*/
+/**
+ * Class allowing to retrieve the computing power of a
+ * computer; this power is represented by MFlops
+ *
+ * @author Bonnie Toy, Reed Wade
+ */
+
+public class Linpack
+{
+
+ /**
+ * Empty default constructor.
+ */
+ public Linpack(){}
+
+ final double abs (double d) {
+ return (d >= 0) ? d : -d;
+ }
-public class Linpack {
+ double second_orig = -1;
- final double abs (double d) {
- return (d >= 0) ? d : -d;
- }
+ double second()
+ {
+ if (second_orig==-1) {
+ second_orig = System.currentTimeMillis();
+ }
+ return (System.currentTimeMillis() - second_orig)/1000;
+ }
- double second_orig = -1;
-
- double second()
- {
- if (second_orig==-1) {
- second_orig = System.currentTimeMillis();
- }
- return (System.currentTimeMillis() - second_orig)/1000;
- }
-
- public double getMFlops()
- {
- double mflops_result = 0.0;
- double residn_result = 0.0;
- double time_result = 0.0;
- double eps_result = 0.0;
-
- double a[][] = new double[1000][1001];
- double b[] = new double[1000];
- double x[] = new double[1000];
- double ops,total,norma,normx;
- double resid,time;
- int n,i,lda;
- int ipvt[] = new int[1000];
-
- //double mflops_result;
- //double residn_result;
- //double time_result;
- //double eps_result;
-
- lda = 1001;
- n = 500;
-
- ops = (2.0e0*(n*n*n))/3.0 + 2.0*(n*n);
-
- norma = matgen(a,lda,n,b);
- time = second();
- dgefa(a,lda,n,ipvt);
- dgesl(a,lda,n,ipvt,b,0);
- total = second() - time;
-
- for (i = 0; i < n; i++) {
- x[i] = b[i];
- }
- norma = matgen(a,lda,n,b);
- for (i = 0; i < n; i++) {
- b[i] = -b[i];
- }
- dmxpy(n,b,n,lda,x,a);
- resid = 0.0;
- normx = 0.0;
- for (i = 0; i < n; i++) {
- resid = (resid > abs(b[i])) ? resid : abs(b[i]);
- normx = (normx > abs(x[i])) ? normx : abs(x[i]);
- }
-
- eps_result = epslon((double)1.0);
-/*
+ /**
+ * Estimate the computing power of the local computer
+ * and return as result the obtained MFlops.
+ * @return The MFlops of the computer
+ */
+ public double getMFlops()
+ {
+ double mflops_result = 0.0;
+ double residn_result = 0.0;
+ double time_result = 0.0;
+ double eps_result = 0.0;
+
+ double a[][] = new double[1000][1001];
+ double b[] = new double[1000];
+ double x[] = new double[1000];
+ double ops,total,norma,normx;
+ double resid,time;
+ int n,i,lda;
+ int ipvt[] = new int[1000];
+
+ //double mflops_result;
+ //double residn_result;
+ //double time_result;
+ //double eps_result;
+
+ lda = 1001;
+ n = 500;
+
+ ops = (2.0e0*(n*n*n))/3.0 + 2.0*(n*n);
+
+ norma = matgen(a,lda,n,b);
+ time = second();
+ dgefa(a,lda,n,ipvt);
+ dgesl(a,lda,n,ipvt,b,0);
+ total = second() - time;
+
+ for (i = 0; i < n; i++) {
+ x[i] = b[i];
+ }
+ norma = matgen(a,lda,n,b);
+ for (i = 0; i < n; i++) {
+ b[i] = -b[i];
+ }
+ dmxpy(n,b,n,lda,x,a);
+ resid = 0.0;
+ normx = 0.0;
+ for (i = 0; i < n; i++) {
+ resid = (resid > abs(b[i])) ? resid : abs(b[i]);
+ normx = (normx > abs(x[i])) ? normx : abs(x[i]);
+ }
+
+ eps_result = epslon((double)1.0);
+ /*
residn_result = resid/( n*norma*normx*eps_result );
time_result = total;
" Time: " + time_result + " secs" +
" Norm Res: " + residn_result +
" Precision: " + eps_result);
-*/
- residn_result = resid/( n*norma*normx*eps_result );
- residn_result += 0.005; // for rounding
- residn_result = (int)(residn_result*100);
