bench_lu_unblk.c (session06/example01/bench_lu

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <sys/times.h>
#include <unistd.h>

//-- timer for benchmarks ------------------------------------------------------

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;
}

//-- setup and print matrices --------------------------------------------------

void
initGeMatrix(int m, int n, double *A, int incRowA, int incColA)
{
    int i, j;

    for (i=0; i<m; ++i) {
        for (j=0; j<n; ++j) {
            A[i*incRowA+j*incColA] = i*n + j + 1;
        }
    }
}

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
makeTrlDiagDom(int n, int unitDiag, double *A, int incRowA, int incColA)
{
    int i, j;

    for (j=0; j<n; ++j) {
        double asum = 0;
        double A_jj = (unitDiag) ? 1
                                 : A[j*(incRowA+incColA)];
        for (i=j+1; i<n; ++i) {
            asum += fabs(A[i*incRowA+j*incColA]);
        }
        for (i=j+1; i<n; ++i) {
            A[i*incRowA+j*incColA] *= A_jj/(asum*1.1);
        }
    }
}

void
makeGeDiagDom(int n, int m, double *A, int incRowA, int incColA)
{
    int i, j;

    for (j=0; j<n; ++j) {
        double asum = 0;

        for (i=0; i<m; ++i) {
            if (i!=j) {
                asum += fabs(A[i*incRowA+j*incColA]);
            }
        }
        for (i=0; i<m; ++i) {
            if (i!=j) {
                A[i*incRowA+j*incColA] *= A[j*(incRowA+incColA)]/(asum*1.1);
            }
        }
    }
}

void
printGeMatrix(int m, int n, const double *A, int incRowA, int incColA)
{
    int i, j;

    for (i=0; i<m; ++i) {
        for (j=0; j<n; ++j) {
            printf("%10.4lf ", A[i*incRowA+j*incColA]);
        }
        printf("\n");
    }
    printf("\n\n");
}

void
printTrMatrix(int m, int n, int unitDiag, int lower,
              const double *A, int incRowA, int incColA)
{
    int i, j;

    for (i=0; i<m; ++i) {
        for (j=0; j<n; ++j) {
            if (unitDiag && (i==j)) {
                printf("%10.4lf ", 1.0);
            } else if ((lower && (i>=j)) || (!lower && (i<=j))) {
                printf("%10.4lf ", A[i*incRowA+j*incColA]);
            } else {
                printf("%10.4lf ", 0.0);
            }
        }
        printf("\n");
    }
    printf("\n\n");
}

//-- some BLAS Level 1 procedures and functions --------------------------------

double
ddot(int n, const double *x, int incX, const double *y, int incY)
{
    int     i;
    double  alpha = 0;

    for (i=0; i<n; ++i) {
        alpha += x[i*incX]*y[i*incY];

    }
    return alpha;
}

void
daxpy(int n, double alpha, const double *x, int incX, double *y, int incY)
{
    int i;

    if (alpha==0) {
        return;
    }
    for (i=0; i<n; ++i) {
        y[i*incY] += alpha*x[i*incX];
    }
}

void
dgeaxpy(int m, int n, double alpha,
        const double *X, int incRowX, int incColX,
        double *Y, int incRowY, int incColY)
{
    int i, j;

    if (alpha==0 || m==0 || n==0) {
        return;
    }
    for (j=0; j<n; ++j) {
        for (i=0; i<m; ++i) {
            Y[i*incRowY+j*incColY] += alpha*X[i*incRowX+j*incColX];
        }
    }
}

void
dscal(int n, double alpha, double *x, int incX)
{
    int i;

    if (alpha==1) {
        return;
    }
    for (i=0; i<n; ++i) {
        x[i*incX] *= alpha;
    }
}

void
dcopy(int n, const double *x, int incX, double *y, int incY)
{
    int i;

    for (i=0; i<n; ++i) {
        y[i*incY] = x[i*incX];
    }
}

void
dgecopy(int m, int n,
        const double *X, int incRowX, int incColX,
        double *Y, int incRowY, int incColY)
{
    int 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
dswap(int n, double *x, int incX, double *y, int incY)
{
    int i;

