/*
|
******************************************************************************
|
Project: OWA EPANET
|
Version: 2.2
|
Module: smatrix.c
|
Description: solves a sparse set of linear equations
|
Authors: see AUTHORS
|
Copyright: see AUTHORS
|
License: see LICENSE
|
Last Updated: 05/15/2019
|
******************************************************************************
|
*/
|
/*
|
This module contains the sparse matrix routines used to solve a network's
|
hydraulic equations. The functions exported by this module are:
|
createsparse() -- called from openhyd() in HYDRAUL.C
|
freesparse() -- called from closehyd() in HYDRAUL.C
|
linsolve() -- called from netsolve() in HYDRAUL.C
|
*/
|
|
#include <stdlib.h>
|
#include <stdio.h>
|
#include <string.h>
|
#include <math.h>
|
#include <limits.h>
|
|
#include <time.h> //For optional timer macros
|
|
#include "text.h"
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#include "types.h"
|
#include "funcs.h"
|
|
// The multiple minimum degree re-ordering routine (see genmmd.c)
|
extern int genmmd(int *neqns, int *xadj, int *adjncy, int *invp, int *perm,
|
int *delta, int *dhead, int *qsize, int *llist, int *marker,
|
int *maxint, int *nofsub);
|
|
// Exported functions
|
int createsparse(Project *);
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void freesparse(Project *);
|
int linsolve(Project *,Smatrix *, int);
|
|
// Local functions
|
static int allocsmatrix(Smatrix *, int, int);
|
static int alloclinsolve(Smatrix *, int);
|
static int localadjlists(Network *, Smatrix *);
|
static int paralink(Network *, Smatrix *, int, int, int k);
|
static void xparalinks(Network *);
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static int reordernodes(Project *);
|
static int factorize(Project *);
|
static int growlist(Project *, int);
|
static int newlink(Project *, Padjlist);
|
static int linked(Network *, int, int);
|
static int addlink(Network *, int, int, int);
|
static int storesparse(Project *, int);
|
static int sortsparse(Smatrix *, int);
|
static void transpose(int, int *, int *, int *, int *,
|
int *, int *, int *);
|
|
|
/*************************************************************************
|
* Timer macros
|
**************************************************************************/
|
//#define cleartimer(tmr) (tmr = 0.0)
|
//#define starttimer(tmr) (tmr -= ((double) clock()/CLOCKS_PER_SEC));
|
//#define stoptimer(tmr) (tmr += ((double) clock()/CLOCKS_PER_SEC));
|
//#define gettimer(tmr) (tmr)
|
|
|
/*************************************************************************
|
* The following data type implements a timer
|
**************************************************************************/
|
// typedef double timer;
|
// timer SmatrixTimer;
|
|
|
int createsparse(Project *pr)
|
/*
|
**--------------------------------------------------------------
|
** Input: none
|
** Output: returns error code
|
** Purpose: creates sparse representation of coeff. matrix
|
**--------------------------------------------------------------
|
*/
|
{
|
Network *net = &pr->network;
|
Smatrix *sm = &pr->hydraul.smatrix;
|
|
int errcode = 0;
|
|
// cleartimer(SmatrixTimer);
|
// starttimer(SmatrixTimer);
|
|
// Allocate sparse matrix data structures
|
errcode = allocsmatrix(sm, net->Nnodes, net->Nlinks);
|
if (errcode) return errcode;
|
|
// Build a local version of node-link adjacency lists
|
// with parallel links removed
|
errcode = localadjlists(net, sm);
|
if (errcode) return errcode;
|
|
// Re-order nodes to minimize number of non-zero coeffs.
