Possible Solution

#include <ulmblas.h>
#include <ulmaux.h>

#include <math.h>           // for nan(), fabs()
#include <stdlib.h>         // for malloc(), free()

//-- BLAS Level 1 functions ----------------------------------------------------

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
daxpy(size_t n, double alpha,
      const double *x, ptrdiff_t incX,
      double *y, ptrdiff_t incY)
{
    for (size_t i=0; i<n; ++i) {
        y[i*incY] += alpha*x[i*incX];
    }
}

double
ddot(size_t n,
     const double *x, ptrdiff_t incX,
     const double *y, ptrdiff_t incY)
{
    double result = 0;

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

    return result;
}

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] *= alpha;
        }
    } else {
        for (size_t i=0; i<n; ++i) {
            x[i*incX] = 0;
        }
    }
}

size_t
idamax(size_t n, const double *x, ptrdiff_t incX)
{
    double max = 0;
    size_t I   = 0;

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

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;
    }
}

//-- BLAS Level 2 functions ----------------------------------------------------

#ifndef AXPYF
#define AXPYF 4
#endif

// y <- alpha*A*x + y where A is a m x AXPYF matrix
void
daxpyf(size_t m, double alpha,
       const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
       const double *x, ptrdiff_t incX,
       double *y, ptrdiff_t incY)
{
    for (size_t i=0; i<m; ++i) {
        for (size_t l=0; l<AXPYF; ++l) {
            y[i*incY] += alpha * A[i*incRowA+l*incColA] * x[l*incX];
        }
    }
}

void
dgemv_axpyf(size_t m, size_t n,
            double alpha,
            const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
            const double *x, ptrdiff_t incX,
            double *y, ptrdiff_t incY)
{
    size_t nb = n / AXPYF;
    for (size_t j=0; j<nb; ++j) {
        daxpyf(m, alpha,
               &A[j*AXPYF*incColA], incRowA, incColA,
               &x[j*AXPYF*incX], incX,
               y, incY);
    }
    for (size_t j=nb*AXPYF; j<n; ++j) {
        daxpy(m, alpha*x[j*incX], &A[j*incColA], incRowA, y, incY);
    }
}

#ifndef DOTF
#define DOTF 4
#endif

void
dgemv_dotf(size_t m, size_t n,
           double alpha,
           const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
           const double *x, ptrdiff_t incX,
           double *y, ptrdiff_t incY)
{
    size_t mb = m / DOTF;

    for (size_t i=0; i<mb; ++i) {
        for (size_t j=0; j<n; ++j) {
            for (size_t l=0; l<DOTF; ++l) {
                y[(DOTF*i+l)*incY]
                    += alpha*A[(DOTF*i+l)*incRowA+j*incColA]*x[j*incX];
            }
        }
    }

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

void
dgemv(size_t m, size_t n,
      double alpha,
      const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
      const double *x, ptrdiff_t incX,
      double beta,
      double *y, ptrdiff_t incY)
{
    dscal(m, beta, y, incY);

    if (alpha==0 || m==0 || n==0) {
        return;
    }

    if (incRowA<incColA) {
        dgemv_axpyf(m, n, alpha, A, incRowA, incColA, x, incX, y, incY);
    } else {
        dgemv_dotf(m, n, alpha, A, incRowA, incColA, x, incX, y, incY);
    }
}

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) {
        dger(n, m, alpha, y, incY, x, incX, A, incColA, incRowA);
        return;
    }

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

void
dtrsv(size_t n, bool lower, bool unit,
      const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
      double *x, ptrdiff_t incX)
{
    if (lower) {
        if (incRowA<incColA) {
            // A is col major

            size_t nb = n / AXPYF;
            for (size_t j=0; j<nb; ++j) {
                for (size_t l=0; l<AXPYF; ++l) {
                    size_t J = j*AXPYF + l;

