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.

Math

Comprehensive collection of mathematical functions including calculus, linear algebra, number theory, and optimization.

Statistics

Powerful statistical tools for data analysis, probability distributions, hypothesis testing, and Bayesian inference.

Engineering

Technical computing tools for fluids, heat transfer, structural analysis, thermodynamics, and photovoltaics.

Charts

Modern scientific and statistical visualization tools for 2D, 3D, and specialty technical plotting.

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.
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).
BIOT	Calculate the Biot number for heat transfer.
BOILING	Calculate the Boiling number (Bg), a dimensionless number for boiling heat transfer.
BOND	Calculate the Bond number (Bo), also known as the Eötvös number (Eo).
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.
FROUDE_DENSIMETRIC	Calculate the densimetric Froude number.
GRAETZ_HEAT	Calculate the Graetz number.
GRASHOF	Calculate the Grashof number.
HAGEN	Calculate the Hagen number.
JAKOB	Calculate the Jakob number for boiling fluid.
KNUDSEN	Calculate the Knudsen number.
LEWIS	Calculate the Lewis number.
MACH	Calculate the Mach number.
MORTON	Calculate the Morton number.
NUSSELT	Calculate the Nusselt number.
OHNESORGE	Calculate the Ohnesorge number.
PECLET_HEAT	Calculate the Peclet number for heat transfer.
PECLET_MASS	Calculate the Peclet number for mass transfer.
POWER_NUMBER	Calculate the Power number for an agitator.
PRANDTL	Calculate the Prandtl number.
RAYLEIGH	Calculate the Rayleigh number.
RELATIVE_ROUGHNESS	Calculate the relative roughness.
REYNOLDS	Calculate the Reynolds number.
SCHMIDT	Calculate the Schmidt number.
SHERWOOD	Calculate the Sherwood number.
STANTON	Calculate the Stanton number.
STOKES_NUMBER	Calculate the Stokes number.
STROUHAL	Calculate the Strouhal number.
SURATMAN	Calculate the Suratman number.
WEBER	Calculate the Weber number.

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.

Heat Transfer

Air Cooler

Tool	Description
AIR_NOISE_GPSA	Compute air cooler noise using the GPSA correlation.
AIR_NOISE_MUKHERJEE	Compute air cooler noise using the Mukherjee correlation.
DP_ESDU_HIGH_FIN	Compute air-side pressure drop for high-fin tube banks.
DP_ESDU_LOW_FIN	Compute air-side pressure drop for low-fin tube banks.
ESDU_TUBE_ROW_CORR	Compute the ESDU tube row correction factor for a tube bundle.
FIN_EFF_KERN_KRAUS	Compute circular fin efficiency for constant-thickness fins.
FT_AIRCOOLER	Compute the LMTD correction factor for an air cooler crossflow exchanger.
H_BRIGGS_YOUNG	Compute air-side heat transfer coefficient using Briggs and Young correlations.
H_ESDU_HIGH_FIN	Compute air-side heat transfer coefficient for high-fin tube banks.
H_ESDU_LOW_FIN	Compute air-side heat transfer coefficient for low-fin tube banks.
H_GANGULI_VDI	Compute air-side heat transfer coefficient using the Ganguli VDI method.
LMTD	Compute the log-mean temperature difference for a heat exchanger.
WALL_FACTOR	Compute wall property correction factors for heat transfer correlations.

Boiling Flow

Tool	Description
CHEN_BENNETT	Compute the Chen-Bennett boiling heat transfer coefficient.
CHEN_EDELSTEIN	Compute the Chen-Edelstein boiling heat transfer coefficient.
COOPER	Compute the Cooper nucleate boiling heat transfer coefficient.
FORSTER_ZUBER	Compute the Forster-Zuber nucleate boiling heat transfer coefficient.
LAZAREK_BLACK	Compute the Lazarek-Black boiling heat transfer coefficient.
LI_WU	Compute the Li-Wu boiling heat transfer coefficient.
LIU_WINTERTON	Compute the Liu-Winterton boiling heat transfer coefficient.
LOCKHART_XTT	Compute the Lockhart-Martinelli Xtt two-phase flow parameter.
SUN_MISHIMA	Compute the Sun-Mishima boiling heat transfer coefficient.
THOME	Compute the Thome microchannel boiling heat transfer coefficient.
TO_SOLVE_Q_THOME	Compute the Thome heat flux residual for a specified wall temperature.
TURBULENT_DITTUS	Compute the Dittus-Boelter turbulent Nusselt number.
TURBULENT_GNIEL	Compute the Gnielinski turbulent Nusselt number.
YUN_HEO_KIM	Compute the Yun-Heo-Kim boiling heat transfer coefficient.

Boiling Nucleic

Tool	Description
BIER	Compute nucleate boiling heat transfer coefficient using the Bier correlation.
GORENFLO	Compute nucleate boiling heat transfer coefficient using the Gorenflo correlation.
H_NUCLEIC	Compute nucleate boiling heat transfer coefficient with method selection.
H_NUCLEIC_METHODS	List available nucleate boiling correlations based on provided inputs.
HEDH_MONTINSKY	Compute nucleate boiling critical heat flux using the HEDH-Montinsky correlation.
HEDH_TABOREK	Compute nucleate boiling heat transfer coefficient using the HEDH-Taborek correlation.
MCNELLY	Compute nucleate boiling heat transfer coefficient using the McNelly correlation.
MONTINSKY	Compute nucleate boiling heat transfer coefficient using the Montinsky correlation.
QMAX_BOIL_METHODS	List available nucleate boiling critical heat flux correlations.
QMAX_BOILING	Compute nucleate boiling critical heat flux with method selection.
ROHSENOW	Compute nucleate boiling heat transfer coefficient using the Rohsenow correlation.
SERTH_HEDH	Compute nucleate boiling critical heat flux for tube bundles using the Serth-HEDH correlation.
STEPHAN_ABDELSALAM	Compute nucleate boiling heat transfer coefficient using the Stephan-Abdelsalam correlation.
ZUBER	Compute nucleate boiling critical heat flux using the Zuber correlation.

Boiling Plate

Tool	Description
H_BOIL_HAN_LEE_KIM	Calculate boiling heat transfer coefficient using Han Lee Kim correlation.
H_BOIL_HANLEEKIM	Calculate boiling heat transfer coefficient using Han Lee Kim correlation.
H_BOIL_HUANG_SHEER	Calculate boiling heat transfer coefficient using Huang Sheer correlation.
H_BOIL_HUANGSHEER	Calculate boiling heat transfer coefficient using Huang Sheer correlation.
H_BOIL_LEE_KANG_KIM	Calculate boiling heat transfer coefficient using Lee Kang Kim correlation.
H_BOIL_LEEKANGKIM	Calculate boiling heat transfer coefficient using Lee Kang Kim correlation.
H_BOILING_AMALFI	Calculate boiling heat transfer coefficient using Amalfi correlation.
H_BOILING_YAN_LIN	Calculate boiling heat transfer coefficient using Yan Lin correlation.
THERMAL_DIFFUSIVITY	Calculate thermal diffusivity for a fluid.

