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https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
add LU decomposition
This commit is contained in:
Fredrik Johansson
parent
e6ed5d2f08
commit
4d6082e935
5 changed files with 342 additions and 5 deletions
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@ -135,6 +135,32 @@ void fmprb_mat_mul(fmprb_mat_t res, const fmprb_mat_t mat1,
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const fmprb_mat_t mat2, long prec)
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Sets res to the matrix product of mat1 and mat2. The operands must have
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compatible dimensions for matrix multiplication. Aliasing of input
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and output is currently not supported.
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compatible dimensions for matrix multiplication.
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*******************************************************************************
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LU decomposition
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*******************************************************************************
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int fmprb_mat_lu(long * P, fmprb_mat_t LU, const fmprb_mat_t A, long prec)
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Given an $n \times n$ matrix $A$, computes an LU decomposition $PLU = A$
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using Gaussian elimination with partial pivoting.
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The input and output matrices can be the same, performing the
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decomposition in-place.
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Entry $i$ in the permutation vector is set to the row index in
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the input matrix corresponding to row $i$ in the output matrix.
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The algorithm succeeds and returns nonzero if it can find $n$ invertible
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(i.e. not containing zero) pivot entries. This guarantees that the matrix
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is invertible.
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The algorithm fails and returns zero, leaving the values in $P$ and $LU$
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undefined, if it cannot find $n$ invertible pivot elements.
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In this case, either the matrix is singular, the input matrix was
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computed to insufficient precision, or the LU decomposition was
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attempted at insufficient precision.
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9
fmprb.h
9
fmprb.h
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@ -286,9 +286,12 @@ fmprb_print(const fmprb_t x)
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static __inline__ void
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fmprb_printd(const fmprb_t x, long digits)
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{
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fmpr_printd(fmprb_midref(x), digits);
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printf(" +/- ");
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fmpr_printd(fmprb_radref(x), 5);
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fmpr_printd(fmprb_midref(x), FLINT_ABS(digits));
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if (digits > 0)
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{
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printf(" +/- ");
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fmpr_printd(fmprb_radref(x), 5);
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}
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}
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static __inline__ void
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12
fmprb_mat.h
12
fmprb_mat.h
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@ -52,6 +52,14 @@ void fmprb_mat_init(fmprb_mat_t mat, long r, long c);
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void fmprb_mat_clear(fmprb_mat_t mat);
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static __inline__ void
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fmprb_mat_swap(fmprb_mat_t mat1, fmprb_mat_t mat2)
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{
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fmprb_mat_struct t = *mat1;
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*mat1 = *mat2;
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*mat2 = t;
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}
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/* Conversions */
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void fmprb_mat_set(fmprb_mat_t dest, const fmprb_mat_t src);
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@ -86,5 +94,9 @@ void fmprb_mat_sub(fmprb_mat_t res, const fmprb_mat_t mat1, const fmprb_mat_t ma
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void fmprb_mat_mul(fmprb_mat_t res, const fmprb_mat_t mat1, const fmprb_mat_t mat2, long prec);
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/* LU decomposition */
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int fmprb_mat_lu(long * P, fmprb_mat_t LU, const fmprb_mat_t A, long prec);
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#endif
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136
fmprb_mat/lu.c
Normal file
136
fmprb_mat/lu.c
Normal file
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@ -0,0 +1,136 @@
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/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Fredrik Johansson
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******************************************************************************/
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#include "fmprb_mat.h"
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static __inline__ void
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fmprb_mat_swap_rows(fmprb_mat_t mat, long * perm, long r, long s)
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{
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if (r != s)
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{
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fmprb_struct * u;
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long t;
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if (perm != NULL)
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{
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t = perm[s];
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perm[s] = perm[r];
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perm[r] = t;
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}
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u = mat->rows[s];
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mat->rows[s] = mat->rows[r];
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mat->rows[r] = u;
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}
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}
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static __inline__ long
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fmprb_mat_find_pivot_partial(const fmprb_mat_t mat,
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long start_row, long end_row, long c)
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{
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long best_row, i;
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best_row = -1;
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for (i = start_row; i < end_row; i++)
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{
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if (!fmprb_contains_zero(fmprb_mat_entry(mat, i, c)))
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{
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if (best_row == -1)
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{
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best_row = i;
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}
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/* todo: should take the radius into account */
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else if (fmpr_cmpabs(fmprb_midref(fmprb_mat_entry(mat, i, c)),
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fmprb_midref(fmprb_mat_entry(mat, best_row, c))) > 0)
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{
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best_row = i;
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}
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}
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}
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return best_row;
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}
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int
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fmprb_mat_lu(long * P, fmprb_mat_t LU, const fmprb_mat_t A, long prec)
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{
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fmprb_t d, e;
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fmprb_struct ** a;
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long i, j, m, n, r, length, row, col;
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int result;
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m = fmprb_mat_nrows(A);
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n = fmprb_mat_ncols(A);
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result = 1;
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if (m == 0 || n == 0)
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return result;
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fmprb_mat_set(LU, A);
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a = LU->rows;
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row = col = 0;
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for (i = 0; i < m; i++)
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P[i] = i;
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fmprb_init(d);
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fmprb_init(e);
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while (row < m && col < n)
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{
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r = fmprb_mat_find_pivot_partial(LU, row, m, col);
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if (r == -1)
