upper ; /* TRUE if ordering triu(A)+triu(A)' */ + Int lower ; /* TRUE if ordering tril(A)+tril(A)' */ + +#ifndef NDEBUG + ccolamd_get_debug ("csymamd") ; +#endif + + both = (stype == 0) ; + upper = (stype > 0) ; + lower = (stype < 0) ; + + /* === Check the input arguments ======================================== */ + + if (!stats) + { + DEBUG1 (("csymamd: stats not present\n")) ; + return (FALSE) ; + } + for (i = 0 ; i < CCOLAMD_STATS ; i++) + { + stats [i] = 0 ; + } + stats [CCOLAMD_STATUS] = CCOLAMD_OK ; + stats [CCOLAMD_INFO1] = -1 ; + stats [CCOLAMD_INFO2] = -1 ; + + if (!A) + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_not_present ; + DEBUG1 (("csymamd: A not present\n")) ; + return (FALSE) ; + } + + if (!p) /* p is not present */ + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p_not_present ; + DEBUG1 (("csymamd: p not present\n")) ; + return (FALSE) ; + } + + if (n < 0) /* n must be >= 0 */ + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_ncol_negative ; + stats [CCOLAMD_INFO1] = n ; + DEBUG1 (("csymamd: n negative "ID" \n", n)) ; + return (FALSE) ; + } + + nnz = p [n] ; + if (nnz < 0) /* nnz must be >= 0 */ + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nnz_negative ; + stats [CCOLAMD_INFO1] = nnz ; + DEBUG1 (("csymamd: number of entries negative "ID" \n", nnz)) ; + return (FALSE) ; + } + + if (p [0] != 0) + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p0_nonzero ; + stats [CCOLAMD_INFO1] = p [0] ; + DEBUG1 (("csymamd: p[0] not zero "ID"\n", p [0])) ; + return (FALSE) ; + } + + /* === If no knobs, set default knobs =================================== */ + + if (!knobs) + { + CCOLAMD_set_defaults (default_knobs) ; + knobs = default_knobs ; + } + + /* === Allocate count and mark ========================================== */ + + count = (Int *) ((*allocate) (n+1, sizeof (Int))) ; + if (!count) + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ; + DEBUG1 (("csymamd: allocate count (size "ID") failed\n", n+1)) ; + return (FALSE) ; + } + + mark = (Int *) ((*allocate) (n+1, sizeof (Int))) ; + if (!mark) + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ; + (*release) ((void *) count) ; + DEBUG1 (("csymamd: allocate mark (size "ID") failed\n", n+1)) ; + return (FALSE) ; + } + + /* === Compute column counts of M, check if A is valid ================== */ + + stats [CCOLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ + + for (i = 0 ; i < n ; i++) + { + mark [i] = -1 ; + } + + for (j = 0 ; j < n ; j++) + { + last_row = -1 ; + + length = p [j+1] - p [j] ; + if (length < 0) + { + /* column pointers must be non-decreasing */ + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_col_length_negative ; + stats [CCOLAMD_INFO1] = j ; + stats [CCOLAMD_INFO2] = length ; + (*release) ((void *) count) ; + (*release) ((void *) mark) ; + DEBUG1 (("csymamd: col "ID" negative length "ID"\n", j, length)) ; + return (FALSE) ; + } + + for (pp = p [j] ; pp < p [j+1] ; pp++) + { + i = A [pp] ; + if (i < 0 || i >= n) + { + /* row index i, in column j, is out of bounds */ + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_row_index_out_of_bounds ; + stats [CCOLAMD_INFO1] = j ; + stats [CCOLAMD_INFO2] = i ; + stats [CCOLAMD_INFO3] = n ; + (*release) ((void *) count) ; + (*release) ((void *) mark) ; + DEBUG1 (("csymamd: row "ID" col "ID" out of bounds\n", i, j)) ; + return (FALSE) ; + } + + if (i <= last_row || mark [i] == j) + { + /* row index is unsorted or repeated (or both), thus col */ + /* is jumbled. This is a notice, not an error condition. */ + stats [CCOLAMD_STATUS] = CCOLAMD_OK_BUT_JUMBLED ; + stats [CCOLAMD_INFO1] = j ; + stats [CCOLAMD_INFO2] = i ; + (stats [CCOLAMD_INFO3]) ++ ; + DEBUG1 (("csymamd: row "ID" col "ID" unsorted/dupl.\n", i, j)) ; + } + + if (mark [i] != j) + { + if ((both && i != j) || (lower && i > j) || (upper && i < j)) + { + /* row k of M will contain column indices i and j */ + count [i]++ ; + count [j]++ ; + } + } + + /* mark the row as having been seen in this column */ + mark [i] = j ; + + last_row = i ; + } + } + + /* === Compute column pointers of M ===================================== */ + + /* use output permutation, perm, for column pointers of M */ + perm [0] = 0 ; + for (j = 1 ; j <= n ; j++) + { + perm [j] = perm [j-1] + count [j-1] ; + } + for (j = 0 ; j < n ; j++) + { + count [j] = perm [j] ; + } + + /* === Construct M ====================================================== */ + + mnz = perm [n] ; + n_row = mnz / 2 ; + Mlen = CCOLAMD_recommended (mnz, n_row, n) ; + M = (Int *) ((*allocate) (Mlen, sizeof (Int))) ; + DEBUG1 (("csymamd: M is "ID"-by-"ID" with "ID" entries, Mlen = %g\n", + n_row, n, mnz, (double) Mlen)) ; + + if (!M) + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ; + (*release) ((void *) count) ; + (*release) ((void *) mark) ; + DEBUG1 (("csymamd: allocate M (size %g) failed\n", (double) Mlen)) ; + return (FALSE) ; + } + + k = 0 ; + + if (stats [CCOLAMD_STATUS] == CCOLAMD_OK) + { + /* Matrix is OK */ + for (j = 0 ; j < n ; j++) + { + ASSERT (p [j+1] - p [j] >= 0) ; + for (pp = p [j] ; pp < p [j+1] ; pp++) + { + i = A [pp] ; + ASSERT (i >= 0 && i < n) ; + if ((both && i != j) || (lower && i > j) || (upper && i < j)) + { + /* row k of M contains column indices i and j */ + M [count [i]++] = k ; + M [count [j]++] = k ; + k++ ; + } + } + } + } + else + { + /* Matrix is jumbled. Do not add duplicates to M. Unsorted cols OK. */ + DEBUG1 (("csymamd: Duplicates in A.\n")) ; + for (i = 0 ; i < n ; i++) + { + mark [i] = -1 ; + } + for (j = 0 ; j < n ; j++) + { + ASSERT (p [j+1] - p [j] >= 0) ; + for (pp = p [j] ; pp < p [j+1] ; pp++) + { + i = A [pp] ; + ASSERT (i >= 0 && i < n) ; + if (mark [i] != j) + { + if ((both && i != j) || (lower && i > j) || (upper && i= 0 */ + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nrow_negative ; + stats [CCOLAMD_INFO1] = n_row ; + DEBUG1 (("ccolamd: nrow negative "ID"\n", n_row)) ; + return (FALSE) ; + } + + if (n_col < 0) /* n_col must be >= 0 */ + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_ncol_negative ; + stats [CCOLAMD_INFO1] = n_col ; + DEBUG1 (("ccolamd: ncol negative "ID"\n", n_col)) ; + return (FALSE) ; + } + + nnz = p [n_col] ; + if (nnz < 0) /* nnz must be >= 0 */ + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nnz_negative ; + stats [CCOLAMD_INFO1] = nnz ; + DEBUG1 (("ccolamd: number of entries negative "ID"\n", nnz)) ; + return (FALSE) ; + } + + if (p [0] != 0) + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p0_nonzero ; + stats [CCOLAMD_INFO1] = p [0] ; + DEBUG1 (("ccolamd: p[0] not zero "ID"\n", p [0])) ; + return (FALSE) ; + } + + /* === If no knobs, set default knobs =================================== */ + + if (!knobs) + { + CCOLAMD_set_defaults (default_knobs) ; + knobs = default_knobs ; + } + + aggressive = (knobs [CCOLAMD_AGGRESSIVE] != FALSE) ; + order_for_lu = (knobs [CCOLAMD_LU] != FALSE) ; + + /* === Allocate workspace from array A ================================== */ + + ok = TRUE ; + Col_size = CCOLAMD_C (n_col, &ok) ; + Row_size = CCOLAMD_R (n_row, &ok) ; + + /* min size of A is 2nnz+ncol. cset and cset_start are of size 2ncol+1 */ + /* Each of the 5 fronts is of size n_col + 1. InFront is of size nrow. */ + + /* + need = MAX (2*nnz, 4*n_col) + n_col + + Col_size + Row_size + + (3*n_col+1) + (5*(n_col+1)) + n_row ; + */ + need = ccolamd_need (nnz, n_row, n_col, &ok) ; + + if (!ok || need > (size_t) Alen || need > Int_MAX) + { + /* not enough space in array A to perform the ordering */ + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_too_small ; + stats [CCOLAMD_INFO1] = need ; + stats [CCOLAMD_INFO2] = Alen ; + DEBUG1 (("ccolamd: Need Alen >= "ID", given "ID"\n", need, Alen)) ; + return (FALSE) ; + } + + /* since integer overflow has been check, the following cannot overflow: */ + Alen -= Col_size + Row_size + (3*n_col + 1) + 5*(n_col+1) + n_row ; + + /* Size of A is now Alen >= MAX (2*nnz, 4*n_col) + n_col. The ordering + * requires Alen >= 2*nnz + n_col, and the postorder requires + * Alen >= 5*n_col. */ + + ap = Alen ; + + /* Front array workspace: 5*(n_col+1) + n_row */ + if (!Front_npivcol || !Front_nrows || !Front_ncols || !Front_parent || + !Front_cols || !Front_cols || !InFront) + { + Front_npivcol = &A [ap] ; ap += (n_col + 1) ; + Front_nrows = &A [ap] ; ap += (n_col + 1) ; + Front_ncols = &A [ap] ; ap += (n_col + 1) ; + Front_parent = &A [ap] ; ap += (n_col + 1) ; + Front_cols = &A [ap] ; ap += (n_col + 1) ; + InFront = &A [ap] ; ap += (n_row) ; + } + else + { + /* Fronts are present. Leave the additional space as elbow room. */ + ap += 5*(n_col+1) + n_row ; + ap = Alen ; + } + + /* Workspace for cset management: 3*n_col+1 */ + /* cset_start is of size n_col + 1 */ + cset_start = &A [ap] ; + ap += n_col + 1 ; + + /* dead_col is of size n_col */ + dead_cols = &A [ap] ; + ap += n_col ; + + /* cset is of size n_col */ + cset = &A [ap] ; + ap += n_col ; + + /* Col is of size Col_size. The space is shared by temp_cstart and csize */ + Col = (CColamd_Col *) &A [ap] ; + temp_cstart = (Int *) Col ; /* [ temp_cstart is of size n_col+1 */ + csize = temp_cstart + (n_col+1) ; /* csize is of size n_col+1 */ + ap += Col_size ; + ASSERT (Col_size >= 2*n_col+1) ; + + /* Row is of size Row_size */ + Row = (CColamd_Row *) &A [ap] ; + ap += Row_size ; + + /* Initialize csize & dead_cols to zero */ + for (i = 0 ; i < n_col ; i++) + { + csize [i] = 0 ; + dead_cols [i] = 0 ; + } + + /* === Construct the constraint set ===================================== */ + + if (n_col == 0) + { + n_cset = 0 ; + } + else if (cmember == (Int *) NULL) + { + /* no constraint set; all columns belong to set zero */ + n_cset = 1 ; + csize [0] = n_col ; + DEBUG1 (("no cmember present\n")) ; + } + else + { + n_cset = 0 ; + for (i = 0 ; i < n_col ; i++) + { + if (cmember [i] < 0 || cmember [i] > n_col) + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_invalid_cmember ; + DEBUG1 (("ccolamd: malformed cmember \n")) ; + return (FALSE) ; + } + n_cset = MAX (n_cset, cmember [i]) ; + csize [cmember [i]]++ ; + } + /* cset is zero based */ + n_cset++ ; + } + + ASSERT ((n_cset >= 0) && (n_cset <= n_col)) ; + + cset_start [0] = temp_cstart [0] = 0 ; + for (i = 1 ; i <= n_cset ; i++) + { + cset_start [i] = cset_start [i-1] + csize [i-1] ; + DEBUG4 ((" cset_start ["ID"] = "ID" \n", i , cset_start [i])) ; + temp_cstart [i] = cset_start [i] ; + } + + /* do in reverse order to encourage natural tie-breaking */ + if (cmember == (Int *) NULL) + { + for (i = n_col-1 ; i >= 0 ; i--) + { + cset [temp_cstart [0]++] = i ; + } + } + else + { + for (i = n_col-1 ; i >= 0 ; i--) + { + cset [temp_cstart [cmember [i]]++] = i ; + } + } + + /* ] temp_cstart and csize are no longer used */ + + /* === Construct the row and column data structures ===================== */ + + if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats)) + { + /* input matrix is invalid */ + DEBUG1 (("ccolamd: Matrix invalid\n")) ; + return (FALSE) ; + } + + /* === Initialize front info ============================================ */ + + for (col = 0 ; col < n_col ; col++) + { + Front_npivcol [col] = 0 ; + Front_nrows [col] = 0 ; + Front_ncols [col] = 0 ; + Front_parent [col] = EMPTY ; + Front_cols [col] = EMPTY ; + } + + /* === Initialize scores, kill dense rows/columns ======================= */ + + init_scoring (n_row, n_col, Row, Col, A, p, knobs, + &n_row2, &n_col2, &max_deg, cmember, n_cset, cset_start, dead_cols, + &ndense_row, &nempty_row, &nnewlyempty_row, + &ndense_col, &nempty_col, &nnewlyempty_col) ; + + ASSERT (n_row2 == n_row - nempty_row - nnewlyempty_row - ndense_row) ; + ASSERT (n_col2 == n_col - nempty_col - nnewlyempty_col - ndense_col) ; + DEBUG1 (("# dense rows "ID" cols "ID"\n", ndense_row, ndense_col)) ; + + /* === Order the supercolumns =========================================== */ + + ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p, +#ifndef NDEBUG + n_col2, +#endif + max_deg, 2*nnz, cset, cset_start, +#ifndef NDEBUG + n_cset, +#endif + cmember, Front_npivcol, Front_nrows, Front_ncols, Front_parent, + Front_cols, &nfr, aggressive, InFront, order_for_lu) ; + + ASSERT (Alen >= 5*n_col) ; + + /* === Postorder ======================================================== */ + + /* A is no longer needed, so use A [0..5*nfr-1] as workspace [ [ */ + /* This step requires Alen >= 5*n_col */ + Front_child = A ; + Front_sibling = Front_child + nfr ; + Front_stack = Front_sibling + nfr ; + Front_order = Front_stack + nfr ; + Front_size = Front_order + nfr ; + + CCOLAMD_fsize (nfr, Front_size, Front_nrows, Front_ncols, + Front_parent, Front_npivcol) ; + + CCOLAMD_postorder (nfr, Front_parent, Front_npivcol, Front_size, + Front_order, Front_child, Front_sibling, Front_stack, Front_cols, + cmember) ; + + /* Front_size, Front_stack, Front_child, Front_sibling no longer needed ] */ + + /* use A [0..nfr-1] as workspace */ + CCOLAMD_apply_order (Front_npivcol, Front_order, A, nfr, nfr) ; + CCOLAMD_apply_order (Front_nrows, Front_order, A, nfr, nfr) ; + CCOLAMD_apply_order (Front_ncols, Front_order, A, nfr, nfr) ; + CCOLAMD_apply_order (Front_parent, Front_order, A, nfr, nfr) ; + CCOLAMD_apply_order (Front_cols, Front_order, A, nfr, nfr) ; + + /* fix the parent to refer to the new numbering */ + for (i = 0 ; i < nfr ; i++) + { + parent = Front_parent [i] ; + if (parent != EMPTY) + { + Front_parent [i] = Front_order [parent] ; + } + } + + /* fix InFront to refer to the new numbering */ + for (row = 0 ; row < n_row ; row++) + { + i = InFront [row] ; + ASSERT (i >= EMPTY && i < nfr) ; + if (i != EMPTY) + { + InFront [row] = Front_order [i] ; + } + } + + /* Front_order longer needed ] */ + + /* === Order the columns in the fronts ================================== */ + + /* use A [0..n_col-1] as inverse permutation */ + for (i = 0 ; i < n_col ; i++) + { + A [i] = EMPTY ; + } + + k = 0 ; + set1 = 0 ; + for (i = 0 ; i < nfr ; i++) + { + ASSERT (Front_npivcol [i] > 0) ; + + set2 = CMEMBER (Front_cols [i]) ; + while (set1 < set2) + { + k += dead_cols [set1] ; + DEBUG3 (("Skip null/dense columns of set "ID"\n",set1)) ; + set1++ ; + } + set1 = set2 ; + + for (col = Front_cols [i] ; col != EMPTY ; col = Col [col].nextcol) + { + ASSERT (col >= 0 && col < n_col) ; + DEBUG1 (("ccolamd output ordering: k "ID" col "ID"\n", k, col)) ; + p [k] = col ; + ASSERT (A [col] == EMPTY) ; + + cs = CMEMBER (col) ; + ASSERT (k >= cset_start [cs] && k < cset_start [cs+1]) ; + + A [col] = k ; + k++ ; + } + } + + /* === Order the "dense" and null columns =============================== */ + + if (n_col2 < n_col) + { + for (col = 0 ; col < n_col ; col++) + { + if (A [col] == EMPTY) + { + k = Col [col].shared2.order ; + cs = CMEMBER (col) ; +#ifndef NDEBUG + dead_cols [cs]-- ; +#endif + ASSERT (k >= cset_start [cs] && k < cset_start [cs+1]) ; + DEBUG1 (("ccolamd output ordering: k "ID" col "ID + " (dense or null col)\n", k, col)) ; + p [k] = col ; + A [col] = k ; + } + } + } + +#ifndef NDEBUG + for (i = 0 ; i < n_cset ; i++) + { + ASSERT (dead_cols [i] == 0) ; + } +#endif + + /* === Return statistics in stats ======================================= */ + + stats [CCOLAMD_DENSE_ROW] = ndense_row ; + stats [CCOLAMD_DENSE_COL] = nempty_row ; + stats [CCOLAMD_NEWLY_EMPTY_ROW] = nnewlyempty_row ; + stats [CCOLAMD_DENSE_COL] = ndense_col ; + stats [CCOLAMD_EMPTY_COL] = nempty_col ; + stats [CCOLAMD_NEWLY_EMPTY_COL] = nnewlyempty_col ; + ASSERT (ndense_col + nempty_col + nnewlyempty_col == n_col - n_col2) ; + if (p_nfr) + { + *p_nfr = nfr ; + } + stats [CCOLAMD_DEFRAG_COUNT] = ngarbage ; + DEBUG1 (("ccolamd: done.\n")) ; + return (TRUE) ; +} + + +/* ========================================================================== */ +/* === colamd_report ======================================================== */ +/* ========================================================================== */ + +PUBLIC void CCOLAMD_report +( + Int stats [CCOLAMD_STATS] +) +{ + print_report ("ccolamd", stats) ; +} + + +/* ========================================================================== */ +/* === symamd_report ======================================================== */ +/* ========================================================================== */ + +PUBLIC void CSYMAMD_report +( + Int stats [CCOLAMD_STATS] +) +{ + print_report ("csymamd", stats) ; +} + + +/* ========================================================================== */ +/* === NON-USER-CALLABLE ROUTINES: ========================================== */ +/* ========================================================================== */ + +/* There are no user-callable routines beyond this point in the file */ + + +/* ========================================================================== */ +/* === init_rows_cols ======================================================= */ +/* ========================================================================== */ + +/* + Takes the column form of the matrix in A and creates the row form of the + matrix. Also, row and column attributes are stored in the Col and Row + structs. If the columns are un-sorted or contain duplicate row indices, + this routine will also sort and remove duplicate row indices from the + column form of the matrix. Returns FALSE if the matrix is invalid, + TRUE otherwise. Not user-callable. +*/ + +PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */ +( + /* === Parameters ======================================================= */ + + Int n_row, /* number of rows of A */ + Int n_col, /* number of columns of A */ + CColamd_Row Row [ ], /* of size n_row+1 */ + CColamd_Col Col [ ], /* of size n_col+1 */ + Int A [ ], /* row indices of A, of size Alen */ + Int p [ ], /* pointers to columns in A, of size n_col+1 */ + Int stats [CCOLAMD_STATS] /* colamd statistics */ +) +{ + /* === Local variables ================================================== */ + + Int col ; /* a column index */ + Int row ; /* a row index */ + Int *cp ; /* a column pointer */ + Int *cp_end ; /* a pointer to the end of a column */ + Int *rp ; /* a row pointer */ + Int *rp_end ; /* a pointer to the end of a row */ + Int last_row ; /* previous row */ + + /* === Initialize columns, and check column pointers ==================== */ + + for (col = 0 ; col < n_col ; col++) + { + Col [col].start = p [col] ; + Col [col].length = p [col+1] - p [col] ; + + if (Col [col].length < 0) + { + /* column pointers must be non-decreasing */ + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_col_length_negative ; + stats [CCOLAMD_INFO1] = col ; + stats [CCOLAMD_INFO2] = Col [col].length ; + DEBUG1 (("ccolamd: col "ID" length "ID" < 0\n", + col, Col [col].length)) ; + return (FALSE) ; + } + + Col [col].shared1.thickness = 1 ; + Col [col].shared2.score = 0 ; + Col [col].shared3.prev = EMPTY ; + Col [col].shared4.degree_next = EMPTY ; + Col [col].nextcol = EMPTY ; + Col [col].lastcol = col ; + } + + /* p [0..n_col] no longer needed, used as "head" in subsequent routines */ + + /* === Scan columns, compute row degrees, and check row indices ========= */ + + stats [CCOLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ + + for (row = 0 ; row < n_row ; row++) + { + Row [row].length = 0 ; + Row [row].shared2.mark = -1 ; + Row [row].thickness = 1 ; + Row [row].front = EMPTY ; + } + + for (col = 0 ; col < n_col ; col++) + { + DEBUG1 (("\nCcolamd input column "ID":\n", col)) ; + last_row = -1 ; + + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + + while (cp < cp_end) + { + row = *cp++ ; + DEBUG1 (("row: "ID"\n", row)) ; + + /* make sure row indices within range */ + if (row < 0 || row >= n_row) + { + stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_row_index_out_of_bounds ; + stats [CCOLAMD_INFO1] = col ; + stats [CCOLAMD_INFO2] = row ; + stats [CCOLAMD_INFO3] = n_row ; + DEBUG1 (("row "ID" col "ID" out of bounds\n", row, col)) ; + return (FALSE) ; + } + + if (row <= last_row || Row [row].shared2.mark == col) + { + /* row index are unsorted or repeated (or both), thus col */ + /* is jumbled. This is a notice, not an error condition. */ + stats [CCOLAMD_STATUS] = CCOLAMD_OK_BUT_JUMBLED ; + stats [CCOLAMD_INFO1] = col ; + stats [CCOLAMD_INFO2] = row ; + (stats [CCOLAMD_INFO3]) ++ ; + DEBUG1 (("row "ID" col "ID" unsorted/duplicate\n", row, col)) ; + } + + if (Row [row].shared2.mark != col) + { + Row [row].length++ ; + } + else + { + /* this is a repeated entry in the column, */ + /* it will be removed */ + Col [col].length-- ; + } + + /* mark the row as having been seen in this column */ + Row [row].shared2.mark = col ; + + last_row = row ; + } + } + + /* === Compute row pointers ============================================= */ + + /* row form of the matrix starts directly after the column */ + /* form of matrix in A */ + Row [0].start = p [n_col] ; + Row [0].shared1.p = Row [0].start ; + Row [0].shared2.mark = -1 ; + for (row = 1 ; row < n_row ; row++) + { + Row [row].start = Row [row-1].start + Row [row-1].length ; + Row [row].shared1.p = Row [row].start ; + Row [row].shared2.mark = -1 ; + } + + /* === Create row form ================================================== */ + + if (stats [CCOLAMD_STATUS] == CCOLAMD_OK_BUT_JUMBLED) + { + /* if cols jumbled, watch for repeated row indices */ + for (col = 0 ; col < n_col ; col++) + { + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + while (cp < cp_end) + { + row = *cp++ ; + if (Row [row].shared2.mark != col) + { + A [(Row [row].shared1.p)++] = col ; + Row [row].shared2.mark = col ; + } + } + } + } + else + { + /* if cols not jumbled, we don't need the mark (this is faster) */ + for (col = 0 ; col < n_col ; col++) + { + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + while (cp < cp_end) + { + A [(Row [*cp++].shared1.p)++] = col ; + } + } + } + + /* === Clear the row marks and set row degrees ========================== */ + + for (row = 0 ; row < n_row ; row++) + { + Row [row].shared2.mark = 0 ; + Row [row].shared1.degree = Row [row].length ; + } + + /* === See if we need to re-create columns ============================== */ + + if (stats [CCOLAMD_STATUS] == CCOLAMD_OK_BUT_JUMBLED) + { + DEBUG1 (("ccolamd: reconstructing column form, matrix jumbled\n")) ; + +#ifndef NDEBUG + /* make sure column lengths are correct */ + for (col = 0 ; col < n_col ; col++) + { + p [col] = Col [col].length ; + } + for (row = 0 ; row < n_row ; row++) + { + rp = &A [Row [row].start] ; + rp_end = rp + Row [row].length ; + while (rp < rp_end) + { + p [*rp++]-- ; + } + } + for (col = 0 ; col < n_col ; col++) + { + ASSERT (p [col] == 0) ; + } + /* now p is all zero (different than when debugging is turned off) */ +#endif + + /* === Compute col pointers ========================================= */ + + /* col form of the matrix starts at A [0]. */ + /* Note, we may have a gap between the col form and the row */ + /* form if there were duplicate entries, if so, it will be */ + /* removed upon the first garbage collection */ + Col [0].start = 0 ; + p [0] = Col [0].start ; + for (col = 1 ; col < n_col ; col++) + { + /* note that the lengths here are for pruned columns, i.e. */ + /* no duplicate row indices will exist for these columns */ + Col [col].start = Col [col-1].start + Col [col-1].length ; + p [col] = Col [col].start ; + } + + /* === Re-create col form =========================================== */ + + for (row = 0 ; row < n_row ; row++) + { + rp = &A [Row [row].start] ; + rp_end = rp + Row [row].length ; + while (rp < rp_end) + { + A [(p [*rp++])++] = row ; + } + } + } + + /* === Done. Matrix is not (or no longer) jumbled ====================== */ + + + return (TRUE) ; +} + + +/* ========================================================================== */ +/* === init_scoring ========================================================= */ +/* ========================================================================== */ + +/* + Kills dense or empty columns and rows, calculates an initial score for + each column, and places all columns in the degree lists. Not user-callable. +*/ + +PRIVATE void init_scoring +( + /* === Parameters ======================================================= */ + + Int n_row, /* number of rows of A */ + Int n_col, /* number of columns of A */ + CColamd_Row Row [ ], /* of size n_row+1 */ + CColamd_Col Col [ ], /* of size n_col+1 */ + Int A [ ], /* column form and row form of A */ + Int head [ ], /* of size n_col+1 */ + double knobs [CCOLAMD_KNOBS],/* parameters */ + Int *p_n_row2, /* number of non-dense, non-empty rows */ + Int *p_n_col2, /* number of non-dense, non-empty columns */ + Int *p_max_deg, /* maximum row degree */ + Int cmember [ ], + Int n_cset, + Int cset_start [ ], + Int dead_cols [ ], + Int *p_ndense_row, /* number of dense rows */ + Int *p_nempty_row, /* number of original empty rows */ + Int *p_nnewlyempty_row, /* number of newly empty rows */ + Int *p_ndense_col, /* number of dense cols (excl "empty" cols) */ + Int *p_nempty_col, /* number of original empty cols */ + Int *p_nnewlyempty_col /* number of newly empty cols */ +) +{ +/* === Local variables ================================================== */ + + Int c ; /* a column index */ + Int r, row ; /* a row index */ + Int *cp ; /* a column pointer */ + Int deg ; /* degree of