|
// in factorized solution matrix
|
ERRCODE(reordernodes(pr));
|
|
// Factorize solution matrix by updating adjacency lists
|
// with non-zero connections due to fill-ins
|
sm->Ncoeffs = net->Nlinks;
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ERRCODE(factorize(pr));
|
|
// Allocate memory for sparse storage of positions of non-zero
|
// coeffs. and store these positions in vector NZSUB
|
ERRCODE(storesparse(pr, net->Njuncs));
|
|
// Free memory used for local adjacency lists and sort
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// row indexes in NZSUB to optimize linsolve()
|
freeadjlists(net);
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ERRCODE(sortsparse(sm, net->Njuncs));
|
|
// Allocate memory used by linear eqn. solver
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ERRCODE(alloclinsolve(sm, net->Nnodes));
|
|
// Re-build adjacency lists for future use
|
ERRCODE(buildadjlists(net));
|
return errcode;
|
}
|
|
|
int allocsmatrix(Smatrix *sm, int Nnodes, int Nlinks)
|
/*
|
**--------------------------------------------------------------
|
** Input: none
|
** Output: returns error code
|
** Purpose: allocates memory for representing a sparse matrix
|
**--------------------------------------------------------------
|
*/
|
{
|
int errcode = 0;
|
|
// Memory for linear eqn. solver allocated in alloclinsolve().
|
sm->Aij = NULL;
|
sm->Aii = NULL;
|
sm->F = NULL;
|
sm->temp = NULL;
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sm->link = NULL;
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sm->first = NULL;
|
|
// Memory for representing sparse matrix data structure
|
sm->Order = (int *) calloc(Nnodes+1, sizeof(int));
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sm->Row = (int *) calloc(Nnodes+1, sizeof(int));
|
sm->Ndx = (int *) calloc(Nlinks+1, sizeof(int));
|
ERRCODE(MEMCHECK(sm->Order));
|
ERRCODE(MEMCHECK(sm->Row));
|
ERRCODE(MEMCHECK(sm->Ndx));
|
return errcode;
|
}
|
|
|
int alloclinsolve(Smatrix *sm, int n)
|
/*
|
**--------------------------------------------------------------
|
** Input: none
|
** Output: returns error code
|
** Purpose: allocates memory used by linear eqn. solver.
|
**--------------------------------------------------------------
|
*/
|
{
|
int errcode = 0;
|
n = n + 1; // All arrays are 1-based
|
|
sm->Aij = (double *)calloc(sm->Ncoeffs + 1, sizeof(double));
|
sm->Aii = (double *)calloc(n, sizeof(double));
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sm->F = (double *)calloc(n, sizeof(double));
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sm->temp = (double *)calloc(n, sizeof(double));
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sm->link = (int *)calloc(n, sizeof(int));
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sm->first = (int *)calloc(n, sizeof(int));
|
ERRCODE(MEMCHECK(sm->Aij));
|
ERRCODE(MEMCHECK(sm->Aii));
|
ERRCODE(MEMCHECK(sm->F));
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ERRCODE(MEMCHECK(sm->temp));
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ERRCODE(MEMCHECK(sm->link));
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ERRCODE(MEMCHECK(sm->first));
|
return errcode;
|
}
|
|
|
void freesparse(Project *pr)
|
/*
|
**----------------------------------------------------------------
|
** Input: None
|
** Output: None
|
** Purpose: Frees memory used for sparse matrix storage
|
**----------------------------------------------------------------
|
*/
|
{
|
Smatrix *sm = &pr->hydraul.smatrix;
|
|
// stoptimer(SmatrixTimer);
|
// printf("\n");
|
// printf("\n Processing Time = %7.3f s", gettimer(SmatrixTimer));
|
// printf("\n");
|
|
FREE(sm->Order);
|
FREE(sm->Row);
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FREE(sm->Ndx);
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FREE(sm->XLNZ);
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FREE(sm->NZSUB);
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FREE(sm->LNZ);
|
|
FREE(sm->Aij);
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FREE(sm->Aii);
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FREE(sm->F);
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FREE(sm->temp);
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FREE(sm->link);
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FREE(sm->first);
|
}
|
|
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int localadjlists(Network *net, Smatrix *sm)
|
/*
|
**--------------------------------------------------------------
|
** Input: none
|
** Output: returns error code
|
** Purpose: builds linked list of non-parallel links adjacent to each node
|
**--------------------------------------------------------------
|
*/
|
{
|
int i, j, k;
|
int pmark = 0; // parallel link marker
|
int errcode = 0;
|
Padjlist alink;
|
|
