Tools
Overview
Boardflare provides a comprehensive library of Python-powered tools designed to extend Excel’s analytical capabilities. By bridging the gap between the world’s most popular spreadsheet and the powerful Python ecosystem (including SciPy, NumPy, and Pandas), Boardflare enables users to perform complex mathematical modeling, statistical analysis, and data processing directly within their familiar Excel environment.
Engineering
Fluids
Atmosphere
| Tool | Description |
|---|---|
| AIRMASS | Calculate the mass of air per square meter in the atmosphere along a given angle using a density profile. |
| ATMOS_NRLMSISE00 | Compute temperature, density, and pressure using the NRLMSISE-00 atmospheric model. |
| ATMOSPHERE_1976 | Calculate standard atmospheric properties at a given altitude using the US Standard Atmosphere 1976 model. |
Compressible
| Tool | Description |
|---|---|
| FRITZSCHE_FLOW | Calculate gas flow rate using the Fritzsche formula. |
| IGT_FLOW | Calculate gas flow rate using the IGT (Institute of Gas Technology) formula. |
| IS_CHOKED_FLOW | Determine if a flow is choked (critical) based on pressure ratio. |
| ISENTROPIC_EFF | Convert between isentropic and polytropic efficiency for compression. |
| ISENTROPIC_T_RISE | Calculate the temperature rise for isentropic compression or expansion. |
| ISENTROPIC_WORK | Calculate work of compression or expansion for a gas in an isentropic process. |
| ISOTHERMAL_GAS | Calculate mass flow rate for isothermal compressible gas flow in a pipe. |
| ISOTHERMAL_WORK | Calculate work of compression or expansion for a gas in an isothermal process. |
| MULLER_FLOW | Calculate gas flow rate using the Muller formula. |
| P_CRITICAL_FLOW | Calculate critical flow pressure for a fluid at Mach 1. |
| P_STAGNATION | Calculate stagnation pressure from static conditions. |
| PANHANDLE_A | Calculate gas flow rate in a pipeline using the Panhandle A formula. |
| PANHANDLE_B | Calculate gas flow rate in a pipeline using the Panhandle B formula. |
| POLYTROPIC_EXP | Calculate polytropic exponent or polytropic efficiency for compression. |
| STAGNATION_ENERGY | Calculate the increase in enthalpy due to fluid velocity. |
| T_CRITICAL_FLOW | Calculate critical flow temperature for a fluid at Mach 1. |
| T_STAG_IDEAL | Calculate ideal stagnation temperature from velocity and heat capacity. |
| T_STAGNATION | Calculate stagnation temperature from pressure ratio. |
| WEYMOUTH_FLOW | Calculate gas flow rate in a pipeline using the Weymouth formula. |
Control Valve
| Tool | Description |
|---|---|
| CV_CAV_INDEX | Calculates the cavitation index of a control valve. |
| CV_CHAR_EQ_PERC | Calculates the flow coefficient characteristic for an equal percentage control valve. |
| CV_CHAR_LINEAR | Calculates the flow coefficient characteristic for a linear control valve. |
| CV_CHAR_QUICK_OP | Calculates the flow coefficient characteristic for a quick opening control valve. |
| CV_CHOKE_PRESS_GAS | Calculates the pressure at which choked flow occurs in a gas control valve. |
| CV_CHOKE_PRESS_LIQ | Calculates the pressure at which choked flow occurs in a liquid control valve. |
| CV_CONVERT_COEFF | Converts between different flow coefficient scales (Kv, Cv, Av). |
| CV_NOISE_GAS_2011 | Calculate the A-weighted sound pressure level for gas flow through a control valve per IEC 60534-8-3 (2011). |
| CV_NOISE_LIQ_2015 | Calculates the sound made by a liquid flowing through a control valve according to the standard IEC 60534-8-4 (2015) using fluids.control_valve.control_valve_noise_l_2015. |
| FF_CRIT_PRESS_L | Calculates FF, the liquid critical pressure ratio factor, for use in IEC 60534 liquid valve sizing calculations using fluids.control_valve.FF_critical_pressure_ratio_l. See https://fluids.readthedocs.io/fluids.control_valve.html#fluids.control_valve.FF_critical_pressure_ratio_l for details. |
| IS_CHOKED_GAS | Determines if a gas flow in a control valve is choked (critical) or not according to IEC 60534. |
| IS_CHOKED_LIQ | Determines if a liquid flow in a control valve is choked (critical) or not according to IEC 60534. |
| LOSS_COEFF_PIPING | Calculates the sum of loss coefficients for reducers/expanders around a control valve. |
| REYNOLDS_FACTOR | Calculates the Reynolds number factor FR for a valve according to IEC 60534. |
| REYNOLDS_VALVE | Calculates the Reynolds number of a control valve according to IEC 60534. |
| SIZE_CV_GAS | Calculates flow coefficient of a control valve passing a gas according to IEC 60534 using fluids.control_valve.size_control_valve_g. |
| SIZE_CV_LIQUID | Calculates the flow coefficient (Kv) of a control valve passing a liquid according to IEC 60534. |
Dimensionless
