350 lines
12 KiB
Plaintext
350 lines
12 KiB
Plaintext
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/*=============================================================================
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This file is part of FLINT.
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FLINT 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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FLINT 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 FLINT; 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) 2011, 2012, 2013 Sebastian Pancratz
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******************************************************************************/
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*******************************************************************************
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Module documentation
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We represent a matrix over $\mathbf{Q}_p$ as a product $p^v M$,
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where $p$ is a prime number, $v \in \mathbf{Z}$ and $M$ a matrix
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over $\mathbf{Z}$.
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We say this matrix is in \emph{canonical form} if either $M$ is zero,
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in which case we choose $v = 0$, too, or if $M$ contains at least one
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$p$-adic unit.
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We say this matrix is \emph{reduced} modulo $p^N$ if it is canonical
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form and if all coefficients of $M$ lie in the range $[0, p^{N-v})$.
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*******************************************************************************
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*******************************************************************************
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Macros
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*******************************************************************************
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fmpz_mat_struct * padic_mat(const padic_mat_t A)
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Returns a pointer to the unit part of the matrix, which
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is a matrix over $\mathbf{Z}$.
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The return value can be used as an argument to
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the functions in the \code{fmpz_mat} module.
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fmpz * padic_mat_entry(const padic_mat_t A, slong i, slong j)
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Returns a pointer to unit part of the entry in position $(i, j)$.
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Note that this is not necessarily a unit.
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The return value can be used as an argument to
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the functions in the \code{fmpz} module.
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slong padic_mat_val(const padic_mat_t A)
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Returns the valuation of the matrix.
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This is implemented as a macro and can be used as an \emph{lvalue}
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as well as an \emph{rvalue}.
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slong padic_mat_nrows(const padic_mat_t A)
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Returns the number of rows of the matrix $A$.
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slong padic_mat_ncols(const padic_mat_t A)
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Returns the number of columns of the matrix $A$.
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*******************************************************************************
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Memory management
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*******************************************************************************
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void padic_mat_init(padic_mat_t A, slong r, slong c)
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Initialises the matrix $A$ as a zero matrix with the specified numbers
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of rows and columns and precision \code{PADIC_DEFAULT_PREC}.
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void padic_mat_init2(padic_mat_t A, slong r, slong c, slong prec)
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Initialises the matrix $A$ as a zero matrix with the specified numbers
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of rows and columns and the given precision.
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void padic_mat_clear(padic_mat_t A)
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Clears the matrix $A$.
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void _padic_mat_canonicalise(padic_mat_t A, const padic_ctx_t ctx)
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Ensures that the matrix $A$ is in canonical form.
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void _padic_mat_reduce(padic_mat_t A, const padic_ctx_t ctx)
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Ensures that the matrix $A$ is reduced modulo $p^N$,
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assuming that it is in canonical form already.
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void padic_mat_reduce(padic_mat_t A, const padic_ctx_t ctx)
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Ensures that the matrix $A$ is reduced modulo $p^N$,
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without assuming that it is necessarily in canonical form.
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int padic_mat_is_empty(const padic_mat_t A)
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Returns whether the matrix $A$ is empty, that is,
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whether it has zero rows or zero columns.
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int padic_mat_is_square(const padic_mat_t A)
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Returns whether the matrix $A$ is square.
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int padic_mat_is_canonical(const padic_mat_t A, const fmpz_t p)
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Returns whether the matrix $A$ is in canonical form.
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*******************************************************************************
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Basic assignment
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*******************************************************************************
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void padic_mat_set(padic_mat_t B, const padic_mat_t A)
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Sets $B$ to a copy of $A$, respecting the precision of $B$.
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void padic_mat_swap(padic_mat_t A, padic_mat_t B)
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Swaps the two matrices $A$ and $B$. This is done efficiently by
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swapping pointers.
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void padic_mat_zero(padic_mat_t A)
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Sets the matrix $A$ to zero.
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void padic_mat_one(padic_mat_t A)
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Sets the matrix $A$ to the identity matrix. If the precision
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is negative then the matrix will be the zero matrix.
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*******************************************************************************
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Conversions
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*******************************************************************************
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void padic_mat_set_fmpq_mat(padic_mat_t B,
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const fmpq_mat_t A, const padic_ctx_t ctx)
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Sets the $p$-adic matrix $B$ to the rational matrix $A$, reduced
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according to the given context.
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void padic_mat_get_fmpq_mat(fmpq_mat_t B,
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const padic_mat_t A, const padic_ctx_t ctx)
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Sets the rational matrix $B$ to the $p$-adic matrices $A$;
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no reduction takes place.
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*******************************************************************************
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Entries
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Because of the choice of the data structure, representing the matrix
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as $p^v M$, setting an entry of the matrix might lead to changes in
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all entries in the matrix $M$. Also, a specific entry is not readily
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available as a $p$-adic number. Thus, there are separate functions
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available for getting and setting entries.
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*******************************************************************************
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void padic_mat_get_entry_padic(padic_t rop,
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const padic_mat_t op, slong i, slong j,
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const padic_ctx_t ctx)
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Sets \code{rop} to the entry in position $(i, j)$ in the matrix \code{op}.