// Create an array of adjacency lists
|
freeadjlists(net);
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net->Adjlist = (Padjlist *)calloc(net->Nnodes + 1, sizeof(Padjlist));
|
if (net->Adjlist == NULL) return 101;
|
|
// For each link, update adjacency lists of its end nodes
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for (k = 1; k <= net->Nlinks; k++)
|
{
|
i = net->Link[k].N1;
|
j = net->Link[k].N2;
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pmark = paralink(net, sm, i, j, k); // Parallel link check
|
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// Include link in start node i's list
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alink = (struct Sadjlist *) malloc(sizeof(struct Sadjlist));
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if (alink == NULL) return(101);
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if (!pmark) alink->node = j;
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else alink->node = 0; // Parallel link marker
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alink->link = k;
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alink->next = net->Adjlist[i];
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net->Adjlist[i] = alink;
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// Include link in end node j's list
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alink = (struct Sadjlist *) malloc(sizeof(struct Sadjlist));
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if (alink == NULL) return(101);
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if (!pmark) alink->node = i;
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else alink->node = 0; // Parallel link marker
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alink->link = k;
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alink->next = net->Adjlist[j];
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net->Adjlist[j] = alink;
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}
|
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// Remove parallel links from adjacency lists
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xparalinks(net);
|
return errcode;
|
}
|
|
|
int paralink(Network *net, Smatrix *sm, int i, int j, int k)
|
/*
|
**--------------------------------------------------------------
|
** Input: i = index of start node of link
|
** j = index of end node of link
|
** k = link index
|
** Output: returns 1 if link k parallels another link, else 0
|
** Purpose: checks for parallel links between nodes i and j
|
**
|
**--------------------------------------------------------------
|
*/
|
{
|
Padjlist alink;
|
for (alink = net->Adjlist[i]; alink != NULL; alink = alink->next)
|
{
|
// Link || to k (same end nodes)
|
if (alink->node == j)
|
{
|
// Assign Ndx entry to this link
|
sm->Ndx[k] = alink->link;
|
return(1);
|
}
|
}
|
// Ndx entry if link not parallel
|
sm->Ndx[k] = k;
|
return(0);
|
}
|
|
|
void xparalinks(Network *net)
|
/*
|
**--------------------------------------------------------------
|
** Input: none
|
** Output: none
|
** Purpose: removes parallel links from nodal adjacency lists
|
**--------------------------------------------------------------
|
*/
|
{
|
int i;
|
Padjlist alink, // Current item in adjacency list
|
blink; // Previous item in adjacency list
|
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// Scan adjacency list of each node
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for (i = 1; i <= net->Nnodes; i++)
|
{
|
alink = net->Adjlist[i]; // First item in list
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blink = NULL;
|
while (alink != NULL)
|
{
|
if (alink->node == 0) // Parallel link marker found
|
{
|
if (blink == NULL) // This holds at start of list
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{
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net->Adjlist[i] = alink->next;
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free(alink); // Remove item from list
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alink = net->Adjlist[i];
|
}
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else // This holds for interior of list
|
{
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blink->next = alink->next;
|
free(alink); // Remove item from list
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alink = blink->next;
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}
|
}
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else
|
{
|
blink = alink; // Move to next item in list
|
alink = alink->next;
|
}
|
}
|
}
|
}
|
|
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int reordernodes(Project *pr)
|
/*
|
**--------------------------------------------------------------
|
** Input: none
|
** Output: returns 1 if successful, 0 if not
|