Condensation

Tool	Description
AKERS_DEANS_CROSSER	Calculate condensation heat transfer coefficient in tubes using the Akers-Deans-Crosser correlation.
BOYKO_KRUZHILIN	Calculate condensation heat transfer coefficient using the Boyko-Kruzhilin correlation.
CAVALLINI_SMITH_Z	Calculate condensation heat transfer coefficient using the Cavallini-Smith-Zecchin correlation.
CAVALLINI_SZ	Calculate condensation heat transfer coefficient using the Cavallini-Smith-Zecchin correlation.
H_KINETIC	Calculate kinetic theory condensation heat transfer coefficient.
NUSSELT_LAMINAR	Calculate laminar film condensation heat transfer on a flat plate using Nusselt theory.
SHAH	Calculate condensation heat transfer coefficient using the Shah correlation.

Conduction

Tool	Description
ACOSH	Compute the inverse hyperbolic cosine.
CYL_HEAT_TRANSFER	Compute heat transfer through a multilayer cylindrical wall.
K_TO_R	Compute thermal resistance from thermal conductivity.
K_TO_R_VALUE	Convert thermal conductivity to R-value.
K_TO_THERM_RESIST	Convert thermal conductivity to thermal resistivity.
LEGACY_CYL_HT	Deprecated alias for cyl_heat_transfer.
LEGACY_K_THERM_RES	Deprecated alias for k_to_therm_resist.
LEGACY_S_PIPE_ECC	Deprecated alias for S_pipe_ecc_to_pipe.
LEGACY_S_PIPE_NORM	Deprecated alias for S_pipe_norm_plane.
LEGACY_S_PIPE_PAIR	Deprecated alias for S_pipe_to_pipe.
LEGACY_S_PIPE_PLANE	Deprecated alias for S_pipe_to_plane.
LEGACY_S_PIPE_PLNS	Deprecated alias for S_pipe_two_planes.
LEGACY_S_SPH_PLANE	Deprecated alias for S_sphere_to_plane.
LEGACY_THERM_RES_K	Deprecated alias for therm_resist_to_k.
LOG	Compute the logarithm of a value with optional base.
R_CYLINDER	Compute thermal resistance of a cylindrical wall.
R_TO_K	Compute thermal conductivity from thermal resistance.
R_VALUE_TO_K	Convert R-value to thermal conductivity.
S_PIPE_ECC_TO_PIPE	Compute the shape factor for eccentric isothermal pipes.
S_PIPE_NORM_PLANE	Compute the shape factor for a pipe normal to a plane.
S_PIPE_TO_PIPE	Compute the shape factor for two isothermal pipes.
S_PIPE_TO_PLANE	Compute the shape factor for a pipe near a plane.
S_PIPE_TWO_PLANES	Compute the shape factor for a pipe between two planes.
S_SPHERE_TO_PLANE	Compute the shape factor for a sphere near a plane.
THERM_RESIST_TO_K	Convert thermal resistivity to thermal conductivity.

Conv External

Tool	Description
NU_CYL_CB	Calculate the Nusselt number for crossflow across a single cylinder using the Churchill-Bernstein correlation.
NU_CYL_PL62	Calculate the Nusselt number for crossflow across a single cylinder using the Perkins-Leppert 1962 correlation.
NU_CYL_PL64	Calculate the Nusselt number for crossflow across a single cylinder using the Perkins-Leppert 1964 correlation.
NU_CYL_SG	Calculate the Nusselt number for crossflow across a single cylinder using the Sanitjai-Goldstein correlation.
NU_CYL_WHITAKER	Calculate the Nusselt number for crossflow across a single cylinder using the Whitaker correlation.
NU_CYL_ZUKAUSKAS	Calculate the Nusselt number for crossflow across a single cylinder using the Zukauskas correlation.
NU_CYLINDER_FAND	Calculate the Nusselt number for crossflow across a single cylinder using the Fand correlation.
NU_CYLINDER_MCADAMS	Calculate the Nusselt number for crossflow across a single cylinder using the McAdams correlation.
NU_EXT_CYL	Calculate the Nusselt number for crossflow across a single cylinder using a selected correlation.
NU_EXT_CYL_METHODS	List available correlations for external cylinder forced convection.
NU_EXT_HORZ_METHODS	List available correlations for forced convection across a horizontal plate.
NU_EXT_HORZ_PLATE	Calculate the Nusselt number for forced convection across a horizontal plate.
NU_HORZ_LAM_BAEHR	Calculate the Nusselt number for laminar flow across an isothermal flat plate using the Baehr correlation.
NU_HORZ_LAM_COZOE	Calculate the Nusselt number for laminar flow across an isothermal flat plate using the Churchill-Ozoe correlation.
NU_HORZ_TURB_KREITH	Calculate the Nusselt number for turbulent flow across an isothermal flat plate using the Kreith correlation.
NU_HORZ_TURB_SCHL	Calculate the Nusselt number for turbulent flow across an isothermal flat plate using the Schlichting correlation.

Conv Free Enclosed

Tool	Description
NU_RA_HOLLANDS	Calculate the Nusselt number between horizontal plates using the Hollands correlation.
NU_RA_HOLLINGHERWIG	Calculate the Nusselt number between infinite horizontal plates using the Holling-Herwig correlation.
NU_RA_PROBERT	Calculate the Nusselt number between infinite horizontal plates using the Probert correlation.
NU_VERT_THESS	Calculate the Nusselt number between vertical plates using the Thess correlation.
NU_VHELIX_ALI	Calculate the Nusselt number for natural convection around a vertical helical coil using the Ali correlation.
NU_VHELIX_PRR	Calculate the Nusselt number for natural convection around a vertical helical coil using the Prabhanjan-Rennie-Raghavan correlation.
RAC_RAYLEIGH	Calculate the critical Rayleigh number for enclosed parallel plates.
RAC_RAYLEIGH_DISK	Calculate the critical Rayleigh number for enclosed parallel disks.

