#include <float.h>
#include <math.h>
#include <stddef.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/times.h>
#include <unistd.h>
void
initMatrix(size_t m, size_t n,
double *A,
ptrdiff_t incRow, ptrdiff_t incCol)
{
for (size_t i=0; i<m; ++i) {
for (size_t j=0; j<n; ++j) {
A[i*incRow+j*incCol] = i*n+j+1;
}
}
}
void
printMatrix(size_t m, size_t n,
const double *A,
ptrdiff_t incRow, ptrdiff_t incCol)
{
for (size_t i=0; i<m; ++i) {
for (size_t j=0; j<n; ++j) {
printf("%10.3lf", A[i*incRow+j*incCol]);
}
printf("\n");
}
printf("\n");
}
size_t
idamax(size_t n, const double *x, ptrdiff_t incX)
{
size_t iMax = 0;
for (size_t i=1; i<n; ++i) {
if (fabs(x[i*incX]) > fabs(x[iMax*incX])) {
iMax = i;
}
}
return iMax;
}
void
dcopy(size_t n,
const double *x, ptrdiff_t incX,
double *y, ptrdiff_t incY)
{
for (size_t i=0; i<n; ++i) {
y[i*incY] = x[i*incX];
}
}
void
dswap(size_t n,
double *x, ptrdiff_t incX,
double *y, ptrdiff_t incY)
{
for (size_t i=0; i<n; ++i) {
double tmp = x[i*incX];
x[i*incX] = y[i*incY];
y[i*incY] = tmp;
}
}
void
daxpy(size_t n, double alpha,
const double *x, ptrdiff_t incX,
double *y, ptrdiff_t incY)
{
if (alpha==0) {
return;
}
for (size_t i=0; i<n; ++i) {
y[i*incY] += alpha*x[i*incX];
}
}
void
dscal(size_t n, double alpha,
double *x, ptrdiff_t incX)
{
if (alpha==1) {
return;
}
if (alpha==0) {
for (size_t i=0; i<n; ++i) {
x[i*incX] = 0;
}
} else {
for (size_t i=0; i<n; ++i) {
x[i*incX] *= alpha;
}
}
}
double
ddot(size_t n,
const double *x, ptrdiff_t incX,
const double *y, ptrdiff_t incY)
{
double alpha = 0;
for (size_t i=0; i<n; ++i) {
alpha += x[i*incX]*y[i*incY];
}
return alpha;
}
void
dger(size_t m, size_t n, double alpha,
const double *x, ptrdiff_t incX,
const double *y, ptrdiff_t incY,
double *A, ptrdiff_t incRowA, ptrdiff_t incColA)
{
if (alpha==0 || m==0 || n==0) {
return;
}
if (incRowA<incColA) {
for (size_t j=0; j<n; ++j) {
daxpy(m, alpha*y[j*incY], x, incX, &A[j*incColA], incRowA);
}
} else {
for (size_t i=0; i<m; ++i) {
daxpy(n, alpha*x[i*incX], y, incY, &A[i*incRowA], incColA);
}
}
}
ptrdiff_t
lu_unblk(size_t m, size_t n,
double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
size_t *p, ptrdiff_t incP)
{
size_t min_mn = (m<n) ? m : n;
ptrdiff_t info = -1;
for (size_t j=0; j<min_mn; ++j) {
size_t jp = j + idamax(m-j, &A[j*(incRowA+incColA)], incRowA);
p[j*incP] = jp;
if (A[jp*incRowA + j*incColA] != 0) {
if (j!=jp) {
dswap(n, &A[j*incRowA], incColA, &A[jp*incRowA], incColA);
}
dscal(m-j-1,
1.0/A[j*(incRowA+incColA)],
&A[(j+1)*incRowA+j*incColA], incRowA);
dger(m-j-1, n-j-1,
-1.0,
&A[(j+1)*incRowA+j*incColA], incRowA,
&A[j*incRowA+(j+1)*incColA], incColA,
&A[(j+1)*(incRowA+incColA)], incRowA, incColA);
} else if (info==-1) {
info = j;
}
}
return info;
}
double
walltime()
{
struct tms ts;
static double ClockTick=0.0;
if (ClockTick==0.0) {
ClockTick = 1.0 / ((double) sysconf(_SC_CLK_TCK));
}
return ((double) times(&ts)) * ClockTick;
}
void
randGeMatrix(int m, int n, double *A, int incRowA, int incColA)
{
int i, j;
for (j=0; j<n; ++j) {
for (i=0; i<m; ++i) {
A[i*incRowA+j*incColA] = ((double)rand()-RAND_MAX/2)*200/RAND_MAX;
}
}
}
void