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{
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result = 0;
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break;
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}
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else if (r != row)
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fmprb_mat_swap_rows(LU, P, row, r);
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fmprb_set(d, a[row] + col);
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for (j = row + 1; j < m; j++)
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{
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fmprb_div(e, a[j] + col, d, prec);
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fmprb_neg(e, e);
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_fmprb_vec_scalar_addmul(a[j] + col,
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a[row] + col, n - col, e, prec);
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fmprb_zero(a[j] + col);
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fmprb_neg(a[j] + row, e);
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}
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row++;
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col++;
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}
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fmprb_clear(d);
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fmprb_clear(e);
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return result;
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}
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160
fmprb_mat/test/t-lu.c
Normal file
160
fmprb_mat/test/t-lu.c
Normal file
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@ -0,0 +1,160 @@
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/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Fredrik Johansson
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******************************************************************************/
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#include "fmprb_mat.h"
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#include "perm.h"
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int fmpq_mat_is_invertible(const fmpq_mat_t A)
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{
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int r;
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fmpq_t t;
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fmpq_init(t);
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fmpq_mat_det(t, A);
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r = !fmpq_is_zero(t);
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fmpq_clear(t);
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return r;
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}
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int main()
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{
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long iter;
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flint_rand_t state;
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printf("lu....");
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fflush(stdout);
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flint_randinit(state);
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for (iter = 0; iter < 100000; iter++)
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{
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fmpq_mat_t Q;
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fmprb_mat_t A, LU, P, L, U, T;
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long i, j, n, qbits, prec, *perm;
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int result, q_invertible, r_invertible;
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n = n_randint(state, 8);
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qbits = 1 + n_randint(state, 100);
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prec = 2 + n_randint(state, 202);
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fmpq_mat_init(Q, n, n);
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fmprb_mat_init(A, n, n);
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fmprb_mat_init(LU, n, n);
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fmprb_mat_init(P, n, n);
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fmprb_mat_init(L, n, n);
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fmprb_mat_init(U, n, n);
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fmprb_mat_init(T, n, n);
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perm = _perm_init(n);
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fmpq_mat_randtest(Q, state, qbits);
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q_invertible = fmpq_mat_is_invertible(Q);
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result = 1;
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if (!q_invertible)
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{
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fmprb_mat_set_fmpq_mat(A, Q, prec);
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r_invertible = fmprb_mat_lu(perm, LU, A, prec);
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if (r_invertible)
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{
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printf("FAIL: matrix is singular over Q but not over R\n");
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printf("n = %ld, prec = %ld\n", n, prec);
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printf("\n");
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printf("Q = \n"); fmpq_mat_print(Q); printf("\n\n");
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printf("A = \n"); fmprb_mat_printd(A, 15); printf("\n\n");
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printf("LU = \n"); fmprb_mat_printd(LU, 15); printf("\n\n");
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}
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}
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else
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{
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/* now this must converge */
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while (1)
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{
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fmprb_mat_set_fmpq_mat(A, Q, prec);
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r_invertible = fmprb_mat_lu(perm, LU, A, prec);
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if (r_invertible)
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{
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break;
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}
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else
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{
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if (prec > 10000)
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{
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printf("FAIL: failed to converge at 10000 bits\n");
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abort();
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}
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prec *= 2;
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}
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}
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fmprb_mat_one(L);
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for (i = 0; i < n; i++)
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for (j = 0; j < i; j++)
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fmprb_set(fmprb_mat_entry(L, i, j),
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fmprb_mat_entry(LU, i, j));
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for (i = 0; i < n; i++)
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for (j = i; j < n; j++)
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fmprb_set(fmprb_mat_entry(U, i, j),
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fmprb_mat_entry(LU, i, j));
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for (i = 0; i < n; i++)
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fmprb_one(fmprb_mat_entry(P, perm[i], i));
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fmprb_mat_mul(T, P, L, prec);
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fmprb_mat_mul(T, T, U, prec);
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if (!fmprb_mat_contains_fmpq_mat(T, Q))
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{
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printf("FAIL (containment, iter = %ld)\n", iter);
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printf("n = %ld, prec = %ld\n", n, prec);
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printf("\n");
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printf("Q = \n"); fmpq_mat_print(Q); printf("\n\n");
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printf("A = \n"); fmprb_mat_printd(A, 15); printf("\n\n");
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printf("LU = \n"); fmprb_mat_printd(LU, 15); printf("\n\n");
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printf("L = \n"); fmprb_mat_printd(L, 15); printf("\n\n");
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printf("U = \n"); fmprb_mat_printd(U, 15); printf("\n\n");
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printf("P*L*U = \n"); fmprb_mat_printd(T, 15); printf("\n\n");
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abort();
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}
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}
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fmpq_mat_clear(Q);
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fmprb_mat_clear(A);
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fmprb_mat_clear(LU);
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fmprb_mat_clear(P);
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fmprb_mat_clear(L);
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fmprb_mat_clear(U);
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fmprb_mat_clear(T);
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_perm_clear(perm);
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}
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flint_randclear(state);
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_fmpz_cleanup();
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printf("PASS\n");
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return EXIT_SUCCESS;
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}
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