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/** \file opennl/superlu/smyblas2.c
* \ingroup opennl
*/
/*
* -- SuperLU routine (version 2.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* November 15, 1997
*
*/
/*
* File name: smyblas2.c
* Purpose:
* Level 2 BLAS operations: solves and matvec, written in C.
* Note:
* This is only used when the system lacks an efficient BLAS library.
*/
/*
* Solves a dense UNIT lower triangular system. The unit lower
* triangular matrix is stored in a 2D array M(1:nrow,1:ncol).
* The solution will be returned in the rhs vector.
*/
/* local prototypes*/
void slsolve ( int, int, float *, float *);
void susolve ( int, int, float *, float *);
void smatvec ( int, int, int, float *, float *, float *);
void slsolve ( int ldm, int ncol, float *M, float *rhs )
{
int k;
float x0, x1, x2, x3, x4, x5, x6, x7;
float *M0;
register float *Mki0, *Mki1, *Mki2, *Mki3, *Mki4, *Mki5, *Mki6, *Mki7;
register int firstcol = 0;
M0 = &M[0];
while ( firstcol < ncol - 7 ) { /* Do 8 columns */
Mki0 = M0 + 1;
Mki1 = Mki0 + ldm + 1;
Mki2 = Mki1 + ldm + 1;
Mki3 = Mki2 + ldm + 1;
Mki4 = Mki3 + ldm + 1;
Mki5 = Mki4 + ldm + 1;
Mki6 = Mki5 + ldm + 1;
Mki7 = Mki6 + ldm + 1;
x0 = rhs[firstcol];
x1 = rhs[firstcol+1] - x0 * *Mki0++;
x2 = rhs[firstcol+2] - x0 * *Mki0++ - x1 * *Mki1++;
x3 = rhs[firstcol+3] - x0 * *Mki0++ - x1 * *Mki1++ - x2 * *Mki2++;
x4 = rhs[firstcol+4] - x0 * *Mki0++ - x1 * *Mki1++ - x2 * *Mki2++
- x3 * *Mki3++;
x5 = rhs[firstcol+5] - x0 * *Mki0++ - x1 * *Mki1++ - x2 * *Mki2++
- x3 * *Mki3++ - x4 * *Mki4++;
x6 = rhs[firstcol+6] - x0 * *Mki0++ - x1 * *Mki1++ - x2 * *Mki2++
- x3 * *Mki3++ - x4 * *Mki4++ - x5 * *Mki5++;
x7 = rhs[firstcol+7] - x0 * *Mki0++ - x1 * *Mki1++ - x2 * *Mki2++
- x3 * *Mki3++ - x4 * *Mki4++ - x5 * *Mki5++
- x6 * *Mki6++;
rhs[++firstcol] = x1;
rhs[++firstcol] = x2;
rhs[++firstcol] = x3;
rhs[++firstcol] = x4;
rhs[++firstcol] = x5;
rhs[++firstcol] = x6;
rhs[++firstcol] = x7;
++firstcol;
for (k = firstcol; k < ncol; k++)
rhs[k] = rhs[k] - x0 * *Mki0++ - x1 * *Mki1++
- x2 * *Mki2++ - x3 * *Mki3++
- x4 * *Mki4++ - x5 * *Mki5++
- x6 * *Mki6++ - x7 * *Mki7++;
M0 += 8 * ldm + 8;
}
while ( firstcol < ncol - 3 ) { /* Do 4 columns */
Mki0 = M0 + 1;
Mki1 = Mki0 + ldm + 1;
Mki2 = Mki1 + ldm + 1;
Mki3 = Mki2 + ldm + 1;
x0 = rhs[firstcol];
x1 = rhs[firstcol+1] - x0 * *Mki0++;
x2 = rhs[firstcol+2] - x0 * *Mki0++ - x1 * *Mki1++;
x3 = rhs[firstcol+3] - x0 * *Mki0++ - x1 * *Mki1++ - x2 * *Mki2++;
rhs[++firstcol] = x1;
rhs[++firstcol] = x2;
rhs[++firstcol] = x3;
++firstcol;
for (k = firstcol; k < ncol; k++)
rhs[k] = rhs[k] - x0 * *Mki0++ - x1 * *Mki1++
- x2 * *Mki2++ - x3 * *Mki3++;
M0 += 4 * ldm + 4;
}
if ( firstcol < ncol - 1 ) { /* Do 2 columns */
Mki0 = M0 + 1;
Mki1 = Mki0 + ldm + 1;
x0 = rhs[firstcol];
x1 = rhs[firstcol+1] - x0 * *Mki0++;
rhs[++firstcol] = x1;
++firstcol;
for (k = firstcol; k < ncol; k++)
rhs[k] = rhs[k] - x0 * *Mki0++ - x1 * *Mki1++;
}
}
/*
* Solves a dense upper triangular system. The upper triangular matrix is
* stored in a 2-dim array M(1:ldm,1:ncol). The solution will be returned
* in the rhs vector.
