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.

Visualization

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

Engineering

Chemical

Chemical Properties

Tool	Description
CAS_FROM_ANY	Resolve a chemical identifier to its standardized CAS number.
CHEMICAL_PROPS	Retrieve physical and thermodynamic properties for a chemical specimen.
DIPOLE	Retrieve the dipole moment of a chemical by CAS number.
OMEGA	Retrieve the acentric factor of a chemical by CAS number.
PC	Retrieve the critical pressure of a chemical by CAS number.
SEARCH_CHEMICAL	Resolve a chemical identifier and return a compact metadata summary.
TB	Retrieve the normal boiling temperature of a chemical by CAS number.
TC	Retrieve the critical temperature of a chemical by CAS number.
TM	Retrieve the melting temperature of a chemical by CAS number.
VC	Retrieve the critical molar volume of a chemical by CAS number.

Combustion Fuels

Tool	Description
AIR_FUEL_RATIO	Calculates molar flow rate of air or fuel from the other, using a specified air-fuel ratio.
COMBUSTION_STOICH	Returns a dictionary of stoichiometric coefficients of chemical combustion from an atoms dictionary.
FUEL_AIR_SPEC	Solves the system of equations describing a flow of air mixing with a flow of combustibles and burning completely.
HHV_STOICHIOMETRY	Returns the higher heating value based on theoretical combustion stoichiometry and heat of formation.
IS_COMBUSTIBLE	Checks if a chemical is combustible based on its CAS and atoms.
LHV_FROM_HHV	Returns the lower heating value (LHV) of a chemical given the higher heating value (HHV) and number of water molecules formed.
MON	This function handles the retrieval of a chemical’s motor octane number (MON), using CASRN.
RON	This function handles the retrieval of a chemical’s research octane number (RON), using CASRN.

Process Safety

Tool	Description
CARCINOGEN_STATUS	Looks up if a chemical is listed as a carcinogen according to specific methods.
CEILING_LIMIT	Handles the retrieval of ceiling limits on worker exposure to dangerous chemicals.
LFL	Handles the retrieval or calculation of a chemical’s Lower Flammability Limit.
STEL	Handles the retrieval of Short-term Exposure Limit (STEL) for worker exposure.
T_AUTOIGNITION	Handles the retrieval or calculation of a chemical’s autoignition temperature.
T_FLASH	Handles the retrieval or calculation of a chemical’s flash point.
TWA_LIMIT	Return the Time-Weighted Average exposure limits (TWA) for the desired chemical.
UFL	Handles the retrieval or calculation of a chemical’s Upper Flammability Limit.

Control Systems

Analysis

Tool	Description
DAMP	Compute the system’s natural frequencies, damping ratios, and poles.
FORCED_RESPONSE	Compute the output of a linear system given an arbitrary input signal.
IMPULSE_RESPONSE	Compute the impulse response for a linear system.
INITIAL_RESPONSE	Compute the initial condition response for a state-space system.
MARGIN	Calculate the gain and phase margins and crossover frequencies of a system.
POLES	Compute the poles of a linear system.
PZMAP	Compute the poles and zeros of a linear system.
ZEROS	Compute the zeros of a linear system.

Design

Tool	Description
ACKER	Pole placement using Ackermann’s formula.
DLQE	Linear quadratic estimator (Kalman filter) for discrete-time systems.
DLQR	Linear quadratic regulator design for discrete-time systems.
LQE	Linear quadratic estimator (Kalman filter) for continuous-time systems.
LQR	Linear quadratic regulator design for continuous-time systems.
MIXSYN	Mixed-sensitivity H-infinity controller synthesis.
PLACE	Pole placement for state feedback gain design.
ROOT_LOCUS	Calculate the root locus for an LTI system.

Fuzzy

Tool	Description
DEFUZZ	Defuzzify a membership function to return a crisp value.
FUZZY_AND	Calculate the fuzzy AND operator (intersection) of two fuzzy sets.
FUZZY_NOT	Calculate the fuzzy NOT operator (complement) of a fuzzy set.
FUZZY_OR	Calculate the fuzzy OR operator (union) of two fuzzy sets.
GAUSS2MF	Generate a Gaussian fuzzy membership function of two combined Gaussians.
GAUSSMF	Generate a Gaussian fuzzy membership function.
GBELLMF	Generate a Generalized Bell fuzzy membership function.
PIECEMF	Generate a piecewise linear fuzzy membership function.
PIMF	Generate a Pi-function fuzzy membership generator.
PSIGMF	Generate the product of two sigmoid membership functions.
SIGMF	Generate a basic sigmoid membership function.
SMF	Generate an S-function fuzzy membership generator.
TRAPMF	Generate a trapezoidal fuzzy membership function.
TRIMF	Generate a triangular fuzzy membership function.
ZMF	Generate a Z-function fuzzy membership generator.

Interconnection

Tool	Description
FEEDBACK	Feedback interconnection of two LTI systems.
PARALLEL	Parallel interconnection of two LTI systems.
SERIES	Series interconnection of two LTI systems.

Matrix Computations

Tool	Description
CARE	Solve the continuous-time algebraic Riccati equation.
CTRB	Compute the controllability matrix.
DARE	Solve the discrete-time algebraic Riccati equation.
DLYAP	Solve the discrete-time Lyapunov equation.
GRAM	Compute the Gramian (controllability or observability).
LYAP	Solve the continuous-time Lyapunov equation.
OBSV	Compute the observability matrix.

Modeling

Tool	Description
C2D	Convert a continuous-time system to discrete-time by sampling.
FRD	Create a frequency response data (FRD) model from measured response data.
PADE_DELAY	Calculate the Pade approximation of a continuous time delay.
SS2TF	Transform a state-space system into a transfer function.
STATE_SPACE	Create a state-space system model from system, control, output, and feedforward matrices.
TF2SS	Convert a transfer function object back into a state-space system object.
TRANSFER_FUNCTION	Create a transfer function system from its numerator and denominator polynomial coefficients.
ZPK	Create a transfer function model from zeros, poles, and gain.

Reduction

Tool	Description
BALRED	Balanced reduced order model of a system.
MINREAL	Eliminate uncontrollable or unobservable states.