Conv Free Immersed

Tool	Description
NU_COIL_XIN_EBADIAN	Calculate the Nusselt number for natural convection around a helical coil.
NU_FREE_HPLATE	Calculate the Nusselt number for free convection from a horizontal plate.
NU_FREE_HPLATE_METH	List available correlations for free convection from a horizontal plate.
NU_FREE_VPLATE	Calculate the Nusselt number for free convection from a vertical plate.
NU_FREE_VPLATE_METH	List available correlations for free convection from a vertical plate.
NU_HCYL_CHURCHILL	Calculate the Nusselt number for a horizontal cylinder using Churchill-Chu.
NU_HCYL_KUEHNGOLD	Calculate the Nusselt number for a horizontal cylinder using Kuehn-Goldstein.
NU_HCYL_METHODS	List available correlations for free convection from a horizontal cylinder.
NU_HCYL_MORGAN	Calculate the Nusselt number for a horizontal cylinder using Morgan.
NU_HORIZ_CYL	Select and calculate a Nusselt number correlation for a horizontal cylinder.
NU_HPLATE_MCADAMS	Calculate the Nusselt number for a horizontal plate using McAdams.
NU_HPLATE_ROHSENOW	Calculate the Nusselt number for a horizontal plate using Rohsenow.
NU_HPLATE_VDI	Calculate the Nusselt number for a horizontal plate using VDI.
NU_SPHERE_CHURCHILL	Calculate the Nusselt number for a sphere using Churchill.
NU_VCYL_ALARABI	Calculate the Nusselt number for a vertical cylinder using Al-Arabi and Khamis.
NU_VCYL_CARNEMORGAN	Calculate the Nusselt number for a vertical cylinder using Carne-Morgan.
NU_VCYL_EIGENSON	Calculate the Nusselt number for a vertical cylinder using Eigenson-Morgan.
NU_VCYL_GRIFFITHS	Calculate the Nusselt number for a vertical cylinder using Griffiths-Davis-Morgan.
NU_VCYL_HANESIAN	Calculate the Nusselt number for a vertical cylinder using Hanesian-Kalish-Morgan.
NU_VCYL_JAKOB	Calculate the Nusselt number for a vertical cylinder using Jakob-Linke-Morgan.
NU_VCYL_KREITH	Calculate the Nusselt number for a vertical cylinder using Kreith-Eckert.
NU_VCYL_MCADAMS	Calculate the Nusselt number for a vertical cylinder using McAdams-Weiss-Saunders.
NU_VCYL_METHODS	List available correlations for free convection from a vertical cylinder.
NU_VCYL_POPIEL	Calculate the Nusselt number for a vertical cylinder using Popiel-Churchill.
NU_VCYL_TOULOUKIAN	Calculate the Nusselt number for a vertical cylinder using Touloukian-Morgan.
NU_VERT_CYL	Select and calculate a Nusselt number correlation for a vertical cylinder.
NU_VPLATE_CHURCHILL	Calculate the Nusselt number for a vertical plate using Churchill-Chu.

Conv Internal

Tool	Description
HEL_TURB_NU_MORI	Calculate the turbulent helical coil Nusselt number using Mori-Nakayama.
HEL_TURB_NU_SCHM	Calculate the turbulent helical coil Nusselt number using Schmidt.
HEL_TURB_NU_XIN	Calculate the turbulent helical coil Nusselt number using Xin-Ebadian.
LAM_ENTRY_BAEHR	Calculate laminar entry Nusselt number using Baehr-Stephan.
LAM_ENTRY_HAUSEN	Calculate laminar thermal entry Nusselt number using Hausen.
LAM_ENTRY_SEIDER	Calculate laminar entry Nusselt number using Seider-Tate.
LAMINAR_Q_CONST	Return the laminar constant-heat-flux Nusselt number for a pipe.
LAMINAR_T_CONST	Return the laminar constant-wall-temperature Nusselt number for a pipe.
MORIMOTO_HOTTA	Calculate the Nusselt number for flow in a spiral heat exchanger.
NU_CONV_INT_METHODS	List available internal convection correlations for a pipe.
NU_CONV_INTERNAL	Compute the Nusselt number for internal pipe convection.
NU_LAM_RECT_SHAN	Calculate the laminar Nusselt number for a rectangular duct.
TURB_BHATTI_SHAH	Calculate turbulent Nusselt number using the Bhatti-Shah correlation.
TURB_CHURCHILL	Calculate turbulent Nusselt number using Churchill-Zajic.
TURB_COLBURN	Calculate turbulent Nusselt number using the Colburn correlation.
TURB_DIPPREY	Calculate turbulent Nusselt number using Dipprey-Sabersky.
TURB_DITTUS	Calculate turbulent Nusselt number using Dittus-Boelter.
TURB_DREXEL	Calculate turbulent Nusselt number using Drexel-McAdams.
TURB_ENTRY_HAUSEN	Calculate turbulent entry-region Nusselt number using Hausen.
TURB_ESDU	Calculate turbulent Nusselt number using the ESDU correlation.
TURB_FRIEND	Calculate turbulent Nusselt number using Friend-Metzner.
TURB_GNIEL_S1	Calculate turbulent Nusselt number using Gnielinski smooth pipe case 1.
TURB_GNIEL_S2	Calculate turbulent Nusselt number using Gnielinski smooth pipe case 2.
TURB_GNIELINSKI	Calculate turbulent Nusselt number using the Gnielinski correlation.
TURB_PETUKHOV	Calculate turbulent Nusselt number using Petukhov-Kirillov-Popov.
TURB_PRANDTL	Calculate turbulent Nusselt number using the Prandtl correlation.
TURB_SIEDER	Calculate turbulent Nusselt number using the Sieder-Tate correlation.
TURB_VON_KARMAN	Calculate turbulent Nusselt number using the von Karman correlation.
TURB_WEBB	Calculate turbulent Nusselt number using the Webb correlation.

Conv Jacket

Tool	Description
LEHRER	Calculate the average heat transfer coefficient for a jacket around a vessel.
STEIN_SCHMIDT	Calculate the average heat transfer coefficient for a jacket around a vessel.

Conv Packed Bed

Tool	Description
NU_ACHENBACH	Calculate Nusselt number for a packed bed using the Achenbach correlation.
NU_KTA	Calculate Nusselt number for a packed bed using the KTA correlation.
NU_PACKED_BED_GN	Calculate Nusselt number for a packed bed using the Gnielinski correlation.
NU_WAKAO_KAGEI	Calculate Nusselt number for a packed bed using the Wakao-Kagei correlation.

Conv Plate

Tool	Description
FRIC_PLATE_MARTIN99	Calculate Darcy friction factor for chevron plate exchangers (Martin 1999).
FRIC_PLATE_MARTINV	Calculate Darcy friction factor for chevron plate exchangers (VDI Heat Atlas variant).
NU_PLATE_KHAN_KHAN	Calculate Nusselt number for single-phase flow in a chevron-style plate heat exchanger (Khan and Khan).
NU_PLATE_KUMAR	Calculate Nusselt number for a well-designed chevron plate heat exchanger (Kumar correlation).
NU_PLATE_MARTIN	Calculate Nusselt number for chevron plate exchangers using the Martin correlation.
NU_PLATE_MULEYMANG	Calculate Nusselt number for chevron plate exchangers using the Muley-Manglik correlation.

