.. _gr-vec: **gr_vec.h** -- vectors over generic rings =============================================================================== Types and basic operations -------------------------------------------------------------------------------- .. type:: gr_vec_struct .. type:: gr_vec_t .. function:: void gr_vec_init(gr_vec_t vec, slong len, gr_ctx_t ctx) Initializes *vec* to a vector of length *len* with elements in the ring *ctx*. The length must be nonnegative. All entries are set to zero. .. function:: void gr_vec_clear(gr_vec_t vec, gr_ctx_t ctx) Clears the vector *vec*. .. macro:: GR_VEC_ENTRY(vec, i, sz) Macro to access the *i*-th element in the vector *vec*, indexed from zero, assuming that entries have size ``sz``. The index must be in bounds. .. function:: gr_ptr gr_vec_entry_ptr(gr_vec_t vec, slong i, gr_ctx_t ctx) Returns a pointer to the *i*-th element in the vector *vec*, indexed from zero. The index must be in bounds. .. function:: slong gr_vec_length(const gr_vec_t vec, gr_ctx_t ctx) Returns the length of the vector *vec*. .. function:: void gr_vec_fit_length(gr_vec_t vec, slong len, gr_ctx_t ctx) Allocates space for at least *len* elements in the vector *vec*. This does not change the size of the vector. .. function:: void gr_vec_set_length(gr_vec_t vec, slong len, gr_ctx_t ctx) Resizes the vector to length *len*, which must be nonnegative. The vector will be extended with zeros. .. function:: int gr_vec_set(gr_vec_t res, const gr_vec_t src, gr_ctx_t ctx) Sets *res* to a copy of the vector *src*. .. function:: int gr_vec_append(gr_vec_t vec, gr_srcptr x, gr_ctx_t ctx) Appends the element *x* to the end of vector *vec*. .. function:: int _gr_vec_write(gr_stream_t out, gr_srcptr vec, slong len, gr_ctx_t ctx) int gr_vec_write(gr_stream_t out, const gr_vec_t vec, gr_ctx_t ctx) int gr_vec_print(const gr_vec_t vec, gr_ctx_t ctx) .. macro:: GR_ENTRY(vec, i, size) Macro to access the *i*-th entry of a ``gr_ptr`` or ``gr_srcptr`` vector *vec*, where each element is ``size`` bytes. .. function:: void _gr_vec_init(gr_ptr vec, slong len, gr_ctx_t ctx) Initialize *len* elements of *vec* to the value 0. The pointer *vec* must already refer to allocated memory. .. function:: void _gr_vec_clear(gr_ptr vec, slong len, gr_ctx_t ctx) Clears *len* elements of *vec*. This frees memory allocated by individual elements, but does not free the memory allocated by *vec* itself. .. function:: void _gr_vec_swap(gr_ptr vec1, gr_ptr vec2, slong len, gr_ctx_t ctx) Swap the entries of *vec1* and *vec2*. .. function:: int _gr_vec_randtest(gr_ptr res, flint_rand_t state, slong len, gr_ctx_t ctx) .. function:: int _gr_vec_set(gr_ptr res, gr_srcptr src, slong len, gr_ctx_t ctx) .. function:: truth_t _gr_vec_equal(gr_srcptr vec1, gr_srcptr vec2, slong len, gr_ctx_t ctx) .. function:: int _gr_vec_zero(gr_ptr vec, slong len, gr_ctx_t ctx) .. function:: truth_t _gr_vec_is_zero(gr_srcptr vec, slong len, gr_ctx_t ctx) .. function:: int _gr_vec_normalise(slong * res, gr_srcptr vec, slong len, gr_ctx_t ctx) .. function:: slong _gr_vec_normalise_weak(gr_srcptr vec, slong len, gr_ctx_t ctx) Arithmetic -------------------------------------------------------------------------------- .. function:: int _gr_vec_neg(gr_ptr res, gr_srcptr src, slong len, gr_ctx_t ctx) .. function:: int _gr_vec_add(gr_ptr res, gr_srcptr src1, gr_srcptr src2, slong len, gr_ctx_t ctx) int _gr_vec_sub(gr_ptr res, gr_srcptr src1, gr_srcptr src2, slong len, gr_ctx_t ctx) int _gr_vec_mul(gr_ptr res, gr_srcptr src1, gr_srcptr src2, slong len, gr_ctx_t ctx) int _gr_vec_div(gr_ptr res, gr_srcptr src1, gr_srcptr src2, slong len, gr_ctx_t ctx) int _gr_vec_divexact(gr_ptr res, gr_srcptr src1, gr_srcptr src2, slong len, gr_ctx_t ctx) int _gr_vec_pow(gr_ptr res, gr_srcptr src1, gr_srcptr src2, slong len, gr_ctx_t ctx) Binary operations applied elementwise. .. function:: int _gr_vec_add_scalar(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t ctx) int _gr_vec_sub_scalar(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t ctx) int _gr_vec_mul_scalar(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t ctx) int _gr_vec_div_scalar(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t ctx) int _gr_vec_divexact_scalar(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t ctx) int _gr_vec_pow_scalar(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t ctx) int _gr_scalar_add_vec(gr_ptr vec1, gr_srcptr c, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_sub_vec(gr_ptr vec1, gr_srcptr c, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_mul_vec(gr_ptr vec1, gr_srcptr c, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_div_vec(gr_ptr vec1, gr_srcptr c, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_divexact_vec(gr_ptr vec1, gr_srcptr c, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_pow_vec(gr_ptr vec1, gr_srcptr c, gr_srcptr vec2, slong len, gr_ctx_t ctx) Binary operations applied elementwise with a fixed scalar operand. .. function:: int _gr_vec_add_other(gr_ptr vec1, gr_srcptr vec2, gr_srcptr vec3, gr_ctx_t ctx3, slong len, gr_ctx_t ctx) int _gr_vec_sub_other(gr_ptr vec1, gr_srcptr vec2, gr_srcptr vec3, gr_ctx_t ctx3, slong len, gr_ctx_t ctx) int _gr_vec_mul_other(gr_ptr vec1, gr_srcptr vec2, gr_srcptr vec3, gr_ctx_t ctx3, slong len, gr_ctx_t ctx) int _gr_vec_div_other(gr_ptr vec1, gr_srcptr vec2, gr_srcptr vec3, gr_ctx_t ctx3, slong len, gr_ctx_t ctx) int _gr_vec_divexact_other(gr_ptr vec1, gr_srcptr vec2, gr_srcptr vec3, gr_ctx_t ctx3, slong len, gr_ctx_t ctx) int _gr_vec_pow_other(gr_ptr vec1, gr_srcptr vec2, gr_srcptr vec3, gr_ctx_t ctx3, slong len, gr_ctx_t ctx) int _gr_other_add_vec(gr_ptr vec1, gr_srcptr vec2, gr_ctx_t ctx2, gr_srcptr vec3, slong len, gr_ctx_t ctx) int _gr_other_sub_vec(gr_ptr vec1, gr_srcptr vec2, gr_ctx_t ctx2, gr_srcptr vec3, slong len, gr_ctx_t ctx) int _gr_other_mul_vec(gr_ptr vec1, gr_srcptr vec2, gr_ctx_t ctx2, gr_srcptr vec3, slong len, gr_ctx_t ctx) int _gr_other_div_vec(gr_ptr vec1, gr_srcptr vec2, gr_ctx_t ctx2, gr_srcptr vec3, slong len, gr_ctx_t ctx) int _gr_other_divexact_vec(gr_ptr vec1, gr_srcptr vec2, gr_ctx_t ctx2, gr_srcptr vec3, slong len, gr_ctx_t ctx) int _gr_other_pow_vec(gr_ptr vec1, gr_srcptr vec2, gr_ctx_t ctx2, gr_srcptr vec3, slong len, gr_ctx_t ctx) Binary operations applied elementwise, allowing a different type for one of the vectors. .. function:: int _gr_vec_add_scalar_other(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t cctx, gr_ctx_t ctx) int _gr_vec_sub_scalar_other(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t cctx, gr_ctx_t ctx) int _gr_vec_mul_scalar_other(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t cctx, gr_ctx_t ctx) int _gr_vec_div_scalar_other(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t cctx, gr_ctx_t ctx) int _gr_vec_divexact_scalar_other(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t cctx, gr_ctx_t ctx) int _gr_vec_pow_scalar_other(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t cctx, gr_ctx_t ctx) int _gr_scalar_other_add_vec(gr_ptr vec1, gr_srcptr c, gr_ctx_t cctx, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_other_sub_vec(gr_ptr vec1, gr_srcptr c, gr_ctx_t cctx, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_other_mul_vec(gr_ptr vec1, gr_srcptr c, gr_ctx_t cctx, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_other_div_vec(gr_ptr vec1, gr_srcptr c, gr_ctx_t cctx, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_other_divexact_vec(gr_ptr vec1, gr_srcptr c, gr_ctx_t cctx, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_scalar_other_pow_vec(gr_ptr vec1, gr_srcptr c, gr_ctx_t cctx, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_vec_add_scalar_si(gr_ptr vec1, gr_srcptr vec2, slong len, slong c, gr_ctx_t ctx) int _gr_vec_sub_scalar_si(gr_ptr vec1, gr_srcptr vec2, slong len, slong c, gr_ctx_t ctx) int _gr_vec_mul_scalar_si(gr_ptr vec1, gr_srcptr vec2, slong len, slong c, gr_ctx_t ctx) int _gr_vec_div_scalar_si(gr_ptr vec1, gr_srcptr vec2, slong len, slong c, gr_ctx_t ctx) int _gr_vec_divexact_scalar_si(gr_ptr vec1, gr_srcptr vec2, slong len, slong c, gr_ctx_t