mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
137 lines
3.4 KiB
C
137 lines
3.4 KiB
C
/*
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Copyright (C) 2018 Fredrik Johansson
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "arb_mat.h"
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static void
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arb_approx_set(arb_t z, const arb_t x)
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{
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arf_set(arb_midref(z), arb_midref(x));
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}
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static void
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arb_approx_sub(arb_t z, const arb_t x, const arb_t y, slong prec)
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{
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arf_sub(arb_midref(z),
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arb_midref(x), arb_midref(y), prec, ARF_RND_DOWN);
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}
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static void
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arb_approx_addmul(arb_t z, const arb_t x, const arb_t y, slong prec)
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{
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arf_addmul(arb_midref(z),
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arb_midref(x), arb_midref(y), prec, ARF_RND_DOWN);
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}
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static void
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arb_approx_div(arb_t z, const arb_t x, const arb_t y, slong prec)
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{
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arf_div(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARB_RND);
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}
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void
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arb_mat_approx_solve_triu_classical(arb_mat_t X, const arb_mat_t U,
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const arb_mat_t B, int unit, slong prec)
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{
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slong i, j, k, n, m;
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arb_ptr tmp;
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arb_t s;
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n = U->r;
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m = B->c;
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tmp = _arb_vec_init(n);
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arb_init(s);
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for (i = 0; i < m; i++)
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{
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for (j = 0; j < n; j++)
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arb_approx_set(tmp + j, arb_mat_entry(X, j, i));
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for (j = n - 1; j >= 0; j--)
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{
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arb_zero(s);
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for (k = 0; k < n - j - 1; k++)
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arb_approx_addmul(s, U->rows[j] + j + 1 + k, tmp + j + 1 + k, prec);
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arb_approx_sub(s, arb_mat_entry(B, j, i), s, prec);
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if (!unit)
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arb_approx_div(s, s, arb_mat_entry(U, j, j), prec);
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arb_approx_set(tmp + j, s);
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}
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for (j = 0; j < n; j++)
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arb_approx_set(arb_mat_entry(X, j, i), tmp + j);
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}
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_arb_vec_clear(tmp, n);
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arb_clear(s);
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}
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void
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arb_mat_approx_solve_triu_recursive(arb_mat_t X,
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const arb_mat_t U, const arb_mat_t B, int unit, slong prec)
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{
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arb_mat_t UA, UB, UD, XX, XY, BX, BY, T;
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slong r, n, m;
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n = U->r;
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m = B->c;
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r = n / 2;
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if (n == 0 || m == 0)
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return;
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/*
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Denoting inv(M) by M^, we have:
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[A B]^ [X] == [A^ (X - B D^ Y)]
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[0 D] [Y] == [ D^ Y ]
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*/
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arb_mat_window_init(UA, U, 0, 0, r, r);
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arb_mat_window_init(UB, U, 0, r, r, n);
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arb_mat_window_init(UD, U, r, r, n, n);
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arb_mat_window_init(BX, B, 0, 0, r, m);
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arb_mat_window_init(BY, B, r, 0, n, m);
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arb_mat_window_init(XX, X, 0, 0, r, m);
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arb_mat_window_init(XY, X, r, 0, n, m);
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arb_mat_approx_solve_triu(XY, UD, BY, unit, prec);
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arb_mat_init(T, UB->r, XY->c);
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arb_mat_mul(T, UB, XY, prec);
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arb_mat_get_mid(T, T);
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arb_mat_sub(XX, BX, T, prec);
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arb_mat_get_mid(XX, XX);
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arb_mat_clear(T);
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arb_mat_approx_solve_triu(XX, UA, XX, unit, prec);
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arb_mat_window_clear(UA);
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arb_mat_window_clear(UB);
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arb_mat_window_clear(UD);
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arb_mat_window_clear(BX);
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arb_mat_window_clear(BY);
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arb_mat_window_clear(XX);
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arb_mat_window_clear(XY);
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}
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void
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arb_mat_approx_solve_triu(arb_mat_t X, const arb_mat_t U,
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const arb_mat_t B, int unit, slong prec)
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{
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if (B->r < 8 || B->c < 8)
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arb_mat_approx_solve_triu_classical(X, U, B, unit, prec);
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else
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arb_mat_approx_solve_triu_recursive(X, U, B, unit, prec);
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}
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