- residn_result /= 100;
-
- time_result = total;
- time_result += 0.005; // for rounding
- time_result = (int)(time_result*100);
- time_result /= 100;
-
- mflops_result = ops/(1.0e6*total);
- mflops_result += 0.0005; // for rounding
- mflops_result = (int)(mflops_result*1000);
- mflops_result /= 1000;
-
-// System.out.println("Mflops/s: " + mflops_result +
-// " Time: " + time_result + " secs" +
-// " Norm Res: " + residn_result +
-// " Precision: " + eps_result);
-
- return mflops_result ;
- }
-
-
-
- final double matgen (double a[][], int lda, int n, double b[])
- {
- double norma;
- int init, i, j;
-
- init = 1325;
- norma = 0.0;
-/* Next two for() statements switched. Solver wants
+ */
+ residn_result = resid/( n*norma*normx*eps_result );
+ residn_result += 0.005; // for rounding
+ residn_result = (int)(residn_result*100);
+ residn_result /= 100;
+
+ time_result = total;
+ time_result += 0.005; // for rounding
+ time_result = (int)(time_result*100);
+ time_result /= 100;
+
+ mflops_result = ops/(1.0e6*total);
+ mflops_result += 0.0005; // for rounding
+ mflops_result = (int)(mflops_result*1000);
+ mflops_result /= 1000;
+
+ // System.out.println("Mflops/s: " + mflops_result +
+ // " Time: " + time_result + " secs" +
+ // " Norm Res: " + residn_result +
+ // " Precision: " + eps_result);
+
+ return mflops_result ;
+ }
+
+
+
+ final double matgen (double a[][], int lda, int n, double b[])
+ {
+ double norma;
+ int init, i, j;
+
+ init = 1325;
+ norma = 0.0;
+ /* Next two for() statements switched. Solver wants
matrix in column order. --dmd 3/3/97
-*/
- for (i = 0; i < n; i++) {
- for (j = 0; j < n; j++) {
- init = 3125*init % 65536;
- a[j][i] = (init - 32768.0)/16384.0;
- norma = (a[j][i] > norma) ? a[j][i] : norma;
- }
- }
- for (i = 0; i < n; i++) {
- b[i] = 0.0;
- }
- for (j = 0; j < n; j++) {
- for (i = 0; i < n; i++) {
- b[i] += a[j][i];
- }
- }
-
- return norma;
- }
-
+ */
+ for (i = 0; i < n; i++) {
+ for (j = 0; j < n; j++) {
+ init = 3125*init % 65536;
+ a[j][i] = (init - 32768.0)/16384.0;
+ norma = (a[j][i] > norma) ? a[j][i] : norma;
+ }
+ }
+ for (i = 0; i < n; i++) {
+ b[i] = 0.0;
+ }
+ for (j = 0; j < n; j++) {
+ for (i = 0; i < n; i++) {
+ b[i] += a[j][i];
+ }
+ }
+
+ return norma;
+ }
+
+
-
- /*
+ /*
dgefa factors a double precision matrix by gaussian elimination.
-
+
dgefa is usually called by dgeco, but it can be called
directly with a saving in time if rcond is not needed.
(time for dgeco) = (1 + 9/n)*(time for dgefa) .
-
+
on entry
-
+
a double precision[n][lda]
the matrix to be factored.
-
+
lda integer
the leading dimension of the array a .
-
+
n integer
the order of the matrix a .
-
+
on return
-
+
a an upper triangular matrix and the multipliers
which were used to obtain it.
the factorization can be written a = l*u where
l is a product of permutation and unit lower
triangular matrices and u is upper triangular.
-
+
ipvt integer[n]
an integer vector of pivot indices.
-
+
info integer
= 0 normal value.
= k if u[k][k] .eq. 0.0 . this is not an error
indicate that dgesl or dgedi will divide by zero
if called. use rcond in dgeco for a reliable
indication of singularity.
-
+
linpack. this version dated 08/14/78.
cleve moler, university of new mexico, argonne national lab.