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 the liquid critical pressure ratio factor FF for IEC 60534 liquid valve sizing.
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

Data Quality

Tool	Description
CHECK_DHI_QCRAD	Return a pass/fail QC flag array for each DHI reading against QCRad physical or extreme limits.
CHECK_DNI_QCRAD	Return a pass/fail QC flag array for each DNI reading against QCRad physical or extreme limits.
CHECK_GHI_QCRAD	Return a pass/fail QC flag array for each GHI reading against QCRad physical or extreme limits.
CHECK_IRRAD_QCRAD	Return consistency flags for irradiance-component balance from GHI, DNI, DHI, and zenith ranges.
COMPLETENESS_SCORE	Calculate a data completeness score for each day from a timestamped PV series.
PERF_RATIO_NREL	Calculate the NREL weather-corrected performance ratio from irradiance, temperature, and power data.
SPACING	Check that the spacing between timestamps conforms to an expected frequency.
STALE_VALUES_ROUND	Identify stale or stuck-sensor values by rounding and checking for repeating sequences.
TRIM_INCOMPLETE	Return a boolean mask to trim leading and trailing low-completeness periods from a PV series.

Irradiance Models

Tool	Description
DIRINT	Estimate Direct Normal Irradiance (DNI) from GHI using the DIRINT model.
DISC	Convert GHI to DNI using the Direct Insolation Simulation Code (DISC) model.
ERBS	Estimate DNI and DHI from GHI and solar zenith using the Erbs model.
GET_EXTRA_RADIATION	Determine extraterrestrial radiation (DNI_extra) for a given day of the year.
GET_GROUND_DIFFUSE	Estimate diffuse irradiance on a tilted surface from ground reflections.
HAYDAVIES	Determine diffuse irradiance from the sky on a tilted surface using the Hay and Davies model.
PEREZ	Determine diffuse irradiance from the sky on a tilted surface using one of the Perez models.
TOTAL_IRRADIANCE	Determine total in-plane irradiance and its beam, sky diffuse and ground reflected components.

Module Models

Tool	Description
CALCPARAMS_DESOTO	Calculate five single-diode model parameter values using the De Soto model.
CALCPARAMS_PVSYST	Calculate five single-diode parameter values using the PVsyst v6 model.
MAX_POWER_POINT	Calculate the maximum power point (MPP) from single-diode equation coefficients.
PVWATTS_LOSSES	Implement NREL’s PVWatts system loss model.
SAPM	Sandia Photovoltaic Array Performance Model (SAPM) solver.
SAPM_EFF_IRRAD	Calculate SAPM effective irradiance accounting for spectral and incidence losses.
SINGLEDIODE	Solve the single-diode equation to obtain a photovoltaic IV curve and its key operating points.
V_FROM_I	Calculate device voltage at a given current for the single-diode model.

Solar Geometry

Tool	Description
AOI	Calculate the angle of incidence (AOI) for a surface.
AOI_PROJECTION	Calculate the dot product of the sun position and surface normal (cosine of AOI).
CALC_AXIS_TILT	Calculate tracker axis tilt on sloped terrain.
CROSS_AXIS_TILT	Calculate cross-axis tilt for single-axis trackers on sloped terrain.
MASK_ANGLE_PASSIAS	Calculate the average masking angle over the slant height of a row.
MASKING_ANGLE	Calculate the elevation angle below which diffuse irradiance is blocked.
PROJ_SOLAR_ZENITH	Calculate the projected solar zenith angle in the tracker reference plane.
SHADED_FRACTION1D	Calculate the fraction of a collector width shaded by an adjacent row.
SINGLEAXIS	Determine the rotation angle and incidence angle for a single-axis tracker.
SURFACE_ORIENT	Calculate surface tilt and azimuth for a given tracker rotation.

Solar Position

Tool	Description
DECLINATION_SPENCER	Compute the solar declination angle using Spencer’s (1971) formula.
EARTHSUN_DISTANCE	Calculate the Earth-Sun distance in AU using the NREL SPA algorithm.
EOT_SPENCER	Compute the equation of time (EOT) using Spencer’s (1971) formula.
SOLAR_AZIM_AN	Calculate the solar azimuth angle using an analytical expression.
SOLAR_ZEN_AN	Calculate the solar zenith angle using an analytical expression.
SOLARPOSITION	Calculate solar azimuth, elevation, and apparent zenith for given times and location.
SUN_RISE_SET_GEOM	Geometric calculation of solar sunrise, sunset, and transit.
SUN_RISE_SET_SPA	Calculate sunrise, sunset, and solar transit times using the NREL SPA algorithm.

Signal Processing

Filtering

Tool	Description
BUTTER	Butterworth digital and analog filter design.
CHEBY1	Chebyshev Type I digital and analog filter design (passband ripple).
CHEBY2	Chebyshev Type II digital and analog filter design (stopband ripple).
ELLIP	Elliptic (Cauer) digital and analog filter design.
FILTFILT	Apply a digital filter forward and backward to a signal for zero phase distortion.
FIRWIN	FIR filter design using the window method.
FREQZ	Compute the frequency response of a digital filter.
GAUSSIAN_FILTER1D	1-D Gaussian filter for signal denoising and smoothing.
GET_WINDOW	Generate a window function vector for signal processing.
IIRDESIGN	Complete IIR digital and analog filter design from passband and stopband specs.
MEDFILT	Perform a median filter on a signal array to remove spike noise.
REMEZ	Calculate the minimax optimal filter using the Remez exchange algorithm.
SAVGOL_FILTER	Apply a Savitzky-Golay filter to a signal array for smoothing.
SOSFILTFILT	Forward-backward digital filter using cascaded second-order sections.

Resampling

Tool	Description
DECIMATE	Downsample the signal after applying an anti-aliasing filter.
RESAMPLE	Resample x to num samples using Fourier method.
RESAMPLE_POLY	Resample x along the matrix using polyphase filtering.
UPFIRDN	Upsample, FIR filter, and downsample.

Spectral Analysis

Tool	Description
COHERENCE	Estimate the magnitude squared coherence (Cxy) using Welch’s method.
CSD	Estimate the cross power spectral density (Pxy) using Welch’s method.
ENG_PERIODOGRAM	Estimate power spectral density using a periodogram.
ENG_WELCH	Estimate power spectral density using Welch’s method.
ISTFT	Perform the Inverse Short-Time Fourier Transform (ISTFT).
LOMBSCARGLE	Estimate a Lomb-Scargle periodogram for unevenly sampled data.
RFFT	Compute the one-dimensional discrete Fourier transform for real input.
RFFTFREQ	Return sample frequencies for one-sided real FFT bins.
SPECTROGRAM	Compute a spectrogram with consecutive Fourier transforms.
STFT	Compute the Short Time Fourier Transform (STFT).