** Purpose: re-orders nodes to minimize # of non-zeros that
|
** will appear in factorized solution matrix
|
**--------------------------------------------------------------
|
*/
|
{
|
Network *net = &pr->network;
|
Smatrix *sm = &pr->hydraul.smatrix;
|
|
int k, knode, m, njuncs, nlinks;
|
int delta = -1;
|
int nofsub = 0;
|
int maxint = INT_MAX; //defined in limits.h
|
int errcode;
|
Padjlist alink;
|
|
// Local versions of node adjacency lists
|
int *adjncy = NULL;
|
int *xadj = NULL;
|
|
// Work arrays
|
int *dhead = NULL;
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int *qsize = NULL;
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int *llist = NULL;
|
int *marker = NULL;
|
|
// Default ordering
|
for (k = 1; k <= net->Nnodes; k++)
|
{
|
sm->Row[k] = k;
|
sm->Order[k] = k;
|
}
|
njuncs = net->Njuncs;
|
nlinks = net->Nlinks;
|
|
// Allocate memory
|
adjncy = (int *) calloc(2*nlinks+1, sizeof(int));
|
xadj = (int *) calloc(njuncs+2, sizeof(int));
|
dhead = (int *) calloc(njuncs+1, sizeof(int));
|
qsize = (int *) calloc(njuncs + 1, sizeof(int));
|
llist = (int *) calloc(njuncs + 1, sizeof(int));
|
marker = (int *) calloc(njuncs + 1, sizeof(int));
|
if (adjncy && xadj && dhead && qsize && llist && marker)
|
{
|
// Create local versions of node adjacency lists
|
xadj[1] = 1;
|
m = 1;
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for (k = 1; k <= njuncs; k++)
|
{
|
for (alink = net->Adjlist[k]; alink != NULL; alink = alink->next)
|
{
|
knode = alink->node;
|
if (knode > 0 && knode <= njuncs)
|
{
|
adjncy[m] = knode;
|
m++;
|
}
|
}
|
xadj[k+1] = m;
|
}
|
|
// Generate a multiple minimum degree node re-ordering
|
genmmd(&njuncs, xadj, adjncy, sm->Row, sm->Order, &delta,
|
dhead, qsize, llist, marker, &maxint, &nofsub);
|
errcode = 0;
|
}
|
else errcode = 101; //insufficient memory
|
|
// Free memory
|
FREE(adjncy);
|
FREE(xadj);
|
FREE(dhead);
|
FREE(qsize);
|
FREE(llist);
|
FREE(marker);
|
return errcode;
|
}
|
|
|
int factorize(Project *pr)
|
/*
|
**--------------------------------------------------------------
|
** Input: none
|
** Output: returns error code
|
** Purpose: symbolically factorizes the solution matrix in
|
** terms of its adjacency lists
|
**--------------------------------------------------------------
|
*/
|
{
|
Network *net = &pr->network;
|
Smatrix *sm = &pr->hydraul.smatrix;
|
|
int k, knode;
|
int errcode = 0;
|
Padjlist alink;
|
|
// Find degree of each junction node
|
sm->Degree = (int *)calloc(net->Nnodes + 1, sizeof(int));
|
if (sm->Degree == NULL) return 101;
|
|
// NOTE: For purposes of node re-ordering, Tanks (nodes with
|
// indexes above Njuncs) have zero degree of adjacency.
|
|
for (k = 1; k <= net->Njuncs; k++)
|
{
|
for (alink = net->Adjlist[k]; alink != NULL; alink = alink->next)
|
{
|
if (alink->node > 0) sm->Degree[k]++;
|
}
|
}
|
|
// Augment each junction's adjacency list to account for
|
// new connections created when solution matrix is solved.
|
// NOTE: Only junctions (indexes <= Njuncs) appear in solution matrix.
|
for (k = 1; k <= net->Njuncs; k++) // Examine each junction
|
{
|
knode = sm->Order[k]; // Re-ordered index
|
if (!growlist(pr, knode)) // Augment adjacency list
|
{
|
errcode = 101;
|
break;
|
}
|
sm->Degree[knode] = 0; // In-activate node
|
}
|
free(sm->Degree);
|
return errcode;
|
}
|
|
|
int growlist(Project *pr, int knode)
|
/*
|
**--------------------------------------------------------------
|
** Input: knode = node index
|
** Output: returns 1 if successful, 0 if not
|
** Purpose: creates new entries in knode's adjacency list for
|
** all unlinked pairs of active nodes that are
|
** adjacent to knode
|
**--------------------------------------------------------------
|
*/
|
{
|
Network *net = &pr->network;
|
Smatrix *sm = &pr->hydraul.smatrix;
|
|
int node;
|
Padjlist alink;
|
|
// Iterate through all nodes connected to knode
|
for (alink = net->Adjlist[knode]; alink != NULL; alink = alink -> next)
|
{
|
node = alink->node; // End node of connecting link
|
if (node > 0 && sm->Degree[node] > 0) // End node is active
|
{
|
sm->Degree[node]--; // Reduce degree of adjacency
|
if (!newlink(pr, alink)) // Add to adjacency list
|
{
|
return 0;
|
}
|
}
|
}
|
return 1;
|
}
|
|
|
int newlink(Project *pr, Padjlist alink)
|
/*
|
**--------------------------------------------------------------
|
** Input: alink = element of node's adjacency list
|
** Output: returns 1 if successful, 0 if not
|
** Purpose: links end of current adjacent link to end nodes of
|
** all links that follow it on adjacency list
|
**--------------------------------------------------------------
|
*/
|
{
|
Network *net = &pr->network;
|
Smatrix *sm = &pr->hydraul.smatrix;
|
|
int inode, jnode;
|
Padjlist blink;
|
|
// Scan all entries in adjacency list that follow anode.