| Tool | Description |
|---|---|
| ARCHIMEDES | Calculate the Archimedes number (Ar) for a fluid and particle. |
| BEJAN | Compute the Bejan number (length-based or permeability-based). |
| BOILING | Calculate the Boiling number (Bg), a dimensionless number for boiling heat transfer. |
| BOND | Calculate the Bond number using fluids.core.Bond. |
| CAPILLARY | Calculate the Capillary number (Ca) for a fluid system using fluids.core.Capillary. |
| CAVITATION | Calculate the Cavitation number (Ca) for a flowing fluid. |
| CONFINEMENT | Calculate the Confinement number (Co) for two-phase flow in a channel. |
| DEAN | Calculate the Dean number (De) for flow in a curved pipe or channel. |
| DRAG | Calculate the drag coefficient (dimensionless) for an object in a fluid. |
| ECKERT | Calculate the Eckert number using fluids.core.Eckert. |
| EULER | Calculate the Euler number (Eu) for a fluid flow. |
| FOURIER_HEAT | Calculate the Fourier number for heat transfer. |
| FOURIER_MASS | Calculate the Fourier number for mass transfer (Fo). |
| FROUDE | Calculate the Froude number (Fr) for a given velocity, length, and gravity. |
Drag
| Tool | Description |
|---|---|
| CD_ALMEDEIJ | Calculate drag coefficient of a sphere using the Almedeij correlation. |
| CD_BARATI | Calculate drag coefficient of a sphere using the Barati correlation. |
| CD_BARATI_HIGH | Calculate drag coefficient of a sphere using the Barati high-Re correlation (valid to Re=1E6). |
| CD_CEYLAN | Calculate drag coefficient of a sphere using the Ceylan correlation. |
| CD_CHENG | Calculate drag coefficient of a sphere using the Cheng correlation. |
| CD_CLIFT | Calculate drag coefficient of a sphere using the Clift correlation. |
| CD_CLIFT_GAUVIN | Calculate drag coefficient of a sphere using the Clift-Gauvin correlation. |
| CD_ENGELUND | Calculate drag coefficient of a sphere using the Engelund-Hansen correlation. |
| CD_FLEMMER_BANKS | Calculate drag coefficient of a sphere using the Flemmer-Banks correlation. |
| CD_GRAF | Calculate drag coefficient of a sphere using the Graf correlation. |
| CD_HAIDER_LEV | Calculate drag coefficient of a sphere using the Haider-Levenspiel correlation. |
| CD_KHAN_RICH | Calculate drag coefficient of a sphere using the Khan-Richardson correlation. |
| CD_MIKHAILOV | Calculate drag coefficient of a sphere using the Mikhailov-Freire correlation. |
| CD_MORRISON | Calculate drag coefficient of a sphere using the Morrison correlation. |
| CD_MORSI_ALEX | Calculate drag coefficient of a sphere using the Morsi-Alexander correlation. |
| CD_ROUSE | Calculate drag coefficient of a sphere using the Rouse correlation. |
| CD_SONG_XU | Calculate drag coefficient of a particle using the Song-Xu correlation for spherical and non-spherical particles. |
| CD_STOKES | Calculate drag coefficient of a sphere using Stokes law (Cd = 24/Re). |
| CD_SWAMEE_OJHA | Calculate drag coefficient of a sphere using the Swamee-Ojha correlation. |
| CD_TERFOUS | Calculate drag coefficient of a sphere using the Terfous correlation. |
| CD_YEN | Calculate drag coefficient of a sphere using the Yen correlation. |
| DRAG_SPHERE | Calculate the drag coefficient of a sphere using various correlations based on Reynolds number. |
| SPHERE_FALL_DIST | Calculate distance traveled by a falling sphere after a given time. |
| SPHERE_VEL_AT_T | Calculate the velocity of a falling sphere after a given time. |
| TIME_V_TERMINAL | Calculate time for a particle in Stokes regime to reach terminal velocity. |
| V_TERMINAL | Calculate terminal velocity of a falling sphere using drag coefficient correlations. |
Filters
| Tool | Description |
|---|---|
| RND_EDGE_GRILL | Calculate the loss coefficient for a rounded edge grill or perforated plate. |
| RND_EDGE_MESH | Calculate the loss coefficient for a round edged open net or screen mesh. |
| RND_EDGE_SCREEN | Calculate the loss coefficient for a round edged wire screen or bar screen. |
| SQ_EDGE_GRILL | Calculate the loss coefficient for a square edged grill or perforated plate. |
| SQ_EDGE_SCREEN | Calculate the loss coefficient for a square edged wire screen, bar screen, or perforated plate. |
Fittings
| Tool | Description |
|---|---|
| BEND_MITER | Calculate the loss coefficient (K) for a single-joint miter bend in a pipe. |
| BEND_ROUNDED | Calculate the loss coefficient (K) for a rounded pipe bend (elbow) using various methods. |
| CONTRACTION_ROUND | Calculate the loss coefficient (K) for a rounded pipe contraction (reducer). |
| CONTRACTION_SHARP | Calculate the loss coefficient (K) for a sharp edged pipe contraction (reducer). |
| CV_TO_K | Convert imperial valve flow coefficient (Cv) to loss coefficient (K). |