Wavelets

Tool	Description
CASCADE	Compute scaling and wavelet functions at dyadic points from filter coefficients.
CWT	Perform a Continuous Wavelet Transform (CWT).
DAUB	Get coefficients for the low-pass filter producing Daubechies wavelets.
MORLET2	Generate a complex Morlet wavelet for a given length and width.
QMF	Return a Quadrature Mirror Filter (QMF) from low-pass coefficients.
RICKER	Return a Ricker wavelet (Mexican hat wavelet).
THRESHOLD	Apply elementwise wavelet thresholding to numeric data.
WAVEDEC	Compute a multilevel one-dimensional discrete wavelet decomposition.

Structural

Beam Numerical

Tool	Description
ANALYZE_BEAM	Perform numerical analysis of a structural beam to determine reactions and internal forces.
BEAM_DEFLECTION	Calculate the deflection of a beam at a specific coordinate.
BEAM_REACTION	Calculate the reaction force or moment at a specific support position.

Beam Symbolic

Tool	Description
SOLVE_BEAM_SYMBOLIC	Solve a statically determinate beam symbolically and return reactions plus internal-force equations.

Finite Elements

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

Fluid Properties

Tool	Description
CP_FLUID_PARAM	Retrieve a CoolProp metadata string for a specified fluid and metadata field.
CP_FLUIDS_LIST	Return a list of CoolProp fluid names, optionally capped to a maximum count.
CP_SAT_ANC	Evaluate a CoolProp saturation ancillary property for a fluid and branch quality.
IAPWS11_PSUB	Compute water-ice sublimation pressure from temperature using IAPWS-11.
IAPWS92_DPSAT_DT	Compute saturation pressure derivative with respect to temperature using IAPWS-92.
IAPWS92_RHOG_SAT	Compute saturated vapor water density from temperature using IAPWS-92.
IAPWS92_RHOL_SAT	Compute saturated liquid water density from temperature using IAPWS-92.
IAPWS95_PROPERTIES	Return key water thermodynamic properties from temperature and pressure using IAPWS-95.
IAPWS95_PSAT	Compute saturation pressure from temperature using IAPWS-95 polynomial fits.
IAPWS95_RHO	Compute water density from temperature and pressure using IAPWS-95.
IAPWS95_SATURATION	Solve IAPWS-95 saturation state from temperature.
IAPWS95_T	Compute water temperature from pressure and density using IAPWS-95.
IAPWS95_TSAT	Compute saturation temperature from pressure using IAPWS-95.
IAPWS97_REGION_TP	Identify the IF-97 region from temperature and pressure.
IAPWS97_RHO	Compute water density from temperature and pressure using IAPWS-97.
PHASE_SI	Identify the phase of a fluid at a given state using CoolProp.
PROPS_SI	Calculate thermophysical properties of fluids using CoolProp.
PSAT_IAPWS	Compute water saturation pressure from temperature with the explicit IAPWS equation.
TSAT_IAPWS	Compute water saturation temperature from pressure with the explicit IAPWS equation.

Phase Equilibrium

Tool	Description
FLASH_INNER_LOOP	Solve flash inner-loop vapor fraction and phase compositions from overall composition and K-values.
FLASH_TB_TC_PC	Perform a low-data flash calculation using boiling and critical properties.
FLASH_WILSON	Perform a Wilson-model flash calculation and return state and phase compositions.
K_VALUE	Calculate a component equilibrium K-value from available pressure, fugacity, and activity inputs.
LI_JOHNS_AHMADI	Solve the Li-Johns-Ahmadi flash equation for vapor fraction and phase compositions.
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.
PR	Solve pure-component Peng-Robinson EOS and return key phase-state properties.
PR_WATER_K_VALUE	Estimate hydrocarbon-water equilibrium K-value with the Peng-Robinson heuristic.
PRMIX	Solve Peng-Robinson mixture EOS and return key phase and fugacity metrics.
PRSV	Solve pure-component PRSV EOS and return key phase-state properties.
PRSVMIX	Solve PRSV mixture EOS and return key phase and fugacity metrics.
RACHFORD_RICE	Solve the classical Rachford-Rice flash equation.
SAT_ANCILLARY	Evaluate a CoolProp saturation ancillary correlation value.
SRK	Solve pure-component Soave-Redlich-Kwong EOS and return key phase-state properties.
SRKMIX	Solve SRK mixture EOS and return key phase and fugacity metrics.
WILSON_K_VALUE	Estimate a component equilibrium K-value using Wilson’s correlation.

Psychrometrics

Tool	Description
HA_PROPS_AUX	Compute auxiliary humid-air properties from CoolProp.
HA_PROPS_SI	Calculate humid air properties using CoolProp psychrometrics.
IAPWS92_PSAT	Compute saturation vapor pressure using the IAPWS-92 correlation.
PSYCHRO_DPSATDT	Compute temperature derivative of saturation pressure using IAPWS-92.

Machine Learning

Clustering

Tool	Description
CMEANS	Perform fuzzy c-means clustering on data.
CMEANS_PREDICT	Predict cluster membership for new data given a trained fuzzy c-means model.

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
CLOUGH_TOCHER	Piecewise cubic C1 interpolation for scattered 2D data.
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.
LSQ_BIVAR_SPL	Weighted least-squares bivariate spline with user-specified knots.
NEAREST_ND_INTERP	Nearest neighbor interpolation in N > 1 dimensions.
RBF_INTERPOLATOR	Radial basis function interpolation in N dimensions.
SMOOTH_BIVAR_SPL	Smooth bivariate spline fit for scattered 2D observations.

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.

Symbolic

Tool	Description
DIFF	Compute a symbolic derivative of an expression.
DSOLVE	Solve an ordinary differential equation symbolically.
EXPAND	Expand products and powers in a symbolic expression.
FACTOR	Factor a symbolic expression into simpler multiplicative terms.
INTEGRATE	Compute an indefinite or definite symbolic integral.
LIMIT	Compute the symbolic limit of an expression.
SIMPLIFY	Simplify a symbolic expression.
SYM_SOLVE	Solve an algebraic equation for a variable.