|
inode = alink->node; // End node of connection to anode
|
for (blink = alink->next; blink != NULL; blink = blink->next)
|
{
|
jnode = blink->node; // End node of next connection
|
|
// If jnode still active, and inode not connected to jnode,
|
// then add a new connection between inode and jnode.
|
if (jnode > 0 && sm->Degree[jnode] > 0) // jnode still active
|
{
|
if (!linked(net, inode, jnode)) // inode not linked to jnode
|
{
|
// Since new connection represents a non-zero coeff.
|
// in the solution matrix, update the coeff. count.
|
sm->Ncoeffs++;
|
|
// Update adjacency lists for inode & jnode to
|
// reflect the new connection.
|
if (!addlink(net, inode, jnode, sm->Ncoeffs)) return 0;
|
if (!addlink(net, jnode, inode, sm->Ncoeffs)) return 0;
|
sm->Degree[inode]++;
|
sm->Degree[jnode]++;
|
}
|
}
|
}
|
return 1;
|
}
|
|
|
int linked(Network *net, int i, int j)
|
/*
|
**--------------------------------------------------------------
|
** Input: i = node index
|
** j = node index
|
** Output: returns 1 if nodes i and j are linked, 0 if not
|
** Purpose: checks if nodes i and j are already linked.
|
**--------------------------------------------------------------
|
*/
|
{
|
Padjlist alink;
|
for (alink = net->Adjlist[i]; alink != NULL; alink = alink->next)
|
{
|
if (alink->node == j) return 1;
|
}
|
return 0;
|
}
|
|
|
int addlink(Network *net, int i, int j, int n)
|
/*
|
**--------------------------------------------------------------
|
** Input: i = node index
|
** j = node index
|
** n = link index
|
** Output: returns 1 if successful, 0 if not
|
** Purpose: augments node i's adjacency list with node j
|
**--------------------------------------------------------------
|
*/
|
{
|
Padjlist alink;
|
alink = (struct Sadjlist *) malloc(sizeof(struct Sadjlist));
|
if (alink == NULL) return 0;
|
alink->node = j;
|
alink->link = n;
|
alink->next = net->Adjlist[i];
|
net->Adjlist[i] = alink;
|
return 1;
|
}
|
|
|
int storesparse(Project *pr, int n)
|
/*
|
**--------------------------------------------------------------
|
** Input: n = number of rows in solution matrix
|
** Output: returns error code
|
** Purpose: stores row indexes of non-zeros of each column of
|
** lower triangular portion of factorized matrix
|
**--------------------------------------------------------------
|
*/
|
{
|
Network *net = &pr->network;
|
Smatrix *sm = &pr->hydraul.smatrix;
|
|
int i, ii, j, k, l, m;
|
int errcode = 0;
|
Padjlist alink;
|
|
// Allocate sparse matrix storage
|
sm->XLNZ = (int *) calloc(n+2, sizeof(int));
|
sm->NZSUB = (int *) calloc(sm->Ncoeffs+2, sizeof(int));
|
sm->LNZ = (int *) calloc(sm->Ncoeffs+2, sizeof(int));