    for (i=0; i<n; ++i) {
        double tmp;

        tmp = x[i*incX];
        x[i*incX] = y[i*incY];
        y[i*incY] = tmp;
    }
}

double
damax(int n, const double *x, int incX)
{
    int     i;
    double  result = 0;

    for (i=0; i<n; ++i) {
        if (fabs(x[i*incX])>result) {
            result = fabs(x[i*incX]);
        }
    }
    return result;
}

double
dgenrm1(int m, int n, const double *A, int incRowA, int incColA)
{
    int     i, j;
    double  result = 0;

    for (j=0; j<n; ++j) {
        double sum = 0;
        for (i=0; i<m; ++i) {
            sum += fabs(A[i*incRowA+j*incColA]);
        }
        if (sum>result) {
            result = sum;
        }
    }
    return result;
}

double
dtrnrm1(int m, int n,  int unitDiag, int lower,
        const double *A, int incRowA, int incColA)
{
    int     i, j;
    double  result = 0;

    for (j=0; j<n; ++j) {
        double sum = 0;
        for (i=0; i<m; ++i) {
            if (unitDiag && (i==j)) {
                sum += 1.0;
            } else if ((lower && (i>=j)) || (!lower && (i<=j))) {
                sum += fabs(A[i*incRowA+j*incColA]);
            }
        }
        if (sum>result) {
            result = sum;
        }
    }
    return result;
}

//-- error bounds --------------------------------------------------------------

double
err_dgemv(int m, int n, double alpha,
          const double *A, int incRowA, int incColA,
          const double *x, int incX,
          double beta,
          const double *y0, int incY0,
          double *y1, int incY1)
{
    int    max_mn = (m>n) ? m : n;
    double normA  = fabs(alpha)*dgenrm1(m, n, A, incRowA, incColA);
    double normX  = damax(n, x, incX);
    double normY0 = fabs(beta)*damax(m, y0, incY0);
    double normD;

    daxpy(m, -1.0, y0, incY0, y1, incY1);
    normD = damax(n, y1, incY1);

    return normD/(normA*normX*normY0*max_mn);
}

double
err_dtrmv(int n, int unitDiag, int lower,
          const double *A, int incRowA, int incColA,
          const double *x0, int incX0,
          double *x1, int incX1)
{
    double normA  = dtrnrm1(n, n, unitDiag, lower, A, incRowA, incColA);
    double normX0 = damax(n, x0, incX0);
    double normD;

    daxpy(n, -1.0, x0, incX0, x1, incX1);
    normD = damax(n, x1, incX1);

    return normD/(n*normA*normX0);
}

double
err_dtrsv(int n, int unitDiag, int lower,
          const double *A, int incRowA, int incColA,
          const double *x0, int incX0,
          double *x1, int incX1)
{
    double normA  = dtrnrm1(n, n, unitDiag, lower, A, incRowA, incColA);
    double normX0 = damax(n, x0, incX0);
    double normD;

    daxpy(n, -1.0, x0, incX0, x1, incX1);
    normD = damax(n, x1, incX1);

    return normD/(n*normA*normX0);
}

double
err_dger(int m, int n, double alpha,
         const double *x, int incX,
         const double *y, int incY,
         const double *A0, int incRowA0, int incColA0,
         double *A, int incRowA, int incColA)
{
    double normA0 = dgenrm1(m, n, A0, incRowA0, incColA0);
    double normX  = fabs(alpha)*damax(m, x, incX);
    double normY  = damax(n, y, incY);
    double normD;
    int    mn     = (m>n) ? m : n;

    dgeaxpy(m, n, -1.0, A0, incRowA0, incColA0, A, incRowA, incColA);
    normD = dgenrm1(m, n, A, incRowA, incColA);

    return normD/(mn*normA0*normX*normY);
}

void
dgemm(int m, int n, int k,
      double alpha,
      const double *A, int incRowA, int incColA,
      const double *B, int incRowB, int incColB,
      double beta,
      double *C, int incRowC, int incColC)
{
    int 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(int m, int n,
       const double *A, int incRowA, int incColA,
       double *LU, int incRowLU, int incColLU)
{
    double aNrm1 = 0;
    double err   = 0;

    int    i,j;
    int    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 (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;
}