*/
void
susolve ( ldm, ncol, M, rhs )
int ldm; /* in */
int ncol; /* in */
float *M; /* in */
float *rhs; /* modified */
{
float xj;
int jcol, j, irow;
jcol = ncol - 1;
for (j = 0; j < ncol; j++) {
xj = rhs[jcol] / M[jcol + jcol*ldm]; /* M(jcol, jcol) */
rhs[jcol] = xj;
for (irow = 0; irow < jcol; irow++)
rhs[irow] -= xj * M[irow + jcol*ldm]; /* M(irow, jcol) */
jcol--;
}
}
/*
* Performs a dense matrix-vector multiply: Mxvec = Mxvec + M * vec.
* The input matrix is M(1:nrow,1:ncol); The product is returned in Mxvec[].
*/
void smatvec ( ldm, nrow, ncol, M, vec, Mxvec )
int ldm; /* in -- leading dimension of M */
int nrow; /* in */
int ncol; /* in */
float *M; /* in */
float *vec; /* in */
float *Mxvec; /* in/out */
{
float vi0, vi1, vi2, vi3, vi4, vi5, vi6, vi7;
float *M0;
register float *Mki0, *Mki1, *Mki2, *Mki3, *Mki4, *Mki5, *Mki6, *Mki7;
register int firstcol = 0;
int k;
M0 = &M[0];
while ( firstcol < ncol - 7 ) { /* Do 8 columns */
Mki0 = M0;
Mki1 = Mki0 + ldm;
Mki2 = Mki1 + ldm;
Mki3 = Mki2 + ldm;
Mki4 = Mki3 + ldm;
Mki5 = Mki4 + ldm;
Mki6 = Mki5 + ldm;
Mki7 = Mki6 + ldm;
vi0 = vec[firstcol++];
vi1 = vec[firstcol++];
vi2 = vec[firstcol++];
vi3 = vec[firstcol++];
vi4 = vec[firstcol++];
vi5 = vec[firstcol++];
vi6 = vec[firstcol++];
vi7 = vec[firstcol++];
for (k = 0; k < nrow; k++)
Mxvec[k] += vi0 * *Mki0++ + vi1 * *Mki1++
+ vi2 * *Mki2++ + vi3 * *Mki3++
+ vi4 * *Mki4++ + vi5 * *Mki5++
+ vi6 * *Mki6++ + vi7 * *Mki7++;
M0 += 8 * ldm;
}
while ( firstcol < ncol - 3 ) { /* Do 4 columns */
Mki0 = M0;
Mki1 = Mki0 + ldm;
Mki2 = Mki1 + ldm;
Mki3 = Mki2 + ldm;
vi0 = vec[firstcol++];
vi1 = vec[firstcol++];
vi2 = vec[firstcol++];
vi3 = vec[firstcol++];
for (k = 0; k < nrow; k++)
Mxvec[k] += vi0 * *Mki0++ + vi1 * *Mki1++
+ vi2 * *Mki2++ + vi3 * *Mki3++ ;
M0 += 4 * ldm;
}
while ( firstcol < ncol ) { /* Do 1 column */
Mki0 = M0;
vi0 = vec[firstcol++];
for (k = 0; k < nrow; k++)
Mxvec[k] += vi0 * *Mki0++;
M0 += ldm;
}
}
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