mzd_t *mzd_kernel_left_pluq(mzd_t *A, int const cutoff) {
mzp_t *P = mzp_init(A->nrows);
mzp_t *Q = mzp_init(A->ncols);
rci_t r = mzd_pluq(A, P, Q, cutoff);
if (r == A->ncols) {
mzp_free(P);
mzp_free(Q);
__M4RI_DD_MZD(A);
return NULL;
}
mzd_t *U = mzd_init_window(A, 0, 0, r, r);
mzd_t *B = mzd_init_window(A, 0, r, r, A->ncols);
mzd_trsm_upper_left(U, B, cutoff);
mzd_t *R = mzd_init(A->ncols, A->ncols - r);
mzd_t *RU = mzd_init_window(R, 0, 0, r, R->ncols);
mzd_copy(RU, B);
for(rci_t i = 0; i < R->ncols; ++i) {
mzd_write_bit(R, r + i, i, 1);
}
mzd_apply_p_left_trans(R, Q);
mzp_free(P);
mzp_free(Q);
mzd_free_window(RU);
mzd_free_window(U);
mzd_free_window(B);
__M4RI_DD_MZD(A);
__M4RI_DD_MZD(R);
return R;
}
int test_pluq_solve_left(rci_t m, rci_t n, int offsetA, int offsetB) {
mzd_t* Abase = mzd_init(2048, 2048);
mzd_t* Bbase = mzd_init(2048, 2048);
mzd_randomize(Abase);
mzd_randomize(Bbase);
mzd_t* A = mzd_init_window(Abase, 0, offsetA, m, m + offsetA);
mzd_t* B = mzd_init_window(Bbase, 0, offsetB, m, n + offsetB);
// copy B
mzd_t* Bcopy = mzd_init(B->nrows, B->ncols);
for (rci_t i = 0; i < B->nrows; ++i)
for (rci_t j = 0; j < B->ncols; ++j)
mzd_write_bit(Bcopy,i,j, mzd_read_bit (B,i,j));
for (rci_t i = 0; i < m; ++i) {
mzd_write_bit(A,i,i, 1);
}
mzd_t *Acopy = mzd_copy(NULL, A);
rci_t r = mzd_echelonize(Acopy,1);
printf("solve_left m: %4d, n: %4d, r: %4d da: %4d db: %4d ", m, n, r, offsetA, offsetB);
mzd_free(Acopy);
Acopy = mzd_copy(NULL, A);
int consistency = mzd_solve_left(A, B, 0, 1);
//copy B
mzd_t *X = mzd_init(B->nrows,B->ncols);
for (rci_t i = 0; i < B->nrows; ++i)
for (rci_t j = 0; j < B->ncols; ++j)
mzd_write_bit(X,i,j, mzd_read_bit (B,i,j));
mzd_t *B1 = mzd_mul(NULL, Acopy, X, 0);
mzd_t *Z = mzd_add(NULL, Bcopy, B1);
int status = 0;
if(consistency == 0) {
status = 1 - mzd_is_zero(Z);
if (status == 0) {
printf("passed\n");
} else {
printf("FAILED\n");
}
} else {
printf("skipped (no solution)\n");
}
mzd_free(Bcopy);
mzd_free(B1);
mzd_free(Z);
mzd_free_window(A);
mzd_free_window(B);
mzd_free(Acopy);
mzd_free(Abase);
mzd_free(Bbase);
mzd_free(X);
return status;
}
int test_trsm_upper_right (int m, int n, int offset, const char* description){
printf("upper_right: %s m: %4d n: %4d offset: %4d ... ",description, m, n, offset);
mzd_t* Ubase = mzd_init (2048,2048);
mzd_t* Bbase = mzd_init (2048,2048);
mzd_randomize (Ubase);
mzd_randomize (Bbase);
mzd_t* Bbasecopy = mzd_copy (NULL, Bbase);
mzd_t* U = mzd_init_window (Ubase, 0, offset, n, offset + n);
mzd_t* B = mzd_init_window (Bbase, 0, offset, m, offset + n);
mzd_t* W = mzd_copy (NULL, B);
size_t i,j;
for (i=0; i<n; ++i){
for (j=0; j<i;++j)
mzd_write_bit(U,i,j, 0);
mzd_write_bit(U,i,i, 1);
}
mzd_trsm_upper_right (U, B, 2048);
mzd_addmul(W, B, U, 2048);
int status = 0;
for ( i=0; i<m; ++i)
for ( j=0; j<n; ++j){
if (mzd_read_bit (W,i,j)){
status = 1;
}
}
// Verifiying that nothing has been changed around the submatrices
mzd_addmul(W, B, U, 2048);
mzd_copy (B, W);
for ( i=0; i<2048; ++i)
for ( j=0; j<2048/RADIX; ++j){
if (Bbase->rows[i][j] != Bbasecopy->rows[i][j]){
