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-rw-r--r--Build/source/utils/asymptote/base/rationalSimplex.asy152
1 files changed, 91 insertions, 61 deletions
diff --git a/Build/source/utils/asymptote/base/rationalSimplex.asy b/Build/source/utils/asymptote/base/rationalSimplex.asy
index 5175b87ba74..d694843289c 100644
--- a/Build/source/utils/asymptote/base/rationalSimplex.asy
+++ b/Build/source/utils/asymptote/base/rationalSimplex.asy
@@ -2,21 +2,23 @@
import rational;
void simplexTableau(rational[][] E, int[] Bindices, int I=-1, int J=-1) {}
+void simplexPhase1(rational[] c, rational[][] A, rational[] b,
+ int[] Bindices) {}
void simplexPhase2() {}
-void simplexWrite(rational[][] E, int[] Bindicies, int, int)
+void simplexWrite(rational[][] E, int[] Bindices, int, int)
{
int m=E.length-1;
int n=E[0].length-1;
- write(E[m][n],tab);
- for(int j=0; j < n; ++j)
+ write(E[m][0],tab);
+ for(int j=1; j <= n; ++j)
write(E[m][j],tab);
write();
for(int i=0; i < m; ++i) {
- write(E[i][n],tab);
- for(int j=0; j < n; ++j) {
+ write(E[i][0],tab);
+ for(int j=1; j <= n; ++j) {
write(E[i][j],tab);
}
write();
@@ -68,10 +70,10 @@ struct simplex {
while(true) {
// Find first negative entry in bottom (reduced cost) row
rational[] Em=E[m];
- for(J=0; J < N; ++J)
+ for(J=1; J <= N; ++J)
if(Em[J] < 0) break;
- if(J == N)
+ if(J > N)
break;
int I=-1;
@@ -79,7 +81,7 @@ struct simplex {
for(int i=0; i < m; ++i) {
rational e=E[i][J];
if(e > 0) {
- M=E[i][N]/e;
+ M=E[i][0]/e;
I=i;
break;
}
@@ -87,7 +89,7 @@ struct simplex {
for(int i=I+1; i < m; ++i) {
rational e=E[i][J];
if(e > 0) {
- rational v=E[i][N]/e;
+ rational v=E[i][0]/e;
if(v < M) {M=v; I=i;} // Bland's rule: choose smallest argmin
}
}
@@ -105,19 +107,19 @@ struct simplex {
int iterateDual(rational[][] E, int N, int[] Bindices) {
while(true) {
- // Find first negative entry in right (basic variable) column
+ // Find first negative entry in zeroth (basic variable) column
rational[] Em=E[m];
int I;
for(I=0; I < m; ++I) {
- if(E[I][N] < 0) break;
+ if(E[I][0] < 0) break;
}
if(I == m)
break;
- int J=-1;
+ int J=0;
rational M;
- for(int j=0; j < N; ++j) {
+ for(int j=1; j <= N; ++j) {
rational e=E[I][j];
if(e < 0) {
M=-E[m][j]/e;
@@ -125,14 +127,14 @@ struct simplex {
break;
}
}
- for(int j=J+1; j < N; ++j) {
+ for(int j=J+1; j <= N; ++j) {
rational e=E[I][j];
if(e < 0) {
rational v=-E[m][j]/e;
if(v < M) {M=v; J=j;} // Bland's rule: choose smallest argmin
}
}
- if(J == -1)
+ if(J == 0)
return INFEASIBLE; // Can only happen in Phase 2.
simplexTableau(E,Bindices,I,J);
@@ -157,66 +159,94 @@ struct simplex {
n=A[0].length;
if(n == 0) {case=INFEASIBLE; return;}
- int N=phase1 ? n+m : n;
- rational[][] E=new rational[m+1][N+1];
+ rational[][] E=new rational[m+1][n+1];
rational[] Em=E[m];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Em[j]=0;
for(int i=0; i < m; ++i) {
rational[] Ai=A[i];
rational[] Ei=E[i];
if(b[i] >= 0 || dual) {
- for(int j=0; j < n; ++j) {
- rational Aij=Ai[j];
+ for(int j=1; j <= n; ++j) {
+ rational Aij=Ai[j-1];
Ei[j]=Aij;
Em[j] -= Aij;
}
} else {
- for(int j=0; j < n; ++j) {
- rational Aij=-Ai[j];
+ for(int j=1; j <= n; ++j) {
+ rational Aij=-Ai[j-1];
Ei[j]=Aij;
Em[j] -= Aij;
}
}
}
- if(phase1) {
- for(int i=0; i < m; ++i) {
- rational[] Ei=E[i];
- for(int j=0; j < i; ++j)
- Ei[n+j]=0;
- Ei[n+i]=1;
- for(int j=i+1; j < m; ++j)
- Ei[n+j]=0;
+ void basicValues() {
+ rational sum=0;
+ for(int i=0; i < m; ++i) {
+ rational B=dual ? b[i] : abs(b[i]);
+ E[i][0]=B;
+ sum -= B;
}
+ Em[0]=sum;
}
- rational sum=0;
- for(int i=0; i < m; ++i) {
- rational B=dual ? b[i] : abs(b[i]);
- E[i][N]=B;
- sum -= B;
- }
- Em[N]=sum;
-
- if(phase1)
- for(int j=0; j < m; ++j)
- Em[n+j]=0;
-
int[] Bindices;
if(phase1) {
- Bindices=sequence(new int(int x){return x;},m)+n;
- iterate(E,N,Bindices);
+ Bindices=new int[m];
+ int p=0;
+
+ // Check for redundant basis vectors.