| DIFFUSER_CONICAL | Calculate the loss coefficient (K) for a conical pipe expansion (diffuser). |
| DIFFUSER_SHARP | Calculate the loss coefficient (K) for a sudden pipe expansion (diffuser). |
| ENTRANCE_ANGLED | Calculate the loss coefficient (K) for an angled sharp entrance to a pipe flush with a reservoir wall. |
| ENTRANCE_BEVELED | Calculate the loss coefficient (K) for a beveled or chamfered entrance to a pipe flush with a reservoir wall. |
| ENTRANCE_ROUNDED | Calculate the loss coefficient (K) for a rounded entrance to a pipe flush with a reservoir wall. |
| ENTRANCE_SHARP | Calculate the loss coefficient (K) for a sharp entrance to a pipe flush with a reservoir wall. |
| EXIT_NORMAL | Calculate the loss coefficient (K) for a normal pipe exit discharging into a reservoir. |
| HELIX | Calculate the loss coefficient (K) for a helical coil pipe section. |
| K_BALL_VALVE | Calculate the loss coefficient (K) for a ball valve using the Crane method. |
| K_BUTTERFLY_VALVE | Calculate the loss coefficient (K) for a butterfly valve using the Crane method. |
| K_GATE_VALVE | Calculate the loss coefficient (K) for a gate valve using the Crane method. |
| K_GLOBE_VALVE | Calculate the loss coefficient (K) for a globe valve using the Crane method. |
| K_SWING_CHECK_VALVE | Calculate the loss coefficient (K) for a swing check valve using the Crane method. |
| K_TO_CV | Convert loss coefficient (K) to imperial valve flow coefficient (Cv). |
| K_TO_KV | Convert loss coefficient (K) to metric valve flow coefficient (Kv). |
| KV_TO_K | Convert metric valve flow coefficient (Kv) to loss coefficient (K). |
| SPIRAL | Calculate the loss coefficient (K) for a spiral coil pipe section. |
Flow Meter
| Tool | Description |
|---|---|
| DIFF_PRESS_BETA | Calculate the beta ratio (diameter ratio) for a differential pressure flow meter. |
| DIFF_PRESS_C_EPS | Calculate discharge coefficient and expansibility factor for differential pressure flow meters. |
| DIFF_PRESS_DP | Calculate non-recoverable pressure drop across a differential pressure flow meter. |
| FLOW_METER_DISCH | Calculate mass flow rate through a differential pressure flow meter based on measured pressures and meter geometry. |
| ORIFICE_DISCHARGE_C | Calculate the discharge coefficient for an orifice plate using the Reader-Harris-Gallagher correlation (ISO 5167 standard). |
| ORIFICE_EXPAND | Calculate the expansibility factor for an orifice plate based on geometry and pressure conditions. |
| ORIFICE_PRESS_DROP | Calculate non-recoverable pressure drop across an orifice plate based on geometry and discharge coefficient. |
Friction
| Tool | Description |
|---|---|
| BLASIUS | Calculates Darcy friction factor for turbulent flow in smooth pipes using the Blasius correlation. |
| CHURCHILL | Calculate Darcy friction factor using the Churchill (1977) universal equation for all flow regimes. |
| CLAMOND | Calculate Darcy friction factor using Clamond’s high-precision solution accurate to nearly machine precision. |
| COLEBROOK | Calculate Darcy friction factor using exact solution to the Colebrook equation. |
| DP_GRAV | Calculate gravitational pressure drop component for single-phase flow in inclined pipes. |
| FF_CURVED | Calculate friction factor for fluid flowing in a curved pipe or helical coil, supporting both laminar and turbulent regimes. |
| FP_MARTIN | Calculate Darcy friction factor for single-phase flow in Chevron-style plate heat exchangers using Martin (1999) correlation. |
| FP_MULEY_MANGLIK | Calculate Darcy friction factor for single-phase flow in Chevron-style plate heat exchangers using Muley-Manglik correlation. |
| FRICTION_FACTOR | Calculate the Darcy friction factor for fluid flow in a pipe using various correlations, automatically selecting appropriate method based on Reynolds number and relative roughness. |
| FRICTION_LAMINAR | Calculate the Darcy friction factor for laminar flow using the theoretical solution fd = 64/Re. |
| FT_CRANE | Calculate the Crane fully turbulent Darcy friction factor for flow in commercial pipe. |
| HAALAND | Calculate Darcy friction factor using the Haaland (1983) approximation. |
| HELICAL_RE_CRIT | Calculate the transition Reynolds number for fluid flowing in a curved or helical pipe between laminar and turbulent flow. |
| MOODY | Calculate Darcy friction factor using the Moody (1947) correlation. |
| ONE_PHASE_DP | Calculate single-phase pressure drop in a pipe using the Darcy-Weisbach equation. |
| SWAMEE_JAIN | Calculate Darcy friction factor using the Swamee-Jain (1976) equation. |
| TRANS_FACTOR | Convert between Darcy friction factor and transmission factor for compressible gas pipeline flow. |