//-- Fused BLAS Level 1 procedures and functions -------------------------------

#ifndef DGEMV_MxBS
#define DGEMV_MxBS 4
#endif

void
dgemv_mxBS(int m, double alpha,
           const double *A, int incRowA, int incColA,
           const double *x, int incX,
           double *y, int incY)
{
    int i, j;

    if (alpha==0) {
        return;
    }
    for (i=0; i<m; ++i) {
        double dot = 0;
        for (j=0; j<DGEMV_MxBS; ++j) {
            dot += A[i*incRowA+j*incColA]*x[j*incX];
        }
        y[i*incY] += alpha*dot;
    }
}

#ifndef DGEMV_BSxN
#define DGEMV_BSxN 4
#endif

void
dgemv_BSxn(int n, double alpha,
           const double *A, int incRowA, int incColA,
           const double *x, int incX,
           double beta,
           double *y, int incY)
{
    int i, j;

    if (alpha==0) {
        return;
    }
    if (beta!=1) {
        for (i=0; i<DGEMV_BSxN; ++i) {
            y[i*incY] *= beta;
        }
    }
    for (j=0; j<n; ++j) {
        for (i=0; i<DGEMV_BSxN; ++i) {
            y[i*incY] += alpha*A[i*incRowA+j*incColA]*x[j*incX];
        }
    }
}

//-- GEMV implementations ------------------------------------------------------

void
dgemv_ref(int m, int n, double alpha,
          const double *A, int incRowA, int incColA,
          const double *x, int incX,
          double beta,
          double *y, int incY)
{
    int i, j;

    for (i=0; i<m; ++i) {
        if (beta==0) {
            y[i*incY] = 0;
        } else {
            y[i*incY] *= beta;
        }
        for (j=0; j<n; ++j) {
            y[i*incY] += alpha*A[i*incRowA+j*incColA]*x[j*incX];
        }
    }
}

void
dgemv_unblk(int m, int n, double alpha,
            const double *A, int incRowA, int incColA,
            const double *x, int incX,
            double beta,
            double *y, int incY)
{
    if (incRowA<incColA) {
        int j;

        dscal(m, beta, y, incY);

        for (j=0; j<n; ++j) {
            daxpy(m, alpha*x[j*incX], &A[j*incColA], incRowA, y, incY);
        }
    } else {
        int i;

        for (i=0; i<m; ++i) {
            y[i*incY] *= beta;
            y[i*incY] += alpha*ddot(n, &A[i*incRowA], incColA, x, incX);
        }
    }
}

void
dgemv(int m, int n, double alpha,
      const double *A, int incRowA, int incColA,
      const double *x, int incX,
      double beta,
      double *y, int incY)
{
    if (incRowA<incColA) {
        int bs = DGEMV_MxBS;
        int j;

        dscal(m, beta, y, incY);

        for (j=0; j+bs<=n; j+=bs) {
            dgemv_mxBS(m, alpha,
                       &A[j*incColA], incRowA, incColA,
                       &x[j*incX], incX,
                       y, incY);
        }
        dgemv_unblk(m, n-j, alpha,
                    &A[j*incColA], incRowA, incColA,
                    &x[j*incX], incX,
                    1.0,
                    y, incY);
    } else {
        int bs = DGEMV_BSxN;
        int i;

        for (i=0; i+bs<=m; i+=bs) {
            dgemv_BSxn(n, alpha,
                       &A[i*incRowA], incRowA, incColA,
                       x, incX,
                       beta,
                       &y[i*incY], incY);
        }
        dgemv_unblk(m-i, n, alpha,
                    &A[i*incRowA], incRowA, incColA,
                    x, incX,
                    beta,
                    &y[i*incY], incY);
    }
}