|
ERRCODE(MEMCHECK(sm->XLNZ));
|
ERRCODE(MEMCHECK(sm->NZSUB));
|
ERRCODE(MEMCHECK(sm->LNZ));
|
if (errcode) return errcode;
|
|
// Generate row index pointers for each column of matrix
|
k = 0;
|
sm->XLNZ[1] = 1;
|
for (i = 1; i <= n; i++) // column
|
{
|
m = 0;
|
ii = sm->Order[i];
|
for (alink = net->Adjlist[ii]; alink != NULL; alink = alink->next)
|
{
|
if (alink->node == 0) continue;
|
j = sm->Row[alink->node]; // row
|
l = alink->link;
|
if (j > i && j <= n)
|
{
|
m++;
|
k++;
|
sm->NZSUB[k] = j;
|
sm->LNZ[k] = l;
|
}
|
}
|
sm->XLNZ[i+1] = sm->XLNZ[i] + m;
|
}
|
return errcode;
|
}
|
|
|
int sortsparse(Smatrix *sm, int n)
|
/*
|
**--------------------------------------------------------------
|
** Input: n = number of rows in solution matrix
|
** Output: returns eror code
|
** Purpose: puts row indexes in ascending order in NZSUB
|
**--------------------------------------------------------------
|
*/
|
{
|
int i, k;
|
int *xlnzt, *nzsubt, *lnzt, *nzt;
|
int errcode = 0;
|
|
int *LNZ = sm->LNZ;
|
int *XLNZ = sm->XLNZ;
|
int *NZSUB = sm->NZSUB;
|
|
xlnzt = (int *) calloc(n+2, sizeof(int));
|
nzsubt = (int *) calloc(sm->Ncoeffs+2, sizeof(int));
|
lnzt = (int *) calloc(sm->Ncoeffs+2, sizeof(int));
|
nzt = (int *) calloc(n+2, sizeof(int));
|
ERRCODE(MEMCHECK(xlnzt));
|
ERRCODE(MEMCHECK(nzsubt));
|
ERRCODE(MEMCHECK(lnzt));
|
ERRCODE(MEMCHECK(nzt));
|
if (!errcode)
|
{
|
// Count # non-zeros in each row
|
for (i = 1; i <= n; i++) nzt[i] = 0;
|
for (i = 1; i <= n; i++)
|
{
|
for (k = XLNZ[i]; k < XLNZ[i+1]; k++) nzt[NZSUB[k]]++;
|
}
|
xlnzt[1] = 1;
|
for (i = 1; i <= n; i++) xlnzt[i+1] = xlnzt[i] + nzt[i];
|
|
// Transpose matrix twice to order column indexes
|
transpose(n, XLNZ, NZSUB, LNZ, xlnzt, nzsubt, lnzt, nzt);
|
transpose(n, xlnzt, nzsubt, lnzt, XLNZ, NZSUB, LNZ, nzt);
|
}
|
|
// Reclaim memory
|
free(xlnzt);
|
free(nzsubt);
|
free(lnzt);
|
free(nzt);
|
return errcode;
|
}
|
|
|
void transpose(int n, int *il, int *jl, int *xl, int *ilt, int *jlt,
|
int *xlt, int *nzt)
|
/*
|
**---------------------------------------------------------------------
|
** Input: n = matrix order
|
** il,jl,xl = sparse storage scheme for original matrix
|
** nzt = work array
|
** Output: ilt,jlt,xlt = sparse storage scheme for transposed matrix
|
** Purpose: Determines sparse storage scheme for transpose of a matrix
|
**---------------------------------------------------------------------
|
*/
|
{
|
int i, j, k, kk;
|
|
for (i = 1; i <= n; i++) nzt[i] = 0;
|
for (i = 1; i <= n; i++)
|
{
|
for (k = il[i]; k < il[i+1]; k++)
|
{
|
j = jl[k];
|
kk = ilt[j] + nzt[j];
|
jlt[kk] = i;
|
xlt[kk] = xl[k];
|
nzt[j]++;
|
}
|
}
|
}
|
|