| VON_KARMAN | Calculate Darcy friction factor for rough pipes at infinite Reynolds number from the von Karman equation. |
Photovoltaics
| Tool | Description |
|---|---|
| CALCPARAMS_CEC | Calculate five CEC model parameters for the single diode equation at given irradiance and cell temperature. |
| I_FROM_V | Calculate the device current at a given device voltage for a PV cell/module using the single diode model. |
| IRRADIANCE | Calculate the plane of array irradiance components on a tilted surface using PVLib. |
| PVWATTS_DC | Calculate the DC power output of a PV module using the PVWatts DC model. |
| SOLARPOSITION | Calculate solar azimuth, elevation, and apparent zenith for given times and location. |
Math
Calculus
Differentiation
| Tool | Description |
|---|---|
| HESSIAN | Compute the Hessian matrix (second derivatives) of a scalar function using CasADi symbolic differentiation. |
| JACOBIAN | Calculate the Jacobian matrix of mathematical expressions with respect to specified variables. |
| SENSITIVITY | Compute the sensitivity of a scalar model with respect to its parameters using CasADi. |
Integration
| Tool | Description |
|---|---|
| DBLQUAD | Compute the double integral of a function over a two-dimensional region. |
| QUAD | Numerically integrate a function defined by a table of x, y values over [a, b] using adaptive quadrature. |
| TRAPEZOID | Integrate sampled data using the composite trapezoidal rule. |
Ode Models
| Tool | Description |
|---|---|
| BRUSSELATOR | Numerically solves the Brusselator system of ordinary differential equations for autocatalytic chemical reactions. |
| COMPARTMENTAL_PK | Numerically solves the basic one-compartment pharmacokinetics ODE using scipy.integrate.solve_ivp. |
| FITZHUGH_NAGUMO | Numerically solves the FitzHugh-Nagumo system of ordinary differential equations for neuron action potentials using scipy.integrate.solve_ivp. |
| HODGKIN_HUXLEY | Numerically solves the Hodgkin-Huxley system of ordinary differential equations for neuron action potentials. |
| LORENZ | Numerically solves the Lorenz system of ordinary differential equations for chaotic dynamics. |
| LOTKA_VOLTERRA | Numerically solves the Lotka-Volterra predator-prey system of ordinary differential equations. |
| MICHAELIS_MENTEN | Numerically solves the Michaelis-Menten system of ordinary differential equations for enzyme kinetics using scipy.integrate.solve_ivp. |
| SEIR | Numerically solves the SEIR system of ordinary differential equations for infectious disease modeling using scipy.integrate.solve_ivp. |
| SIR | Solves the SIR system of ordinary differential equations for infection dynamics using scipy.integrate.solve_ivp (see scipy.integrate.solve_ivp). |
| VAN_DER_POL | Numerically solves the Van der Pol oscillator system of ordinary differential equations. |
Ode Systems
| Tool | Description |
|---|---|
| SOLVE_BVP | Solve a boundary value problem for a second-order system of ODEs. |
| SOLVE_IVP | Solve an initial value problem for a system of ODEs of the form dy/dt = A @ y. |
Curve Fitting
Least Squares
| Tool | Description |
|---|---|
| CA_CURVE_FIT | Fit an arbitrary symbolic model to data using CasADi and automatic differentiation. |
| CURVE_FIT | Fit a model expression to xdata, ydata using scipy.optimize.curve_fit. |
| LM_FIT | Fit data using lmfit’s built-in models with optional model composition. |
| MINUIT_FIT | Fit an arbitrary model expression to data using iminuit least-squares minimization with uncertainty estimates. |
Models
| Tool | Description |
|---|---|
| ADSORPTION | Fits adsorption models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| AGRICULTURE | Fits agriculture models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| BINDING_MODEL | Fits binding_model models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| CHROMA_PEAKS | Fits chroma_peaks models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| DOSE_RESPONSE | Fits dose_response models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| ELECTRO_ION | Fits electro_ion models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| ENZYME_BASIC | Fits enzyme_basic models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| ENZYME_INHIBIT | Fits enzyme_inhibit models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| EXP_ADVANCED | Fits exp_advanced models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| EXP_DECAY | Fits exp_decay models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| EXP_GROWTH | Fits exponential growth models to data using scipy.optimize.curve_fit. |