a row or column */ + Int *cp_end ; /* a pointer to the end of a column */ + Int *new_cp ; /* new column pointer */ + Int col_length ; /* length of pruned column */ + Int score ; /* current column score */ + Int n_col2 ; /* number of non-dense, non-empty columns */ + Int n_row2 ; /* number of non-dense, non-empty rows */ + Int dense_row_count ; /* remove rows with more entries than this */ + Int dense_col_count ; /* remove cols with more entries than this */ + Int max_deg ; /* maximum row degree */ + Int s ; /* a cset index */ + Int ndense_row ; /* number of dense rows */ + Int nempty_row ; /* number of empty rows */ + Int nnewlyempty_row ; /* number of newly empty rows */ + Int ndense_col ; /* number of dense cols (excl "empty" cols) */ + Int nempty_col ; /* number of original empty cols */ + Int nnewlyempty_col ; /* number of newly empty cols */ + Int ne ; + +#ifndef NDEBUG + Int debug_count ; /* debug only. */ +#endif + + /* === Extract knobs ==================================================== */ + + /* Note: if knobs contains a NaN, this is undefined: */ + if (knobs [CCOLAMD_DENSE_ROW] < 0) + { + /* only remove completely dense rows */ + dense_row_count = n_col-1 ; + } + else + { + dense_row_count = DENSE_DEGREE (knobs [CCOLAMD_DENSE_ROW], n_col) ; + } + if (knobs [CCOLAMD_DENSE_COL] < 0) + { + /* only remove completely dense columns */ + dense_col_count = n_row-1 ; + } + else + { + dense_col_count = + DENSE_DEGREE (knobs [CCOLAMD_DENSE_COL], MIN (n_row, n_col)) ; + } + + DEBUG1 (("densecount: "ID" "ID"\n", dense_row_count, dense_col_count)) ; + max_deg = 0 ; + + n_col2 = n_col ; + n_row2 = n_row ; + + /* Set the head array for bookkeeping of dense and empty columns. */ + /* This will be used as hash buckets later. */ + for (s = 0 ; s < n_cset ; s++) + { + head [s] = cset_start [s+1] ; + } + + ndense_col = 0 ; + nempty_col = 0 ; + nnewlyempty_col = 0 ; + ndense_row = 0 ; + nempty_row = 0 ; + nnewlyempty_row = 0 ; + + /* === Kill empty columns =============================================== */ + + /* Put the empty columns at the end in their natural order, so that LU */ + /* factorization can proceed as far as possible. */ + for (c = n_col-1 ; c >= 0 ; c--) + { + deg = Col [c].length ; + if (deg == 0) + { + /* this is a empty column, kill and order it last of its cset */ + Col [c].shared2.order = --head [CMEMBER (c)] ; + --n_col2 ; + dead_cols [CMEMBER (c)] ++ ; + nempty_col++ ; + KILL_PRINCIPAL_COL (c) ; + } + } + DEBUG1 (("ccolamd: null columns killed: "ID"\n", n_col - n_col2)) ; + + /* === Kill dense columns =============================================== */ + + /* Put the dense columns at the end, in their natural order */ + for (c = n_col-1 ; c >= 0 ; c--) + { + /* skip any dead columns */ + if (COL_IS_DEAD (c)) + { + continue ; + } + deg = Col [c].length ; + if (deg > dense_col_count) + { + /* this is a dense column, kill and order it last of its cset */ + Col [c].shared2.order = --head [CMEMBER (c)] ; + --n_col2 ; + dead_cols [CMEMBER (c)] ++ ; + ndense_col++ ; + /* decrement the row degrees */ + cp = &A [Col [c].start] ; + cp_end = cp + Col [c].length ; + while (cp < cp_end) + { + Row [*cp++].shared1.degree-- ; + } + KILL_PRINCIPAL_COL (c) ; + } + } + DEBUG1 (("Dense and null columns killed: "ID"\n", n_col - n_col2)) ; + + /* === Kill dense and empty rows ======================================== */ + + /* Note that there can now be empty rows, since dense columns have + * been deleted. These are "newly" empty rows. */ + + ne = 0 ; + for (r = 0 ; r < n_row ; r++) + { + deg = Row [r].shared1.degree ; + ASSERT (deg >= 0 && deg <= n_col) ; + if (deg > dense_row_count) + { + /* There is at least one dense row. Continue ordering, but */ + /* symbolic factorization will be redone after ccolamd is done.*/ + ndense_row++ ; + } + if (deg == 0) + { + /* this is a newly empty row, or original empty row */ + ne++ ; + } + if (deg > dense_row_count || deg == 0) + { + /* kill a dense or empty row */ + KILL_ROW (r) ; + Row [r].thickness = 0 ; + --n_row2 ; + } + else + { + /* keep track of max degree of remaining rows */ + max_deg = MAX (max_deg, deg) ; + } + } + nnewlyempty_row = ne - nempty_row ; + DEBUG1 (("ccolamd: Dense and null rows killed: "ID"\n", n_row - n_row2)) ; + + /* === Compute initial column scores ==================================== */ + + /* At this point the row degrees are accurate. They reflect the number */ + /* of "live" (non-dense) columns in each row. No empty rows exist. */ + /* Some "live" columns may contain only dead rows, however. These are */ + /* pruned in the code below. */ + + /* now find the initial COLMMD score for each column */ + for (c = n_col-1 ; c >= 0 ; c--) + { + /* skip dead column */ + if (COL_IS_DEAD (c)) + { + continue ; + } + score = 0 ; + cp = &A [Col [c].start] ; + new_cp = cp ; + cp_end = cp + Col [c].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + /* skip if dead */ + if (ROW_IS_DEAD (row)) + { + continue ; + } + /* compact the column */ + *new_cp++ = row ; + /* add row's external degree */ + score += Row [row].shared1.degree - 1 ; + /* guard against integer overflow */ + score = MIN (score, n_col) ; + } + /* determine pruned column length */ + col_length = (Int) (new_cp - &A [Col [c].start]) ; + if (col_length == 0) + { + /* a newly-made null column (all rows in this col are "dense" */ + /* and have already been killed) */ + DEBUG1 (("Newly null killed: "ID"\n", c)) ; + Col [c].shared2.order = -- head [CMEMBER (c)] ; + --n_col2 ; + dead_cols [CMEMBER (c)] ++ ; + nnewlyempty_col++ ; + KILL_PRINCIPAL_COL (c) ; + } + else + { + /* set column length and set score */ + ASSERT (score >= 0) ; + ASSERT (score <= n_col) ; + Col [c].length = col_length ; + Col [c].shared2.score = score ; + } + } + DEBUG1 (("ccolamd: Dense, null, and newly-null columns killed: "ID"\n", + n_col-n_col2)) ; + + /* At this point, all empty rows and columns are dead. All live columns */ + /* are "clean" (containing no dead rows) and simplicial (no supercolumns */ + /* yet). Rows may contain dead columns, but all live rows contain at */ + /* least one live column. */ + +#ifndef NDEBUG + debug_count = 0 ; +#endif + + /* clear the hash buckets */ + for (c = 0 ; c <= n_col ; c++) + { + head [c] = EMPTY ; + } + +#ifndef NDEBUG + debug_structures (n_row, n_col, Row, Col, A, cmember, cset_start) ; +#endif + + /* === Return number of remaining columns, and max row degree =========== */ + + *p_n_col2 = n_col2 ; + *p_n_row2 = n_row2 ; + *p_max_deg = max_deg ; + *p_ndense_row = ndense_row ; + *p_nempty_row = nempty_row ; /* original empty rows */ + *p_nnewlyempty_row = nnewlyempty_row ; + *p_ndense_col = ndense_col ; + *p_nempty_col = nempty_col ; /* original empty cols */ + *p_nnewlyempty_col = nnewlyempty_col ; +} + + +/* ========================================================================== */ +/* === find_ordering ======================================================== */ +/* ========================================================================== */ + +/* + * Order the principal columns of the supercolumn form of the matrix + * (no supercolumns on input). Uses a minimum approximate column minimum + * degree ordering method. Not user-callable. + */ + +PRIVATE Int find_ordering /* return the number of garbage collections */ +( + /* === Parameters ======================================================= */ + + Int n_row, /* number of rows of A */ + Int n_col, /* number of columns of A */ + Int Alen, /* size of A, 2*nnz + n_col or larger */ + CColamd_Row Row [ ], /* of size n_row+1 */ + CColamd_Col Col [ ], /* of size n_col+1 */ + Int A [ ], /* column form and row form of A */ + Int head [ ], /* of size n_col+1 */ +#ifndef NDEBUG + Int n_col2, /* Remaining columns to order */ +#endif + Int max_deg, /* Maximum row degree */ + Int pfree, /* index of first free slot (2*nnz on entry) */ + Int cset [ ], /* constraint set of A */ + Int cset_start [ ], /* pointer to the start of every cset */ +#ifndef NDEBUG + Int n_cset, /* number of csets */ +#endif + Int cmember [ ], /* col -> cset mapping */ + Int Front_npivcol [ ], + Int Front_nrows [ ], + Int Front_ncols [ ], + Int Front_parent [ ], + Int Front_cols [ ], + Int *p_nfr, /* number of fronts */ + Int aggressive, + Int InFront [ ], + Int order_for_lu +) +{ + /* === Local variables ================================================== */ + + Int k ; /* current pivot ordering step */ + Int pivot_col ; /* current pivot column */ + Int *cp ; /* a column pointer */ + Int *rp ; /* a row pointer */ + Int pivot_row ; /* current pivot row */ + Int *new_cp ; /* modified column pointer */ + Int *new_rp ; /* modified row pointer */ + Int pivot_row_start ; /* pointer to start of pivot row */ + Int pivot_row_degree ; /* number of columns in pivot row */ + Int pivot_row_length ; /* number of supercolumns in pivot row */ + Int pivot_col_score ; /* score of pivot column */ + Int needed_memory ; /* free space needed for pivot row */ + Int *cp_end ; /* pointer to the end of a column */ + Int *rp_end ; /* pointer to the end of a row */ + Int row ; /* a row index */ + Int col ; /* a column index */ + Int max_score ; /* maximum possible score */ + Int cur_score ; /* score of current column */ + unsigned Int hash ; /* hash value for supernode detection */ + Int head_column ; /* head of hash bucket */ + Int first_col ; /* first column in hash bucket */ + Int tag_mark ; /* marker value for mark array */ + Int row_mark ; /* Row [row].shared2.mark */ + Int set_difference ; /* set difference size of row with pivot row */ + Int min_score ; /* smallest column score */ + Int col_thickness ; /* "thickness" (no. of columns in a supercol) */ + Int max_mark ; /* maximum value of tag_mark */ + Int pivot_col_thickness ; /* number of columns represented by pivot col */ + Int prev_col ; /* Used by Dlist operations. */ + Int next_col ; /* Used by Dlist operations. */ + Int ngarbage ; /* number of garbage collections performed */ + Int current_set ; /* consraint set that is being ordered */ + Int score ; /* score of a column */ + Int colstart ; /* pointer to first column in current cset */ + Int colend ; /* pointer to last column in current cset */ + Int deadcol ; /* number of dense & null columns in a cset */ + +#ifndef NDEBUG + Int debug_d ; /* debug loop counter */ + Int debug_step = 0 ; /* debug loop counter */ + Int cols_thickness = 0 ; /* the thickness of the columns in current */ + /* cset degreelist and in pivot row pattern. */ +#endif + + Int pivot_row_thickness ; /* number of rows represented by pivot row */ + Int nfr = 0 ; /* number of fronts */ + Int child ; + + /* === Initialization and clear mark ==================================== */ + + max_mark = Int_MAX - n_col ; /* Int_MAX defined in */ + tag_mark = clear_mark (0, max_mark, n_row, Row) ; + min_score = 0 ; + ngarbage = 0 ; + current_set = -1 ; + deadcol = 0 ; + DEBUG1 (("ccolamd: Ordering, n_col2="ID"\n", n_col2)) ; + + for (row = 0 ; row < n_row ; row++) + { + InFront [row] = EMPTY ; + } + + /* === Order the columns ================================================ */ + + for (k = 0 ; k < n_col ; /* 'k' is incremented below */) + { + + /* make sure degree list isn't empty */ + ASSERT (min_score >= 0) ; + ASSERT (min_score <= n_col) ; + ASSERT (head [min_score] >= EMPTY) ; + +#ifndef NDEBUG + for (debug_d = 0 ; debug_d < min_score ; debug_d++) + { + ASSERT (head [debug_d] == EMPTY) ; + } +#endif + + /* Initialize the degree list with columns from next non-empty cset */ + + while ((k+deadcol) == cset_start [current_set+1]) + { + current_set++ ; + DEBUG1 (("\n\n\n============ CSET: "ID"\n", current_set)) ; + k += deadcol ; /* jump to start of next cset */ + deadcol = 0 ; /* reset dead column count */ + + ASSERT ((current_set == n_cset) == (k == n_col)) ; + + /* return if all columns are ordered. */ + if (k == n_col) + { + *p_nfr = nfr ; + return (ngarbage) ; + } + +#ifndef NDEBUG + for (col = 0 ; col <= n_col ; col++) + { + ASSERT (head [col] == EMPTY) ; + } +#endif + + min_score = n_col ; + colstart = cset_start [current_set] ; + colend = cset_start [current_set+1] ; + + while (colstart < colend) + { + col = cset [colstart++] ; + + if (COL_IS_DEAD(col)) + { + DEBUG1 (("Column "ID" is dead\n", col)) ; + /* count dense and null columns */ + if (Col [col].shared2.order != EMPTY) + { + deadcol++ ; + } + continue ; + } + + /* only add principal columns in current set to degree lists */ + ASSERT (CMEMBER (col) == current_set) ; + + score = Col [col].shared2.score ; + DEBUG1 (("Column "ID" is alive, score "ID"\n", col, score)) ; + + ASSERT (min_score >= 0) ; + ASSERT (min_score <= n_col) ; + ASSERT (score >= 0) ; + ASSERT (score <= n_col) ; + ASSERT (head [score] >= EMPTY) ; + + /* now add this column to dList at proper score location */ + next_col = head [score] ; + Col [col].shared3.prev = EMPTY ; + Col [col].shared4.degree_next = next_col ; + + /* if there already was a column with the same score, set its */ + /* previous pointer to this new column */ + if (next_col != EMPTY) + { + Col [next_col].shared3.prev = col ; + } + head [score] = col ; + + /* see if this score is less than current min */ + min_score = MIN (min_score, score) ; + } + +#ifndef NDEBUG + DEBUG1 (("degree lists initialized \n")) ; + debug_deg_lists (n_row, n_col, Row, Col, head, min_score, + ((cset_start [current_set+1]-cset_start [current_set])-deadcol), + max_deg) ; +#endif + } + +#ifndef NDEBUG + if (debug_step % 100 == 0) + { + DEBUG2 (("\n... Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ; + } + else + { + DEBUG3 (("\n------Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ; + } + debug_step++ ; + DEBUG1 (("start of step k="ID": ", k)) ; + debug_deg_lists (n_row, n_col, Row, Col, head, + min_score, cset_start [current_set+1]-(k+deadcol), max_deg) ; + debug_matrix (n_row, n_col, Row, Col, A) ; +#endif + + /* === Select pivot column, and order it ============================ */ + + while (head [min_score] == EMPTY && min_score < n_col) + { + min_score++ ; + } + + pivot_col = head [min_score] ; + + ASSERT (pivot_col >= 0 && pivot_col <= n_col) ; + next_col = Col [pivot_col].shared4.degree_next ; + head [min_score] = next_col ; + if (next_col != EMPTY) + { + Col [next_col].shared3.prev = EMPTY ; + } + + ASSERT (COL_IS_ALIVE (pivot_col)) ; + + /* remember score for defrag check */ + pivot_col_score = Col [pivot_col].shared2.score ; + + /* the pivot column is the kth column in the pivot order */ + Col [pivot_col].shared2.order = k ; + + /* increment order count by column thickness */ + pivot_col_thickness = Col [pivot_col].shared1.thickness ; + k += pivot_col_thickness ; + ASSERT (pivot_col_thickness > 0) ; + DEBUG3 (("Pivot col: "ID" thick "ID"\n", pivot_col, + pivot_col_thickness)) ; + + /* === Garbage_collection, if necessary ============================= */ + + needed_memory = MIN (pivot_col_score, n_col - k) ; + if (pfree + needed_memory >= Alen) + { + pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ; + ngarbage++ ; + /* after garbage collection we will have enough */ + ASSERT (pfree + needed_memory < Alen) ; + /* garbage collection has wiped out Row [ ].shared2.mark array */ + tag_mark = clear_mark (0, max_mark, n_row, Row) ; + +#ifndef NDEBUG + debug_matrix (n_row, n_col, Row, Col, A) ; +#endif + } + + /* === Compute pivot row pattern ==================================== */ + + /* get starting location for this new merged row */ + pivot_row_start = pfree ; + + /* initialize new row counts to zero */ + pivot_row_degree = 0 ; + pivot_row_thickness = 0 ; + + /* tag pivot column as having been visited so it isn't included */ + /* in merged pivot row */ + Col [pivot_col].shared1.thickness = -pivot_col_thickness ; + + /* pivot row is the union of all rows in the pivot column pattern */ + cp = &A [Col [pivot_col].start] ; + cp_end = cp + Col [pivot_col].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + ASSERT (row >= 0 && row < n_row) ; + DEBUG4 (("Pivcol pattern "ID" "ID"\n", ROW_IS_ALIVE (row), row)) ; + /* skip if row is dead */ + if (ROW_IS_ALIVE (row)) + { + /* sum the thicknesses of all the rows */ + pivot_row_thickness += Row [row].thickness ; + + rp = &A [Row [row].start] ; + rp_end = rp + Row [row].length ; + while (rp < rp_end) + { + /* get a column */ + col = *rp++ ; + /* add the column, if alive and untagged */ + col_thickness = Col [col].shared1.thickness ; + if (col_thickness > 0 && COL_IS_ALIVE (col)) + { + /* tag column in pivot row */ + Col [col].shared1.thickness = -col_thickness ; + ASSERT (pfree < Alen) ; + /* place column in pivot row */ + A [pfree++] = col ; + pivot_row_degree += col_thickness ; + DEBUG4 (("\t\t\tNew live col in pivrow: "ID"\n",col)) ; + } +#ifndef NDEBUG + if (col_thickness < 0 && COL_IS_ALIVE (col)) + { + DEBUG4 (("\t\t\tOld live col in pivrow: "ID"\n",col)) ; + } +#endif + } + } + } + + /* pivot_row_thickness is the number of rows in frontal matrix */ + /* including both pivotal rows and nonpivotal rows */ + + /* clear tag on pivot column */ + Col [pivot_col].shared1.thickness = pivot_col_thickness ; + max_deg = MAX (max_deg, pivot_row_degree) ; + +#ifndef NDEBUG + DEBUG3 (("check2\n")) ; + debug_mark (n_row, Row, tag_mark, max_mark) ; +#endif + + /* === Kill all rows used to construct pivot row ==================== */ + + /* also kill pivot row, temporarily */ + cp = &A [Col [pivot_col].start] ; + cp_end = cp + Col [pivot_col].length ; + while (cp < cp_end) + { + /* may be killing an already dead row */ + row = *cp++ ; + DEBUG3 (("Kill row in pivot col: "ID"\n", row)) ; + ASSERT (row >= 0 && row < n_row) ; + if (ROW_IS_ALIVE (row)) + { + if (Row [row].front != EMPTY) + { + /* This row represents a frontal matrix. */ + /* Row [row].front is a child of current front */ + child = Row [row].front ; + Front_parent [child] = nfr ; + DEBUG1 (("Front "ID" => front "ID", normal\n", child, nfr)); + } + else + { + /* This is an original row. Keep track of which front + * is its parent in the row-merge tree. */ + InFront [row] = nfr ; + DEBUG1 (("Row "ID" => front "ID", normal\n", row, nfr)) ; + } + } + + KILL_ROW (row) ; + Row [row].thickness = 0 ; + } + + /* === Select a row index to use as the new pivot row =============== */ + + pivot_row_length = pfree - pivot_row_start ; + if (pivot_row_length > 0) + { + /* pick the "pivot" row arbitrarily (first row in col) */ + pivot_row = A [Col [pivot_col].start] ; + DEBUG3 (("Pivotal row is "ID"\n", pivot_row)) ; + } + else + { + /* there is no pivot row, since it is of zero length */ + pivot_row = EMPTY ; + ASSERT (pivot_row_length == 0) ; + } + ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ; + + /* === Approximate degree computation =============================== */ + + /* Here begins the computation of the approximate degree. The column */ + /* score is the sum of the pivot row "length", plus the size of the */ + /* set differences of each row in the column minus the pattern of the */ + /* pivot row itself. The column ("thickness") itself is also */ + /* excluded from the column score (we thus use an approximate */ + /* external degree). */ + + /* The time taken by the following code (compute set differences, and */ + /* add them up) is proportional to the size of the data structure */ + /* being scanned - that is, the sum of the sizes of each column in */ + /* the pivot row. Thus, the amortized time to compute a column score */ + /* is proportional to the size of that column (where size, in this */ + /* context, is the column "length", or the number of row indices */ + /* in that column). The number of row indices in a column is */ + /* monotonically non-decreasing, from the length of the original */ + /* column on input to colamd. */ + + /* === Compute set differences ====================================== */ + + DEBUG3 (("** Computing set differences phase. **\n")) ; + + /* pivot row is currently dead - it will be revived later. */ + + DEBUG3 (("Pivot row: ")) ; + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + col = *rp++ ; + ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; + DEBUG3 (("Col: "ID"\n", col)) ; + + /* clear tags used to construct pivot row pattern */ + col_thickness = -Col [col].shared1.thickness ; + ASSERT (col_thickness > 0) ; + Col [col].shared1.thickness = col_thickness ; + + /* === Remove column from degree list =========================== */ + + /* only columns in current_set will be in degree list */ + if (CMEMBER (col) == current_set) + { +#ifndef NDEBUG + cols_thickness += col_thickness ; +#endif + cur_score = Col [col].shared2.score ; + prev_col = Col [col].shared3.prev ; + next_col = Col [col].shared4.degree_next ; + DEBUG3 ((" cur_score "ID" prev_col "ID" next_col "ID"\n", + cur_score, prev_col, next_col)) ; + ASSERT (cur_score >= 0) ; + ASSERT (cur_score <= n_col) ; + ASSERT (cur_score >= EMPTY) ; + if (prev_col == EMPTY) + { + head [cur_score] = next_col ; + } + else + { + Col [prev_col].shared4.degree_next = next_col ; + } + if (next_col != EMPTY) + { + Col [next_col].shared3.prev = prev_col ; + } + } + + /* === Scan the column ========================================== */ + + cp = &A [Col [col].start] ; + cp_end = cp + Col [col].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + row_mark = Row [row].shared2.mark ; + /* skip if dead */ + if (ROW_IS_MARKED_DEAD (row_mark)) + { + continue ; + } + ASSERT (row != pivot_row) ; + set_difference = row_mark - tag_mark ; + /* check if the row has been seen yet */ + if (set_difference < 0) + { + ASSERT (Row [row].shared1.degree <= max_deg) ; + set_difference = Row [row].shared1.degree ; + } + /* subtract column thickness from this row's set difference */ + set_difference -= col_thickness ; + ASSERT (set_difference >= 0) ; + /* absorb this row if the set difference becomes zero */ + if (set_difference == 0 && aggressive) + { + DEBUG3 (("aggressive absorption. Row: "ID"\n", row)) ; + + if (Row [row].front != EMPTY) + { + /* Row [row].front is a child of current front. */ + child = Row [row].front ; + Front_parent [child] = nfr ; + DEBUG1 (("Front "ID" => front "ID", aggressive\n", + child, nfr)) ; + } + else + { + /* this is an original row. Keep track of which front + * assembles it, for the row-merge tree */ + InFront [row] = nfr ; + DEBUG1 (("Row "ID" => front "ID", aggressive\n", + row, nfr)) ; + } + + KILL_ROW (row) ; + + /* sum the thicknesses of all the rows */ + pivot_row_thickness += Row [row].thickness ; + Row [row].thickness = 0 ; + } + else + { + /* save the new mark */ + Row [row].shared2.mark = set_difference + tag_mark ; + } + } + } + +#ifndef NDEBUG + debug_deg_lists (n_row, n_col, Row, Col, head, min_score, + cset_start [current_set+1]-(k+deadcol)-(cols_thickness), + max_deg) ; + cols_thickness = 0 ; +#endif + + /* === Add up set differences for each column ======================= */ + + DEBUG3 (("** Adding set differences phase. **\n")) ; + + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + /* get a column */ + col = *rp++ ; + ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; + hash = 0 ; + cur_score = 0 ; + cp = &A [Col [col].start] ; + /* compact the column */ + new_cp = cp ; + cp_end = cp + Col [col].length ; + + DEBUG4 (("Adding set diffs for Col: "ID".\n", col)) ; + + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + ASSERT (row >= 0 && row < n_row) ; + row_mark = Row [row].shared2.mark ; + /* skip if dead */ + if (ROW_IS_MARKED_DEAD (row_mark)) + { + DEBUG4 ((" Row "ID", dead\n", row)) ; + continue ; + } + DEBUG4 ((" Row "ID", set diff "ID"\n", row, row_mark-tag_mark)); + ASSERT (row_mark >= tag_mark) ; + /* compact the column */ + *new_cp++ = row ; + /* compute hash function */ + hash += row ; + /* add set difference */ + cur_score += row_mark - tag_mark ; + /* integer overflow... */ + cur_score = MIN (cur_score, n_col) ; + } + + /* recompute the column's length */ + Col [col].length = (Int) (new_cp - &A [Col [col].start]) ; + + /* === Further mass elimination ================================= */ + + if (Col [col].length == 0 && CMEMBER (col) == current_set) + { + DEBUG4 (("further mass elimination. Col: "ID"\n", col)) ; + /* nothing left but the pivot row in this column */ + KILL_PRINCIPAL_COL (col) ; + pivot_row_degree -= Col [col].shared1.thickness ; + ASSERT (pivot_row_degree >= 0) ; + /* order it */ + Col [col].shared2.order = k ; + /* increment order count by column thickness */ + k += Col [col].shared1.thickness ; + pivot_col_thickness += Col [col].shared1.thickness ; + /* add to column list of front */ +#ifndef NDEBUG + DEBUG1 (("Mass")) ; + dump_super (col, Col, n_col) ; +#endif + Col [Col [col].lastcol].nextcol = Front_cols [nfr] ; + Front_cols [nfr] = col ; + } + else + { + /* === Prepare for supercolumn detection ==================== */ + + DEBUG4 (("Preparing supercol detection for Col: "ID".\n", col)); + + /* save score so far */ + Col [col].shared2.score = cur_score ; + + /* add column to hash table, for supercolumn detection */ + hash %= n_col + 1 ; + + DEBUG4 ((" Hash = "ID", n_col = "ID".