tenzr::scipy::special¶

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Functions¶

Detailed Description¶

High-level scientific and numerical computing ecosystem (tenzr::scipy / tsp). Modeled after SciPy / JAX SciPy: - tenzr::scipy::special: special functions (erf, erfc, logit, expit, logsumexp, softmax, gamma, gammaln) - tenzr::scipy::linalg: linear algebra routines (det, inv, solve, cholesky) - tenzr::scipy::optimize: gradient optimizers (minimize_cg, minimize_bfgs) leveraging autodiff

Functions Documentation¶

function Erf¶

TENZR_APIArray Erf(
    const Array & x
)

Parameters:

• x The input array.
• x Input array.

Return:

• The error function values.
• erf(x).

Computes the Gauss error function elementwise. Elementwise error function via the Abramowitz & Stegun 7.1.26 approximation.

function Erfc¶

TENZR_APIArray Erfc(
    const Array & x
)

Parameters:

• x The input array.
• x Input array.

Return:

• The complementary error function values.
• 1 - erf(x).

Computes the complementary error function elementwise. Elementwise complementary error function.

function Gamma¶

TENZR_APIArray Gamma(
    const Array & x
)

Parameters:

• x The input array.
• x Input array.

Return:

• The gamma function values.
• gamma(x).

Computes the gamma function elementwise. Elementwise gamma function.

function Gammaln¶

TENZR_APIArray Gammaln(
    const Array & x
)

Parameters:

• x The input array.
• x Input array.

Return:

• The log-gamma values.
• lgamma(x).

Computes the natural log of the absolute gamma function elementwise. Elementwise log-gamma via a Stirling/Ramanujan asymptotic expansion.

function Logit¶

TENZR_APIArray Logit(
    const Array & x
)

Parameters:

• x The input array with values in (0, 1).
• x Input array with values in (0, 1).

Return:

• The log-odds values.
• log(x / (1 - x)).

Computes the logit function elementwise. Elementwise inverse logistic function.

function Expit¶

TENZR_APIArray Expit(
    const Array & x
)

Parameters:

• x The input array.
• x Input array.

Return:

• The sigmoid values.
• 1 / (1 + exp(-x)).

Computes the logistic sigmoid function elementwise. Elementwise logistic sigmoid.

function Logsumexp¶

TENZR_APIArray Logsumexp(
    const Array & x,
    std::optional< std::vector< int64_t > > axis =std::nullopt,
    bool keepdims =false
)

Parameters:

• x The input array.
• axis Axes to reduce, or all axes when unset.
• keepdims Whether to retain reduced dimensions as size 1.
• x Input array.
• axis Optional reduction axes.
• keepdims Whether reduced axes are retained.

Return:

• The reduced result.
• log(sum(exp(x))).

Computes the log-sum-exp reduction with numerical stabilization. Numerically stable log of the sum of exponentials.

function softmax¶

TENZR_APIArray softmax(
    const Array & x,
    int64_t axis =-1
)

Parameters:

• x The input array.
• axis The axis to normalize over.
• x Input array.
• axis Reduction axis.

Return:

• The softmax probabilities.
• Softmax-normalized array.

Computes a numerically stable softmax along axis. Numerically stable softmax along axis.