Wavelets

Tool	Description
CWT_PYWT	Compute the continuous wavelet transform and associated pseudo-frequencies.
DOWNCOEF	Compute approximation or detail coefficients at a specified decomposition level.
DWT	Perform a single-level one-dimensional discrete wavelet transform.
DWT2	Perform a single-level two-dimensional discrete wavelet transform.
IDWT	Reconstruct a one-dimensional signal from approximation and detail coefficients.
THRESHOLD_PYWT	Apply elementwise wavelet thresholding to numeric data.
UPCOEF	Reconstruct approximation or detail contribution from one-dimensional coefficients.
WAVEDEC_PYWT	Compute a multilevel one-dimensional discrete wavelet decomposition.
WAVEREC	Reconstruct a one-dimensional signal from multilevel wavelet coefficients.

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

Tool	Description
ANOVA	Perform one-way ANOVA on tabular data using Pingouin.
GAMESHOWELL	Run Games-Howell pairwise comparisons using Pingouin.
HOMOSCEDASTICITY	Test equality of variances across groups using Pingouin.
MIXED_ANOVA	Perform mixed ANOVA with within- and between-subject factors using Pingouin.
NORMALITY	Test normality by group or overall using Pingouin.
PAIRWISE_TUKEY	Run Tukey HSD pairwise comparisons using Pingouin.
RM_ANOVA	Perform repeated-measures ANOVA on tabular data using Pingouin.
WELCH_ANOVA	Perform Welch ANOVA for unequal variances using Pingouin.

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

Tool	Description
MEDIATION_ANALYSIS	Perform causal mediation analysis with bootstrap confidence intervals.

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
CRONBACH_ALPHA	Compute Cronbach’s alpha reliability coefficient for a set of items.
DESCRIBE	Compute descriptive statistics using scipy.stats.describe.
DISTANCE_CORR	Compute distance correlation between two numeric variables.
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.
PARTIAL_CORR	Compute partial or semi-partial correlation between two variables.
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.

Dashboards

Geo Allocation

Tool	Description
Capacity Coverage Balance	Balances workforce and asset capacity allocation against geographic coverage goals to avoid solving one deficit while creating another.
Catchment Analysis View	Examines each location’s catchment profile using deterministic trade-area demand, penetration, and overlap indicators.
Coverage Overlap Audit	Audits account and postal-code coverage to detect overlapping ownership, uncovered white space, and routing conflicts between adjacent territories.
Coverage Planning Map	Provides a map-first operating view that compares serviceable capacity against demand by zone, cluster, and service tier.
Coverage Variance Monitor	Monitors whether coverage performance is stable or drifting away from expected operating ranges across regions and service tiers.
Expansion Action Queue	Converts identified coverage deficits into an executable queue of actions with effort, impact, and dependency visibility.
Exposure Variance Monitor	Tracks exposure movement across periods and compares realized variance against approved tolerance bands by region and asset class.
Hazard Scenario Simulator	Simulates plausible hazard scenarios and estimates resulting exposure, service disruption, and recovery burden across regions.
Local Risk Overlay	Overlays local risk signals on top of location performance to reveal where operational fragility and external exposure intersect.
Location Performance Map	Provides a map-first operating view of site, store, and facility performance with deterministic scoring for revenue, throughput, quality, and service reliability.
Mitigation Action Queue	Converts diagnosed risk issues into an execution-ready action queue ranked by expected reduction, urgency, and implementation effort.
New Location Scenario Planner	Evaluates multiple new-site scenarios and compares expected coverage gain, travel-time reduction, and financial feasibility under common assumptions.
Path Efficiency Simulator	Simulates how path redesign choices affect trip time, transfer burden, fuel use, and service reliability before committing schedule changes.
Peak Window Risk Tracker	Tracks route-level risk during predefined peak windows by combining demand spikes, delay volatility, fleet readiness, and staffing exposure.
Quota Variance Monitor	Tracks quota variance continuously across territories and regions against plan, commit, and prior-period baselines.
Region Gap Diagnostics	Decomposes regional attainment gaps into coverage, conversion, deal-size, and cycle-time contributors with signed impact values.
Regional Alert Timeline	Provides a time-ordered view of risk alerts, escalation decisions, and response milestones to evaluate operational responsiveness.
Regional Potential Tracker	Tracks realized revenue against modeled addressable potential to show where each region is overperforming, saturated, or underpenetrated.
Regional Risk Map	Presents a map-first view of regional exposure, hazard intensity, and control readiness so leaders can rapidly identify where risk is clustering.
Resilience Score Tracker	Tracks resilience capability scores by region across preparedness, response, recovery, and adaptation dimensions.
Risk Hotspot Diagnostics	Decomposes each hotspot into hazard, concentration, control, and recovery components so teams can isolate the dominant driver of current risk.
Route Action Queue	Translates congestion and variance findings into a ranked execution queue with owners, due dates, and expected throughput lift.
Route Congestion Diagnostics	Decomposes corridor congestion into traffic friction, boarding pressure, intersection delay, and dispatch spacing effects with signed impact values.
Route Density Map	Presents a map-first view of route movement density, active vehicle concentration, and stop-load intensity across the operating network.
Service Gap Diagnostics	Focuses on why service gaps persist after routine dispatch and route changes, separating structural gaps from temporary operational noise.
Service Radius Optimizer	Optimizes service radius policies by balancing incremental demand capture against travel-time reliability and utilization constraints.
Site Comparison Explorer	Enables structured side-by-side comparison of selected sites across outcome metrics, operating inputs, and quality signals.
Site Driver Diagnostics	Decomposes site performance gaps into explicit demand, staffing, process, and asset reliability drivers with signed impact values.
Site Intervention Queue	Converts diagnostic and variance findings into an actionable queue of interventions with ranked priority, named owners, and expected business impact.
Stop Density Analyzer	Analyzes stop density, spacing variability, and boarding concentration to identify where stop patterns are too sparse, too dense, or unevenly loaded.
Target Variance Monitor	Monitors variance between plan targets and observed results for each location with deterministic escalation states.
Territory Action Queue	Converts diagnostic findings into a prioritized queue of territory interventions with owners, due dates, and expected impact.
Territory Performance Map	Presents a map-first operating view of quota attainment, run-rate, and risk across all active territories in the selected period.
Territory Rebalance Simulator	Simulates territory rebalance scenarios to estimate impact on quota equity, coverage load, and projected attainment before execution.
Throughput Variance Monitor	Tracks variance between planned and observed route throughput to detect deterioration before reliability and customer wait times worsen.

