/*! @file dmyblas2.c

 * \brief Level 2 Blas operations

 * 

 * 

 * -- SuperLU routine (version 2.0) --

 * Univ. of California Berkeley, Xerox Palo Alto Research Center,

 * and Lawrence Berkeley National Lab.

 * November 15, 1997

 * 

 * Purpose:

 *     Level 2 BLAS operations: solves and matvec, written in C.

 * Note:

 *     This is only used when the system lacks an efficient BLAS library.

 * 

 */

/*

 * File name:		dmyblas2.c

 */

/*! \brief 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.

 */

void dlsolve ( int ldm, int ncol, double *M, double *rhs )

{

    int k;

    double x0, x1, x2, x3, x4, x5, x6, x7;

    double *M0;

    register double *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++;

    }

}

/*! \brief 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

dusolve ( ldm, ncol, M, rhs )

int ldm;	/* in */

int ncol;	/* in */

double *M;	/* in */

double *rhs;	/* modified */

{

    double 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--;

    }

}

/*! \brief 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 dmatvec ( ldm, nrow, ncol, M, vec, Mxvec )

int ldm;	/* in -- leading dimension of M */

int nrow;	/* in */ 

int ncol;	/* in */

double *M;	/* in */

double *vec;	/* in */

double *Mxvec;	/* in/out */

{

    double vi0, vi1, vi2, vi3, vi4, vi5, vi6, vi7;

    double *M0;

    register double *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;

    }

}