                    if (!unit) {
                        x[J*incX] /= A[J*(incRowA+incColA)];
                    }
                    daxpy(AXPYF-1-l, -x[J*incX],
                          &A[(J+1)*incRowA + J*incColA], incRowA,
                          &x[(J+1)*incX], incX);
                }
                daxpyf(n-(j+1)*AXPYF, -1,
                       &A[((j+1)*incRowA + j*incColA)*AXPYF], incRowA, incColA,
                       &x[j*incX*AXPYF], incX,
                       &x[(j+1)*incX*AXPYF], incX);
            }
            for (size_t j=nb*AXPYF; j<n; ++j) {
                if (!unit) {
                    x[j*incX] /= A[j*(incRowA+incColA)];
                }
                daxpy(n-1-j, -x[j*incX],
                      &A[(j+1)*incRowA+j*incColA], incRowA,
                      &x[(j+1)*incX], incX);
            }
        } else {
            // A is row major
            for (size_t j=0; j<n; ++j) {
                x[j*incX] -= ddot(j, &A[j*incRowA], incColA, x, incX);
                if (!unit) {
                    x[j*incX] /= A[j*(incRowA+incColA)];
                }
            }
        }
    } else {
        if (incRowA<incColA) {
            // A is col major
            for (size_t j=n; j-- >0; ) {
                if (!unit) {
                    x[j*incX] /= A[j*(incRowA+incColA)];
                }
                daxpy(j, -x[j*incX], &A[j*incColA], incRowA,
                      x, incX);
            }
        } else {
            // A is row major
            for (size_t j=n; j-- >0; ) {
                x[j*incX] -= ddot(n-1-j,
                                  &A[j*incRowA+(j+1)*incColA], incColA,
                                  &x[(j+1)*incX], incX);
                if (!unit) {
                    x[j*incX] /= A[j*(incRowA+incColA)];
                }
            }
        }
    }
}

//-- BLAS Level 3 functions ----------------------------------------------------
void
ge_dscal(size_t m, size_t n,
         double alpha,
         double *A, ptrdiff_t incRowA, ptrdiff_t incColA)
{
    if (alpha!=0) {
        for (size_t j=0; j<n; ++j) {
            for (size_t i=0; i<m; ++i) {
                A[i*incRowA + j*incColA] *= alpha;
            }
        }
    } else {
        for (size_t j=0; j<n; ++j) {
            for (size_t i=0; i<m; ++i) {
                A[i*incRowA + j*incColA] = 0;
            }
        }
    }
}

void
ge_dcopy(size_t m, size_t n,
         const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
         double *B, ptrdiff_t incRowB, ptrdiff_t incColB)
{
    for (size_t j=0; j<n; ++j) {
        for (size_t i=0; i<m; ++i) {
            B[i*incRowB + j*incColB] = A[i*incRowA + j*incColA];
        }
    }
}

void
dgemm_jli(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 *C, ptrdiff_t incRowC, ptrdiff_t incColC)
{
    for (size_t j=0; j<n; ++j) {
        for (size_t l=0; l<k; ++l) {
            for (size_t i=0; i<m; ++i) {
                C[i*incRowC + j*incColC] += alpha*A[i*incRowA + l*incColA]
                                                 *B[l*incRowB + j*incColB];
            }
        }
    }
}

#ifndef DGEMM_MC
#define DGEMM_MC 8
#endif

#ifndef DGEMM_KC
#define DGEMM_KC 256
#endif

#ifndef DGEMM_NC
#define DGEMM_NC 1024
#endif

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)
{
    ge_dscal(m, n, beta, C, incRowC, incColC);

    if (k==0 || alpha==0) {
        return;
    }

    double *A_ = malloc(DGEMM_MC*DGEMM_KC*sizeof(double));
    double *B_ = malloc(DGEMM_KC*DGEMM_NC*sizeof(double));

    size_t mb = (m + DGEMM_MC - 1)/DGEMM_MC;
    size_t nb = (n + DGEMM_NC - 1)/DGEMM_NC;
    size_t kb = (k + DGEMM_KC - 1)/DGEMM_KC;

    size_t mr = m % DGEMM_MC;
    size_t nr = n % DGEMM_NC;
    size_t kr = k % DGEMM_KC;

    for (size_t jb=0; jb<nb; ++jb) {
        size_t nc = (jb!=nb-1 || nr==0) ? DGEMM_NC : nr;

        for (size_t lb=0; lb<kb; ++lb) {
            size_t kc = (lb!=kb-1 || kr==0) ? DGEMM_KC : kr;

            ge_dcopy(kc, nc, &B[lb*DGEMM_KC*incRowB + jb*DGEMM_NC*incColB],
                     incRowB, incColB,
                     B_, 1, DGEMM_KC);