-
+
functions
-
+
blas daxpy,dscal,idamax
- */
- final int dgefa( double a[][], int lda, int n, int ipvt[])
- {
- double[] col_k, col_j;
- double t;
- int j,k,kp1,l,nm1;
- int info;
-
- // gaussian elimination with partial pivoting
-
- info = 0;
- nm1 = n - 1;
- if (nm1 >= 0) {
- for (k = 0; k < nm1; k++) {
- col_k = a[k];
- kp1 = k + 1;
-
- // find l = pivot index
-
- l = idamax(n-k,col_k,k,1) + k;
- ipvt[k] = l;
-
- // zero pivot implies this column already triangularized
-
- if (col_k[l] != 0) {
-
- // interchange if necessary
-
- if (l != k) {
- t = col_k[l];
- col_k[l] = col_k[k];
- col_k[k] = t;
- }
-
- // compute multipliers
-
- t = -1.0/col_k[k];
- dscal(n-(kp1),t,col_k,kp1,1);
-
- // row elimination with column indexing
-
- for (j = kp1; j < n; j++) {
- col_j = a[j];
- t = col_j[l];
- if (l != k) {
- col_j[l] = col_j[k];
- col_j[k] = t;
- }
- daxpy(n-(kp1),t,col_k,kp1,1,
- col_j,kp1,1);
- }
- }
- else {
- info = k;
+ */
+ final int dgefa( double a[][], int lda, int n, int ipvt[])
+ {
+ double[] col_k, col_j;
+ double t;
+ int j,k,kp1,l,nm1;
+ int info;
+
+ // gaussian elimination with partial pivoting
+
+ info = 0;
+ nm1 = n - 1;
+ if (nm1 >= 0) {
+ for (k = 0; k < nm1; k++) {
+ col_k = a[k];
+ kp1 = k + 1;
+
+ // find l = pivot index
+
+ l = idamax(n-k,col_k,k,1) + k;
+ ipvt[k] = l;
+
+ // zero pivot implies this column already triangularized
+
+ if (col_k[l] != 0) {
+
+ // interchange if necessary
+
+ if (l != k) {
+ t = col_k[l];
+ col_k[l] = col_k[k];
+ col_k[k] = t;
+ }
+
+ // compute multipliers
+
+ t = -1.0/col_k[k];
+ dscal(n-(kp1),t,col_k,kp1,1);
+
+ // row elimination with column indexing
+
+ for (j = kp1; j < n; j++) {
+ col_j = a[j];
+ t = col_j[l];
+ if (l != k) {
+ col_j[l] = col_j[k];
+ col_j[k] = t;
+ }
+ daxpy(n-(kp1),t,col_k,kp1,1,
+ col_j,kp1,1);
+ }
+ }
+ else {
+ info = k;
+ }
+ }
+ }
+ ipvt[n-1] = n-1;
+ if (a[(n-1)][(n-1)] == 0) info = n-1;
+
+ return info;
}
- }
- }
- ipvt[n-1] = n-1;
- if (a[(n-1)][(n-1)] == 0) info = n-1;
-
- return info;
- }
-
-
-
- /*
+
+
+
+ /*
dgesl solves the double precision system
a * x = b or trans(a) * x = b
using the factors computed by dgeco or dgefa.
-
+
on entry
-
+
a double precision[n][lda]
the output from dgeco or dgefa.
-
+
lda integer
the leading dimension of the array a .
-
+
n integer
the order of the matrix a .
-
+
ipvt integer[n]
the pivot vector from dgeco or dgefa.
b double precision[n]
the right hand side vector.
-
+
job integer
= 0 to solve a*x = b ,
= nonzero to solve trans(a)*x = b where
trans(a) is the transpose.
-
+
on return
-
+
b the solution vector x .
-
+
error condition
-
+
a division by zero will occur if the input factor contains a
zero on the diagonal. technically this indicates singularity
but it is often caused by improper arguments or improper
setting of lda . it will not occur if the subroutines are
called correctly and if dgeco has set rcond .gt. 0.0
or dgefa has set info .eq. 0 .
-
+
to compute inverse(a) * c where c is a matrix
with p columns
dgeco(a,lda,n,ipvt,rcond,z)
for (j=0,j<p,j++)
dgesl(a,lda,n,ipvt,c[j][0],0);
}
-
+
linpack. this version dated 08/14/78 .
cleve moler, university of new mexico, argonne national lab.
