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#include "config.h"
#include "system.h"
#include "coretypes.h"
#include "tm.h"
#include "errors.h"
#include "ggc.h"
#include "tree.h"
#include "target.h"
#include "varray.h"
#include "lambda.h"
/* Allocate a new transformation matrix. */
lambda_trans_matrix
lambda_trans_matrix_new (int colsize, int rowsize)
{
lambda_trans_matrix ret;
ret = xcalloc (1, sizeof (*ret));
LTM_MATRIX (ret) = lambda_matrix_new (rowsize, colsize);
LTM_ROWSIZE (ret) = rowsize;
LTM_COLSIZE (ret) = colsize;
LTM_DENOMINATOR (ret) = 1;
return ret;
}
/* Return true if the transformation matrix is nonsingular. */
bool
lambda_trans_matrix_is_nonsingular (lambda_trans_matrix t)
{
return lambda_trans_matrix_is_fullrank (t);
}
/* Return true if the transformation matrix is full row rank. */
bool
lambda_trans_matrix_is_fullrank (lambda_trans_matrix t)
{
return (lambda_trans_matrix_rank (t) == LTM_ROWSIZE (t));
}
/* Compute the rank of the matrix. */
int
lambda_trans_matrix_rank (lambda_trans_matrix t)
{
lambda_matrix partial;
int rowsize, colsize;
int i, j, nextrow;
lambda_matrix tempmatrix;
lambda_vector row;
int minimum_column, factor;
partial = LTM_MATRIX (t);
rowsize = LTM_ROWSIZE (t);
colsize = LTM_COLSIZE (t);
tempmatrix = lambda_matrix_new (rowsize, colsize);
lambda_matrix_copy (partial, tempmatrix, rowsize, colsize);
j = 0;
while ((j < colsize) && (j < rowsize))
{
/* Considering the submatrix A[j:m, j:n], search for the first
row k >= k such that A[k, j:n] != 0 */
nextrow = lambda_matrix_first_nz_vec (tempmatrix, rowsize, colsize, j);
if (nextrow != j)
return j;
/* Delete rows j .. nextrow - 1 */
lambda_matrix_delete_rows (tempmatrix, rowsize, j, nextrow);
lambda_matrix_delete_rows (partial, rowsize, j, nextrow);
rowsize = rowsize - nextrow + j;
/* Nextrow becomes row j+1 in the matrix, but not necessary row
j + 1 in the array. */
/* Apply elementary column operations to make the diagonal
element non-zero and the others zero. */
row = tempmatrix[j];
/* Make every element of tempmatrix[j, j:colsize] positive. */
for (i = j; i < colsize; i++)
if (row[i] < 0)
lambda_matrix_col_negate (tempmatrix, rowsize, i);
/* Stop only when the diagonal element is non-zero. */
while (lambda_vector_first_nz (row, colsize, j+1) < colsize)
{
minimum_column = lambda_vector_min_nz (row, colsize, j);
lambda_matrix_col_exchange (tempmatrix, rowsize, j, minimum_column);
for (i = j + 1; i < colsize; i++)
{
if (row[i])
{
factor = row[i] / row[j];
/* Add (-1) * factor of column j to column i. */
lambda_matrix_col_add (tempmatrix, rowsize,
j, i, (-1) * factor);
}
}
}
j++;
}
return rowsize;
}
/* Compute the base matrix. */
lambda_trans_matrix
lambda_trans_matrix_base (lambda_trans_matrix mat)
{
int rowsize, colsize;
int i, j, nextrow;
lambda_matrix partial, tempmatrix;
lambda_vector row;
int minimum_column, factor;
lambda_trans_matrix base;
rowsize = LTM_ROWSIZE (mat);
colsize = LTM_COLSIZE (mat);
base = lambda_trans_matrix_new (rowsize, colsize);
partial = LTM_MATRIX (base);
lambda_matrix_copy (LTM_MATRIX (mat), partial, rowsize, colsize);
tempmatrix = lambda_matrix_new (rowsize, colsize);
lambda_matrix_copy (partial, tempmatrix, rowsize, colsize);
j = 0;
while ((j < colsize)
&& (nextrow = lambda_matrix_first_nz_vec (tempmatrix,
rowsize,
colsize, j)) < rowsize)
{
/* Consider the submatrix A[j:m, j:n].