//-- TRMV implementations ------------------------------------------------------

void
dtrlmv_ref(int n, int unitDiag,
           const double *A, int incRowA, int incColA,
           double *x, int incX)
{
    int i, j;

    for (j=n-1; j>=0; --j) {
        for (i=j+1; i<n; ++i) {
            x[i*incX] += A[i*incRowA+j*incColA]*x[j*incX];
        }
        if (!unitDiag) {
            x[j*incX] *= A[j*(incRowA+incColA)];
        }
    }
}

void
dtrlmv_col(int n, int unitDiag,
           const double *A, int incRowA, int incColA,
           double *x, int incX)
{
    int k;

    if (unitDiag) {
        for (k=n-1; k>=0; --k) {
            daxpy(n-k-1, x[k*incX],
                  &A[(k+1)*incRowA+k*incColA], incRowA,
                  &x[(k+1)*incX], incX);
        }
    } else {
        for (k=n-1; k>=0; --k) {
            daxpy(n-k-1, x[k*incX],
                  &A[(k+1)*incRowA+k*incColA], incRowA,
                  &x[(k+1)*incX], incX);
            x[k*incX] *= A[k*(incRowA+incColA)];
        }
    }
}

void
dtrlmv_row(int n, int unitDiag,
           const double *A, int incRowA, int incColA,
           double *x, int incX)
{
    int k;

    if (unitDiag) {
        for (k=n-1; k>=0; --k) {
            x[k*incX] += ddot(k, &A[k*incRowA], incColA, x, incX);
        }
    } else {
        for (k=n-1; k>=0; --k) {
            x[k*incX] = ddot(k+1, &A[k*incRowA], incColA, x, incX);
        }
    }
}

void
dtrlmv(int n, int unitDiag,
       const double *A, int incRowA, int incColA,
       double *x, int incX)
{
    if (incRowA<incColA) {
        int bs = DGEMV_MxBS;
        int k  = (n/bs)*bs;

        dtrlmv_col(n-k, unitDiag,
                   &A[k*(incRowA+incColA)], incRowA, incColA,
                   &x[k*incX], incX);

        for (k-=bs; k>=0; k-=bs) {
            dgemv_mxBS(n-k-bs, 1.0,
                       &A[(k+bs)*incRowA+k*incColA], incRowA, incColA,
                       &x[k*incX], incX,
                       &x[(k+bs)*incX], incX);
            dtrlmv_col(bs, unitDiag,
                       &A[k*(incRowA+incColA)], incRowA, incColA,
                       &x[k*incX], incX);
        }
    } else {
        double buffer[DGEMV_BSxN];
        int    bs = DGEMV_BSxN;
        int    k  = (n/bs)*bs;

        dgemv(n-k, k, 1.0,
              &A[k*incRowA], incRowA, incColA,
              x, incX,
              0.0,
              buffer,1);
        dtrlmv_row(n-k, unitDiag,
                   &A[k*(incRowA+incColA)], incRowA, incColA,
                   &x[k*incX], incX);
        daxpy(n-k, 1.0, buffer, 1, &x[k*incX], incX);

        for (k-=bs; k>=0; k-=bs) {
            dgemv_BSxn(k, 1.0,
                       &A[k*incRowA], incRowA, incColA,
                       x, incX,
                       0.0,
                       buffer, 1);
            dtrlmv_col(bs, unitDiag,
                       &A[k*(incRowA+incColA)], incRowA, incColA,
                       &x[k*incX], incX);
            daxpy(bs, 1.0, buffer, 1, &x[k*incX], incX);
        }
    }
}