dgecopy(size_t m, size_t n,
const double *X, ptrdiff_t incRowX, ptrdiff_t incColX,
double *Y, ptrdiff_t incRowY, ptrdiff_t incColY)
{
size_t i, j;
for (i=0; i<m; ++i) {
for (j=0; j<n; ++j) {
Y[i*incRowY+j*incColY] = X[i*incRowX+j*incColX];
}
}
}
void
dgemm(size_t m, size_t n, size_t k,
double alpha,
const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
const double *B, ptrdiff_t incRowB, ptrdiff_t incColB,
double beta,
double *C, ptrdiff_t incRowC, ptrdiff_t incColC)
{
size_t i, j, l;
if (beta!=1) {
for (i=0; i<m; ++i) {
for (j=0; j<n; ++j) {
C[i*incRowC+j*incColC] *= beta;
}
}
}
if (alpha!=0) {
for (i=0; i<m; ++i) {
for (j=0; j<n; ++j) {
for (l=0; l<k; ++l) {
C[i*incRowC+j*incColC] += alpha*A[i*incRowA+l*incColA]
*B[l*incRowB+j*incColB];
}
}
}
}
}
double
err_lu(size_t m, size_t n,
const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
double *LU, ptrdiff_t incRowLU, ptrdiff_t incColLU,
size_t *P, ptrdiff_t incP)
{
double aNrm1 = 0;
double err = 0;
size_t i,j;
size_t k = (m<n) ? m : n;
double *L = (double *)malloc(m*k*sizeof(double));
double *U = (double *)malloc(k*n*sizeof(double));
for (j=0; j<k; ++j) {
for (i=0; i<m; ++i) {
L[i+j*m] = (i>j) ? LU[i*incRowLU+j*incColLU]
: (i==j) ? 1
: 0;
}
}
for (j=0; j<n; ++j) {
for (i=0; i<k; ++i) {
U[i+j*k] = (i<=j) ? LU[i*incRowLU+j*incColLU]
: 0;
}
}
for (j=0; j<n; ++j) {
for (i=0; i<m; ++i) {
aNrm1 += fabs(A[i*incRowA+j*incColA]);
}
}
dgemm(m, n, k, 1.0,
L, 1, m,
U, 1, k,
0.0,
LU, incRowLU, incColLU);
for (size_t i=m; i>0; --i) {
if (i-1 != P[(i-1)*incP]) {
dswap(n,
&LU[(i-1)*incRowLU], incColLU,
&LU[P[(i-1)*incP]*incRowLU], incColLU);
}
}
for (j=0; j<n; ++j) {
for (i=0; i<m; ++i) {
err += fabs(A[i*incRowA+j*incColA]-LU[i*incRowLU+j*incColLU]);
}
}
err /= (aNrm1*k);
free(L);
free(U);
return err;
}
#ifndef MIN_N
#define MIN_N 100
#endif
#ifndef MAX_N
#define MAX_N 8000
#endif
#ifndef INC_N
#define INC_N 100
#endif
#ifndef MIN_M
#define MIN_M 100
#endif
#ifndef MAX_M
#define MAX_M 8000
#endif
#ifndef INC_M
#define INC_M 100
#endif
#ifndef ROWMAJOR
#define ROWMAJOR 0
#endif
double A_[MAX_M*MAX_N];
double A_0[MAX_M*MAX_N];
size_t P_0[(MAX_M<MAX_N) ? MAX_M : MAX_N];
int
main()
{
randGeMatrix(MAX_N, MAX_N, A_, 1, MAX_M);
printf("#%9s %9s %9s %9s", "m", "n", "INCROW_A", "INCCOL_A");
printf(" %12s %12s %17s", "t", "MFLOPS", "Residual Error");
printf("\n");
for (size_t m=MIN_M, n=MIN_N; n<=MAX_N && m<=MAX_M; m+=INC_M, n+=INC_N) {
double t, dt, err;
size_t runs = 1;
size_t minMN = (m<n) ? m : n;
size_t maxMN = (m>n) ? m : n;
double ops = minMN*minMN*maxMN
-(minMN*minMN*minMN/3.)
-(minMN*minMN/2.);
ptrdiff_t incRowA = (ROWMAJOR==1) ? n : 1;
ptrdiff_t incColA = (ROWMAJOR==1) ? 1 : m;
printf(" %9zu %9zu %9td %9td", m, n, incRowA, incColA);
t = 0;
runs = 0;
do {
dgecopy(m, n, A_, 1, MAX_M, A_0, incRowA, incColA);
dt = walltime();
lu_unblk(m, n, A_0, incRowA, incColA, P_0, 1);
dt = walltime() - dt;
t += dt;
++runs;
} while (t<0.3);
t /= runs;
err = err_lu(m, n,
A_, 1, MAX_M,
A_0, incRowA, incColA,
P_0, 1);
printf(" %12.2e %12.2lf %12.2e %4s", t, ops/(1000*1000*t), err, (err<DBL_EPSILON) ? "PASS" : "FAIL");
printf("\n");
}
return 0;
}