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Module: tfp.math

TensorFlow Probability math functions.

Modules

`hypergeometric` module: Implements hypergeometric functions in TensorFlow.

`ode` module: TensorFlow Probability ODE solvers.

`psd_kernels` module: Positive-semidefinite kernels package.

Classes

`class MinimizeTraceableQuantities`: Namedtuple of quantities that may be traced from `tfp.math.minimize`.

Functions

`atan_difference(...)`: Difference of arctan(x) and arctan(y).

`batch_interp_regular_1d_grid(...)`: Linear `1-D` interpolation on a regular (constant spacing) grid.

`batch_interp_regular_nd_grid(...)`: Multi-linear interpolation on a regular (constant spacing) grid.

`bessel_iv_ratio(...)`: Computes `I_{v} (z) / I_{v - 1} (z)` in a numerically stable way.

`bessel_ive(...)`: Computes exponentially scaled modified Bessel function of the first kind.

`bessel_kve(...)`: Computes exponentially scaled modified Bessel function of the 2nd kind.

`bracket_root(...)`: Finds bounds that bracket a root of the objective function.

`cholesky_concat(...)`: Concatenates `chol @ chol.T` with additional rows and columns.

`cholesky_update(...)`: Returns cholesky of chol @ chol.T + multiplier * u @ u.T.

`clip_by_value_preserve_gradient(...)`: Clips values to a specified min and max while leaving gradient unaltered.

`custom_gradient(...)`: Embeds a custom gradient into a `Tensor`.

`dawsn(...)`: Computes Dawson's integral element-wise.

`dense_to_sparse(...)`: Converts dense `Tensor` to `SparseTensor`, dropping `ignore_value` cells.

`diag_jacobian(...)`: Computes diagonal of the Jacobian matrix of `ys=fn(xs)` wrt `xs`.

`erfcinv(...)`: Computes the inverse of `tf.math.erfc` of `z` element-wise.

`erfcx(...)`: Computes the scaled complementary error function exp(x**) * erfc(x).

`fill_triangular(...)`: Creates a (batch of) triangular matrix from a vector of inputs.

`fill_triangular_inverse(...)`: Creates a vector from a (batch of) triangular matrix.

`find_root_chandrupatla(...)`: Finds root(s) of a scalar function using Chandrupatla's method.

`find_root_secant(...)`: Finds root(s) of a function of single variable using the secant method.

`gram_schmidt(...)`: Implementation of the modified Gram-Schmidt orthonormalization algorithm.

`igammacinv(...)`: Computes the inverse to `tf.math.igammac` with respect to `p`.

`igammainv(...)`: Computes the inverse to `tf.math.igamma` with respect to `p`.

`interp_regular_1d_grid(...)`: Linear `1-D` interpolation on a regular (constant spacing) grid.

`lambertw(...)`: Computes Lambert W of `z` element-wise.

`lambertw_winitzki_approx(...)`: Computes Winitzki approximation to Lambert W function at z >= -1/exp(1).

`lbeta(...)`: Returns log(Beta(x, y)).

`log1mexp(...)`: Compute `log(1 - exp(-|x|))` elementwise in a numerically stable way.

`log1psquare(...)`: Numerically stable calculation of `log(1 + x**2)` for small or large `|x|`.

`log_add_exp(...)`: Computes `log(exp(x) + exp(y))` in a numerically stable way.

`log_bessel_ive(...)`: Computes `log(tfp.math.bessel_ive(v, z))`.

`log_bessel_kve(...)`: Computes `log(tfp.math.bessel_kve(v, z))`.

`log_combinations(...)`: Log multinomial coefficient.

`log_cosh(...)`: Compute `log(cosh(x))` in a numerically stable way.

`log_cumsum_exp(...)`: Computes log(cumsum(exp(x))).

`log_gamma_correction(...)`: Returns the error of the Stirling approximation to lgamma(x) for x >= 8.

`log_gamma_difference(...)`: Returns lgamma(y) - lgamma(x + y), accurately.

`log_sub_exp(...)`: Compute `log(exp(max(x, y)) - exp(min(x, y)))` in a numerically stable way.

`logerfc(...)`: Computes the logarithm of `tf.math.erfc` of `x` element-wise.

`logerfcx(...)`: Computes the logarithm of `tfp.math.erfcx` of `x` element-wise.

`lu_matrix_inverse(...)`: Computes a matrix inverse given the matrix's LU decomposition.

`lu_reconstruct(...)`: The inverse LU decomposition, `X == lu_reconstruct(*tf.linalg.lu(X))`.

`lu_solve(...)`: Solves systems of linear eqns `A X = RHS`, given LU factorizations.

`minimize(...)`: Minimize a loss function using a provided optimizer.

`owens_t(...)`: Computes Owen's T function of `h` and `a` element-wise.

`pivoted_cholesky(...)`: Computes the (partial) pivoted cholesky decomposition of `matrix`.

`random_rademacher(...)`: Generates `Tensor` consisting of `-1` or `+1`, chosen uniformly at random. (deprecated)

`random_rayleigh(...)`: Generates `Tensor` of positive reals drawn from a Rayleigh distributions. (deprecated)

`reduce_kahan_sum(...)`: Reduces the input tensor along the given axis using Kahan summation.

`reduce_log_harmonic_mean_exp(...)`: Computes `log(1 / mean(1 / exp(input_tensor)))`.

`reduce_logmeanexp(...)`: Computes `log(mean(exp(input_tensor)))`.

`reduce_weighted_logsumexp(...)`: Computes `log(abs(sum(weight * exp(elements across tensor dimensions))))`.

`round_exponential_bump_function(...)`: Function supported on [-1, 1], smooth on the real line, with a round top.

`scan_associative(...)`: Perform a scan with an associative binary operation, in parallel.

`secant_root(...)`: Finds root(s) of a function of single variable using the secant method. (deprecated)

`smootherstep(...)`: Computes a sigmoid-like interpolation function on the unit-interval.

`soft_sorting_matrix(...)`: Computes a matrix representing a continuous relaxation of sorting.

`soft_threshold(...)`: Soft Thresholding operator.

`softplus_inverse(...)`: Computes the inverse softplus, i.e., x = softplus_inverse(softplus(x)).

`sparse_or_dense_matmul(...)`: Returns (batched) matmul of a SparseTensor (or Tensor) with a Tensor.

`sparse_or_dense_matvecmul(...)`: Returns (batched) matmul of a (sparse) matrix with a column vector.

`sqrt1pm1(...)`: Compute `sqrt(x + 1) - 1` elementwise in a numerically stable way.

`trapz(...)`: Integrate y(x) on the specified axis using the trapezoidal rule.

`value_and_gradient(...)`: Computes `f(*args, **kwargs)` and its gradients wrt to `args`, `kwargs`.

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