linpack.java

纯java操作系统jnode,安装简单和操作简单的个人使用的Java操作系统

/*
 * $Id: Linpack.java,v 1.1 2003/11/25 11:41:41 epr Exp $
 */
package org.jnode.test;

/*

Modified 3/3/97 by David M. Doolin (dmd) [e-mail]
Fixed error in matgen() method. Added some comments.

Modified 1/22/97 by Paul McMahan [e-mail]
Added more MacOS options to form.

Optimized by Jonathan Hardwick ([e-mail]), 3/28/96
Compare to Linkpack.java.
Optimizations performed:
 - added "final" modifier to performance-critical methods.
 - changed lines of the form "a[i] = a[i] + x" to "a[i] += x".
 - minimized array references using common subexpression elimination.
 - eliminated unused variables.
 - undid an unrolled loop.
 - added temporary 1D arrays to hold frequently-used columns of 2D arrays.
 - wrote my own abs() method
See http://www.cs.cmu.edu/~jch/java/linpack.html for more details.


Ported to Java by Reed Wade  ([e-mail]) 2/96
built using JDK 1.0 on solaris
using "javac -O Linpack.java"


Translated to C by Bonnie Toy 5/88
  (modified on 2/25/94  to fix a problem with daxpy  for
   unequal increments or equal increments not equal to 1.
	 Jack Dongarra)

*/

/**
 * @author epr
 */
public class Linpack {

	public static void main(String[] args) {
		Linpack l = new Linpack();
		l.run_benchmark();
	}

	final double abs(double d) {
		return (d >= 0) ? d : -d;
	}

	double second_orig = -1;

	double second() {
		if (second_orig == -1) {
			second_orig = System.currentTimeMillis();
		}
		return (System.currentTimeMillis() - second_orig) / 1000;
	}

	public void run_benchmark() {
		double mflops_result = 0.0;
		double residn_result = 0.0;
		double time_result = 0.0;
		double eps_result = 0.0;

		double a[][] = new double[200][201];
		double b[] = new double[200];
		double x[] = new double[200];
		double ops, total, norma, normx;
		double resid, time;
		int n, i, lda;
		int ipvt[] = new int[200];

		//double mflops_result;
		//double residn_result;
		//double time_result;
		//double eps_result;

		lda = 201;
		n = 100;

		ops = (2.0e0 * (n * n * n)) / 3.0 + 2.0 * (n * n);

		norma = matgen(a, lda, n, b);
		time = second();
		/*info =*/ 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(1.0);
		/*
		
			residn_result = resid/( n*norma*normx*eps_result );
			time_result = total;
			mflops_result = ops/(1.0e6*total);
		
			return ("Mflops/s: " + mflops_result +
				"  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);
	}

	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;
	}

	/*
		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
		condition for this subroutine, but it does
		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;
				}
			}
		}
		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)
		if (!rcond is too small){
		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

			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;
				}
				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;
				}
			} 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;

		if (n > 0) {
			if (incx != 1) {

				// code for increment not equal to 1

				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;
			}
		}
	}

	/*
		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;
				}
				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
		numbers is not a power of three.
		2.  the quantity  a  in statement 10 is represented to
		the accuracy used in dfloating point variables
		that are stored in memory.
		the statement number 10 and the go to 10 are intended to
		force optimizing compilers to generate code satisfying
		assumption 2.
		under these assumptions, it should be true that,
		a  is not exactly equal to four-thirds,
		b  has a zero for its last bit or digit,
		c  is not exactly equal to one,
		eps  measures the separation of 1.0 from
		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));
	}

	/*
		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];
			}
		}
	}

}