Lifecycle Retention

Tool	Description
Advisor Intervention Queue	Produces a deterministic intervention queue that prioritizes students requiring advisor outreach based on risk severity, intervention readiness, and timing sensitivity.
At-Risk Account Queue	Converts churn analytics into a deterministic intervention queue so frontline teams know exactly which accounts to engage, what intervention to apply, who owns each action, and the latest acceptable due date.
Attendance Outcome Analyzer	Quantifies the relationship between attendance behavior and persistence outcomes at course, section, and cohort levels.
Attrition Driver Diagnostics	Decomposes employee attrition into deterministic cause categories so teams can identify why exits are occurring, where exits are accelerating, and which drivers are economically and operationally material.
Cancel Reason Audit	Audits cancellation reasons for signal quality, consistency, and actionability so churn analysis is based on reliable evidence rather than inconsistent free-text coding.
Churn Driver Diagnostics	Decomposes subscription churn into deterministic drivers so teams can isolate whether losses are caused by onboarding friction, product value gaps, support instability, competitive pressure, pricing mismatch, or procurement constraints.
Renewal Variance Monitor	Tracks renewal performance against committed subscription plan assumptions and identifies where variance is accumulating by month, segment, and plan family.
Churn Scenario Simulator	Simulates deterministic churn outcomes under configurable intervention assumptions so leaders can compare realistic mitigation paths before allocating budget or setting quarterly commitments.
Cohort Retention Diagnostics	Diagnoses retention behavior by signup cohort, tenure band, product adoption profile, and contract model so teams can identify where persistence is deteriorating and why.
Cohort Risk Explorer	Maps persistence risk concentration across cohort definitions such as entry term, major family, aid status, residency, modality, and demographic segments.
Customer Retention Hub	Provides a unified retention command view that consolidates logo retention, gross revenue retention, net revenue retention, renewal attainment, and active risk concentration across segments and geographies.
Employee Retention Hub	Provides a unified command view for workforce retention by combining headcount retention, voluntary attrition, regrettable attrition, critical-role vacancy pressure, and manager-level risk concentration into one deterministic operating layer.
Exit Signal Analyzer	Analyzes deterministic pre-exit signals captured from engagement pulses, manager one-on-one completion, workload telemetry, internal application behavior, and compensation event timing to detect acceleration in exit propensity before resignation events occur.
Expansion Opportunity Tracker	Tracks expansion opportunities embedded in existing customers by combining retention health, product adoption depth, seat utilization, feature gap signals, and buying-center engagement.
Manager Intervention Queue	Converts attrition-risk analytics into a deterministic manager intervention queue that identifies which managers require immediate support, why they are flagged, what intervention should be executed, and the expected retention impact.
Mobility Impact Tracker	Tracks how internal mobility pathways influence retention, regrettable attrition reduction, skill redeployment, and manager stability across the enterprise.
Persistence Driver Diagnostics	Diagnoses which academic, behavioral, and financial factors most strongly influence term persistence for specific cohorts.
Plan Mix Retention Analyzer	Analyzes how subscription plan mix changes influence retention quality and churn exposure so pricing and packaging teams can make deterministic portfolio decisions.
Renewal Variance Monitor	Monitors renewal outcomes against committed operating plan assumptions and flags where variance is accumulating by segment, contract type, and renewal month.
Retention Action Queue	Converts retention risk analytics into a deterministic, account-level intervention queue that clarifies which accounts require immediate action, what action should be taken, who owns it, and by when it must be completed.
Retention Variance Monitor	Monitors retention execution against workforce plan assumptions and flags where variance is accumulating by function, location, and role criticality.
Risk Segment Explorer	Explores how churn and downgrade risk concentrates across customer segments, product tiers, geography, tenure bands, and engagement profiles.
Save Offer Simulator	Simulates the impact of save-offer strategies on renewal probability, gross margin, and net retained ARR so teams can choose interventions that maximize long-term value rather than short-term logo saves alone.
Student Retention Hub	Provides a unified retention command center that consolidates first-year retention, term-to-term persistence, stop-out incidence, credit momentum, and advisor capacity pressure into one deterministic operating layer.
Subscription Churn Hub	Provides a unified executive command center for subscription churn risk by combining logo churn, gross revenue churn, net revenue retention, renewal attainment, and segment-level risk concentration into one deterministic operating view.
Support Program Tracker	Tracks performance of student support programs such as tutoring, emergency aid, peer mentoring, learning communities, and first-year seminars against persistence and completion goals.
Tenure Risk Explorer	Explores how attrition risk concentrates across tenure bands, role families, manager cohorts, performance distributions, and location clusters.
Term Variance Monitor	Tracks variance between retention plan and observed outcomes across terms, colleges, and cohort bands.

Monitoring Anomalies

Tool	Description
Anomaly Detection Console	Centralizes anomaly scoring across key metrics so analysts can confirm whether a current signal is outside expected operating behavior.
Anomaly Triage Queue	Converts detected anomalies into a prioritized work queue with ownership, urgency, and disposition tracking.
Availability Incident Diagnostics	Focuses on active availability incidents with drill-down diagnostics that explain why uptime dropped and how fast impact is spreading.
Baseline Variance Monitor	Monitors variance drift between short-horizon and reference baselines to determine if detection parameters remain trustworthy.
Change Point Explorer	Identifies potential structural breaks in metric trajectories and supports evidence-based acceptance or rejection of each candidate break.
Data Issue Triage Queue	Converts quality detections into an execution queue with severity, ownership, and SLA timers for dependable incident throughput.
Data Quality Monitor Console	Aggregates freshness, completeness, and quality conformance indicators into a single operations surface for hourly monitoring.
Dependency Failure Map	Maps reliability of shared dependencies to downstream service availability so teams can quantify blast radius before failures cascade.
Downstream Impact Analyzer	Quantifies how active upstream quality issues propagate into downstream dashboards, machine-learning features, and operational decisions.
Error Budget Burn Tracker	Tracks error budget spend and burn rate to determine whether services are operating within reliability policy boundaries.
Event Correlation View	Maps temporal and topological relationships between alerts, logs, and metric anomalies to reveal correlated event clusters.
False Positive Audit	Audits closed anomaly cases to quantify false-positive patterns by metric, rule, team, and time window.
Freshness Completeness Diagnostics	Investigates whether each critical feed arrived on time and delivered expected record coverage for its scheduled batch window.
Live Alert Queue	Organizes incoming alerts into a deterministic queue with severity, freshness, assignment, and escalation state so on-call teams can process work in strict order.
Noise Reduction Tuner	Provides a controlled environment for testing suppression rules, deduplication windows, and threshold sensitivity against deterministic historical alert outcomes.
Outlier Cluster Diagnostics	Examines anomaly points as spatial and temporal clusters to determine whether outliers share a common operational mechanism.
Quality Variance Monitor	Monitors short-horizon quality variance against stable historical baselines to detect emerging drift before it becomes operationally severe.
Realtime Status Wall	Presents a continuously updated wallboard view of service availability, latency pressure, and regional degradation so operators can identify instability in seconds.
Recovery Time Analyzer	Analyzes recovery timelines to show where incident response and restoration workflows lose time.
Reliability Action Queue	Converts reliability findings into an execution-ready queue so teams can sequence remediation work with high operational leverage.
Schema Drift Detector	Detects structural and semantic schema changes between current source payloads and governed contract baselines.
Seasonality Break Detector	Detects when established seasonal patterns no longer explain observed behavior, signaling potential process or demand regime shifts.
Signal Variance Monitor	Tracks statistical variance shifts across high-frequency telemetry streams to detect unstable operating regimes before hard failures occur.
SLO Variance Monitor	Tracks variance between observed reliability performance and committed SLO objectives across services and customer journeys.
Source Reliability Tracker	Tracks data source reliability using delivery timeliness, failure incidence, retry behavior, and recovery performance metrics.
Stream Health Tracker	Monitors streaming pipeline reliability through partition lag, throughput balance, consumer commit behavior, and dropped-message risk indicators.
Threshold Breach Diagnostics	Focuses on breach-first triage by ranking active violations against latency, error-rate, and throughput thresholds with deterministic severity scoring.
Uptime Reliability Console	Consolidates service uptime, incident pressure, and reliability trend signals into a single operating console for daily review.