Search for the first row k >= j such that A[k, j:n] != 0. */
/* Delete rows j .. nextrow - 1. */
lambda_matrix_delete_rows (tempmatrix, rowsize, j, nextrow);
lambda_matrix_delete_rows (partial, rowsize, j, nextrow);
/* nextrow becomes row j+1 in the matrix, though not necessarily
row j+1 in the array. */
/* Apply elementary column oeprations to make the diagonal
element nonzero and the others zero. */
row = tempmatrix[j];
/* Make every element of tempmatrix[j, j:colsize] positive. */
for (i = j; i < colsize; i++)
if (row[i] < 0)
lambda_matrix_col_negate (tempmatrix, rowsize, i);
/* Stop when only the diagonal element is nonzero. */
while (lambda_vector_first_nz (row, colsize, j+1) < colsize)
{
minimum_column = lambda_vector_min_nz (row, colsize, j);
lambda_matrix_col_exchange (tempmatrix, rowsize, j, minimum_column);
for (i = j + 1; i < colsize; i++)
{
if (row[i])
{
factor = row[i] / row[j];
/* Add (-1) * factor of column j to column i. */
lambda_matrix_col_add (tempmatrix, rowsize,
j, i, (-1) * factor);
}
}
}
j++;
}
/* Store the rank. */
LTM_ROWSIZE (base) = j;
return base;
}
/* Pad the legal base matrix to an invertable matrix. */
lambda_trans_matrix
lambda_trans_matrix_padding (lambda_trans_matrix matrix)
{
int i, k;
int currrow, minimum_column, factor;
lambda_matrix tempmatrix, padmatrix;
lambda_vector row;
lambda_trans_matrix padded;
lambda_matrix partial;
int rowsize, colsize;
rowsize = LTM_ROWSIZE (matrix);
colsize = LTM_COLSIZE (matrix);
padded = lambda_trans_matrix_new (rowsize, colsize);
partial = LTM_MATRIX (padded);
lambda_matrix_copy(LTM_MATRIX (matrix), partial, rowsize, colsize);
/* full rank, no need for padding */
if (rowsize==colsize)
return(padded);
tempmatrix = lambda_matrix_new (rowsize, colsize);
lambda_matrix_copy (partial, tempmatrix, rowsize, colsize);
padmatrix = lambda_matrix_new (colsize, colsize);
lambda_matrix_id (padmatrix, colsize);
for(currrow = 0; currrow < rowsize; currrow++)
{
/* consider the submatrix A[i:m, i:n]. */
/* apply elementary column operations to make the diag element nonzero
and others zero. */
/* only consider columns from currrow to colsize. */
row = tempmatrix[currrow];
/* make every element of tempmatrix[currrow, currrow:colsize]
positive. */
for(i = currrow; i < colsize; i++)
if(row[i] < 0)
lambda_matrix_col_negate (tempmatrix, rowsize, i);
/* stop when only the diagonal element is nonzero */
while (lambda_vector_first_nz (row, colsize, currrow + 1) < colsize)
{
minimum_column = lambda_vector_min_nz (row, colsize, currrow);
lambda_matrix_col_exchange (tempmatrix, rowsize, currrow,
minimum_column);
lambda_matrix_row_exchange (padmatrix, currrow, minimum_column);
for (i = currrow + 1; i < colsize; i++)
{
if(row[i])
{
factor = row[i] / row[currrow];
lambda_matrix_col_add (tempmatrix, rowsize,
currrow, i, (-1) * factor);
}
}
}
}
for(k = rowsize; k < colsize; k++)
partial[k] = padmatrix[k];
return(padded);
}
/* Compute the inverse of the transformation. */
lambda_trans_matrix
lambda_trans_matrix_inverse (lambda_trans_matrix mat)
{
lambda_trans_matrix inverse;
int determinant;
inverse = lambda_trans_matrix_new (LTM_ROWSIZE (mat), LTM_COLSIZE (mat));
determinant = lambda_matrix_inverse (LTM_MATRIX (mat), LTM_MATRIX (inverse),
LTM_ROWSIZE (mat));
LTM_DENOMINATOR (inverse) = determinant;
return inverse;
}
/* Print out a transformation matrix. */
void
print_lambda_trans_matrix (FILE *outfile, lambda_trans_matrix mat)
{
print_lambda_matrix (outfile, LTM_MATRIX (mat), LTM_ROWSIZE (mat),
LTM_COLSIZE (mat));
}
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