char* smatrix_to_json(Smatrix* smatrix) {
|
char* json = (char*)malloc(102400000 * sizeof(char));
|
|
|
//sm->Aij = (double*)calloc(sm->Ncoeffs + 1, sizeof(double));
|
//sm->Aii = (double*)calloc(n, sizeof(double));
|
//sm->F = (double*)calloc(n, sizeof(double));
|
//sm->temp = (double*)calloc(n, sizeof(double));
|
//sm->link = (int*)calloc(n, sizeof(int));
|
//sm->first = (int*)calloc(n, sizeof(int));
|
|
|
int t = 0;
|
sprintf(json, "{ \"Aii\": [");
|
for (int i = 1; i < smatrix->Ncoeffs; i++) {
|
|
sprintf(json, "%s %f,", json, smatrix->Aii[i]);
|
t++;
|
}
|
sprintf(json, "%s ], \"Aij\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %f,", json, smatrix->Aij[i]);
|
}
|
sprintf(json, "%s ], \"F\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %f,", json, smatrix->F[i]);
|
}
|
sprintf(json, "%s ], \"temp\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %f,", json, smatrix->temp[i]);
|
}
|
sprintf(json, "%s ], \"Ncoeffs\": %d, \"Order\": [", json, smatrix->Ncoeffs);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->Order[i]);
|
}
|
sprintf(json, "%s ], \"Row\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->Row[i]);
|
}
|
sprintf(json, "%s ], \"Ndx\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->Ndx[i]);
|
}
|
sprintf(json, "%s ], \"XLNZ\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->XLNZ[i]);
|
}
|
sprintf(json, "%s ], \"NZSUB\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->NZSUB[i]);
|
}
|
sprintf(json, "%s ], \"LNZ\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->LNZ[i]);
|
}
|
sprintf(json, "%s ], \"Degree\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->Degree[i]);
|
}
|
sprintf(json, "%s ], \"link\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->link[i]);
|
}
|
sprintf(json, "%s ], \"first\": [", json);
|
for (int i = 0; i < smatrix->Ncoeffs; i++) {
|
sprintf(json, "%s %d,", json, smatrix->first[i]);
|
}
|
sprintf(json, "%s ] }", json);
|
return json;
|
}
|
|
|
int MatrixToFile(Smatrix matrix)
|
/*
|
**---------------------------------------------------------------------
|
** Input: n = matrix order
|
** il,jl,xl = sparse storage scheme for original matrix
|
** nzt = work array
|
** Output: ilt,jlt,xlt = sparse storage scheme for transposed matrix
|
** Purpose: Determines sparse storage scheme for transpose of a matrix
|
**---------------------------------------------------------------------
|
*/
|
{
|
|
// Initialize smatrix here
|
char* json = smatrix_to_json(&matrix);
|
FILE* fp = fopen("C:\\Desktop\\¹¤¾ßÏä\\output.txt", "w");
|
fprintf(fp, "%s", json);
|
fclose(fp);
|
free(json);
|
return 0;
|
}
|
|
|
int linsolve(Project *pr, Smatrix *sm, int n)