\n", hash, n_col)) ; + ASSERT (((Int) hash) <= n_col) ; + + head_column = head [hash] ; + if (head_column > EMPTY) + { + /* degree list "hash" is non-empty, use prev (shared3) of */ + /* first column in degree list as head of hash bucket */ + first_col = Col [head_column].shared3.headhash ; + Col [head_column].shared3.headhash = col ; + } + else + { + /* degree list "hash" is empty, use head as hash bucket */ + first_col = - (head_column + 2) ; + head [hash] = - (col + 2) ; + } + Col [col].shared4.hash_next = first_col ; + + /* save hash function in Col [col].shared3.hash */ + Col [col].shared3.hash = (Int) hash ; + ASSERT (COL_IS_ALIVE (col)) ; + } + } + + /* The approximate external column degree is now computed. */ + + /* === Supercolumn detection ======================================== */ + + DEBUG3 (("** Supercolumn detection phase. **\n")) ; + + detect_super_cols ( +#ifndef NDEBUG + n_col, Row, +#endif + Col, A, head, pivot_row_start, pivot_row_length, cmember) ; + + /* === Kill the pivotal column ====================================== */ + + DEBUG1 ((" KILLING column detect supercols "ID" \n", pivot_col)) ; + KILL_PRINCIPAL_COL (pivot_col) ; + + /* add columns to column list of front */ +#ifndef NDEBUG + DEBUG1 (("Pivot")) ; + dump_super (pivot_col, Col, n_col) ; +#endif + Col [Col [pivot_col].lastcol].nextcol = Front_cols [nfr] ; + Front_cols [nfr] = pivot_col ; + + /* === Clear mark =================================================== */ + + tag_mark = clear_mark (tag_mark+max_deg+1, max_mark, n_row, Row) ; + +#ifndef NDEBUG + DEBUG3 (("check3\n")) ; + debug_mark (n_row, Row, tag_mark, max_mark) ; +#endif + + /* === Finalize the new pivot row, and column scores ================ */ + + DEBUG3 (("** Finalize scores phase. **\n")) ; + + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + /* compact the pivot row */ + new_rp = rp ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + col = *rp++ ; + /* skip dead columns */ + if (COL_IS_DEAD (col)) + { + continue ; + } + *new_rp++ = col ; + /* add new pivot row to column */ + A [Col [col].start + (Col [col].length++)] = pivot_row ; + + /* retrieve score so far and add on pivot row's degree. */ + /* (we wait until here for this in case the pivot */ + /* row's degree was reduced due to mass elimination). */ + cur_score = Col [col].shared2.score + pivot_row_degree ; + + /* calculate the max possible score as the number of */ + /* external columns minus the 'k' value minus the */ + /* columns thickness */ + max_score = n_col - k - Col [col].shared1.thickness ; + + /* make the score the external degree of the union-of-rows */ + cur_score -= Col [col].shared1.thickness ; + + /* make sure score is less or equal than the max score */ + cur_score = MIN (cur_score, max_score) ; + ASSERT (cur_score >= 0) ; + + /* store updated score */ + Col [col].shared2.score = cur_score ; + + /* === Place column back in degree list ========================= */ + + if (CMEMBER (col) == current_set) + { + ASSERT (min_score >= 0) ; + ASSERT (min_score <= n_col) ; + ASSERT (cur_score >= 0) ; + ASSERT (cur_score <= n_col) ; + ASSERT (head [cur_score] >= EMPTY) ; + next_col = head [cur_score] ; + Col [col].shared4.degree_next = next_col ; + Col [col].shared3.prev = EMPTY ; + if (next_col != EMPTY) + { + Col [next_col].shared3.prev = col ; + } + head [cur_score] = col ; + /* see if this score is less than current min */ + min_score = MIN (min_score, cur_score) ; + } + else + { + Col [col].shared4.degree_next = EMPTY ; + Col [col].shared3.prev = EMPTY ; + } + } + +#ifndef NDEBUG + debug_deg_lists (n_row, n_col, Row, Col, head, + min_score, cset_start [current_set+1]-(k+deadcol), max_deg) ; +#endif + + /* frontal matrix can have more pivot cols than pivot rows for */ + /* singular matrices. */ + + /* number of candidate pivot columns */ + Front_npivcol [nfr] = pivot_col_thickness ; + + /* all rows (not just size of contrib. block) */ + Front_nrows [nfr] = pivot_row_thickness ; + + /* all cols */ + Front_ncols [nfr] = pivot_col_thickness + pivot_row_degree ; + + Front_parent [nfr] = EMPTY ; + + pivot_row_thickness -= pivot_col_thickness ; + DEBUG1 (("Front "ID" Pivot_row_thickness after pivot cols elim: "ID"\n", + nfr, pivot_row_thickness)) ; + pivot_row_thickness = MAX (0, pivot_row_thickness) ; + + /* === Resurrect the new pivot row ================================== */ + + if ((pivot_row_degree > 0 && pivot_row_thickness > 0 && (order_for_lu)) + || (pivot_row_degree > 0 && (!order_for_lu))) + { + /* update pivot row length to reflect any cols that were killed */ + /* during super-col detection and mass elimination */ + Row [pivot_row].start = pivot_row_start ; + Row [pivot_row].length = (Int) (new_rp - &A[pivot_row_start]) ; + Row [pivot_row].shared1.degree = pivot_row_degree ; + Row [pivot_row].shared2.mark = 0 ; + Row [pivot_row].thickness = pivot_row_thickness ; + Row [pivot_row].front = nfr ; + /* pivot row is no longer dead */ + DEBUG1 (("Resurrect Pivot_row "ID" deg: "ID"\n", + pivot_row, pivot_row_degree)) ; + } + +#ifndef NDEBUG + DEBUG1 (("Front "ID" : "ID" "ID" "ID" ", nfr, + Front_npivcol [nfr], Front_nrows [nfr], Front_ncols [nfr])) ; + DEBUG1 ((" cols:[ ")) ; + debug_d = 0 ; + for (col = Front_cols [nfr] ; col != EMPTY ; col = Col [col].nextcol) + { + DEBUG1 ((" "ID, col)) ; + ASSERT (col >= 0 && col < n_col) ; + ASSERT (COL_IS_DEAD (col)) ; + debug_d++ ; + ASSERT (debug_d <= pivot_col_thickness) ; + } + ASSERT (debug_d == pivot_col_thickness) ; + DEBUG1 ((" ]\n ")) ; +#endif + nfr++ ; /* one more front */ + } + + /* === All principal columns have now been ordered ====================== */ + + *p_nfr = nfr ; + return (ngarbage) ; +} + + +/* ========================================================================== */ +/* === detect_super_cols ==================================================== */ +/* ========================================================================== */ + +/* + * Detects supercolumns by finding matches between columns in the hash buckets. + * Check amongst columns in the set A [row_start ... row_start + row_length-1]. + * The columns under consideration are currently *not* in the degree lists, + * and have already been placed in the hash buckets. + * + * The hash bucket for columns whose hash function is equal to h is stored + * as follows: + * + * if head [h] is >= 0, then head [h] contains a degree list, so: + * + * head [h] is the first column in degree bucket h. + * Col [head [h]].headhash gives the first column in hash bucket h. + * + * otherwise, the degree list is empty, and: + * + * -(head [h] + 2) is the first column in hash bucket h. + * + * For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous + * column" pointer. Col [c].shared3.hash is used instead as the hash number + * for that column. The value of Col [c].shared4.hash_next is the next column + * in the same hash bucket. + * + * Assuming no, or "few" hash collisions, the time taken by this routine is + * linear in the sum of the sizes (lengths) of each column whose score has + * just been computed in the approximate degree computation. + * Not user-callable. + */ + +PRIVATE void detect_super_cols +( + /* === Parameters ======================================================= */ + +#ifndef NDEBUG + /* these two parameters are only needed when debugging is enabled: */ + Int n_col, /* number of columns of A */ + CColamd_Row Row [ ], /* of size n_row+1 */ +#endif + + CColamd_Col Col [ ], /* of size n_col+1 */ + Int A [ ], /* row indices of A */ + Int head [ ], /* head of degree lists and hash buckets */ + Int row_start, /* pointer to set of columns to check */ + Int row_length, /* number of columns to check */ + Int cmember [ ] /* col -> cset mapping */ +) +{ + /* === Local variables ================================================== */ + + Int hash ; /* hash value for a column */ + Int *rp ; /* pointer to a row */ + Int c ; /* a column index */ + Int super_c ; /* column index of the column to absorb into */ + Int *cp1 ; /* column pointer for column super_c */ + Int *cp2 ; /* column pointer for column c */ + Int length ; /* length of column super_c */ + Int prev_c ; /* column preceding c in hash bucket */ + Int i ; /* loop counter */ + Int *rp_end ; /* pointer to the end of the row */ + Int col ; /* a column index in the row to check */ + Int head_column ; /* first column in hash bucket or degree list */ + Int first_col ; /* first column in hash bucket */ + + /* === Consider each column in the row ================================== */ + + rp = &A [row_start] ; + rp_end = rp + row_length ; + while (rp < rp_end) + { + col = *rp++ ; + if (COL_IS_DEAD (col)) + { + continue ; + } + + /* get hash number for this column */ + hash = Col [col].shared3.hash ; + ASSERT (hash <= n_col) ; + + /* === Get the first column in this hash bucket ===================== */ + + head_column = head [hash] ; + if (head_column > EMPTY) + { + first_col = Col [head_column].shared3.headhash ; + } + else + { + first_col = - (head_column + 2) ; + } + + /* === Consider each column in the hash bucket ====================== */ + + for (super_c = first_col ; super_c != EMPTY ; + super_c = Col [super_c].shared4.hash_next) + { + ASSERT (COL_IS_ALIVE (super_c)) ; + ASSERT (Col [super_c].shared3.hash == hash) ; + length = Col [super_c].length ; + + /* prev_c is the column preceding column c in the hash bucket */ + prev_c = super_c ; + + /* === Compare super_c with all columns after it ================ */ + + for (c = Col [super_c].shared4.hash_next ; + c != EMPTY ; c = Col [c].shared4.hash_next) + { + ASSERT (c != super_c) ; + ASSERT (COL_IS_ALIVE (c)) ; + ASSERT (Col [c].shared3.hash == hash) ; + + /* not identical if lengths or scores are different, */ + /* or if in different constraint sets */ + if (Col [c].length != length || + Col [c].shared2.score != Col [super_c].shared2.score + || CMEMBER (c) != CMEMBER (super_c)) + { + prev_c = c ; + continue ; + } + + /* compare the two columns */ + cp1 = &A [Col [super_c].start] ; + cp2 = &A [Col [c].start] ; + + for (i = 0 ; i < length ; i++) + { + /* the columns are "clean" (no dead rows) */ + ASSERT (ROW_IS_ALIVE (*cp1)) ; + ASSERT (ROW_IS_ALIVE (*cp2)) ; + /* row indices will same order for both supercols, */ + /* no gather scatter nessasary */ + if (*cp1++ != *cp2++) + { + break ; + } + } + + /* the two columns are different if the for-loop "broke" */ + /* super columns should belong to the same constraint set */ + if (i != length) + { + prev_c = c ; + continue ; + } + + /* === Got it! two columns are identical =================== */ + + ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ; + + Col [super_c].shared1.thickness += Col [c].shared1.thickness ; + Col [c].shared1.parent = super_c ; + KILL_NON_PRINCIPAL_COL (c) ; + /* order c later, in order_children() */ + Col [c].shared2.order = EMPTY ; + /* remove c from hash bucket */ + Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ; + + /* add c to end of list of super_c */ + ASSERT (Col [super_c].lastcol >= 0) ; + ASSERT (Col [super_c].lastcol < n_col) ; + Col [Col [super_c].lastcol].nextcol = c ; + Col [super_c].lastcol = Col [c].lastcol ; +#ifndef NDEBUG + /* dump the supercolumn */ + DEBUG1 (("Super")) ; + dump_super (super_c, Col, n_col) ; +#endif + } + } + + /* === Empty this hash bucket ======================================= */ + + if (head_column > EMPTY) + { + /* corresponding degree list "hash" is not empty */ + Col [head_column].shared3.headhash = EMPTY ; + } + else + { + /* corresponding degree list "hash" is empty */ + head [hash] = EMPTY ; + } + } +} + + +/* ========================================================================== */ +/* === garbage_collection =================================================== */ +/* ========================================================================== */ + +/* + * Defragments and compacts columns and rows in the workspace A. Used when + * all avaliable memory has been used while performing row merging. Returns + * the index of the first free position in A, after garbage collection. The + * time taken by this routine is linear is the size of the array A, which is + * itself linear in the number of nonzeros in the input matrix. + * Not user-callable. + */ + +PRIVATE Int garbage_collection /* returns the new value of pfree */ +( + /* === Parameters ======================================================= */ + + Int n_row, /* number of rows */ + Int n_col, /* number of columns */ + CColamd_Row Row [ ], /* row info */ + CColamd_Col Col [ ], /* column info */ + Int A [ ], /* A [0 ... Alen-1] holds the matrix */ + Int *pfree /* &A [0] ... pfree is in use */ +) +{ + /* === Local variables ================================================== */ + + Int *psrc ; /* source pointer */ + Int *pdest ; /* destination pointer */ + Int j ; /* counter */ + Int r ; /* a row index */ + Int c ; /* a column index */ + Int length ; /* length of a row or column */ + +#ifndef NDEBUG + Int debug_rows ; + DEBUG2 (("Defrag..