| GROWTH_POWER | Fits growth_power models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| GROWTH_SIGMOID | Fits growth_sigmoid models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| MISC_PIECEWISE | Fits misc_piecewise models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| PEAK_ASYM | Fits peak_asym models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| POLY_BASIC | Fits poly_basic models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| RHEOLOGY | Fits rheology models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| SPECTRO_PEAKS | Fits spectro_peaks models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| STAT_DISTRIB | Fits stat_distrib models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| STAT_PARETO | Fits stat_pareto models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
| WAVEFORM | Fits waveform models to data using scipy.optimize.curve_fit. See https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html for details. |
Interpolation
Approximation
| Tool | Description |
|---|---|
| LAGRANGE_INTERP | Compute the Lagrange interpolating polynomial through a set of points. |
| PADE | Compute Pade rational approximation to a polynomial. |
Multivariate
| Tool | Description |
|---|---|
| GRID_INTERP | Interpolator on a regular grid in 2D. |
| GRIDDATA | Interpolate unstructured D-D data. |
| INTERPN | Multidimensional interpolation on regular grids (2D). |
| LINEAR_ND_INTERP | Piecewise linear interpolator in N > 1 dimensions. |
| NEAREST_ND_INTERP | Nearest neighbor interpolation in N > 1 dimensions. |
| RBF_INTERPOLATOR | Radial basis function interpolation in N dimensions. |
Splines
| Tool | Description |
|---|---|
| INTERP_UV_SPLINE | 1-D interpolating spline for data. |
| MAKE_INTERP_SPLINE | Compute interpolating B-spline and evaluate at new points. |
| MAKE_LSQ_SPLINE | Compute LSQ-based fitting B-spline. |
| SMOOTH_SPLINE | Smoothing cubic spline. |
| UNIVARIATE_SPLINE | 1-D smoothing spline fit to data. |
Univariate
| Tool | Description |
|---|---|
| AKIMA_INTERP | Akima 1D interpolation. |
| BARYCENTRIC_INTERP | Interpolating polynomial for a set of points using barycentric interpolation. |
| CUBIC_SPLINE | Cubic spline data interpolator. |
| HERMITE_SPLINE | Piecewise-cubic interpolator matching values and first derivatives. |
| INTERP1D | Interpolate a 1-D function. |
| KROGH_INTERPOLATE | Krogh polynomial interpolation. |
| PCHIP_INTERPOLATE | PCHIP 1-D monotonic cubic interpolation. |
Linear Algebra
| Tool | Description |
|---|---|
| CHOLESKY | Compute the Cholesky decomposition of a real, symmetric positive-definite matrix. |
| EXPM | Compute the matrix exponential of a square matrix using scipy.linalg.expm |
| LSQ_LINEAR | Solve a bounded linear least-squares problem. |
| LSTSQ | Compute the least-squares solution to Ax = B using scipy.linalg.lstsq. |
| PINV | Compute the Moore-Penrose pseudoinverse of a matrix using singular value decomposition (SVD). |
| QR | Compute the QR decomposition of a matrix and return either Q or R. |
| SVD | Compute the Singular Value Decomposition (SVD) of a matrix using scipy.linalg.svd. |
Optimization
Assignment Problems
| Tool | Description |
|---|---|
| LINEAR_ASSIGNMENT | Solve the linear assignment problem using scipy.optimize.linear_sum_assignment. |
| QUAD_ASSIGN | Solve a quadratic assignment problem using SciPy’s implementation. |
Global Optimization
| Tool | Description |
|---|---|
| BASIN_HOPPING | Minimize a single-variable expression with SciPy’s basinhopping algorithm. |
| BRUTE | Perform a brute-force grid search to approximate the global minimum of a function. |
| DIFF_EVOLUTION | Minimize a multivariate function using differential evolution. |
| DUAL_ANNEALING | Minimize a multivariate function using dual annealing. |
| SHGO | Find global minimum using Simplicial Homology Global Optimization. |
Linear Programming
| Tool | Description |
|---|---|
| CA_QUAD_PROG | Solve a quadratic programming problem using CasADi’s qpsol solver. |
| LINEAR_PROG | Solve a linear programming problem using SciPy’s linprog function. |
| MILP | Solve a mixed-integer linear program using scipy.optimize.milp. |
Local Optimization
| Tool | Description |
|---|---|
| CA_MINIMIZE | Minimize a multivariate function using CasADi with automatic differentiation. |
| MINIMIZE | Minimize a multivariate function using SciPy’s minimize routine. |
| MINIMIZE_SCALAR | Minimize a single-variable function using SciPy’s minimize_scalar. |
Root Finding
| Tool | Description |
|---|---|
| CA_ROOT | Solve a system of nonlinear equations using CasADi with automatic Jacobian. |
| FIXED_POINT | Find a fixed point x such that f(x) = x for a scalar function expression. |
| ROOT | Solve a square nonlinear system using SciPy’s root solver. |
| ROOT_SCALAR | Find a real root of a scalar function using SciPy’s root_scalar. |
Statistics