ctx) int _gr_vec_pow_scalar_si(gr_ptr vec1, gr_srcptr vec2, slong len, slong c, gr_ctx_t ctx) int _gr_vec_add_scalar_ui(gr_ptr vec1, gr_srcptr vec2, slong len, ulong c, gr_ctx_t ctx) int _gr_vec_sub_scalar_ui(gr_ptr vec1, gr_srcptr vec2, slong len, ulong c, gr_ctx_t ctx) int _gr_vec_mul_scalar_ui(gr_ptr vec1, gr_srcptr vec2, slong len, ulong c, gr_ctx_t ctx) int _gr_vec_div_scalar_ui(gr_ptr vec1, gr_srcptr vec2, slong len, ulong c, gr_ctx_t ctx) int _gr_vec_divexact_scalar_ui(gr_ptr vec1, gr_srcptr vec2, slong len, ulong c, gr_ctx_t ctx) int _gr_vec_pow_scalar_ui(gr_ptr vec1, gr_srcptr vec2, slong len, ulong c, gr_ctx_t ctx) int _gr_vec_add_scalar_fmpz(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpz_t c, gr_ctx_t ctx) int _gr_vec_sub_scalar_fmpz(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpz_t c, gr_ctx_t ctx) int _gr_vec_mul_scalar_fmpz(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpz_t c, gr_ctx_t ctx) int _gr_vec_div_scalar_fmpz(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpz_t c, gr_ctx_t ctx) int _gr_vec_divexact_scalar_fmpz(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpz_t c, gr_ctx_t ctx) int _gr_vec_pow_scalar_fmpz(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpz_t c, gr_ctx_t ctx) int _gr_vec_add_scalar_fmpq(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpq_t c, gr_ctx_t ctx) int _gr_vec_sub_scalar_fmpq(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpq_t c, gr_ctx_t ctx) int _gr_vec_mul_scalar_fmpq(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpq_t c, gr_ctx_t ctx) int _gr_vec_div_scalar_fmpq(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpq_t c, gr_ctx_t ctx) int _gr_vec_divexact_scalar_fmpq(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpq_t c, gr_ctx_t ctx) int _gr_vec_pow_scalar_fmpq(gr_ptr vec1, gr_srcptr vec2, slong len, const fmpq_t c, gr_ctx_t ctx) Binary operations applied elementwise with a fixed scalar operand, allowing a different type for the scalar. .. function:: int _gr_vec_addmul_scalar(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t ctx) int _gr_vec_submul_scalar(gr_ptr vec1, gr_srcptr vec2, slong len, gr_srcptr c, gr_ctx_t ctx) int _gr_vec_addmul_scalar_si(gr_ptr vec1, gr_srcptr vec2, slong len, slong c, gr_ctx_t ctx) int _gr_vec_submul_scalar_si(gr_ptr vec1, gr_srcptr vec2, slong len, slong c, gr_ctx_t ctx) .. function:: int _gr_vec_mul_scalar_2exp_si(gr_ptr res, gr_srcptr vec, slong len, slong c, gr_ctx_t ctx) Sums and products -------------------------------------------------------------------------------- .. function:: int _gr_vec_sum(gr_ptr res, gr_srcptr vec, slong len, gr_ctx_t ctx) .. function:: int _gr_vec_product(gr_ptr res, gr_srcptr vec, slong len, gr_ctx_t ctx) Dot products -------------------------------------------------------------------------------- .. function:: int _gr_vec_dot(gr_ptr res, gr_srcptr initial, int subtract, gr_srcptr vec1, gr_srcptr vec2, slong len, gr_ctx_t ctx) int _gr_vec_dot_si(gr_ptr res, gr_srcptr initial, int subtract, gr_srcptr vec1, const slong * vec2, slong len, gr_ctx_t ctx) int _gr_vec_dot_ui(gr_ptr res, gr_srcptr initial, int subtract, gr_srcptr vec1, const ulong * vec2, slong len, gr_ctx_t ctx) int _gr_vec_dot_fmpz(gr_ptr res, gr_srcptr initial, int subtract, gr_srcptr vec1, const fmpz * vec2, slong len, gr_ctx_t ctx) Sets *res* to `c \pm \sum_{i=0}^{n-1} a_i b_i`. .. function:: int _gr_vec_dot_rev(gr_ptr res, gr_srcptr initial, int subtract, gr_srcptr vec1, gr_srcptr vec2, slong len, gr_ctx_t ctx) Sets *res* to `c \pm \sum_{i=0}^{n-1} a_i b_{n-1-i}`. Other functions -------------------------------------------------------------------------------- .. function:: int _gr_vec_step(gr_ptr vec, gr_srcptr start, gr_srcptr step, slong len, gr_ctx_t ctx) .. function:: int _gr_vec_reciprocals(gr_ptr res, slong len, gr_ctx_t ctx) Sets *res* to the vector of reciprocals of the positive integers 1, 2, ... up to *len* inclusive. .. function:: int _gr_vec_set_powers(gr_ptr res, gr_srcptr x, slong len, gr_ctx_t ctx) .. raw:: latex \newpage