\n")) ; + for (psrc = &A[0] ; psrc < pfree ; psrc++) ASSERT (*psrc >= 0) ; + debug_rows = 0 ; +#endif + + /* === Defragment the columns =========================================== */ + + pdest = &A[0] ; + for (c = 0 ; c < n_col ; c++) + { + if (COL_IS_ALIVE (c)) + { + psrc = &A [Col [c].start] ; + + /* move and compact the column */ + ASSERT (pdest <= psrc) ; + Col [c].start = (Int) (pdest - &A [0]) ; + length = Col [c].length ; + for (j = 0 ; j < length ; j++) + { + r = *psrc++ ; + if (ROW_IS_ALIVE (r)) + { + *pdest++ = r ; + } + } + Col [c].length = (Int) (pdest - &A [Col [c].start]) ; + } + } + + /* === Prepare to defragment the rows =================================== */ + + for (r = 0 ; r < n_row ; r++) + { + if (ROW_IS_DEAD (r) || (Row [r].length == 0)) + { + /* This row is already dead, or is of zero length. Cannot compact + * a row of zero length, so kill it. NOTE: in the current version, + * there are no zero-length live rows. Kill the row (for the first + * time, or again) just to be safe. */ + KILL_ROW (r) ; + } + else + { + /* save first column index in Row [r].shared2.first_column */ + psrc = &A [Row [r].start] ; + Row [r].shared2.first_column = *psrc ; + ASSERT (ROW_IS_ALIVE (r)) ; + /* flag the start of the row with the one's complement of row */ + *psrc = ONES_COMPLEMENT (r) ; +#ifndef NDEBUG + debug_rows++ ; +#endif + } + } + + /* === Defragment the rows ============================================== */ + + psrc = pdest ; + while (psrc < pfree) + { + /* find a negative number ... the start of a row */ + if (*psrc++ < 0) + { + psrc-- ; + /* get the row index */ + r = ONES_COMPLEMENT (*psrc) ; + ASSERT (r >= 0 && r < n_row) ; + /* restore first column index */ + *psrc = Row [r].shared2.first_column ; + ASSERT (ROW_IS_ALIVE (r)) ; + + /* move and compact the row */ + ASSERT (pdest <= psrc) ; + Row [r].start = (Int) (pdest - &A [0]) ; + length = Row [r].length ; + for (j = 0 ; j < length ; j++) + { + c = *psrc++ ; + if (COL_IS_ALIVE (c)) + { + *pdest++ = c ; + } + } + Row [r].length = (Int) (pdest - &A [Row [r].start]) ; +#ifndef NDEBUG + debug_rows-- ; +#endif + } + } + + /* ensure we found all the rows */ + ASSERT (debug_rows == 0) ; + + /* === Return the new value of pfree ==================================== */ + + return ((Int) (pdest - &A [0])) ; +} + + +/* ========================================================================== */ +/* === clear_mark =========================================================== */ +/* ========================================================================== */ + +/* + * Clears the Row [ ].shared2.mark array, and returns the new tag_mark. + * Return value is the new tag_mark. Not user-callable. + */ + +PRIVATE Int clear_mark /* return the new value for tag_mark */ +( + /* === Parameters ======================================================= */ + + Int tag_mark, /* new value of tag_mark */ + Int max_mark, /* max allowed value of tag_mark */ + + Int n_row, /* number of rows in A */ + CColamd_Row Row [ ] /* Row [0 ... n_row-1].shared2.mark is set to zero */ +) +{ + /* === Local variables ================================================== */ + + Int r ; + + if (tag_mark <= 0 || tag_mark >= max_mark) + { + for (r = 0 ; r < n_row ; r++) + { + if (ROW_IS_ALIVE (r)) + { + Row [r].shared2.mark = 0 ; + } + } + tag_mark = 1 ; + } + + return (tag_mark) ; +} + + +/* ========================================================================== */ +/* === print_report ========================================================= */ +/* ========================================================================== */ + +/* No printing occurs if NPRINT is defined at compile time. */ + +PRIVATE void print_report +( + char *method, + Int stats [CCOLAMD_STATS] +) +{ + + Int i1, i2, i3 ; + + PRINTF (("\n%s version %d.%d, %s: ", method, + CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE)) ; + + if (!stats) + { + PRINTF (("No statistics available.\n")) ; + return ; + } + + i1 = stats [CCOLAMD_INFO1] ; + i2 = stats [CCOLAMD_INFO2] ; + i3 = stats [CCOLAMD_INFO3] ; + + if (stats [CCOLAMD_STATUS] >= 0) + { + PRINTF(("OK. ")) ; + } + else + { + PRINTF(("ERROR. ")) ; + } + + switch (stats [CCOLAMD_STATUS]) + { + + case CCOLAMD_OK_BUT_JUMBLED: + + PRINTF(("Matrix has unsorted or duplicate row indices.\n")) ; + + PRINTF(("%s: duplicate or out-of-order row indices: "ID"\n", + method, i3)) ; + + PRINTF(("%s: last seen duplicate or out-of-order row: "ID"\n", + method, INDEX (i2))) ; + + PRINTF(("%s: last seen in column: "ID"", + method, INDEX (i1))) ; + + /* no break - fall through to next case instead */ + + case CCOLAMD_OK: + + PRINTF(("\n")) ; + + PRINTF(("%s: number of dense or empty rows ignored: "ID"\n", + method, stats [CCOLAMD_DENSE_ROW])) ; + + PRINTF(("%s: number of dense or empty columns ignored: "ID"\n", + method, stats [CCOLAMD_DENSE_COL])) ; + + PRINTF(("%s: number of garbage collections performed: "ID"\n", + method, stats [CCOLAMD_DEFRAG_COUNT])) ; + break ; + + case CCOLAMD_ERROR_A_not_present: + + PRINTF(("Array A (row indices of matrix) not present.\n")) ; + break ; + + case CCOLAMD_ERROR_p_not_present: + + PRINTF(("Array p (column pointers for matrix) not present.\n")) ; + break ; + + case CCOLAMD_ERROR_nrow_negative: + + PRINTF(("Invalid number of rows ("ID").\n", i1)) ; + break ; + + case CCOLAMD_ERROR_ncol_negative: + + PRINTF(("Invalid number of columns ("ID").\n", i1)) ; + break ; + + case CCOLAMD_ERROR_nnz_negative: + + PRINTF(("Invalid number of nonzero entries ("ID").\n", i1)) ; + break ; + + case CCOLAMD_ERROR_p0_nonzero: + + PRINTF(("Invalid column pointer, p [0] = "ID", must be 0.\n", i1)) ; + break ; + + case CCOLAMD_ERROR_A_too_small: + + PRINTF(("Array A too small.\n")) ; + PRINTF((" Need Alen >= "ID", but given only Alen = "ID".\n", + i1, i2)) ; + break ; + + case CCOLAMD_ERROR_col_length_negative: + + PRINTF(("Column "ID" has a negative number of entries ("ID").\n", + INDEX (i1), i2)) ; + break ; + + case CCOLAMD_ERROR_row_index_out_of_bounds: + + PRINTF(("Row index (row "ID") out of bounds ("ID" to "ID") in" + "column "ID".\n", INDEX (i2), INDEX (0), INDEX (i3-1), + INDEX (i1))) ; + break ; + + case CCOLAMD_ERROR_out_of_memory: + + PRINTF(("Out of memory.\n")) ; + break ; + + case CCOLAMD_ERROR_invalid_cmember: + + PRINTF(("cmember invalid\n")) ; + break ; + } +} + + +/* ========================================================================= */ +/* === "Expert" routines =================================================== */ +/* ========================================================================= */ + +/* The following routines are visible outside this routine, but are not meant + * to be called by the user. They are meant for a future version of UMFPACK, + * to replace UMFPACK internal routines with a similar name. + */ + + +/* ========================================================================== */ +/* === CCOLAMD_apply_order ================================================== */ +/* ========================================================================== */ + +/* + * Apply post-ordering of supernodal elimination tree. + */ + +GLOBAL void CCOLAMD_apply_order +( + Int Front [ ], /* of size nn on input, size nfr on output */ + const Int Order [ ], /* Order [i] = k, i in the range 0..nn-1, + * and k in the range 0..nfr-1, means that node + * i is the kth node in the postordered tree. */ + Int Temp [ ], /* workspace of size nfr */ + Int nn, /* nodes are numbered in the range 0..nn-1 */ + Int nfr /* the number of nodes actually in use */ +) +{ + Int i, k ; + for (i = 0 ; i < nn ; i++) + { + k = Order [i] ; + ASSERT (k >= EMPTY && k < nfr) ; + if (k != EMPTY) + { + Temp [k] = Front [i] ; + } + } + + for (k = 0 ; k < nfr ; k++) + { + Front [k] = Temp [k] ; + } +} + + +/* ========================================================================== */ +/* === CCOLAMD_fsize ======================================================== */ +/* ========================================================================== */ + +/* Determine the largest frontal matrix size for each subtree. + * Only required to sort the children of each + * node prior to postordering the column elimination tree. */ + +GLOBAL void CCOLAMD_fsize +( + Int nn, + Int Fsize [ ], + Int Fnrows [ ], + Int Fncols [ ], + Int Parent [ ], + Int Npiv [ ] +) +{ + double dr, dc ; + Int j, parent, frsize, r, c ; + + for (j = 0 ; j < nn ; j++) + { + Fsize [j] = EMPTY ; + } + + /* ---------------------------------------------------------------------- */ + /* find max front size for tree rooted at node j, for each front j */ + /* ---------------------------------------------------------------------- */ + + DEBUG1 (("\n\n========================================FRONTS:\n")) ; + for (j = 0 ; j < nn ; j++) + { + if (Npiv [j] > 0) + { + /* this is a frontal matrix */ + parent = Parent [j] ; + r = Fnrows [j] ; + c = Fncols [j] ; + /* avoid integer overflow */ + dr = (double) r ; + dc = (double) c ; + frsize = (INT_OVERFLOW (dr * dc)) ? Int_MAX : (r * c) ; + DEBUG1 ((""ID" : npiv "ID" size "ID" parent "ID" ", + j, Npiv [j], frsize, parent)) ; + Fsize [j] = MAX (Fsize [j], frsize) ; + DEBUG1 (("Fsize [j = "ID"] = "ID"\n", j, Fsize [j])) ; + if (parent != EMPTY) + { + /* find the maximum frontsize of self and children */ + ASSERT (Npiv [parent] > 0) ; + ASSERT (parent > j) ; + Fsize [parent] = MAX (Fsize [parent], Fsize [j]) ; + DEBUG1 (("Fsize [parent = "ID"] = "ID"\n", + parent, Fsize [parent])); + } + } + } + DEBUG1 (("fsize done\n")) ; +} + + +/* ========================================================================= */ +/* === CCOLAMD_postorder =================================================== */ +/* ========================================================================= */ + +/* Perform a postordering (via depth-first search) of an assembly tree. */ + +GLOBAL void CCOLAMD_postorder +( + /* inputs, not modified on output: */ + Int nn, /* nodes are in the range 0..nn-1 */ + Int Parent [ ], /* Parent [j] is the parent of j, or EMPTY if root */ + Int Nv [ ], /* Nv [j] > 0 number of pivots represented by node j, + * or zero if j is not a node. */ + Int Fsize [ ], /* Fsize [j]: size of node j */ + + /* output, not defined on input: */ + Int Order [ ], /* output post-order */ + + /* workspaces of size nn: */ + Int Child [ ], + Int Sibling [ ], + Int Stack [ ], + Int Front_cols [ ], + + /* input, not modified on output: */ + Int cmember [ ] +) +{ + Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ; + + for (j = 0 ; j < nn ; j++) + { + Child [j] = EMPTY ; + Sibling [j] = EMPTY ; + } + + /* --------------------------------------------------------------------- */ + /* place the children in link lists - bigger elements tend to be last */ + /* --------------------------------------------------------------------- */ + + for (j = nn-1 ; j >= 0 ; j--) + { + if (Nv [j] > 0) + { + /* this is an element */ + parent = Parent [j] ; + if (parent != EMPTY) + { + /* place the element in link list of the children its parent */ + /* bigger elements will tend to be at the end of the list */ + Sibling [j] = Child [parent] ; + if (CMEMBER (Front_cols[parent]) == CMEMBER (Front_cols[j])) + { + Child [parent] = j ; + } + } + } + } + +#ifndef NDEBUG + { + Int nels, ff, nchild ; + DEBUG1 (("\n\n================================ ccolamd_postorder:\n")); + nels = 0 ; + for (j = 0 ; j < nn ; j++) + { + if (Nv [j] > 0) + { + DEBUG1 ((""ID" : nels "ID" npiv "ID" size "ID + " parent "ID" maxfr "ID"\n", j, nels, + Nv [j], Fsize [j], Parent [j], Fsize [j])) ; + /* this is an element */ + /* dump the link list of children */ + nchild = 0 ; + DEBUG1 ((" Children: ")) ; + for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff]) + { + DEBUG1 ((ID" ", ff)) ; + nchild++ ; + ASSERT (nchild < nn) ; + } + DEBUG1 (("\n")) ; + parent = Parent [j] ; + nels++ ; + } + } + } +#endif + + /* --------------------------------------------------------------------- */ + /* place the largest child last in the list of children for each node */ + /* --------------------------------------------------------------------- */ + + for (i = 0 ; i < nn ; i++) + { + if (Nv [i] > 0 && Child [i] != EMPTY) + { + +#ifndef NDEBUG + Int nchild ; + DEBUG1 (("Before partial sort, element "ID"\n", i)) ; + nchild = 0 ; + for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) + { + DEBUG1 ((" f: "ID" size: "ID"\n", f, Fsize [f])) ; + nchild++ ; + } +#endif + + /* find the biggest element in the child list */ + fprev = EMPTY ; + maxfrsize = EMPTY ; + bigfprev = EMPTY ; + bigf = EMPTY ; + for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) + { + frsize = Fsize [f] ; + if (frsize >= maxfrsize) + { + /* this is the biggest seen so far */ + maxfrsize = frsize ; + bigfprev = fprev ; + bigf = f ; + } + fprev = f ; + } + + fnext = Sibling [bigf] ; + + DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID + " fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ; + + if (fnext != EMPTY) + { + /* if fnext is EMPTY then bigf is already at the end of list */ + + if (bigfprev == EMPTY) + { + /* delete bigf from the element of the list */ + Child [i] = fnext ; + } + else + { + /* delete bigf from the middle of the list */ + Sibling [bigfprev] = fnext ; + } + + /* put bigf at the end of the list */ + Sibling [bigf] = EMPTY ; + Sibling [fprev] = bigf ; + } + +#ifndef NDEBUG + DEBUG1 (("After partial sort, element "ID"\n", i)) ; + for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) + { + DEBUG1 ((" "ID" "ID"\n", f, Fsize [f])) ; + nchild-- ; + } +#endif + } + } + + /* --------------------------------------------------------------------- */ + /* postorder the assembly tree */ + /* --------------------------------------------------------------------- */ + + for (i = 0 ; i < nn ; i++) + { + Order [i] = EMPTY ; + } + + k = 0 ; + + for (i = 0 ; i < nn ; i++) + { + if ((Parent [i] == EMPTY + || (CMEMBER (Front_cols [Parent [i]]) != CMEMBER (Front_cols [i]))) + && Nv [i] > 0) + { + DEBUG1 (("Root of assembly tree "ID"\n", i)) ; + k = CCOLAMD_post_tree (i, k, Child, Sibling, Order, Stack) ; + } + } +} + + +/* ========================================================================= */ +/* === CCOLAMD_post_tree =================================================== */ +/* ========================================================================= */ + +/* Post-ordering of a supernodal column elimination tree. */ + +GLOBAL Int CCOLAMD_post_tree +( + Int root, /* root of the tree */ + Int k, /* start numbering at k */ + Int Child [ ], /* input argument of size nn, undefined on + * output. Child [i] is the head of a link + * list of all nodes that are children of node + * i in the tree. */ + const Int Sibling [ ], /* input argument of size nn, not modified. + * If f is a node in the link list of the + * children of node i, then Sibling [f] is the + * next child of node i. + */ + Int Order [ ], /* output order, of size nn. Order [i] = k + * if node i is the kth node of the reordered + * tree. */ + Int Stack [ ] /* workspace of size nn */ +) +{ + Int f, head, h, i ; + +#if 0 + /* --------------------------------------------------------------------- */ + /* recursive version (Stack [ ] is not used): */ + /* --------------------------------------------------------------------- */ + + /* this is simple, but can cause stack overflow if nn is large */ + i = root ; + for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) + { + k = CCOLAMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ; + } + Order [i] = k++ ; + return (k) ; +#endif + + /* --------------------------------------------------------------------- */ + /* non-recursive version, using an explicit stack */ + /* --------------------------------------------------------------------- */ + + /* push root on the stack */ + head = 0 ; + Stack [0] = root ; + + while (head >= 0) + { + /* get head of stack */ + i = Stack [head] ; + DEBUG1 (("head of stack "ID" \n", i)) ; + + if (Child [i] != EMPTY) + { + /* the children of i are not yet ordered */ + /* push each child onto the stack in reverse order */ + /* so that small ones at the head of the list get popped first */ + /* and the biggest one at the end of the list gets popped last */ + for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) + { + head++ ; + } + h = head ; + for (f = Child [i] ; f != EMPTY ; f = Sibling [f]) + { + ASSERT (h > 0) ; + Stack [h--] = f ; + DEBUG1 (("push "ID" on stack\n", f)) ; + } + ASSERT (Stack [h] == i) ; + + /* delete child list so that i gets ordered next time we see it */ + Child [i] = EMPTY ; + } + else + { + /* the children of i (if there were any) are already ordered */ + /* remove i from the stack and order it. Front i is kth front */ + head-- ; + DEBUG1 (("pop "ID" order "ID"\n", i, k)) ; + Order [i] = k++ ; + } + +#ifndef NDEBUG + DEBUG1 (("\nStack:")) ; + for (h = head ; h >= 0 ; h--) + { + Int j = Stack [h] ; + DEBUG1 ((" "ID, j)) ; + } + DEBUG1 (("\n\n")) ; +#endif + + } + return (k) ; +} + + + +/* ========================================================================== */ +/* === CCOLAMD debugging routines =========================================== */ +/* ========================================================================== */ + +/* When debugging is disabled, the remainder of this file is ignored. */ + +#ifndef NDEBUG + + +/* ========================================================================== */ +/* === debug_structures ===================================================== */ +/* ========================================================================== */ + +/* + * At this point, all empty rows and columns are dead. All live columns + * are "clean" (containing no dead rows) and simplicial (no supercolumns + * yet). Rows may contain dead columns, but all live rows contain at + * least one live column. + */ + +PRIVATE void debug_structures +( + /* === Parameters ======================================================= */ + + Int n_row, + Int n_col, + CColamd_Row Row [ ], + CColamd_Col Col [ ], + Int A [ ], + Int cmember [ ], + Int cset_start [ ] +) +{ + /* === Local variables ================================================== */ + + Int i ; + Int c ; + Int *cp ; + Int *cp_end ; + Int len ; + Int score ; + Int r ; + Int *rp ; + Int *rp_end ; + Int deg ; + Int cs ; + + /* === Check A, Row, and Col ============================================ */ + + for (c = 0 ; c < n_col ; c++) + { + if (COL_IS_ALIVE (c)) + { + len = Col [c].length ; + score = Col [c].shared2.score ; + DEBUG4 (("initial live col %5d %5d %5d\n", c, len, score)) ; + ASSERT (len > 0) ; + ASSERT (score >= 0) ; + ASSERT (Col [c].shared1.thickness == 1) ; + cp = &A [Col [c].start] ; + cp_end = cp + len ; + while (cp < cp_end) + { + r = *cp++ ; + ASSERT (ROW_IS_ALIVE (r)) ; + } + } + else + { + i = Col [c].shared2.order ; + cs = CMEMBER (c) ; + ASSERT (i >= cset_start [cs] && i < cset_start [cs+1]) ; + } + } + + for (r = 0 ; r < n_row ; r++) + { + if (ROW_IS_ALIVE (r)) + { + i = 0 ; + len = Row [r].length ; + deg = Row [r].shared1.degree ; + ASSERT (len > 0) ; + ASSERT (deg > 0) ; + rp = &A [Row [r].start] ; + rp_end = rp + len ; + while (rp < rp_end) + { + c = *rp++ ; + if (COL_IS_ALIVE (c)) + { + i++ ; + } + } + ASSERT (i > 0) ; + } + } +} + + +/* ========================================================================== */ +/* === debug_deg_lists ====================================================== */ +/* ========================================================================== */ + +/* + * Prints the contents of the degree lists. Counts the number of columns + * in the degree list and compares it to the total it should have. Also + * checks the row degrees. + */ + +PRIVATE void debug_deg_lists +( + /* === Parameters ======================================================= */ + + Int n_row, + Int n_col, + CColamd_Row Row [ ], + CColamd_Col Col [ ], + Int head [ ], + Int min_score, + Int should, + Int max_deg +) + +{ + /* === Local variables ================================================== */ + + Int deg ; + Int col ; + Int have ; + Int row ; + + /* === Check the degree lists =========================================== */ + + if (n_col > 10000 && ccolamd_debug <= 0) + { + return ; + } + have = 0 ; + DEBUG4 (("Degree lists: "ID"\n", min_score)) ; + for (deg = 0 ; deg <= n_col ; deg++) + { + col = head [deg] ; + if (col == EMPTY) + { + continue ; + } + DEBUG4 (("%d:", deg)) ; + ASSERT (Col [col].shared3.prev == EMPTY) ; + while (col != EMPTY) + { + DEBUG4 ((" "ID"", col)) ; + have += Col [col].shared1.thickness ; + ASSERT (COL_IS_ALIVE (col)) ; + col = Col [col].shared4.degree_next ; + } + DEBUG4 (("\n")) ; + } + DEBUG4 (("should "ID" have "ID"\n", should, have)) ; + ASSERT (should == have) ; + + /* === Check the row degrees ============================================ */ + + if (n_row > 10000 && ccolamd_debug <= 0) + { + return ; + } + for (row = 0 ; row < n_row ; row++) + { + if (ROW_IS_ALIVE (row)) + { + ASSERT (Row [row].shared1.degree <= max_deg) ; + } + } +} + + +/* ========================================================================== */ +/* === debug_mark =========================================================== */ +/* ========================================================================== */ + +/* + * Ensures that the tag_mark is less that the maximum and also ensures that + * each entry in the mark array is less than the tag mark. + */ + +PRIVATE void debug_mark +( + /* === Parameters ======================================================= */ + + Int n_row, + CColamd_Row Row [ ], + Int tag_mark, + Int max_mark +) +{ + /* === Local variables ================================================== */ + + Int r ; + + /* === Check the Row marks ============================================== */ + + ASSERT (tag_mark > 0 && tag_mark <= max_mark) ; + if (n_row > 10000 && ccolamd_debug <= 0) + { + return ; + } + for (r = 0 ; r < n_row ; r++) + { + ASSERT (Row [r].shared2.mark < tag_mark) ; + } +} + + +/* ========================================================================== */ +/* === debug_matrix ========================================================= */ +/* ========================================================================== */ + +/* Prints out the contents of the columns and the rows. */ + +PRIVATE void debug_matrix +( + /* === Parameters ======================================================= */ + + Int n_row, + Int n_col, + CColamd_Row Row [ ], + CColamd_Col Col [ ], + Int A [ ] +) +{ + /* === Local variables ================================================== */ + + Int r ; + Int c ; + Int *rp ; + Int *rp_end ; + Int *cp ; + Int *cp_end ; + + /* === Dump the rows and columns of the matrix ========================== */ + + if (ccolamd_debug < 3) + { + return ; + } + DEBUG3 (("DUMP MATRIX:\n")) ; + for (r = 0 ; r < n_row ; r++) + { + DEBUG3 (("Row "ID" alive? "ID"\n", r, ROW_IS_ALIVE (r))) ; + if (ROW_IS_DEAD (r)) + { + continue ; + } + + DEBUG3 (("start "ID" length "ID" degree "ID"\nthickness "ID"\n", + Row [r].start, Row [r].length, Row [r].shared1.degree, + Row [r].thickness)) ; + + rp = &A [Row [r].start] ; + rp_end = rp + Row [r].length ; + while (rp < rp_end) + { + c = *rp++ ; + DEBUG4 ((" "ID" col "ID"\n", COL_IS_ALIVE (c), c)) ; + } + } + + for (c = 0 ; c < n_col ; c++) + { + DEBUG3 (("Col "ID" alive? "ID"\n", c, COL_IS_ALIVE (c))) ; + if (COL_IS_DEAD (c)) + { + continue ; + } + DEBUG3 (("start "ID" length "ID" shared1 "ID" shared2 "ID"\n", + Col [c].start, Col [c].length, + Col [c].shared1.thickness, Col [c].shared2.score)) ; + cp = &A [Col [c].start] ; + cp_end = cp + Col [c].length ; + while (cp < cp_end) + { + r = *cp++ ; + DEBUG4 ((" "ID" row "ID"\n", ROW_IS_ALIVE (r), r)) ; + } + } +} + + +/* ========================================================================== */ +/* === dump_super =========================================================== */ +/* ========================================================================== */ + +PRIVATE void dump_super +( + Int super_c, + CColamd_Col Col [ ], + Int n_col +) +{ + Int col, ncols ; + + DEBUG1 ((" =[ ")) ; + ncols = 0 ; + for (col = super_c ; col != EMPTY ; col = Col [col].nextcol) + { + DEBUG1 ((" "ID, col)) ; + ASSERT (col >= 0 && col < n_col) ; + if (col != super_c) + { + ASSERT (COL_IS_DEAD (col)) ; + } + if (Col [col].nextcol == EMPTY) + { + ASSERT (col == Col [super_c].lastcol) ; + } + ncols++ ; + ASSERT (ncols <= Col [super_c].shared1.thickness) ; + } + ASSERT (ncols == Col [super_c].shared1.thickness) ; + DEBUG1 (("]\n")) ; +} + + +/* ========================================================================== */ +/* === ccolamd_get_debug ==================================================== */ +/* ========================================================================== */ + +PRIVATE void ccolamd_get_debug +( + char *method +) +{ + FILE *debug_file ; + ccolamd_debug = 0 ; /* no debug printing */ + + /* Read debug info from the debug file. */ + debug_file = fopen ("debug", "r") ; + if (debug_file) + { + (void) fscanf (debug_file, ""ID"", &ccolamd_debug) ; + (void) fclose (debug_file) ; + } + + DEBUG0 ((":")) ; + DEBUG1 (("%s: debug version, D = "ID" (THIS WILL BE SLOW!)