            for (size_t ib=0; ib<mb; ++ib) {
                size_t mc = (ib!=mb-1 || mr==0) ? DGEMM_MC : mr;

                ge_dcopy(mc, kc, &A[ib*DGEMM_MC*incRowA + lb*DGEMM_KC*incColA],
                         incRowA, incColA,
                         A_, 1, DGEMM_MC);

                dgemm_jli(mc, nc, kc,
                          alpha,
                          A_, 1, DGEMM_MC,
                          B_, 1, DGEMM_KC,
                          &C[ib*DGEMM_MC*incRowC + jb*DGEMM_NC*incColC],
                          incRowC, incColC);
            }
        }
    }

    free(A_);
    free(B_);
}

void
dtrsm(size_t m, size_t n, bool lower, bool unit, double alpha,
      const double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
      double *X, ptrdiff_t incRowX, ptrdiff_t incColX)
{
    if (alpha!=0) {
        for (size_t j=0; j<n; ++j) {
            dtrsv(m, lower, unit, A, incRowA, incColA, &X[j*incColX], incRowX);
        }
    }
    ge_dscal(m, n, alpha, X, incRowX, incColX);
}

//-- LAPACK functions ----------------------------------------------------------

ptrdiff_t
dgetrf_ger(size_t m, size_t n,
           double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
           size_t *p, ptrdiff_t incP)
{
    size_t k = m<n ? m : n;

    for (size_t j=0; j<k; ++j) {
        size_t pj = j + idamax(m-j, &A[j*incRowA + j*incColA], incRowA);

        if (j!=pj) {
            dswap(n, &A[j*incRowA], incColA, &A[pj*incRowA], incColA);
        }
        p[j*incP] = pj;

        double alpha = A[j*incRowA + j*incColA];
        if (alpha==0) {
            return j;
        } else {
            alpha = 1/alpha;
        }

        dscal(m-1-j, alpha, &A[(j+1)*incRowA + j*incColA], incRowA);
        dger(m-1-j, n-1-j, -1,
             &A[(j+1)*incRowA +  j   *incColA], incRowA,
             &A[ j   *incRowA + (j+1)*incColA], incColA,
             &A[(j+1)*incRowA + (j+1)*incColA], incRowA, incColA);
    }

    return -1;
}

ptrdiff_t
dgetrf_gemv(size_t m, size_t n,
            double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
            size_t *p, ptrdiff_t incP)
{
    size_t k = m<n ? m : n;

    for (size_t j=0; j<k; ++j) {
        dtrsv(j, true, true,
              A, incRowA, incColA,
              &A[j*incColA], incRowA);

        dgemv(m-j, j, -1,
              &A[j*incRowA], incRowA, incColA,
              &A[j*incColA], incRowA,
              1,
              &A[j*incRowA+j*incColA], incRowA);

        size_t pj = j + idamax(m-j, &A[j*incRowA + j*incColA], incRowA);

        if (j!=pj) {
            dswap(n, &A[j*incRowA], incColA, &A[pj*incRowA], incColA);
        }
        p[j*incP] = pj;

        double alpha = A[j*incRowA + j*incColA];
        if (alpha==0) {
            return j;
        }

        dscal(m-j-1, 1/alpha, &A[(j+1)*incRowA+j*incColA], incRowA);
    }
    for (size_t j=k; j<n; ++j) {
        dtrsv(m, true, true,
              A, incRowA, incColA,
              &A[j*incColA], incRowA);
    }

    return -1;
}

ptrdiff_t
dgetrf(size_t m, size_t n,
       double *A, ptrdiff_t incRowA, ptrdiff_t incColA,
       size_t *p, ptrdiff_t incP)
{
    return dgetrf_gemv(m, n, A, incRowA, incColA, p, incP);
}

void
dlaswp(size_t n, size_t k0, size_t k1,
       const size_t *p, ptrdiff_t incP,
       double *A, ptrdiff_t incRowA, ptrdiff_t incColA)
{
    ptrdiff_t kInc = k0<k1 ? 1 : -1;

    k1 += kInc;

    for (size_t k=k0; k!=k1; k+=kInc) {
        if (k!=p[k*incP]) {
            dswap(n, &A[k*incRowA], incColA, &A[p[k*incP]], incColA);
        }
    }
}