-
- functions
-
- blas daxpy,ddot
- */
- final void dgesl( double a[][], int lda, int n, int ipvt[], double b[], int job)
- {
- double t;
- int k,kb,l,nm1,kp1;
-
- nm1 = n - 1;
- if (job == 0) {
-
- // job = 0 , solve a * x = b. first solve l*y = b
-
- if (nm1 >= 1) {
- for (k = 0; k < nm1; k++) {
- l = ipvt[k];
- t = b[l];
- if (l != k){
- b[l] = b[k];
- b[k] = t;
- }
- kp1 = k + 1;
- daxpy(n-(kp1),t,a[k],kp1,1,b,kp1,1);
- }
- }
- // now solve u*x = y
+ functions
- for (kb = 0; kb < n; kb++) {
- k = n - (kb + 1);
- b[k] /= a[k][k];
- t = -b[k];
- daxpy(k,t,a[k],0,1,b,0,1);
- }
- }
- else {
-
- // job = nonzero, solve trans(a) * x = b. first solve trans(u)*y = b
-
- for (k = 0; k < n; k++) {
- t = ddot(k,a[k],0,1,b,0,1);
- b[k] = (b[k] - t)/a[k][k];
- }
-
- // now solve trans(l)*x = y
-
- if (nm1 >= 1) {
- for (kb = 1; kb < nm1; kb++) {
- k = n - (kb+1);
- kp1 = k + 1;
- b[k] += ddot(n-(kp1),a[k],kp1,1,b,kp1,1);
- l = ipvt[k];
- if (l != k) {
- t = b[l];
- b[l] = b[k];
- b[k] = t;
- }
+ blas daxpy,ddot
+ */
+ final void dgesl( double a[][], int lda, int n, int ipvt[], double b[], int job)
+ {
+ double t;
+ int k,kb,l,nm1,kp1;
+
+ nm1 = n - 1;
+ if (job == 0) {
+
+ // job = 0 , solve a * x = b. first solve l*y = b
+
+ if (nm1 >= 1) {
+ for (k = 0; k < nm1; k++) {
+ l = ipvt[k];
+ t = b[l];
+ if (l != k){
+ b[l] = b[k];
+ b[k] = t;
+ }
+ kp1 = k + 1;
+ daxpy(n-(kp1),t,a[k],kp1,1,b,kp1,1);
+ }
+ }
+
+ // now solve u*x = y
+
+ for (kb = 0; kb < n; kb++) {
+ k = n - (kb + 1);
+ b[k] /= a[k][k];
+ t = -b[k];
+ daxpy(k,t,a[k],0,1,b,0,1);
+ }
+ }
+ else {
+
+ // job = nonzero, solve trans(a) * x = b. first solve trans(u)*y = b
+
+ for (k = 0; k < n; k++) {
+ t = ddot(k,a[k],0,1,b,0,1);
+ b[k] = (b[k] - t)/a[k][k];
+ }
+
+ // now solve trans(l)*x = y
+
+ if (nm1 >= 1) {
+ for (kb = 1; kb < nm1; kb++) {
+ k = n - (kb+1);
+ kp1 = k + 1;
+ b[k] += ddot(n-(kp1),a[k],kp1,1,b,kp1,1);
+ l = ipvt[k];
+ if (l != k) {
+ t = b[l];
+ b[l] = b[k];
+ b[k] = t;
+ }
+ }
+ }
+ }
}
- }
- }
- }
- /*
+ /*
constant times a vector plus a vector.
jack dongarra, linpack, 3/11/78.