Operational Control

Tool	Description
Aging Inventory Audit	Audits aging inventory to identify excess and obsolescence exposure by age bucket, SKU class, and location.
Allocation Replan Simulator	Simulates deterministic reallocation scenarios that rebalance constrained supply across channels, regions, and priority tiers.
Carrier Performance Audit	Audits carrier execution quality using deterministic service and cost records across lanes, service classes, and claim categories.
Cost-to-Serve Tracker	Tracks cost-to-serve performance by combining transportation spend, handling cost, expedite leakage, claim burden, and customer-specific service overhead into a deterministic lane view.
Delivery Variance Monitor	Monitors delivery promise adherence by quantifying variance between committed delivery windows and actual drop-off completion times across customer tiers, channels, and service classes.
Dependency Risk Map	Maps deterministic dependency networks across projects to show where upstream slippage, vendor uncertainty, and environment readiness can propagate into milestone failures.
Dispatch Action Queue	Converts live exception signals into a deterministic dispatch action queue prioritized by service risk, customer impact, and time-to-deadline urgency.
Escalation Path Analyzer	Evaluates deterministic escalation pathways from initial incident declaration through managerial, specialist, and executive decision nodes.
Expedite Action Queue	Consolidates expediting interventions into a deterministic ranked backlog based on service risk, due-date pressure, financial impact, and unblock readiness.
Incident Control Tower	Provides a deterministic command view of active and recently resolved incidents across severity, customer impact, containment posture, escalation pressure, and restoration confidence.
Incident Flow Diagnostics	Decomposes incident throughput from alert intake to closure by measuring deterministic transition times between acknowledge, diagnose, contain, resolve, and verify stages.
Intervention Queue	Consolidates high-priority project interventions into a deterministic queue ranked by urgency, value at risk, due-date proximity, and execution confidence.
Inventory Control Tower	Provides a unified operating view of inventory health across plants, distribution centers, and channels by combining on-hand position, days of supply, stockout risk, overstock burden, and service-level attainment into a deterministic command layer.
Lead-Time and Fulfillment Diagnostics	Decomposes late fulfillment outcomes into deterministic drivers spanning supplier delay, customs hold, plant release latency, allocation lag, and carrier handoff slippage.
Logistics Control Tower	Provides a single-screen operational command view across active shipments, lane status, delay exposure, dispatch workload, and same-day service risk using deterministic seeded records.
Milestone Blocker Diagnostics	Decomposes milestone slippage into deterministic blocker classes such as dependency wait, scope churn, environment instability, approval latency, and staffing shortfall.
Node Bottleneck Map	Maps deterministic bottleneck pressure across critical network nodes by comparing planned capacity, realized throughput, queue buildup, and downstream service impact.
OTIF Variance Monitor	Tracks deterministic OTIF performance against commitments and highlights where variance is persistent enough to require escalation.
Postmortem Follow-up Tracker	Tracks deterministic execution of postmortem commitments from action definition through owner assignment, due-date governance, validation, and closure evidence.
Project Control Tower	Provides a deterministic operational command view for active projects across schedule, budget, milestone confidence, dependency health, and escalation load.
Delivery Variance Monitor	Tracks deterministic variance between approved baseline and current forecast across schedule, cost, scope completion, and milestone attainment.
Recovery Plan Simulator	Simulates deterministic recovery plans that rebalance scope, staffing, sequencing, and contingency usage to restore milestone commitments.
Replenishment Action Queue	Organizes replenishment interventions into a deterministic execution queue based on service risk, economic impact, and action urgency.
Resolution Variance Monitor	Tracks deterministic variance between actual incident resolution duration and committed restoration targets across severity tiers, services, and incident archetypes.
Resource Conflict Tracker	Tracks deterministic resource allocation conflicts where critical roles are overcommitted across projects, phases, and delivery windows.
Response Action Queue	Prioritizes deterministic response actions across active incidents by balancing urgency, customer impact reduction potential, dependency readiness, and execution effort.
Root Cause Cluster Map	Maps incident root causes into deterministic clusters so teams can identify recurring systemic failure patterns rather than treating each event as isolated.
Route Delay Diagnostics	Diagnoses route-level delay accumulation by decomposing lateness into departure slippage, transit variance, transfer dwell overages, and final-mile execution misses.
Route Efficiency Analyzer	Analyzes route efficiency by linking miles traveled, load utilization, stop productivity, and cycle-time outcomes for each lane and route template.
Safety Stock Simulator	Simulates the effect of safety-stock policy changes on service reliability, stockout probability, and working-capital investment under deterministic demand and lead-time assumptions.
Service Level Variance	Tracks service-level performance against target across channels, customers, and product tiers to surface where fulfillment reliability is drifting outside acceptable limits.
Stockout and Overstock Diagnostics	Diagnoses simultaneous stockout and overstock conditions by isolating where forecast error, MOQ constraints, replenishment delay, and network allocation rules create inventory mismatch at SKU-site level.
Supplier Delay Impact	Quantifies how supplier lead-time delays propagate through inventory positions, customer service levels, and expedite costs at SKU and supplier lane granularity.
Supplier Risk Tracker	Tracks deterministic supplier risk exposure by combining punctuality performance, quality incidents, financial stress signals, and concentration dependency in one repeatable monitoring frame.
Supply Chain Control Tower	Provides the deterministic command view of network health by combining supplier lead-time adherence, node throughput, OTIF attainment, expedite burden, and backlog pressure into a single operational layer.