//-- TRSV implementations ------------------------------------------------------

void
dtrlsv_ref(int n, int unitDiag,
           const double *A, int incRowA, int incColA,
           double *x, int incX)
{
    int i, j;

    for (i=0; i<n; ++i) {
        for (j=0; j<i; ++j) {
            x[i*incX] -= A[i*incRowA+j*incColA]*x[j*incX];
        }
        x[i*incX] /= (unitDiag) ? 1.0 : A[i*(incRowA+incColA)];
    }
}

void
dtrlsv_row(int n, int unitDiag,
           const double *A, int incRowA, int incColA,
           double *x, int incX)
{
    int k;

    for (k=0; k<n; ++k) {
        x[k*incX] -= ddot(k, &A[k*incRowA], incColA, x, incX);
        x[k*incX] /= (unitDiag) ? 1.0 : A[k*(incRowA+incColA)];
    }
}

void
dtrlsv_col(int n, int unitDiag,
           const double *A, int incRowA, int incColA,
           double *x, int incX)
{
    int k;

    for (k=0; k<n; ++k) {
        x[k*incX] /= (unitDiag) ? 1.0 : A[k*(incRowA+incColA)];
        daxpy(n-k-1, -x[k*incX],
              &A[(k+1)*incRowA+k*incColA], incRowA,
              &x[(k+1)*incX], incX);
    }
}

void
dtrlsv(int n, int unitDiag,
       const double *A, int incRowA, int incColA,
       double *x, int incX)
{
    if (incRowA<incColA) {
        // ... your code here ...
    } else {
        // ... your code here ...
    }
}


//-- GER implementations -------------------------------------------------------

void
dger_ref(int m, int n, double alpha,
         const double *x, int incX,
         const double *y, int incY,
         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] += alpha*x[i*incX]*y[j*incY];
        }
    }
}

void
dger_row(int m, int n, double alpha,
         const double *x, int incX,
         const double *y, int incY,
         double *A, int incRowA, int incColA)
{
    int i;

    for (i=0; i<m; ++i) {
        daxpy(n, alpha*x[i*incX], y, incY, &A[i*incRowA], incColA);
    }
}

void
dger_col(int m, int n, double alpha,
         const double *x, int incX,
         const double *y, int incY,
         double *A, int incRowA, int incColA)
{
    int j;

    for (j=0; j<n; ++j) {
        daxpy(m, alpha*y[j*incY], x, incX, &A[j*incColA], incRowA);
    }
}

void
dger(int m, int n, double alpha,
     const double *x, int incX,
     const double *y, int incY,
     double *A, int incRowA, int incColA)
{
    if (incRowA<incColA) {
        // ... your code here ...
    } else {
        // ... your code here ...
    }
}

//-- LU factorization ----------------------------------------------------------

void
lu_unblk_var1(int m, int n, double *A, int incRowA, int incColA)
{
    int min_mn = (m<n) ? m : n;
    int max_mn = (m>n) ? m : n;
    int j;

    // ... your code here ...
}

void
lu_unblk_var2(int m, int n, double *A, int incRowA, int incColA)
{
    int min_mn = (m<n) ? m : n;
    int j;

    // ... your code here ...
}

void
lu_unblk_var3(int m, int n, double *A, int incRowA, int incColA)
{
    int min_mn = (m<n) ? m : n;
    int j;

    // ... your code here ...
}

void
lu_unblk_var4(int m, int n, double *A, int incRowA, int incColA)
{
    int min_mn = (m<n) ? m : n;
    int j;

    // ... your code here ...
}

void
lu_unblk_var5(int m, int n, double *A, int incRowA, int incColA)
{
    int min_mn = (m<n) ? m : n;
    int j;

    // ... your code here ...
}


//------------------------------------------------------------------------------

#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

#if (ROWMAJOR==1)
#   define INCROW_A  MAX_N
#   define INCCOL_A  1
#else
#   define INCROW_A  1
#   define INCCOL_A  MAX_M
#endif