Conv Supercritical

Tool	Description
NU_BISHOP	Calculate Nusselt number for supercritical pipe flow using the Bishop correlation.
NU_BRINGER_SMITH	Calculate Nusselt number for near-supercritical flow using the Bringer-Smith correlation.
NU_GORBAN	Calculate Nusselt number for supercritical flow using the Gorban correlation.
NU_GRIEM	Calculate Nusselt number for supercritical flow using the Griem correlation.
NU_GUPTA	Calculate Nusselt number for supercritical flow using the Gupta correlation.
NU_JACKSON	Calculate Nusselt number for supercritical flow using the Jackson correlation.
NU_KITOH	Calculate Nusselt number for supercritical flow using the Kitoh correlation.
NU_KRASN_PROTO	Calculate Nusselt number for supercritical flow using the Krasnoshchekov-Protopopov correlation.
NU_KRASNOSH_PROTO	Calculate Nusselt number for supercritical flow using the Krasnoshchekov-Protopopov correlation.
NU_KRASNOSHCHEKOV	Calculate Nusselt number for supercritical flow using the Krasnoshchekov correlation.
NU_MCADAMS	Calculate Nusselt number for supercritical flow using the McAdams correlation.
NU_MOKRY	Calculate Nusselt number for supercritical flow using the Mokry correlation.
NU_ORNATSKY	Calculate Nusselt number for supercritical flow using the Ornatsky correlation.
NU_PETUKHOV	Calculate Nusselt number for supercritical flow using the Petukhov correlation.
NU_SHITSMAN	Calculate Nusselt number for supercritical flow using the Shitsman correlation.
NU_SWENSON	Calculate Nusselt number for supercritical flow using the Swenson correlation.
NU_XU	Calculate Nusselt number for supercritical flow using the Xu correlation.
NU_YAMAGATA	Calculate Nusselt number for supercritical flow using the Yamagata correlation.
NU_ZHU	Calculate Nusselt number for supercritical flow using the Zhu correlation.

Conv Tube Bank

Tool	Description
CTB_BAFFLE_CORR	Compute Bell-Delaware baffle correction factor for crossflow.
CTB_BAFFLE_LEAK	Compute Bell-Delaware baffle leakage correction factor.
CTB_BUNDLE_BYPASS	Compute Bell-Delaware bundle bypass correction factor.
CTB_DP_KERN	Compute tube bank pressure drop using the Kern method.
CTB_DP_ZUKAUSKAS	Compute tube bank pressure drop using the Zukauskas method.
CTB_ESDU_ANG_CORR	Compute the ESDU tube bank inclination correction factor.
CTB_ESDU_ROW_CORR	Compute the ESDU tube row correction factor for a tube bundle.
CTB_HORNER	Evaluate a polynomial using Horner’s method.
CTB_LAMINAR_CORR	Compute Bell-Delaware laminar flow correction factor.
CTB_NU_ESDU_73031	Compute tube bank Nusselt number using the ESDU 73031 correlation.
CTB_NU_GRIMISON	Compute tube bank Nusselt number using the Grimison correlation.
CTB_NU_HEDH	Compute tube bank Nusselt number using the HEDH correlation.
CTB_NU_ZUK_BEJAN	Compute tube bank Nusselt number using the Zukauskas-Bejan correlation.
CTB_UNEQUAL_BAFFLE	Compute Bell-Delaware unequal baffle spacing correction factor.
CTB_WALL_FACTOR	Compute wall correction factor for heat transfer properties.
CTB_ZUK_ROW_CORR	Compute Zukauskas tube row correction factor for a tube bundle.

Conv Two Phase

Tool	Description
AGGOUR	Calculate two-phase heat transfer coefficient using the Aggour correlation.
DAVIS_DAVID	Calculate two-phase heat transfer coefficient using the Davis-David correlation.
ELAMVALUTHI_SRIN	Calculate two-phase heat transfer coefficient using the Elamvaluthi-Srinivas correlation.
GROOTHUIS_HENDAL	Calculate two-phase heat transfer coefficient using the Groothuis-Hendal correlation.
H_TWO_PHASE	Calculate two-phase heat transfer coefficient using a selected correlation.
H_TWO_PHASE_METHODS	List available two-phase heat transfer correlations for a tube.
HUGHMARK	Calculate two-phase laminar heat transfer coefficient using the Hughmark correlation.
KNOTT	Calculate two-phase heat transfer coefficient using the Knott correlation.
KUDIRKA_GROSH_MCF	Calculate two-phase heat transfer coefficient using the Kudirka-Grosh-McFadden correlation.
LAMINAR_ENTRY_ST	Calculate laminar entry-region Nusselt number using Seider-Tate.
MARTIN_SIMS	Calculate two-phase heat transfer coefficient using the Martin-Sims correlation.
RAVIPUDI_GODBOLD	Calculate two-phase heat transfer coefficient using the Ravipudi-Godbold correlation.

Core

Tool	Description
CC_HX_TEMP_CHECK	Check whether two fluid temperature profiles are plausible for countercurrent exchange.
FIN_EFFICIENCY_KK	Compute circular fin efficiency using the Kern-Kraus correlation.
IS_HEATING_PROPERTY	Determine whether a wall heats or cools a flow from a property ratio.
IS_HEATING_TEMP	Determine whether a wall heats or cools a flow from temperatures.
WALL_FACTOR_FD	Compute a wall correction factor for frictional pressure loss.
WALL_FACTOR_NU	Compute a wall correction factor for Nusselt number calculations.