status = 1;
}
}
mzd_free_window (U);
mzd_free_window (B);
mzd_free (W);
mzd_free(Ubase);
mzd_free(Bbase);
mzd_free(Bbasecopy);
if (!status)
printf("passed\n");
else
printf("FAILED\n");
return status;
}
int test_trsm_lower_left (int m, int n, int offsetL, int offsetB){
mzd_t* Lbase = mzd_init (2048,2048);
mzd_t* Bbase = mzd_init (2048,2048);
mzd_randomize (Lbase);
mzd_randomize (Bbase);
mzd_t* Bbasecopy = mzd_copy (NULL, Bbase);
mzd_t* L = mzd_init_window (Lbase, 0, offsetL, m, offsetL + m);
mzd_t* B = mzd_init_window (Bbase, 0, offsetB, m, offsetB + n);
mzd_t* W = mzd_copy (NULL, B);
size_t i,j;
for (i=0; i<m; ++i){
for (j=i+1; j<m;++j)
mzd_write_bit(L,i,j, 0);
mzd_write_bit(L,i,i, 1);
}
mzd_trsm_lower_left(L, B, 2048);
mzd_addmul(W, L, B, 2048);
int status = 0;
for ( i=0; i<m; ++i)
for ( j=0; j<n; ++j){
if (mzd_read_bit (W,i,j)){
status = 1;
}
}
// Verifiying that nothing has been changed around the submatrices
mzd_addmul(W, L, B, 2048);
mzd_copy (B, W);
for ( i=0; i<2048; ++i)
for ( j=0; j<2048/RADIX; ++j){
if (Bbase->rows[i][j] != Bbasecopy->rows[i][j]){
status = 1;
}
}
mzd_free_window (L);
mzd_free_window (B);
mzd_free_window (W);
mzd_free(Lbase);
mzd_free(Bbase);
mzd_free(Bbasecopy);
if (!status)
printf(" ... passed\n");
else
printf(" ... FAILED\n");
return status;
}
int _mzd_pluq_solve_left(mzd_t const *A, rci_t rank,
mzp_t const *P, mzp_t const *Q,
mzd_t *B, int const cutoff, int const inconsistency_check) {
/** A is supposed to store L lower triangular and U upper triangular
* B is modified in place
* (Bi's in the comments are just modified versions of B)
* PLUQ = A
* 1) P B2 = B1
* 2) L B3 = B2
* 3) U B4 = B3
* 4) Q B5 = B4
*/
int retval = 0;
/* P B2 = B1 or B2 = P^T B1 */
mzd_apply_p_left(B, P);
/* L B3 = B2 */
/* view on the upper part of L */
mzd_t const *LU = mzd_init_window_const(A, 0, 0, rank, rank);
mzd_t *Y1 = mzd_init_window(B, 0, 0, rank, B->ncols);
mzd_trsm_lower_left(LU, Y1, cutoff);
if (inconsistency_check) { /* Check for inconsistency */
/** FASTER without this check; update with the lower part of L
*/
mzd_t const *H = mzd_init_window_const(A, rank, 0, A->nrows, rank);
mzd_t *Y2 = mzd_init_window(B, rank, 0, A->nrows, B->ncols);
if(A->nrows < B->nrows) {
mzd_t *Y3 = mzd_init_window(B, A->nrows, 0, B->nrows, B->ncols);
mzd_set_ui(Y3, 0);
mzd_free_window(Y3);
}
mzd_addmul(Y2, H, Y1, cutoff);
/*
* test whether Y2 is the zero matrix
*/
if(!mzd_is_zero(Y2)) {
retval = -1;
}
mzd_free_window((mzd_t*)H);
mzd_free_window(Y2);
}
/* U B4 = B3 */
mzd_trsm_upper_left(LU, Y1, cutoff);
mzd_free_window((mzd_t*)LU);
mzd_free_window(Y1);
if (!inconsistency_check) {
/** Default is to set the undefined bits to zero if inconsistency
* has been checked then Y2 bits are already all zeroes thus this
* clearing is not needed
*/
for(rci_t i = rank; i < B->nrows; ++i) {
for(rci_t j = 0; j < B->ncols; j += m4ri_radix) {
mzd_clear_bits(B, i, j, MIN(m4ri_radix, B->ncols - j));
}
}
}
/* Q B5 = B4 or B5 = Q^T B4 */
mzd_apply_p_left_trans(B, Q);
/* P L U Q B5 = B1 */
__M4RI_DD_MZD(B);
__M4RI_DD_INT(retval);
return retval;
}