#define MIN(X,Y)   ((X)<(Y) ? (X) : (Y))
#define MAX(X,Y)   ((X)>(Y) ? (X) : (Y))

double A_[MAX_N*MAX_N];
double A_0[MAX_N*MAX_N*MIN(INCROW_A,INCCOL_A)];

int
main()
{
    int m, n;

    randGeMatrix(MAX_N, MAX_N, A_, 1, MAX_M);

    printf("#%9s %9s %9s %9s", "m", "n", "INCROW_A", "INCCOL_A");
    printf(" %12s %12s %12s", "t", "MFLOPS", "err");
    printf(" %12s %12s %12s", "t", "MFLOPS", "err");
    printf(" %12s %12s %12s", "t", "MFLOPS", "err");
    printf(" %12s %12s %12s", "t", "MFLOPS", "err");
    printf(" %12s %12s %12s", "t", "MFLOPS", "err");
    printf("\n");

    for (m=MIN_M, n=MIN_N; n<=MAX_N && m<=MAX_M; m+=INC_M, n+=INC_N) {
        double t, dt, err;
        int    runs  = 1;
        int    minMN = MIN(m,n);
        int    maxMN = MAX(m,n);
        double ops   = minMN*minMN*maxMN
                     -(minMN*minMN*minMN/3.)
                     -(minMN*minMN/2.);

        printf(" %9d %9d %9d %9d", m, n, INCROW_A, INCCOL_A);

        t    = 0;
        runs = 0;
        do {
            dgecopy(m, n, A_, 1, MAX_M, A_0, INCROW_A, INCCOL_A);
            dt = walltime();
            lu_unblk_var1(m, n, A_0, INCROW_A, INCCOL_A);
            dt = walltime() - dt;
            t += dt;
            ++runs;
        } while (t<0.3);
        t /= runs;

        err = err_lu(m, n,
                     A_, 1, MAX_M,
                     A_0, INCROW_A, INCCOL_A);

        printf(" %12.2e %12.2lf %12.2e", t, ops/(1000*1000*t), err);

        t    = 0;
        runs = 0;
        do {
            dgecopy(m, n, A_, 1, MAX_M, A_0, INCROW_A, INCCOL_A);
            dt = walltime();
            lu_unblk_var2(m, n, A_0, INCROW_A, INCCOL_A);
            dt = walltime() - dt;
            t += dt;
            ++runs;
        } while (t<0.3);
        t /= runs;

        err = err_lu(m, n,
                     A_, 1, MAX_M,
                     A_0, INCROW_A, INCCOL_A);

        printf(" %12.2e %12.2lf %12.2e", t, ops/(1000*1000*t), err);

        t    = 0;
        runs = 0;
        do {
            dgecopy(m, n, A_, 1, MAX_M, A_0, INCROW_A, INCCOL_A);
            dt = walltime();
            lu_unblk_var3(m, n, A_0, INCROW_A, INCCOL_A);
            dt = walltime() - dt;
            t += dt;
            ++runs;
        } while (t<0.3);
        t /= runs;

        err = err_lu(m, n,
                     A_, 1, MAX_M,
                     A_0, INCROW_A, INCCOL_A);

        printf(" %12.2e %12.2lf %12.2e", t, ops/(1000*1000*t), err);

        t    = 0;
        runs = 0;
        do {
            dgecopy(m, n, A_, 1, MAX_M, A_0, INCROW_A, INCCOL_A);
            dt = walltime();
            lu_unblk_var4(m, n, A_0, INCROW_A, INCCOL_A);
            dt = walltime() - dt;
            t += dt;
            ++runs;
        } while (t<0.3);
        t /= runs;

        err = err_lu(m, n,
                     A_, 1, MAX_M,
                     A_0, INCROW_A, INCCOL_A);

        printf(" %12.2e %12.2lf %12.2e", t, ops/(1000*1000*t), err);

        t    = 0;
        runs = 0;
        do {
            dgecopy(m, n, A_, 1, MAX_M, A_0, INCROW_A, INCCOL_A);
            dt = walltime();
            lu_unblk_var5(m, n, A_0, INCROW_A, INCCOL_A);
            dt = walltime() - dt;
            t += dt;
            ++runs;
        } while (t<0.3);
        t /= runs;

        err = err_lu(m, n,
                     A_, 1, MAX_M,
                     A_0, INCROW_A, INCCOL_A);

        printf(" %12.2e %12.2lf %12.2e", t, ops/(1000*1000*t), err);


        printf("\n");
    }

    return 0;
}