Frequency Statistics
| Tool | Description |
|---|---|
| BINNED_STATISTIC | Computes a binned statistic (mean, sum, median, etc.) for the input data. |
| BINNED_STATISTIC_2D | Computes a bidimensional binned statistic (mean, sum, median, etc.) for the input data. |
| CUMFREQ | Compute the cumulative frequency histogram for the input data. |
| PERCENTILEOFSCORE | Computes the percentile rank of a score relative to the input data. |
| RELFREQ | Returns the relative frequency histogram for the input data. |
| SCOREATPERCENTILE | Calculates the score at the given percentile of the input data. |
Hypothesis Tests
Association Correlation
| Tool | Description |
|---|---|
| BARNARD_EXACT | Perform Barnard’s exact test on a 2x2 contingency table. |
| BOSCHLOO_EXACT | Perform Boschloo’s exact test on a 2x2 contingency table. |
| CHI2_CONTINGENCY | Perform the chi-square test of independence for variables in a contingency table. |
| FISHER_EXACT | Perform Fisher’s exact test on a 2x2 contingency table. |
| KENDALLTAU | Calculate Kendall’s tau, a correlation measure for ordinal data. |
| PAGE_TREND_TEST | Perform Page’s L trend test for monotonic trends across treatments. |
| PEARSONR | Calculate the Pearson correlation coefficient and p-value for two datasets. |
| POINTBISERIALR | Calculate a point biserial correlation coefficient and its p-value. |
| SIEGELSLOPES | Compute the Siegel repeated medians estimator for robust linear regression using scipy.stats.siegelslopes. |
| SOMERSD | Calculate Somers’ D, an asymmetric measure of ordinal association between two variables. |
| SPEARMANR | Calculate a Spearman rank-order correlation coefficient with associated p-value. |
| THEILSLOPES | Compute the Theil-Sen estimator for a set of points (robust linear regression). |
| WEIGHTEDTAU | Compute a weighted version of Kendall’s tau correlation coefficient. |
Independent Sample
| Tool | Description |
|---|---|
| ALEXANDERGOVERN | Performs the Alexander-Govern test for equality of means across multiple independent samples with possible heterogeneity of variance. |
| ANDERSON_KSAMP | Performs the k-sample Anderson-Darling test to determine if samples are drawn from the same population. |
| ANSARI | Performs the Ansari-Bradley test for equal scale parameters (non-parametric) using scipy.stats.ansari. |
| BRUNNERMUNZEL | Computes the Brunner-Munzel nonparametric test for two independent samples. |
| BWS_TEST | Performs the Baumgartner-Weiss-Schindler test on two independent samples. |
| CVM_2SAMP | Performs the two-sample Cramér-von Mises test using scipy.stats.cramervonmises_2samp. |
| DUNNETT | Performs Dunnett’s test for multiple comparisons of means against a control group. |
| EPPS_SINGLE_2SAMP | Compute the Epps-Singleton test statistic and p-value for two samples. |
| F_ONEWAY | Performs a one-way ANOVA test for two or more independent samples. |
| FLIGNER | Performs the Fligner-Killeen test for equality of variances across multiple samples. |
| FRIEDMANCHISQUARE | Computes the Friedman test for repeated samples. |
| KRUSKAL | Computes the Kruskal-Wallis H-test for independent samples. |
| KS_2SAMP | Performs the two-sample Kolmogorov-Smirnov test for goodness of fit. |
| LEVENE | Performs the Levene test for equality of variances across multiple samples. |
| MANNWHITNEYU | Performs the Mann-Whitney U rank test on two independent samples using scipy.stats.mannwhitneyu. |
| MEDIAN_TEST | Performs Mood’s median test to determine if two or more independent samples come from populations with the same median. |
| MOOD | Perform Mood’s two-sample test for scale parameters. |
| POISSON_MEANS_TEST | Performs the Poisson means test (E-test) to compare the means of two Poisson distributions. |
| RANKSUMS | Computes the Wilcoxon rank-sum statistic and p-value for two independent samples. |
| TTEST_IND | Performs the independent two-sample t-test for the means of two groups. |
| TTEST_IND_STATS | Perform a t-test for means of two independent samples using summary statistics. |
One Sample
| Tool | Description |
|---|---|
| BINOMTEST | Perform a binomial test for the probability of success in a Bernoulli experiment. |
| JARQUE_BERA | Perform the Jarque-Bera goodness of fit test for normality. |
| KSTEST | Performs the one-sample Kolmogorov-Smirnov test for goodness of fit. |
| KURTOSISTEST | Test whether the kurtosis of a sample is different from that of a normal distribution. |
| NORMALTEST | Test whether a sample differs from a normal distribution (omnibus test). |
| QUANTILE_TEST | Perform a quantile test to determine if a population quantile equals a hypothesized value. |
| SHAPIRO | Perform the Shapiro-Wilk test for normality. |