Performance Diagnostics

Tool	Description
Agent Performance Explorer	Explores agent-level performance by combining productivity, quality, and workload fairness diagnostics in a unified review interface.
Attribution Gap Review	Reviews attribution gaps by comparing deterministic credit assignment outcomes across first-touch, last-touch, linear, and position-based models.
Backlog Aging Diagnostics	Diagnoses backlog pressure by age band, queue, issue type, and assignment state to reveal where work is accumulating faster than resolution throughput.
Channel & Campaign Drilldown	Enables drilldown from aggregate marketing outcomes into channel and campaign-level efficiency, conversion quality, and contribution diagnostics.
Corrective Action Queue	Presents a prioritized queue of corrective and preventive actions ranked by quality risk, regulatory exposure, and closure urgency.
Creative Performance Explorer	Explores creative-level performance by linking message themes, formats, and audience segments to downstream conversion and revenue influence.
CSAT Driver Analysis	Analyzes customer satisfaction outcomes to isolate controllable drivers across response timeliness, resolution quality, communication clarity, and follow-up effectiveness.
Deal Velocity Diagnostics	Diagnoses deal velocity by decomposing cycle time across pipeline stages, regions, and deal-size bands.
Defect Source Drilldown	Enables targeted drilldown from aggregate defect rates into source-level diagnostics by line, station, shift, product variant, and defect category.
Funnel Stage Diagnostics	Diagnoses marketing funnel performance by stage using deterministic conversion, velocity, and leakage metrics from lead capture through closed-won influence.
Intervention Action Queue	Presents a prioritized queue of portfolio interventions ranked by schedule risk, value at risk, governance urgency, and dependency criticality.
Marketing Performance Overview	Provides a single-screen diagnostic view of marketing performance with deterministic KPI tiles for spend, pipeline contribution, sourced revenue, CAC, and ROI across the selected reporting period.
Milestone Slippage Review	Reviews milestone slippage across programs and projects by comparing planned versus actual completion, critical path movement, and gate-readiness quality.
Optimization Action Queue	Presents a prioritized queue of campaign optimization actions ranked by expected pipeline impact, urgency, and implementation effort.
Pipeline Action Queue	Presents a prioritized queue of in-flight opportunities requiring action, ranked by close-date risk, slippage probability, and forecast impact.
Portfolio Performance Overview	Provides a single-screen diagnostic summary of portfolio performance with deterministic KPI cards for strategic initiative attainment, on-time milestone rate, budget adherence, risk exposure, and value capture against plan.
Quality Performance Overview	Provides a single-screen quality diagnostics summary with deterministic KPI cards for first-pass yield, defect rate per thousand units, customer returns rate, corrective action closure rate, and cost of poor quality.
Quota Variance Diagnostics	Breaks down quota variance by region, segment, and rep cohort to show where attainment misses are structural versus execution-related.
Rep & Segment Drilldown	Enables manager-led drilldown from regional outcomes into rep and segment-level performance with conversion and cycle diagnostics.
Resolution Variance Diagnostics	Decomposes resolution-time variance by queue, issue category, priority band, and escalation path.
Resource Mix Analysis	Analyzes portfolio resource mix to determine whether labor, contractor, platform, and vendor allocations are aligned with delivery goals and value outcomes.
Rework Cost Analysis	Quantifies rework cost burden by defect type, line, shift, and product family, linking quality losses to labor, scrap, downtime, and expedited handling components.
ROI Variance Diagnostics	Decomposes marketing ROI variance by channel, campaign objective, audience tier, and conversion stage to show where returns diverge from plan assumptions.
Sales Performance Overview	Provides a single-screen diagnostic overview of sales performance with headline tiles for bookings, quota attainment, win rate, average sales cycle, and pipeline coverage.
Service Performance Overview	Provides a single-screen diagnostic summary of service operations with deterministic KPI tiles for ticket volume, first response SLA attainment, median time to resolution, backlog pressure, escalation rate, and CSAT.
SLA Breach Drilldown	Enables focused drilldown on SLA breaches by queue, ticket priority, support channel, and shift window.
SPC Signal Explorer	Explores statistical process control signals across critical quality characteristics, surfacing special-cause variation and rule violations with deterministic chart-ready datasets.
Supplier Quality Breakdown	Breaks down supplier quality performance across incoming defect rates, lot acceptance outcomes, response timeliness, and corrective action effectiveness.
Target Variance Diagnostics	Decomposes portfolio target variance across business units, initiative classes, and delivery phases to quantify where misses are structural versus temporary.
Territory Gap Explorer	Explores territory-level performance gaps by comparing quota, pipeline, conversion, and account coverage against potential market demand.
Ticket Action Queue	Presents a prioritized queue of active tickets requiring intervention based on SLA risk, customer impact, escalation probability, and dependency blockers.
Unit & Project Drilldown	Enables deterministic drilldown from portfolio outcomes into business-unit, program, and project-level delivery performance.
Value Realization Tracker	Tracks value realization across the portfolio by measuring approved business case benefits, realized outcomes to date, confidence of future capture, and timing of benefit ramp.
Win/Loss Driver Analysis	Analyzes won and lost opportunities to isolate outcome drivers across pricing, product fit, competition, response speed, and stakeholder engagement.
Yield Variance Diagnostics	Decomposes first-pass yield variance by line, shift, product family, and defect mechanism to quantify where target misses are structural versus temporary.