Hx

Tool	Description
BAFFLE_THICKNESS	Compute baffle thickness from shell diameter and support spacing.
BUNDLE_FROM_TUBES	Calculate bundle diameter required for a specified tube count.
CALC_CMAX	Calculate the maximum heat capacity rate of two streams.
CALC_CMIN	Calculate the minimum heat capacity rate of two streams.
CALC_CR	Calculate the heat capacity rate ratio for two streams.
CHECK_TUBING_TEMA	Check whether a tubing size and gauge are valid per TEMA.
D_BAFFLE_HOLES	Calculate baffle hole diameter for tubes using TEMA guidance.
D_FOR_NTUBES_VDI	Estimate tube bundle diameter from tube count using the VDI method.
DBUNDLE_MIN	Estimate a minimum bundle diameter for a given tube outer diameter.
DBUNDLE_NT_HEDH	Estimate tube bundle diameter from tube count using the HEDH correlation.
DBUNDLE_NT_PHADK	Calculate tube bundle diameter for a given tube count using Phadke’s method.
EFF_FROM_NTU	Calculate effectiveness from NTU, capacity ratio, and configuration.
EFF_NTU_METHOD	Solve a heat exchanger with the effectiveness-NTU method.
F_LMTD_FAKHERI	Compute the LMTD correction factor for shell-and-tube exchangers.
L_UNSUPPORTED_MAX	Get the maximum unsupported tube length from TEMA guidance.
NTU_FROM_EFF	Solve NTU from effectiveness, capacity ratio, and configuration.
NTU_FROM_P_BASIC	Solve NTU for a basic exchanger from effectiveness and capacity ratio.
NTU_FROM_P_E	Solve NTU for a TEMA E exchanger from effectiveness and capacity ratio.
NTU_FROM_P_PLATE	Solve NTU for a plate exchanger from effectiveness and capacity ratio.
NTU_FROM_UA	Calculate NTU from UA and the minimum heat capacity rate.
NTUBES	Calculate the number of tubes that fit in a tube bundle.
NTUBES_HEDH	Estimate tube count from bundle diameter using the HEDH correlation.
NTUBES_PHADKEB	Calculate tube count from bundle diameter using Phadke’s method.
NTUBES_VDI	Estimate tube count from bundle diameter using the VDI method.
P_NTU_METHOD	Solve a heat exchanger with the P-NTU method.
SHELL_CLEARANCE	Look up shell-to-bundle clearance from TEMA guidance.
TEMP_EFF_BASIC	Compute temperature effectiveness for a basic exchanger type.
TEMP_EFF_PLATE	Compute temperature effectiveness for a plate exchanger.
TEMP_EFF_TEMA_E	Compute temperature effectiveness for a TEMA E exchanger.
UA_FROM_NTU	Calculate UA from NTU and the minimum heat capacity rate.

Insulation

Tool	Description
ASHRAE_K	Return thermal conductivity for an ASHRAE material.
CP_MATERIAL	Return heat capacity for an insulating or building material.
INTERP	Perform one-dimensional linear interpolation.
K_MATERIAL	Return thermal conductivity for an insulating or building material.
NEAREST_MATERIAL	Return the nearest material match from insulation tables.
REFRACTORY_VDI_CP	Return refractory heat capacity from VDI data.
REFRACTORY_VDI_K	Return refractory thermal conductivity from VDI data.
RHO_MATERIAL	Return density for an insulating or building material.

Radiation

Tool	Description
BB_SPECTRAL_RAD	Compute blackbody spectral radiance at a wavelength.
GREY_TRANSMITTANCE	Compute grey-body transmittance from extinction and path length.
Q_RAD	Compute radiant heat flux between a surface and surroundings.

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.

Structural

Tool	Description
BEAM_2D	Analyze continuous 2D beams with auto-meshing.
FRAME_2D	Analyze 2D rigid frames.
PLATE	Analyze 2D plates and shells.
TRUSS_2D	Analyze 2D pin-jointed trusses.

Thermodynamics

Tool	Description
CHEMICAL_PROPS	Retrieve physical and thermodynamic properties for a chemical specimen.
HA_PROPS_SI	Calculate humid air properties using CoolProp psychrometrics.
MIXTURE_FLASH	Perform a flash calculation for a chemical mixture and return key properties.
MIXTURE_STRING	Create a formatted CoolProp mixture string from component fluids and mole fractions.
PHASE_SI	Identify the phase of a fluid at a given state using CoolProp.
PROPS_SI	Calculate thermophysical properties of fluids using CoolProp.

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.
AGRICULTURE	Fits agriculture models to data using scipy.optimize.curve_fit.
BINDING_MODEL	Fits binding_model models to data using scipy.optimize.curve_fit.
CHROMA_PEAKS	Fits chroma_peaks models to data using scipy.optimize.curve_fit.
DOSE_RESPONSE	Fits dose_response models to data using scipy.optimize.curve_fit.
ELECTRO_ION	Fits electro_ion models to data using scipy.optimize.curve_fit.
ENZYME_BASIC	Fits enzyme_basic models to data using scipy.optimize.curve_fit.
ENZYME_INHIBIT	Fits enzyme_inhibit models to data using scipy.optimize.curve_fit.
EXP_ADVANCED	Fits exp_advanced models to data using scipy.optimize.curve_fit.
EXP_DECAY	Fits exp_decay models to data using scipy.optimize.curve_fit.
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.
GROWTH_SIGMOID	Fits growth_sigmoid models to data using scipy.optimize.curve_fit.
MISC_PIECEWISE	Fits misc_piecewise models to data using scipy.optimize.curve_fit.
PEAK_ASYM	Fits peak_asym models to data using scipy.optimize.curve_fit.
POLY_BASIC	Fits poly_basic models to data using scipy.optimize.curve_fit.
RHEOLOGY	Fits rheology models to data using scipy.optimize.curve_fit.
SPECTRO_PEAKS	Fits spectro_peaks models to data using scipy.optimize.curve_fit.
STAT_DISTRIB	Fits stat_distrib models to data using scipy.optimize.curve_fit.
STAT_PARETO	Fits stat_pareto models to data using scipy.optimize.curve_fit.
WAVEFORM	Fits waveform models to data using scipy.optimize.curve_fit.

Geometry

Gis

Tool	Description
SHAPELY_AREA	Calculate the area of a geometry.
SHAPELY_BUFFER	Returns a representation of all points within a given distance of the this geometric object.
SHAPELY_CONTAINS	Returns True if the first geometry contains the second.
SHAPELY_CONVEX_HULL	Returns the smallest convex polygon that contains all the points in the object.
SHAPELY_DISTANCE	Calculate the minimum distance between two geometries.
SHAPELY_INTERSECT	Returns a representation of the intersection of this object with another geometric object.
SHAPELY_LINESTRING	Create a geometric line string from a list of points.
SHAPELY_PLOT	Plot geometries and return an image.
SHAPELY_POINT	Create a geometric point.
SHAPELY_POLYGON	Create a geometric polygon from a shell of points and optional holes.
SHAPELY_SIMPLIFY	Returns a simplified representation of the geometric object.
SHAPELY_UNION_ALL	Returns the union of all geometries in the input list.

Triangle Solvers

Tool	Description
TRI_AAAS	Solve a triangle from three angles and one side for scale.
TRI_SAS	Solve a triangle from two sides and their included angle.
TRI_SOLVE	Solve a triangle from any valid combination of three known side/angle values.
TRI_SSA	Solve a triangle from two sides and a non-included angle using SSA branch selection.
TRI_SSS	Solve a triangle from three known side lengths.