| SKEWTEST | Test whether the skewness of a sample is different from that of a normal distribution. |
| TTEST_1SAMP | Perform a one-sample t-test for the mean of a group of scores. |
Models
Count
| Tool | Description |
|---|---|
| HURDLE_COUNT_MODEL | Fits a Hurdle model for count data with two-stage process (zero vs. positive counts). |
| ZINB_MODEL | Fits a Zero-Inflated Negative Binomial (ZINB) model for overdispersed count data with excess zeros. |
| ZIP_MODEL | Fits a Zero-Inflated Poisson (ZIP) model for count data with excess zeros. |
Discrete Choice
| Tool | Description |
|---|---|
| LOGIT_MODEL | Fits a binary logistic regression model to predict binary outcomes using maximum likelihood estimation. |
| MULTINOMIAL_LOGIT | Fits a multinomial logistic regression model for multi-category outcomes. |
| ORDERED_LOGIT | Fits an ordered logistic regression model for ordinal outcomes. |
| PROBIT_MODEL | Fits a binary probit regression model using maximum likelihood estimation. |
Generalized Linear
| Tool | Description |
|---|---|
| GLM_BINOMIAL | Fits a Generalized Linear Model with binomial family for binary or proportion data. |
| GLM_GAMMA | Fit a Generalized Linear Model with Gamma family for positive continuous data. |
| GLM_INV_GAUSS | Fits a Generalized Linear Model with Inverse Gaussian family for right-skewed positive data. |
| GLM_NEG_BINOM | Fits a Generalized Linear Model with Negative Binomial family for overdispersed count data. |
| GLM_POISSON | Fits a Generalized Linear Model with Poisson family for count data. |
| GLM_TWEEDIE | Fits a Generalized Linear Model with Tweedie family for flexible distribution modeling. |
Mixed Effects
| Tool | Description |
|---|---|
| GEE_MODEL | Fits a Generalized Estimating Equations (GEE) model for correlated data. |
| GLMM_BINOMIAL | Fits a Generalized Linear Mixed Model (GLMM) with binomial family for binary clustered data. |
| GLMM_POISSON | Fits a Generalized Linear Mixed Model (GLMM) with Poisson family for count clustered data. |
| MIXED_LINEAR_MODEL | Fits a Linear Mixed Effects Model (LMM) with random intercepts and slopes. |
Regression
| Tool | Description |
|---|---|
| GLS_REGRESSION | Fits a Generalized Least Squares (GLS) regression model. |
| INFLUENCE_DIAG | Computes regression influence diagnostics for identifying influential observations. |
| OLS_DIAGNOSTICS | Performs diagnostic tests on OLS regression residuals. |
| OLS_REGRESSION | Fits an Ordinary Least Squares (OLS) regression model. |
| QUANTILE_REGRESSION | Fits a quantile regression model to estimate conditional quantiles of the response distribution. |
| REGRESS_DIAG | Performs comprehensive regression diagnostic tests. |
| ROBUST_LINEAR_MODEL | Fits a robust linear regression model using M-estimators. |
| SPECIFICATION_TESTS | Performs regression specification tests to detect model misspecification. |
| WLS_REGRESSION | Fits a Weighted Least Squares (WLS) regression model. |
Survival
| Tool | Description |
|---|---|
| COX_HAZARDS | Fits a Cox Proportional Hazards regression model for survival data. |
| EXP_SURVIVAL_REG | Fits a parametric exponential survival regression model. |
| KAPLAN_MEIER | Computes the Kaplan-Meier survival function estimate for time-to-event data. |
Multivariate Analysis
| Tool | Description |
|---|---|
| CANCORR | Performs Canonical Correlation Analysis (CCA) between two sets of variables. |
| FACTOR_ANALYSIS | Performs exploratory factor analysis with rotation. |
| MANOVA_TEST | Performs Multivariate Analysis of Variance (MANOVA) for multiple dependent variables. |
| PCA_ANALYSIS | Performs Principal Component Analysis (PCA) for dimensionality reduction. |
Probability Distributions
Continuous Distributions
| Tool | Description |
|---|---|
| BETA | Wrapper for scipy.stats.beta distribution providing multiple statistical methods. |
| CAUCHY | Wrapper for scipy.stats.cauchy distribution providing multiple statistical methods. |
| CHISQ | Compute various statistics and functions for the chi-squared distribution from scipy.stats.chi2. |
| EXPON | Exponential distribution function wrapping scipy.stats.expon. |
| F_DIST | Unified interface to the main methods of the F-distribution, including PDF, CDF, inverse CDF, survival function, and distribution statistics. |
| LAPLACE | Laplace distribution function supporting multiple methods. |
| LOGNORM | Compute lognormal distribution statistics and evaluations. |
| NORM | Normal (Gaussian) distribution function supporting multiple methods. |
| PARETO | Generalized Pareto distribution function supporting multiple methods. |
| T_DIST | Student’s t distribution function supporting multiple methods from scipy.stats.t. |
| UNIFORM | Uniform distribution function supporting multiple methods. |