- */
- final void daxpy( int n, double da, double dx[], int dx_off, int incx,
- double dy[], int dy_off, int incy)
- {
- int i,ix,iy;
-
- if ((n > 0) && (da != 0)) {
- if (incx != 1 || incy != 1) {
-
- // code for unequal increments or equal increments not equal to 1
-
- ix = 0;
- iy = 0;
- if (incx < 0) ix = (-n+1)*incx;
- if (incy < 0) iy = (-n+1)*incy;
- for (i = 0;i < n; i++) {
- dy[iy +dy_off] += da*dx[ix +dx_off];
- ix += incx;
- iy += incy;
+ */
+ final void daxpy( int n, double da, double dx[], int dx_off, int incx,
+ double dy[], int dy_off, int incy)
+ {
+ int i,ix,iy;
+
+ if ((n > 0) && (da != 0)) {
+ if (incx != 1 || incy != 1) {
+
+ // code for unequal increments or equal increments not equal to 1
+
+ ix = 0;
+ iy = 0;
+ if (incx < 0) ix = (-n+1)*incx;
+ if (incy < 0) iy = (-n+1)*incy;
+ for (i = 0;i < n; i++) {
+ dy[iy +dy_off] += da*dx[ix +dx_off];
+ ix += incx;
+ iy += incy;
+ }
+ return;
+ } else {
+
+ // code for both increments equal to 1
+
+ for (i=0; i < n; i++)
+ dy[i +dy_off] += da*dx[i +dx_off];
+ }
+ }
}
- return;
- } else {
-
- // code for both increments equal to 1
-
- for (i=0; i < n; i++)
- dy[i +dy_off] += da*dx[i +dx_off];
- }
- }
- }
- /*
+ /*
forms the dot product of two vectors.
jack dongarra, linpack, 3/11/78.
- */
- final double ddot( int n, double dx[], int dx_off, int incx, double dy[],
- int dy_off, int incy)
- {
- double dtemp;
- int i,ix,iy;
-
- dtemp = 0;
-
- if (n > 0) {
-
- if (incx != 1 || incy != 1) {
-
- // code for unequal increments or equal increments not equal to 1
-
- ix = 0;
- iy = 0;
- if (incx < 0) ix = (-n+1)*incx;
- if (incy < 0) iy = (-n+1)*incy;
- for (i = 0;i < n; i++) {
- dtemp += dx[ix +dx_off]*dy[iy +dy_off];
- ix += incx;
- iy += incy;
+ */
+ final double ddot( int n, double dx[], int dx_off, int incx, double dy[],
+ int dy_off, int incy)
+ {
+ double dtemp;
+ int i,ix,iy;
+
+ dtemp = 0;
+
+ if (n > 0) {
+
+ if (incx != 1 || incy != 1) {
+
+ // code for unequal increments or equal increments not equal to 1
+
+ ix = 0;
+ iy = 0;
+ if (incx < 0) ix = (-n+1)*incx;
+ if (incy < 0) iy = (-n+1)*incy;
+ for (i = 0;i < n; i++) {
+ dtemp += dx[ix +dx_off]*dy[iy +dy_off];
+ ix += incx;
+ iy += incy;
+ }
+ } else {
+
+ // code for both increments equal to 1
+
+ for (i=0;i < n; i++)
+ dtemp += dx[i +dx_off]*dy[i +dy_off];
+ }
+ }
+ return(dtemp);
}
- } else {
- // code for both increments equal to 1
-
- for (i=0;i < n; i++)
- dtemp += dx[i +dx_off]*dy[i +dy_off];
- }
- }
- return(dtemp);
- }
-
-
- /*
+
+ /*
scales a vector by a constant.
jack dongarra, linpack, 3/11/78.
- */
- final void dscal( int n, double da, double dx[], int dx_off, int incx)
- {
- int i,nincx;
+ */
+ final void dscal( int n, double da, double dx[], int dx_off, int incx)
+ {
+ int i,nincx;
- if (n > 0) {
- if (incx != 1) {
+ if (n > 0) {
+ if (incx != 1) {
- // code for increment not equal to 1
+ // code for increment not equal to 1
- nincx = n*incx;
- for (i = 0; i < nincx; i += incx)
- dx[i +dx_off] *= da;
- } else {
+ nincx = n*incx;
+ for (i = 0; i < nincx; i += incx)
+ dx[i +dx_off] *= da;
+ } else {
+
+ // code for increment equal to 1
+
+ for (i = 0; i < n; i++)
+ dx[i +dx_off] *= da;
+ }
+ }
+ }
- // code for increment equal to 1
- for (i = 0; i < n; i++)
- dx[i +dx_off] *= da;
- }
- }
- }
-
-
- /*
+ /*
finds the index of element having max. absolute value.
jack dongarra, linpack, 3/11/78.