|
/*
|
**--------------------------------------------------------------
|
** Input: sm = sparse matrix struct
|
n = number of equations
|
** Output: sm->F = solution values
|
** returns 0 if solution found, or index of
|
** equation causing system to be ill-conditioned
|
** Purpose: solves sparse symmetric system of linear
|
** equations using Cholesky factorization
|
**
|
** NOTE: This procedure assumes that the solution matrix has
|
** been symbolically factorized with the positions of
|
** the lower triangular, off-diagonal, non-zero coeffs.
|
** stored in the following integer arrays:
|
** XLNZ (start position of each column in NZSUB)
|
** NZSUB (row index of each non-zero in each column)
|
** LNZ (position of each NZSUB entry in Aij array)
|
**
|
** This procedure has been adapted from subroutines GSFCT and
|
** GSSLV in the book "Computer Solution of Large Sparse
|
** Positive Definite Systems" by A. George and J. W-H Liu
|
** (Prentice-Hall, 1981).
|
**--------------------------------------------------------------
|
*/
|
{
|
double *Aii = sm->Aii;
|
double *Aij = sm->Aij;
|
double *B = sm->F;
|
double *temp = sm->temp;
|
int *LNZ = sm->LNZ;
|
int *XLNZ = sm->XLNZ;
|
int *NZSUB = sm->NZSUB;
|
int *link = sm->link;
|
int *first = sm->first;
|
|
int i, istop, istrt, isub, j, k, kfirst, newk;
|
double bj, diagj, ljk;
|
|
memset(temp, 0, (n + 1) * sizeof(double));
|
memset(link, 0, (n + 1) * sizeof(int));
|
memset(first, 0, (n + 1) * sizeof(int));
|
|
|
//MatrixToFile(*sm);
|
|
// Begin numerical factorization of matrix A into L
|
// Compute column L(*,j) for j = 1,...n
|
for (j = 1; j <= n; j++)
|
{
|
// For each column L(*,k) that affects L(*,j):
|
diagj = 0.0;
|
newk = link[j];
|
k = newk;
|
while (k != 0)
|
{
|
// Outer product modification of L(*,j) by
|
// L(*,k) starting at first[k] of L(*,k)
|
newk = link[k];
|
kfirst = first[k];
|
ljk = Aij[LNZ[kfirst]];
|
diagj += ljk*ljk;
|
istrt = kfirst + 1;
|
istop = XLNZ[k+1] - 1;
|
if (istop >= istrt)
|
{
|
|
// Before modification, update vectors 'first'
|
// and 'link' for future modification steps
|
first[k] = istrt;
|
isub = NZSUB[istrt];
|
link[k] = link[isub];
|
link[isub] = k;
|
|
// The actual mod is saved in vector 'temp'
|
for (i = istrt; i <= istop; i++)
|
{
|
isub = NZSUB[i];
|
temp[isub] += Aij[LNZ[i]]*ljk;
|
}
|
}
|
k = newk;
|
}
|
|
// Apply the modifications accumulated
|
// in 'temp' to column L(*,j)
|
|
/* if (j == 214700)
|
{
|
int test = 0;
|
}*/
|
|
|
diagj = Aii[j] - diagj;
|
if (diagj <= 0.0) // Check for ill-conditioning
|
{
|
//[CloudflightÐÞ¶©] 2023Äê5ÔÂ17ÈÕ 17:36:47
|
// [CloudflightÐÞ¶©] 2023Äê5ÔÂ18ÈÕ 15:58:58
|
//´¦ÀíEPANET2.2ÎÞ·¨cannot solve hydraulic eqµÄÎÊÌâ by ºÎƽ
|
//Ô
|
//return j;
|
//ÐÂ
|
////[CloudflightÐÞ¸Ä]2023-12-28
|
//Ô
|
//if (pr->hydraul.DemandModel == DDA)
|
// diagj = MAX( ABS(diagj),TINY );
|
//else
|
// return j;
|
//ÐÂ
|
diagj = MAX(ABS(diagj), TINY);
|
}
|
diagj = sqrt(diagj);
|
Aii[j] = diagj;
|
istrt = XLNZ[j];
|
istop = XLNZ[j+1] - 1;
|
if (istop >= istrt)
|
{
|
first[j] = istrt;
|
isub = NZSUB[istrt];
|
link[j] = link[isub];
|
link[isub] = j;
|
for (i = istrt; i <= istop; i++)
|
{
|
isub = NZSUB[i];
|
bj = (Aij[LNZ[i]] - temp[isub])/diagj;
|
Aij[LNZ[i]] = bj;
|
temp[isub] = 0.0;
|
}
|
}
|
} // next j
|
|
// Foward substitution
|
for (j = 1; j <= n; j++)
|
{
|
bj = B[j]/Aii[j];
|
B[j] = bj;
|
istrt = XLNZ[j];
|
istop = XLNZ[j+1] - 1;
|
if (istop >= istrt)
|
{
|
for (i = istrt; i <= istop; i++)
|
{
|
isub = NZSUB[i];
|
B[isub] -= Aij[LNZ[i]]*bj;
|
}
|
}
|
}
|
|
// Backward substitution
|
for (j = n; j >= 1; j--)
|
{
|
bj = B[j];
|
istrt = XLNZ[j];
|
istop = XLNZ[j+1] - 1;
|
if (istop >= istrt)
|
{
|
for (i = istrt; i <= istop; i++)
|
{
|
isub = NZSUB[i];
|
bj -= Aij[LNZ[i]]*B[isub];
|
}
|
}
|
B[j] = bj/Aii[j];
|
}
|
return 0;
|
}
|