+ bool checkBasis(int j) {
+ for(int i=0; i < m; ++i) {
+ rational[] Ei=E[i];
+ if(i != p ? Ei[j] != 0 : Ei[j] <= 0) return false;
+ }
+ return true;
+ }
+
+ int checkTableau() {
+ for(int j=1; j <= n; ++j)
+ if(checkBasis(j)) return j;
+ return 0;
+ }
+
+ int k=0;
+ while(p < m) {
+ int j=checkTableau();
+ if(j > 0)
+ Bindices[p]=j;
+ else { // Add an artificial variable
+ Bindices[p]=n+1+k;
+ for(int i=0; i < p; ++i)
+ E[i].push(0);
+ E[p].push(1);
+ for(int i=p+1; i < m; ++i)
+ E[i].push(0);
+ E[m].push(0);
+ ++k;
+ }
+ ++p;
+ }
+
+ basicValues();
+
+ simplexPhase1(c,A,b,Bindices);
+
+ iterate(E,n+k,Bindices);
- if(Em[J] != 0) {
+ if(Em[0] != 0) {
simplexTableau(E,Bindices);
case=INFEASIBLE;
return;
}
- } else Bindices=sequence(new int(int x){return x;},m)+n-m;
+ } else {
+ Bindices=sequence(new int(int x){return x;},m)+n-m+1;
+ basicValues();
+ }
rational[] cB=phase1 ? new rational[m] : c[n-m:n];
rational[][] D=phase1 ? new rational[m+1][n+1] : E;
@@ -225,12 +255,12 @@ struct simplex {
// Drive artificial variables out of basis.
for(int i=0; i < m; ++i) {
int k=Bindices[i];
- if(k >= n) {
+ if(k > n) {
rational[] Ei=E[i];
int j;
- for(j=0; j < n; ++j)
+ for(j=1; j <= n; ++j)
if(Ei[j] != 0) break;
- if(j == n) continue;
+ if(j > n) continue;
output=false;
simplexTableau(E,Bindices,i,j);
Bindices[i]=j;
@@ -241,22 +271,22 @@ struct simplex {
int ip=0; // reduced i
for(int i=0; i < m; ++i) {
int k=Bindices[i];
- if(k >= n) continue;
+ if(k > n) continue;
Bindices[ip]=k;
- cB[ip]=c[k];
+ cB[ip]=c[k-1];
rational[] Dip=D[ip];
rational[] Ei=E[i];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Dip[j]=Ei[j];
- Dip[n]=Ei[N];
+ Dip[0]=Ei[0];
++ip;
}
rational[] Dip=D[ip];
rational[] Em=E[m];
- for(int j=0; j < n; ++j)
+ for(int j=1; j <= n; ++j)
Dip[j]=Em[j];
- Dip[n]=Em[N];
+ Dip[0]=Em[0];
if(m > ip) {
Bindices.delete(ip,m-1);
@@ -267,17 +297,17 @@ struct simplex {
}
rational[] Dm=D[m];
- for(int j=0; j < n; ++j) {
+ for(int j=1; j <= n; ++j) {
rational sum=0;
for(int k=0; k < m; ++k)
sum += cB[k]*D[k][j];
- Dm[j]=c[j]-sum;
+ Dm[j]=c[j-1]-sum;
}
rational sum=0;
for(int k=0; k < m; ++k)
- sum += cB[k]*D[k][n];
- Dm[n]=-sum;
+ sum += cB[k]*D[k][0];
+ Dm[0]=-sum;
simplexPhase2();
@@ -290,9 +320,9 @@ struct simplex {
x[j]=0;
for(int k=0; k < m; ++k)
- x[Bindices[k]]=D[k][n];
+ x[Bindices[k]-1]=D[k][0];
- cost=-Dm[n];
+ cost=-Dm[0];
}
// Try to find a solution x to sgn(Ax-b)=sgn(s) that minimizes the cost
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-05 22:45:44 +0000