\n", + method, ccolamd_debug)) ; + DEBUG1 ((" Debug printing level: "ID"\n", ccolamd_debug)) ; +} + +#endif diff --git a/colamd/ccolamd.h b/colamd/ccolamd.h new file mode 100644 index 000000000..11a098741 --- /dev/null +++ b/colamd/ccolamd.h @@ -0,0 +1,365 @@ +/* ========================================================================== */ +/* === CCOLAMD/ccolamd.h ==================================================== */ +/* ========================================================================== */ + +/* ---------------------------------------------------------------------------- + * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, + * Sivasankaran Rajamanickam, and Stefan Larimore + * See License.txt for the Version 2.1 of the GNU Lesser General Public License + * http://www.cise.ufl.edu/research/sparse + * -------------------------------------------------------------------------- */ + +/* + * You must include this file (ccolamd.h) in any routine that uses ccolamd, + * csymamd, or the related macros and definitions. + */ + +#ifndef CCOLAMD_H +#define CCOLAMD_H + +/* make it easy for C++ programs to include CCOLAMD */ +#ifdef __cplusplus +extern "C" { +#endif + +/* for size_t definition: */ +#include + +/* ========================================================================== */ +/* === CCOLAMD version ====================================================== */ +/* ========================================================================== */ + +/* All versions of CCOLAMD will include the following definitions. + * As an example, to test if the version you are using is 1.3 or later: + * + * if (CCOLAMD_VERSION >= CCOLAMD_VERSION_CODE (1,3)) ... + * + * This also works during compile-time: + * + * #if CCOLAMD_VERSION >= CCOLAMD_VERSION_CODE (1,3) + * printf ("This is version 1.3 or later\n") ; + * #else + * printf ("This is an early version\n") ; + * #endif + */ + +#define CCOLAMD_DATE "Nov 30, 2009" +#define CCOLAMD_VERSION_CODE(main,sub) ((main) * 1000 + (sub)) +#define CCOLAMD_MAIN_VERSION 2 +#define CCOLAMD_SUB_VERSION 7 +#define CCOLAMD_SUBSUB_VERSION 2 +#define CCOLAMD_VERSION \ + CCOLAMD_VERSION_CODE(CCOLAMD_MAIN_VERSION,CCOLAMD_SUB_VERSION) + +/* ========================================================================== */ +/* === Knob and statistics definitions ====================================== */ +/* ========================================================================== */ + +/* size of the knobs [ ] array. Only knobs [0..3] are currently used. */ +#define CCOLAMD_KNOBS 20 + +/* number of output statistics. Only stats [0..10] are currently used. */ +#define CCOLAMD_STATS 20 + +/* knobs [0] and stats [0]: dense row knob and output statistic. */ +#define CCOLAMD_DENSE_ROW 0 + +/* knobs [1] and stats [1]: dense column knob and output statistic. */ +#define CCOLAMD_DENSE_COL 1 + +/* knobs [2]: aggressive absorption option */ +#define CCOLAMD_AGGRESSIVE 2 + +/* knobs [3]: LU or Cholesky factorization option */ +#define CCOLAMD_LU 3 + +/* stats [2]: memory defragmentation count output statistic */ +#define CCOLAMD_DEFRAG_COUNT 2 + +/* stats [3]: ccolamd status: zero OK, > 0 warning or notice, < 0 error */ +#define CCOLAMD_STATUS 3 + +/* stats [4..6]: error info, or info on jumbled columns */ +#define CCOLAMD_INFO1 4 +#define CCOLAMD_INFO2 5 +#define CCOLAMD_INFO3 6 + +/* stats [7]: number of originally empty rows */ +#define CCOLAMD_EMPTY_ROW 7 +/* stats [8]: number of originally empty cols */ +#define CCOLAMD_EMPTY_COL 8 +/* stats [9]: number of rows with entries only in dense cols */ +#define CCOLAMD_NEWLY_EMPTY_ROW 9 +/* stats [10]: number of cols with entries only in dense rows */ +#define CCOLAMD_NEWLY_EMPTY_COL 10 + +/* error codes returned in stats [3]: */ +#define CCOLAMD_OK (0) +#define CCOLAMD_OK_BUT_JUMBLED (1) +#define CCOLAMD_ERROR_A_not_present (-1) +#define CCOLAMD_ERROR_p_not_present (-2) +#define CCOLAMD_ERROR_nrow_negative (-3) +#define CCOLAMD_ERROR_ncol_negative (-4) +#define CCOLAMD_ERROR_nnz_negative (-5) +#define CCOLAMD_ERROR_p0_nonzero (-6) +#define CCOLAMD_ERROR_A_too_small (-7) +#define CCOLAMD_ERROR_col_length_negative (-8) +#define CCOLAMD_ERROR_row_index_out_of_bounds (-9) +#define CCOLAMD_ERROR_out_of_memory (-10) +#define CCOLAMD_ERROR_invalid_cmember (-11) +#define CCOLAMD_ERROR_internal_error (-999) + +/* ========================================================================== */ +/* === Prototypes of user-callable routines ================================= */ +/* ========================================================================== */ + +/* define UF_long */ +#include "UFconfig.h" + +size_t ccolamd_recommended /* returns recommended value of Alen, */ + /* or 0 if input arguments are erroneous */ +( + int nnz, /* nonzeros in A */ + int n_row, /* number of rows in A */ + int n_col /* number of columns in A */ +) ; + +size_t ccolamd_l_recommended /* returns recommended value of Alen, */ + /* or 0 if input arguments are erroneous */ +( + UF_long nnz, /* nonzeros in A */ + UF_long n_row, /* number of rows in A */ + UF_long n_col /* number of columns in A */ +) ; + +void ccolamd_set_defaults /* sets default parameters */ +( /* knobs argument is modified on output */ + double knobs [CCOLAMD_KNOBS] /* parameter settings for ccolamd */ +) ; + +void ccolamd_l_set_defaults /* sets default parameters */ +( /* knobs argument is modified on output */ + double knobs [CCOLAMD_KNOBS] /* parameter settings for ccolamd */ +) ; + +int ccolamd /* returns (1) if successful, (0) otherwise*/ +( /* A and p arguments are modified on output */ + int n_row, /* number of rows in A */ + int n_col, /* number of columns in A */ + int Alen, /* size of the array A */ + int A [ ], /* row indices of A, of size Alen */ + int p [ ], /* column pointers of A, of size n_col+1 */ + double knobs [CCOLAMD_KNOBS],/* parameter settings for ccolamd */ + int stats [CCOLAMD_STATS], /* ccolamd output statistics and error codes */ + int cmember [ ] /* Constraint set of A, of size n_col */ +) ; + +UF_long ccolamd_l /* same as ccolamd, but with UF_long integers */ +( + UF_long n_row, + UF_long n_col, + UF_long Alen, + UF_long A [ ], + UF_long p [ ], + double knobs [CCOLAMD_KNOBS], + UF_long stats [CCOLAMD_STATS], + UF_long cmember [ ] +) ; + +int csymamd /* return (1) if OK, (0) otherwise */ +( + int n, /* number of rows and columns of A */ + int A [ ], /* row indices of A */ + int p [ ], /* column pointers of A */ + int perm [ ], /* output permutation, size n_col+1 */ + double knobs [CCOLAMD_KNOBS],/* parameters (uses defaults if NULL) */ + int stats [CCOLAMD_STATS], /* output statistics and error codes */ + void * (*allocate) (size_t, size_t), /* pointer to calloc (ANSI C) or */ + /* mxCalloc (for MATLAB mexFunction) */ + void (*release) (void *), /* pointer to free (ANSI C) or */ + /* mxFree (for MATLAB mexFunction) */ + int cmember [ ], /* Constraint set of A */ + int stype /* 0: use both parts, >0: upper, <0: lower */ +) ; + +UF_long csymamd_l /* same as csymamd, but with UF_long integers */ +( + UF_long n, + UF_long A [ ], + UF_long p [ ], + UF_long perm [ ], + double knobs [CCOLAMD_KNOBS], + UF_long stats [CCOLAMD_STATS], + void * (*allocate) (size_t, size_t), + void (*release) (void *), + UF_long cmember [ ], + UF_long stype +) ; + +void ccolamd_report +( + int stats [CCOLAMD_STATS] +) ; + +void ccolamd_l_report +( + UF_long stats [CCOLAMD_STATS] +) ; + +void csymamd_report +( + int stats [CCOLAMD_STATS] +) ; + +void csymamd_l_report +( + UF_long stats [CCOLAMD_STATS] +) ; + + +/* ========================================================================== */ +/* === Prototypes of "expert" routines ====================================== */ +/* ========================================================================== */ + +/* These routines are meant to be used internally, or in a future version of + * UMFPACK. They appear here so that UMFPACK can use them, but they should not + * be called directly by the user. + */ + +int ccolamd2 +( /* A and p arguments are modified on output */ + int n_row, /* number of rows in A */ + int n_col, /* number of columns in A */ + int Alen, /* size of the array A */ + int A [ ], /* row indices of A, of size Alen */ + int p [ ], /* column pointers of A, of size n_col+1 */ + double knobs [CCOLAMD_KNOBS],/* parameter settings for ccolamd */ + int stats [CCOLAMD_STATS], /* ccolamd output statistics and error codes */ + /* each Front_ array is of size n_col+1: */ + int Front_npivcol [ ], /* # pivot cols in each front */ + int Front_nrows [ ], /* # of rows in each front (incl. pivot rows) */ + int Front_ncols [ ], /* # of cols in each front (incl. pivot cols) */ + int Front_parent [ ], /* parent of each front */ + int Front_cols [ ], /* link list of pivot columns for each front */ + int *p_nfr, /* total number of frontal matrices */ + int InFront [ ], /* InFront [row] = f if row in front f */ + int cmember [ ] /* Constraint set of A */ +) ; + +UF_long ccolamd2_l /* same as ccolamd2, but with UF_long integers */ +( + UF_long n_row, + UF_long n_col, + UF_long Alen, + UF_long A [ ], + UF_long p [ ], + double knobs [CCOLAMD_KNOBS], + UF_long stats [CCOLAMD_STATS], + UF_long Front_npivcol [ ], + UF_long Front_nrows [ ], + UF_long Front_ncols [ ], + UF_long Front_parent [ ], + UF_long Front_cols [ ], + UF_long *p_nfr, + UF_long InFront [ ], + UF_long cmember [ ] +) ; + +void ccolamd_apply_order +( + int Front [ ], + const int Order [ ], + int Temp [ ], + int nn, + int nfr +) ; + +void ccolamd_l_apply_order +( + UF_long Front [ ], + const UF_long Order [ ], + UF_long Temp [ ], + UF_long nn, + UF_long nfr +) ; + + +void ccolamd_fsize +( + int nn, + int MaxFsize [ ], + int Fnrows [ ], + int Fncols [ ], + int Parent [ ], + int Npiv [ ] +) ; + +void ccolamd_l_fsize +( + UF_long nn, + UF_long MaxFsize [ ], + UF_long Fnrows [ ], + UF_long Fncols [ ], + UF_long Parent [ ], + UF_long Npiv [ ] +) ; + +void ccolamd_postorder +( + int nn, + int Parent [ ], + int Npiv [ ], + int Fsize [ ], + int Order [ ], + int Child [ ], + int Sibling [ ], + int Stack [ ], + int Front_cols [ ], + int cmember [ ] +) ; + +void ccolamd_l_postorder +( + UF_long nn, + UF_long Parent [ ], + UF_long Npiv [ ], + UF_long Fsize [ ], + UF_long Order [ ], + UF_long Child [ ], + UF_long Sibling [ ], + UF_long Stack [ ], + UF_long Front_cols [ ], + UF_long cmember [ ] +) ; + +int ccolamd_post_tree +( + int root, + int k, + int Child [ ], + const int Sibling [ ], + int Order [ ], + int Stack [ ] +) ; + +UF_long ccolamd_l_post_tree +( + UF_long root, + UF_long k, + UF_long Child [ ], + const UF_long Sibling [ ], + UF_long Order [ ], + UF_long Stack [ ] +) ; + +#ifndef EXTERN +#define EXTERN extern +#endif + +EXTERN int (*ccolamd_printf) (const char *, ...) ; + +#ifdef __cplusplus +} +#endif + +#endif diff --git a/colamd/ccolamd_global.c b/colamd/ccolamd_global.c new file mode 100644 index 000000000..d43985126 --- /dev/null +++ b/colamd/ccolamd_global.c @@ -0,0 +1,25 @@ +/* ========================================================================== */ +/* === ccolamd_global.c ===================================================== */ +/* ========================================================================== */ + +/* ---------------------------------------------------------------------------- + * CCOLAMD Copyright (C), Univ. of Florida. Authors: Timothy A. Davis, + * Sivasankaran Rajamanickam, and Stefan Larimore + * See License.txt for the Version 2.1 of the GNU Lesser General Public License + * http://www.cise.ufl.edu/research/sparse + * -------------------------------------------------------------------------- */ + +/* Global variables for CCOLAMD */ + +#ifndef NPRINT +#ifdef MATLAB_MEX_FILE +#include "mex.h" +int (*ccolamd_printf) (const char *, ...) = mexPrintf ; +#else +#include +int (*ccolamd_printf) (const char *, ...) = printf ; +#endif +#else +int (*ccolamd_printf) (const char *, ...) = ((void *) 0) ; +#endif + diff --git a/cpp/FactorGraph-inl.h b/cpp/FactorGraph-inl.h index b99391b5c..db802dd87 100644 --- a/cpp/FactorGraph-inl.h +++ b/cpp/FactorGraph-inl.h @@ -15,6 +15,10 @@ #include #include +extern "C" { +#include +} + #include #include #include diff --git a/cpp/GaussianFactorGraph.cpp b/cpp/GaussianFactorGraph.cpp index 592426510..60261b440 100644 --- a/cpp/GaussianFactorGraph.cpp +++ b/cpp/GaussianFactorGraph.cpp @@ -11,8 +11,6 @@ #include #include // for operator += in Ordering -#include - #include "GaussianFactorGraph.h" #include "GaussianFactorSet.h" #include "FactorGraph-inl.h"