Trig Identities

Tool	Description
TRIG_EXPAND	Expand trigonometric compound-angle expressions into component terms.
TRIG_FU	Simplify trigonometric expressions using the Fu transformation pipeline.
TRIG_TR1	Rewrite secant and cosecant into reciprocal cosine and sine forms.
TRIG_TR10	Expand sine and cosine of summed angles into separated component terms.
TRIG_TR2	Rewrite tangent and cotangent into sine-cosine ratio forms.
TRIG_TR3	Normalize trig signs and induced odd/even identity forms.
TRIG_TR4	Evaluate exact trigonometric values at standard special angles.
TRIG_TR5	Replace even powers of sine using a cosine-based identity.
TRIG_TR6	Replace even powers of cosine using a sine-based identity.
TRIG_TR7	Apply power-reduction to cosine-squared terms.
TRIG_TR8	Convert products of sine and cosine terms into sum or difference forms.
TRIG_TR9	Convert sums of sine or cosine terms into product forms.
TRIG_TRIGSIMP	Simplify a trigonometric expression using identity transformations.

Graph Theory

Centrality

Tool	Description
BETWEENNESS_CENT	Calculate the shortest-path betweenness centrality for nodes.
CLOSENESS_CENT	Calculate the closeness centrality for nodes.
DEGREE_CENTRALITY	Calculate the degree centrality for nodes in a graph.
EIGENVECTOR_CENT	Calculate the eigenvector centrality for nodes.
PAGERANK	Calculate the PageRank of the nodes in the graph.

Network Flow

Tool	Description
MAX_FLOW_VALUE	Calculate the maximum flow value between a source and sink.
MIN_COST_FLOW_COST	Find the minimum cost to satisfy all demands in a network.
MIN_CUT_VALUE	Calculate the capacity of the minimum (source, sink) cut.

Shortest Path

Tool	Description
MIN_SPANNING_TREE	Find the minimum spanning tree (MST) of an undirected graph.
SHORTEST_PATH	Find the shortest path and its length between two nodes in a network.

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

Decompositions

Tool	Description
CHOLESKY	Compute the Cholesky decomposition of a real, symmetric positive-definite matrix.
HESSENBERG	Compute Hessenberg form of a matrix.
LDL	Compute the LDLt or Bunch-Kaufman factorization of a symmetric matrix.
LU	Compute LU decomposition of a matrix with partial pivoting.
POLAR	Compute the polar decomposition of a matrix.
QR	Compute the QR decomposition of a matrix and return either Q or R.
SCHUR	Compute Schur decomposition of a matrix.
SVD	Compute the Singular Value Decomposition (SVD) of a matrix using scipy.linalg.svd.

Eigenvalues

Tool	Description
EIG	Compute eigenvalues and eigenvectors of a general square matrix.
EIGH	Solve eigenvalue problem for a real symmetric or complex Hermitian matrix.
EIGVALS	Compute eigenvalues of a general square matrix.
EIGVALSH	Compute eigenvalues of a real symmetric or complex Hermitian matrix.

Equations

Tool	Description
LSQ_LINEAR	Solve a bounded linear least-squares problem.
LSTSQ	Compute the least-squares solution to Ax = B using scipy.linalg.lstsq.
SOLVE	Solve a linear matrix equation, or system of linear scalar equations.
SOLVE_BANDED	Solve the equation Ax = b for x, assuming A is a banded matrix.
SOLVE_TOEPLITZ	Solve a Toeplitz system using Levinson Recursion.
SOLVE_TRIANGULAR	Solve the equation Ax = b for x, assuming A is a triangular matrix.

Matrix Functions

Tool	Description
COSM	Compute the matrix cosine.
EXPM	Compute the matrix exponential of a square matrix using scipy.linalg.expm
FRAC_MAT_POW	Compute the fractional power of a square matrix.
LOGM	Compute matrix logarithm.
SINM	Compute the matrix sine.
SQRTM	Compute the matrix square root.

Matrix Operations

Tool	Description
DET	Compute the determinant of a square matrix.
INV	Compute the inverse of a square matrix.
KHATRI_RAO	Compute the Khatri-Rao product of two matrices.
KRON	Compute the Kronecker product of two matrices.
MATRIX_NORM	Compute matrix or vector norm.
PINV	Compute the Moore-Penrose pseudoinverse of a matrix using singular value decomposition (SVD).

Special Matrices

Tool	Description
CIRCULANT	Construct a circulant matrix.
HADAMARD	Construct a Hadamard matrix.
HANKEL	Construct a Hankel matrix.
HILBERT	Construct a Hilbert matrix.
PASCAL	Construct a Pascal matrix.
TOEPLITZ	Construct a Toeplitz matrix.

Number Theory

Gcd Lcm Divisors

Tool	Description
DIVCOUNT	Count divisors of an integer with optional modulus filtering.
DIVISORS	List divisors of an integer with optional proper divisor mode.
GCD	Compute the greatest common divisor of one or more integers.
ISQRT	Compute the integer square root of a nonnegative integer.
LCM	Compute the least common multiple of one or more integers.
PPY_PHI	Compute Euler’s totient function using the primePy implementation.
PROPDIVCNT	Count proper divisors of an integer with optional modulus filtering.
PROPDIVS	List proper divisors of an integer.
REDUCEDTOT	Compute Carmichael’s reduced totient function for an integer.
TOTIENT	Compute Euler’s totient function for an integer.

Modular Arithmetic

Tool	Description
DLOG	Solve discrete logarithms in modular arithmetic.
ISPRIMROOT	Check whether a value is a primitive root modulo n.
ISQUADRES	Check whether a value is a quadratic residue modulo p.
JACOBI	Compute the Jacobi symbol for two integers.
LEGENDRE	Compute the Legendre symbol modulo an odd prime.
NORDER	Find the multiplicative order of an integer modulo n.
NTHROOTMOD	Solve nth-power congruences modulo an integer.
PRIMROOT	Find a primitive root modulo n when one exists.
QUADCONG	Solve quadratic congruences modulo n.
QUADRES	List all quadratic residues modulo p.
SQRTMOD	Solve quadratic congruences of the form x squared congruent to a.

Prime Numbers

Tool	Description
FACTORINT	Compute the prime factorization of an integer with multiplicities.
ISPRIME	Determine whether an integer is prime.
NEXTPRIME	Return the ith prime number greater than a given integer.
PPY_PRIMEBETWEEN	List prime numbers between two bounds using primePy.
PPY_PRIMECHECK	Check primality using the primePy implementation.
PPY_PRIMEUPTO	List all prime numbers up to a maximum value using primePy.
PREVPRIME	Return the largest prime smaller than a given integer.
PRIME	Return the nth prime number.
PRIMEFACTORS	Return distinct prime factors of an integer.
PRIMEPI	Count the number of primes less than or equal to an integer.
PRIMERANGE	Generate all prime numbers in a specified interval.
RANDPRIME	Sample a prime number from a half-open integer interval.

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.