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void padic_mat_set_entry_padic(padic_mat_t rop, slong i, slong j,
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const padic_t op, const padic_ctx_t ctx)
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Sets the entry in position $(i, j)$ in the matrix to \code{rop}.
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*******************************************************************************
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Comparison
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*******************************************************************************
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int padic_mat_equal(const padic_mat_t A, const padic_mat_t B)
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Returns whether the two matrices $A$ and $B$ are equal.
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int padic_mat_is_zero(const padic_mat_t A)
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Returns whether the matrix $A$ is zero.
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*******************************************************************************
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Input and output
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*******************************************************************************
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int padic_mat_fprint(FILE * file,
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const padic_mat_t A, const padic_ctx_t ctx)
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Prints a simple representation of the matrix $A$ to the
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output stream \code{file}. The format is the number of rows,
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a space, the number of columns, two spaces, followed by a list
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of all the entries, one row after the other.
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In the current implementation, always returns $1$.
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int padic_mat_fprint_pretty(FILE * file, const padic_mat_t A,
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const padic_ctx_t ctx)
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Prints a \emph{pretty} representation of the matrix $A$
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to the output stream \code{file}.
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In the current implementation, always returns $1$.
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int padic_mat_print(const padic_mat_t A, const padic_ctx_t ctx)
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int padic_mat_print_pretty(const padic_mat_t A, const padic_ctx_t ctx)
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*******************************************************************************
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Random matrix generation
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*******************************************************************************
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void padic_mat_randtest(padic_mat_t A, flint_rand_t state,
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const padic_ctx_t ctx)
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Sets $A$ to a random matrix.
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The valuation will be in the range $[- \ceil{N/10}, N)$,
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$[N - \ceil{-N/10}, N)$, or $[-10, 0)$ as $N$ is positive,
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negative or zero.
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*******************************************************************************
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Transpose
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*******************************************************************************
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void padic_mat_transpose(padic_mat_t B, const padic_mat_t A)
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Sets $B$ to $A^t$.
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*******************************************************************************
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Addition and subtraction
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*******************************************************************************
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void _padic_mat_add(padic_mat_t C, const padic_mat_t A, const padic_mat_t B,
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const padic_ctx_t ctx)
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Sets $C$ to the exact sum $A + B$, ensuring that the result is in
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canonical form.
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void padic_mat_add(padic_mat_t C, const padic_mat_t A, const padic_mat_t B,
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const padic_ctx_t ctx)
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Sets $C$ to the sum $A + B$ modulo $p^N$.
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void _padic_mat_sub(padic_mat_t C, const padic_mat_t A, const padic_mat_t B,
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const padic_ctx_t ctx)
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Sets $C$ to the exact difference $A - B$, ensuring that the result is in
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canonical form.
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void padic_mat_sub(padic_mat_t C, const padic_mat_t A, const padic_mat_t B,
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const padic_ctx_t ctx)
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Sets $C$ to $A - B$, ensuring that the result is reduced.
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void _padic_mat_neg(padic_mat_t B, const padic_mat_t A)
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Sets $B$ to $-A$ in canonical form.
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void padic_mat_neg(padic_mat_t B, const padic_mat_t A, const padic_ctx_t ctx)
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Sets $B$ to $-A$, ensuring the result is reduced.
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*******************************************************************************
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Scalar operations
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*******************************************************************************
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void _padic_mat_scalar_mul_padic(padic_mat_t B,
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const padic_mat_t A, const padic_t c,
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const padic_ctx_t ctx)
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Sets $B$ to $c A$, ensuring that the result is in canonical form.
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void padic_mat_scalar_mul_padic(padic_mat_t B,
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const padic_mat_t A, const padic_t c,
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const padic_ctx_t ctx)
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Sets $B$ to $c A$, ensuring that the result is reduced.
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void _padic_mat_scalar_mul_fmpz(padic_mat_t B,
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const padic_mat_t A, const fmpz_t c,
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const padic_ctx_t ctx)
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Sets $B$ to $c A$, ensuring that the result is in canonical form.
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void padic_mat_scalar_mul_fmpz(padic_mat_t B,
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const padic_mat_t A, const fmpz_t c,
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const padic_ctx_t ctx)
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Sets $B$ to $c A$, ensuring that the result is reduced.
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void padic_mat_scalar_div_fmpz(padic_mat_t B,
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const padic_mat_t A, const fmpz_t c,
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const padic_ctx_t ctx)
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Sets $B$ to $c^{-1} A$, assuming that $c \neq 0$.
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Ensures that the result $B$ is reduced.
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*******************************************************************************
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Multiplication
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*******************************************************************************
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void _padic_mat_mul(padic_mat_t C, const padic_mat_t A, const padic_mat_t B,
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const padic_ctx_t ctx)
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Sets $C$ to the product $A B$ of the two matrices $A$ and $B$,
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ensuring that $C$ is in canonical form.
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void padic_mat_mul(padic_mat_t C, const padic_mat_t A, const padic_mat_t B,
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const padic_ctx_t ctx)
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Sets $C$ to the product $A B$ of the two matrices $A$ and $B$,
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ensuring that $C$ is reduced.
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