- */
- final int idamax( int n, double dx[], int dx_off, int incx)
- {
- double dmax, dtemp;
- int i, ix, itemp=0;
-
- if (n < 1) {
- itemp = -1;
- } else if (n ==1) {
- itemp = 0;
- } else if (incx != 1) {
-
- // code for increment not equal to 1
-
- dmax = abs(dx[0 +dx_off]);
- ix = 1 + incx;
- for (i = 1; i < n; i++) {
- dtemp = abs(dx[ix + dx_off]);
- if (dtemp > dmax) {
- itemp = i;
- dmax = dtemp;
+ */
+ final int idamax( int n, double dx[], int dx_off, int incx)
+ {
+ double dmax, dtemp;
+ int i, ix, itemp=0;
+
+ if (n < 1) {
+ itemp = -1;
+ } else if (n ==1) {
+ itemp = 0;
+ } else if (incx != 1) {
+
+ // code for increment not equal to 1
+
+ dmax = abs(dx[0 +dx_off]);
+ ix = 1 + incx;
+ for (i = 1; i < n; i++) {
+ dtemp = abs(dx[ix + dx_off]);
+ if (dtemp > dmax) {
+ itemp = i;
+ dmax = dtemp;
+ }
+ ix += incx;
+ }
+ } else {
+
+ // code for increment equal to 1
+
+ itemp = 0;
+ dmax = abs(dx[0 +dx_off]);
+ for (i = 1; i < n; i++) {
+ dtemp = abs(dx[i + dx_off]);
+ if (dtemp > dmax) {
+ itemp = i;
+ dmax = dtemp;
+ }
+ }
+ }
+ return (itemp);
}
- ix += incx;
- }
- } else {
-
- // code for increment equal to 1
-
- itemp = 0;
- dmax = abs(dx[0 +dx_off]);
- for (i = 1; i < n; i++) {
- dtemp = abs(dx[i + dx_off]);
- if (dtemp > dmax) {
- itemp = i;
- dmax = dtemp;
- }
- }
- }
- return (itemp);
- }
-
- /*
+
+ /*
estimate unit roundoff in quantities of size x.
-
+
this program should function properly on all systems
satisfying the following two assumptions,
1. the base used in representing dfloating point
the next larger dfloating point number.
the developers of eispack would appreciate being informed
about any systems where these assumptions do not hold.
-
- *****************************************************************
+
+ *****************************************************************
this routine is one of the auxiliary routines used by eispack iii
to avoid machine dependencies.
- *****************************************************************
-
+ *****************************************************************
+
this version dated 4/6/83.
- */
- final double epslon (double x)
- {
- double a,b,c,eps;
-
- a = 4.0e0/3.0e0;
- eps = 0;
- while (eps == 0) {
- b = a - 1.0;
- c = b + b + b;
- eps = abs(c-1.0);
- }
- return(eps*abs(x));
- }
+ */
+ final double epslon (double x)
+ {
+ double a,b,c,eps;
+
+ a = 4.0e0/3.0e0;
+ eps = 0;
+ while (eps == 0) {
+ b = a - 1.0;
+ c = b + b + b;
+ eps = abs(c-1.0);
+ }
+ return(eps*abs(x));
+ }
-
- /*
+
+ /*
purpose:
multiply matrix m times vector x and add the result to vector y.
-
+
parameters:
-
+
n1 integer, number of elements in vector y, and number of rows in
matrix m
-
+
y double [n1], vector of length n1 to which is added
the product m*x
-
+
n2 integer, number of elements in vector x, and number of columns
in matrix m
-
+
ldm integer, leading dimension of array m
-
+
x double [n2], vector of length n2
-
+
m double [ldm][n2], matrix of n1 rows and n2 columns
- */
- final void dmxpy ( int n1, double y[], int n2, int ldm, double x[], double m[][])
- {
- int j,i;
-
- // cleanup odd vector
- for (j = 0; j < n2; j++) {
- for (i = 0; i < n1; i++) {
- y[i] += x[j]*m[j][i];
- }
- }
- }
+ */
+ final void dmxpy ( int n1, double y[], int n2, int ldm, double x[], double m[][])
+ {
+ int j,i;
+
+ // cleanup odd vector
+ for (j = 0; j < n2; j++) {
+ for (i = 0; i < n1; i++) {
+ y[i] += x[j]*m[j][i];
+ }
+ }
+ }
}