Special Functions

Bessel Functions

Tool	Description
BESSEL_HANKEL1	Compute the cylindrical Hankel function of the first kind and return real and imaginary parts.
BESSEL_HANKEL2	Compute the cylindrical Hankel function of the second kind and return real and imaginary parts.
BESSEL_IV	Compute the modified cylindrical Bessel function of the first kind for real order.
BESSEL_JN_ZEROS	Compute the first positive zeros of the integer-order Bessel function of the first kind.
BESSEL_JV	Compute the cylindrical Bessel function of the first kind for real order.
BESSEL_KV	Compute the modified cylindrical Bessel function of the second kind for real order.
BESSEL_YN_ZEROS	Compute the first positive zeros of the integer-order Bessel function of the second kind.
BESSEL_YV	Compute the cylindrical Bessel function of the second kind for real order.
SPHERICAL_IN	Compute the modified spherical Bessel function of the first kind or its derivative.
SPHERICAL_JN	Compute the spherical Bessel function of the first kind or its derivative.
SPHERICAL_KN	Compute the modified spherical Bessel function of the second kind or its derivative.
SPHERICAL_YN	Compute the spherical Bessel function of the second kind or its derivative.

Elliptic Integrals

Tool	Description
ELLIPE	Compute the complete elliptic integral of the second kind.
ELLIPEINC	Compute the incomplete elliptic integral of the second kind.
ELLIPJ	Compute Jacobi elliptic functions sn, cn, dn and amplitude for scalar input.
ELLIPK	Compute the complete elliptic integral of the first kind.
ELLIPKINC	Compute the incomplete elliptic integral of the first kind.
ELLIPKM1	Compute the complete elliptic integral of the first kind near m equals one.
ELLIPRC	Compute Carlson’s degenerate symmetric elliptic integral RC.
ELLIPRD	Compute Carlson’s symmetric elliptic integral RD.
ELLIPRF	Compute Carlson’s completely symmetric elliptic integral RF.
ELLIPRG	Compute Carlson’s completely symmetric elliptic integral RG.
ELLIPRJ	Compute Carlson’s symmetric elliptic integral RJ.

Error And Fresnel

Tool	Description
DAWSN	Evaluate Dawson’s integral for a real input.
ERF	Evaluate the Gauss error function for a real input.
ERFC	Evaluate the complementary error function for a real input.
ERFCINV	Compute the inverse complementary error function on its real domain.
ERFCX	Evaluate the exponentially scaled complementary error function.
ERFI	Evaluate the imaginary error function for a real input.
ERFINV	Compute the inverse error function on its real domain.
FRESNEL	Compute Fresnel sine and cosine integrals for a real input.
WOFZ	Compute the Faddeeva function and return real and imaginary parts.

Gamma Beta Functions

Tool	Description
BETAINC	Compute the regularized incomplete beta function.
BETAINCINV	Invert the regularized incomplete beta function with respect to x.
BETALN	Compute the natural logarithm of the absolute beta function.
DIGAMMA	Compute the digamma function for a real input.
EULER_BETA	Evaluate the Euler beta function for two real parameters.
GAMMA	Evaluate the gamma function for a real input.
GAMMAINC	Compute the regularized lower incomplete gamma function.
GAMMAINCC	Compute the regularized upper incomplete gamma function.
GAMMAINCCINV	Invert the regularized upper incomplete gamma function.
GAMMAINCINV	Invert the regularized lower incomplete gamma function.
GAMMALN	Compute the natural logarithm of the absolute gamma function.
POCH	Evaluate the rising factorial using the Pochhammer symbol.
POLYGAMMA	Compute the n-th derivative of the digamma function.
RGAMMA	Compute the reciprocal of the gamma function.

Statistics

Bayesian

Conjugate Priors

Tool	Description
BB_LOGBETA	Compute the log-Beta term used in conjugate posterior calculations.
BB_POST_UPDATE	Update Beta-Binomial posterior hyperparameters from observed counts.
BB_QBETA	Compute a Beta posterior quantile for Beta-Binomial models.
GAMMA_POST_Q	Compute a Gamma posterior quantile from shape-rate parameters.
INVGAMMA_POST_Q	Compute an inverse-Gamma posterior quantile.
NIG_POST_UPDATE	Update Normal-Inverse-Gamma posterior hyperparameters from sample summaries.
NN_POST_UPDATE	Update Normal posterior parameters for unknown mean with known variance.

Credible Intervals

Tool	Description
BAYES_MVS_CI	Compute Bayesian credible intervals for mean, variance, and standard deviation from sample data.
BETA_CI_BOUNDS	Compute an equal-tailed Bayesian credible interval for a proportion using a Beta posterior.
GAMMA_CI_BOUNDS	Compute an equal-tailed Bayesian credible interval for a positive rate parameter using Gamma quantiles.
INVGAMMA_CI_BOUNDS	Compute an equal-tailed Bayesian credible interval for a positive scale or variance parameter using Inverse-Gamma quantiles.
MVSDIST_CI	Compute Bayesian credible intervals from posterior distributions of mean, variance, and standard deviation.
SAMPLE_EQTAIL_CI	Compute an equal-tailed credible interval from posterior samples using empirical quantiles.
SAMPLE_HPD_CI	Approximate a highest posterior density interval from posterior samples using the narrowest empirical window.

Dirichlet Multinomial

Tool	Description
DM_CRED_INT	Compute category-wise credible intervals from posterior Dirichlet parameters.
DM_DIRICHLET_SUM	Compute Dirichlet density and moments for a category-probability vector.
DM_LOGBETA	Compute the Dirichlet log-normalization term using log-gamma values.
DM_LOGSUM_NORM	Compute a stable log normalizer and normalized probabilities from log-values.
DM_POST_UPDATE	Update Dirichlet posterior parameters from prior hyperparameters and observed counts.
DM_PREDICTIVE	Compute posterior predictive category probabilities from Dirichlet parameters.

Posterior Summarization

Tool	Description
POSTERIOR_BMV	Compute Bayesian posterior summaries for mean, variance, and standard deviation.
POSTERIOR_ENTROPY	Compute Shannon or relative entropy for posterior probability tables.
POSTERIOR_LOGSUMEXP	Compute stable log-sum-exp aggregates for posterior normalization and evidence calculations.
POSTERIOR_MAP	Extract the MAP estimate from a tabulated posterior distribution.
POSTERIOR_TAILPROB	Compute posterior tail probabilities relative to a decision threshold.
POSTERIOR_WMEANVAR	Compute posterior weighted mean and variance summaries from values and weights.
POSTERIOR_XLOGY	Compute numerically stable x times log y terms for posterior information calculations.

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.
LINREGRESS	Calculate a linear least-squares regression for two sets of measurements.
MULTISCALE_GRAPH	Compute the Multiscale Graph Correlation (MGC) test statistic and p-value.
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.
BARTLETT	Performs Bartlett’s test for equal variances across multiple samples.
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.
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	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.
VAL_DISCRETE	Select a value from a list based on a discrete probability distribution.
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.
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	Return the modal (most common) numeric value in the input data, returning the smallest if there are multiple modes.
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.