| WEIBULL_MIN | Compute various functions of the Weibull minimum distribution using scipy.stats.weibull_min. |
Discrete Distributions
| Tool | Description |
|---|---|
| BERNOULLI | Calculates properties of a Bernoulli discrete random variable. |
| BETABINOM | Compute Beta-binomial distribution values from scipy.stats.betabinom. |
| BETANBINOM | Compute Beta-negative-binomial distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
| BINOM | Compute Binomial distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
| BOLTZMANN | Compute Boltzmann distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
| DLAPLACE | Compute Discrete Laplace distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
| GEOM | Compute Geometric distribution values using scipy.stats.geom. |
| HYPERGEOM | Compute Hypergeometric distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
| LOGSER | Compute Log-Series distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
| NBINOM | Compute Negative Binomial distribution values using scipy.stats.nbinom. |
| NHYPERGEOM | Compute Negative Hypergeometric distribution values using scipy.stats.nhypergeom. |
| PLANCK | Compute Planck distribution values using scipy.stats.planck. |
| POISSON_DIST | Compute Poisson distribution values using scipy.stats.poisson. |
| RANDINT | Compute Uniform discrete distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
| SKELLAM | Compute Skellam distribution values using scipy.stats.skellam. |
| YULESIMON | Compute Yule-Simon distribution values using scipy.stats.yulesimon. |
| ZIPF | Compute Zipf distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
| ZIPFIAN | Compute Zipfian distribution values: PMF, CDF, SF, ICDF, ISF, mean, variance, std, or median. |
Multivariate Distributions
| Tool | Description |
|---|---|
| DIRICHLET | Computes the PDF, log-PDF, mean, variance, covariance, entropy, or draws random samples from a Dirichlet distribution. |
| DIRICHLET_MULTINOM | Computes the probability mass function, log probability mass function, mean, variance, or covariance of the Dirichlet multinomial distribution. |
| MATRIX_NORMAL | Computes the PDF, log-PDF, or draws random samples from a matrix normal distribution. |
| MULTINOMIAL | Compute the probability mass function, log-PMF, entropy, covariance, or draw random samples from a multinomial distribution. |
| MULTIVARIATE_NORMAL | Computes the PDF, CDF, log-PDF, log-CDF, entropy, or draws random samples from a multivariate normal distribution. |
| MULTIVARIATE_T | Computes the PDF, CDF, or draws random samples from a multivariate t-distribution. |
| MV_HYPERGEOM | Computes probability mass function, log-PMF, mean, variance, covariance, or draws random samples from a multivariate hypergeometric distribution. |
| ORTHO_GROUP | Draws random samples of orthogonal matrices from the O(N) Haar distribution using scipy.stats.ortho_group. |
| RANDOM_CORRELATION | Generates a random correlation matrix with specified eigenvalues. |
| SPECIAL_ORTHO_GROUP | Draws random samples from the special orthogonal group SO(N), returning orthogonal matrices with determinant +1. |
| UNIFORM_DIRECTION | Draws random unit vectors uniformly distributed on the surface of a hypersphere in the specified dimension. |
| UNITARY_GROUP | Generate a random unitary matrix of dimension N from the Haar distribution. |
| VONMISES_FISHER | Computes the PDF, log-PDF, entropy, or draws random samples from a von Mises-Fisher distribution on the unit hypersphere. |
| WISHART | Computes the PDF, log-PDF, or draws random samples from the Wishart distribution using scipy.stats.wishart. |
Summary Statistics
| Tool | Description |
|---|---|
| DESCRIBE | Compute descriptive statistics using scipy.stats.describe module. |
| EFFECT_SIZES | Computes effect size measures for comparing two groups. |
| EXPECTILE | Calculates the expectile of a dataset using scipy.stats.expectile. |
| GMEAN | Compute the geometric mean of the input data, flattening the input and ignoring non-numeric values. |
| HMEAN | Calculates the harmonic mean of the input data, flattening the input and ignoring non-numeric values. |
| KURTOSIS | Compute the kurtosis (Fisher or Pearson) of a dataset. |
| MODE | Returns the modal (most common) value in the passed array. Wraps scipy.stats.mode to flatten the input, ignore non-numeric values, and always return a single mode (the smallest if multiple). If no mode is found (all values occur only once), returns an error. |
| MOMENT | Calculates the nth moment about the mean for a sample. |
| PMEAN | Computes the power mean (generalized mean) of the input data for a given power p. |
| SKEWNESS | Calculate the skewness of a dataset. |