Time Series

Autocorrelation And Stationarity Tests

Tool	Description
ACF	Compute autocorrelation values across lags with optional confidence intervals and Ljung-Box statistics.
ACOVF	Estimate autocovariance values of a time series across lags.
ADFULLER	Run the Augmented Dickey-Fuller unit-root test for stationarity diagnostics.
CCF	Compute cross-correlation between two time series across nonnegative lags.
CCOVF	Estimate cross-covariance values between two time series across lags.
KPSS	Run the KPSS stationarity test under level or trend null hypotheses.
PACF	Compute partial autocorrelation values across lags for lag-order diagnostics.
Q_STAT	Compute Ljung-Box Q statistics and p-values from autocorrelation coefficients.
RURTEST	Run the range unit-root test as an alternative stationarity diagnostic.
ZIVOT_ANDREWS	Run the Zivot-Andrews unit-root test allowing one endogenous structural break.

Decomposition And Seasonality

Tool	Description
DETREND	Remove linear or constant trend from input data.
MSTL	Perform multi-seasonal STL decomposition on a time series.
PERIODOGRAM	Estimate the power spectral density of a time series using a periodogram.
SEASDECOMP	Decompose a time series into trend, seasonal, and residual components.
STL	Perform STL decomposition of a univariate time series.
WELCH	Estimate the power spectral density of a time series using Welch’s method.

Forecasting Models

Tool	Description
ARIMA_FORECAST	Fit an ARIMA model and return out-of-sample forecasts.
ARMA_ORDER_IC	Select ARMA order using an information criterion.
HANNAN_RISSANEN	Estimate ARMA parameters using the Hannan-Rissanen procedure.
HOLT_FORECAST	Fit Holt trend exponential smoothing and return forecasts.
HW_FORECAST	Fit Holt-Winters exponential smoothing and return forecasts.
INNOVATIONS_MLE	Estimate SARIMA parameters using innovations maximum likelihood.
SARIMAX_FORECAST	Fit a SARIMAX model and return out-of-sample forecasts.
SES_FORECAST	Fit simple exponential smoothing and return forecasts.

Moving Averages

Tool	Description
EMA_LFILTER	Compute an exponential moving average using recursive linear filtering.
EMA_PERIOD	Compute an exponential moving average using a period-derived smoothing constant.
SMA_CONV	Compute a simple moving average using discrete convolution with a uniform window.
SMA_CUMSUM	Compute a simple moving average using cumulative-sum differencing.
WINMA_CONV	Compute a weighted moving average by convolving data with a user-defined weight window.
WMA	Compute a rolling weighted moving average using user-supplied weights.

Visualization

Charts

3d

Tool	Description
AREA_3D	Create a 3D filled area chart between two 3D lines.
BAR_3D	Create a 3D bar chart.
LINE_3D	Create a 3D line plot.
QUIVER_3D	Create a 3D quiver (vector) plot.
SCATTER_3D	Create a 3D scatter plot.
STEM_3D	Create a 3D stem plot.
SURFACE_3D	Create a 3D surface plot.
TRISURF_3D	Create a 3D triangular surface plot.
VOXELS	Create a 3D voxel plot from a 3D grid of values.
WIREFRAME_3D	Create a 3D wireframe plot.

Basic

Tool	Description
AREA	Create a filled area chart from data.
BAR	Create a bar chart (vertical or horizontal) from data.
GROUPED_BAR	Create a grouped/dodged bar chart from data.
LINE	Create a line chart from data.
PIE	Create a pie chart from data.
SCATTER	Create an XY scatter plot from data.
STACKED_BAR	Create a stacked bar chart from data.
STEP	Create a step plot from data.

Categorical

Tool	Description
DONUT	Create a donut chart from data.
DOT_PLOT	Create a Cleveland dot plot from data.
DUMBBELL	Create a dumbbell plot (range comparison) from data.
FUNNEL	Create a funnel chart for stages in a process.
PARETO_CHART	Create a Pareto chart (bar chart + cumulative line).
SLOPE	Create a slope chart for comparing paired changes across categories.
STEM	Create a stem/lollipop plot from data.
WATERFALL	Create a waterfall chart (change analysis) from data.

Matrix

Tool	Description
CLUSTER_MAP	Create a hierarchically-clustered heatmap.
CORRELATION	Create a correlation matrix heatmap from data.
HEATMAP	Create a heatmap from a matrix of data.
TRIANGULAR_HEATMAP	Create a lower or upper triangular heatmap.

Scientific

Tool	Description
BARBS	Plot a 2D field of wind barbs.
CONTOUR	Create a contour plot.
CONTOUR_FILLED	Create a filled contour plot.
LOGLOG	Create a log-log plot from data.
PCOLORMESH	Create a pseudocolor plot with a rectangular grid.
POLAR_BAR	Create a bar chart in polar coordinates (also known as a Rose diagram).
POLAR_LINE	Create a line plot in polar coordinates.
POLAR_SCATTER	Create a scatter plot in polar coordinates.
QUIVER	Create a quiver plot (vector field arrows).
RADAR	Create a radar (spider) chart.
SEMILOGX	Create a plot with a log-scale X-axis.
SEMILOGY	Create a plot with a log-scale Y-axis.
STREAMPLOT	Create a streamplot (vector field streamlines).
TRICONTOUR	Draw contour lines on an unstructured triangular grid.
TRICONTOUR_FILLED	Draw filled contour regions on an unstructured triangular grid.
TRIPCOLOR	Create a pseudocolor plot of an unstructured triangular grid.
TRIPLOT	Draw an unstructured triangular grid as lines and/or markers.

Specialty

Tool	Description
BULLET	Create a bullet chart for visual comparison against a target.
GANTT	Create a Gantt chart (timeline of tasks).
GAUGE	Create a speedometer/gauge style chart.
SANKEY	Create a Sankey flow diagram.
TABLE	Render data as a graphical table image.
WORDCLOUD	Generates a word cloud image from provided text data and returns a PNG image as a base64 string.

Statistical

Tool	Description
BOXPLOT	Create a box-and-whisker plot from data.
DENDROGRAM	Performs hierarchical (agglomerative) clustering and returns a dendrogram as an image.
DENSITY	Create a Kernel Density Estimate (KDE) plot.
ECDF	Create an Empirical Cumulative Distribution Function plot.
ERRORBAR	Create an XY plot with error bars.
EVENTPLOT	Create a spike raster or event plot from data.
HEXBIN	Create a hexagonal binning plot from data.
HIST2D	Create a 2D histogram plot from data.
HISTOGRAM	Create a frequency distribution histogram from data.
VIOLIN	Create a violin plot from data.