Pipeline Funnel

Tool	Description
Activation Variance Monitor	Monitors plan-versus-actual activation performance across onboarding stages, segments, and motion types, with explicit decomposition of where variance pressure is accumulating.
Backlog Pressure Audit	Audits deterministic backlog pressure by combining inflow-outflow imbalance, aging distribution, severity-weighted exposure, and available handling capacity.
Campaign Follow-Up Queue	Produces an ordered, deterministic action queue of campaigns and lead cohorts requiring immediate follow-up, ranked by expected pipeline recovery and SLA breach risk.
Candidate Stage Diagnostics	Isolates stage-by-stage loss and delay signals so recruiting teams can identify whether conversion friction is driven by qualification mismatch, interviewer latency, compensation misalignment, or candidate experience issues.
Channel Conversion Audit	Audits conversion quality across paid, owned, partner, and organic channels with an emphasis on consistency between volume generation and downstream qualification outcomes.
Cohort Funnel Analyzer	Analyzes funnel outcomes by acquisition cohort to reveal whether conversion quality is improving, decaying, or remaining stable as campaigns scale.
Conversion Variance Monitor	Monitors conversion performance versus plan across each funnel step, decomposing variance into volume mix, response-time effects, and campaign-quality effects.
Creative Drop-Off Inspector	Diagnoses where individual creatives lose audience quality between click, inquiry, and qualified lead stages, helping teams separate high-CTR but low-intent assets from creatives that sustain downstream conversion quality.
Customer Follow-Up Queue	Produces a deterministic action queue for account-level outreach by combining onboarding stage, inactivity age, milestone risk, expansion potential, and assigned owner capacity.
Deal Followup Queue	Converts pipeline risk analysis into a deterministic follow-up queue so managers and reps can execute the highest-impact deal actions first.
Escalation Path Inspector	Evaluates the deterministic performance of escalation pathways from frontline queues to specialist teams, focusing on transfer delay, loopback frequency, ownership clarity, and resolution quality after escalation.
Forecast Commit Inspector	Evaluates forecast commit integrity by reconciling committed deals against stage readiness, historical slippage patterns, and confidence-scoring rules.
Friction Point Inspector	Identifies high-friction checkpoints in the onboarding experience by combining event completion, retry frequency, abandonment signals, and support touchpoint demand.
Intake to Resolve Diagnostics	Isolates where tickets stall, reroute, or exit expected workflows between intake and resolution, allowing teams to pinpoint whether losses are driven by classification accuracy, assignment latency, dependency wait states, or escalation routing friction.
Lead Stage Leakage Diagnostics	Isolates and ranks leakage by stage transition so operators can determine whether conversion loss is driven by audience fit, lead quality, response latency, routing issues, or qualification criteria drift.
Marketing Funnel Tracker	Provides a deterministic, executive-grade view of the entire demand funnel from first inquiry to closed won, combining stage volumes, stage-to-stage conversion rates, influenced pipeline value, and elapsed time to progression in a single operating screen.
Offer Acceptance Audit	Audits offer outcomes to identify acceptance risk drivers across compensation competitiveness, decision latency, candidate seniority, and competing-offer pressure.
Onboarding Funnel Tracker	Provides an executive-grade, deterministic view of customer onboarding progression from signed account through kickoff scheduling, workspace setup, first key action, and verified activation.
Persona Path Analyzer	Compares onboarding path performance across buyer and end-user personas to reveal where each group experiences different completion behavior, timing, and activation quality.
Pipeline Quality Audit	Audits pipeline record quality to ensure opportunities used in forecast and funnel analytics meet defined completeness, consistency, and timeliness standards.
Pipeline Velocity Analyzer	Measures pipeline velocity by combining stage dwell time, stage throughput, and transition probability into a unified flow-efficiency view.
Queue Mix Analyzer	Decomposes queue volume into deterministic mix components so teams can understand whether pressure is caused by demand growth, case-complexity shift, channel-routing change, or service-policy updates.
Recruiter Action Queue	Converts funnel risk diagnostics into a deterministic recruiter work queue ranked by time sensitivity, candidate quality, requisition criticality, and expected contribution to near-term hires.
Conversion Variance Monitor	Monitors conversion plan-versus-actual outcomes across recruiting stages and quantifies hiring impact attributable to each stage variance.
Recruiting Funnel Tracker	Provides an executive-grade, deterministic view of the end-to-end recruiting funnel across requisitions, from initial application volume to accepted offers.
Conversion Variance Monitor	Monitors conversion variance by stage, region, and segment against committed operating plan assumptions, with explicit decomposition into favorable and unfavorable contributors.
Sales Pipeline Funnel	Provides an executive view of the full opportunity funnel from lead qualification through closed won, combining stage counts, weighted pipeline value, conversion rates, and average days-in-stage in one deterministic operating view.
SLA Variance Monitor	Monitors plan-versus-actual SLA performance across severity tiers, support queues, and handoff stages, with explicit decomposition of where breach pressure is accumulating.
Source Quality Analyzer	Audits candidate source performance across referral, job board, outbound, campus, and agency channels, with emphasis on downstream quality, interview progression, and accepted-offer yield instead of top-of-funnel volume alone.
Stage Leakage Diagnostics	Isolates where and why opportunities leak between pipeline stages by decomposing conversion loss into volume decay, qualification mismatch, pricing friction, and legal/procurement delay signals.
Step Completion Diagnostics	Isolates where customers fail to complete onboarding milestones so teams can determine whether drop-off is driven by missing configuration data, delayed stakeholder response, unresolved integration prerequisites, or unclear in-product guidance.
Support Queue Funnel	Provides an executive-grade, deterministic view of the full support lifecycle from new intake through triage, assignment, active work, escalation, and resolved closure.
Ticket Triage Queue	Converts queue risk signals into a deterministic triage worklist ranked by severity, age, customer impact, and predicted breach proximity.
Time-to-Fill Inspector	Inspects time-to-fill performance across requisitions and stage segments to identify where hiring cycle duration exceeds staffing commitments.
Time to Value Audit	Audits whether customers reach first measurable business value within committed onboarding windows, and quantifies where delays are concentrated by segment, implementation type, and value milestone.

Planning Forecasting

Tool	Description
Allocation Action Queue	Centralizes allocation interventions into a deterministic queue ranked by customer impact, due-date urgency, and expected capacity recovery.
Budget Action Queue	Centralizes budget interventions into a deterministic action queue sorted by financial impact, deadline risk, and owner accountability.
Budget Plan Control Center	Provides a single control surface for budget plan governance with deterministic KPI cards, period trend lines, and department status indicators aligned to monthly operating cadence.
Budget Timeline Variance	Quantifies deterministic variance between planned and actual project performance across budget consumption and timeline adherence in a single integrated bridge.
Capacity Gap Variance	Quantifies the gap between required demand load and feasible capacity across plants, lines, and shift structures using a deterministic bridge from nominal capacity to realized output.
Cash Action Queue	Centralizes liquidity interventions into a deterministic action queue sorted by impact, due-date risk, and controllability to support daily treasury execution.
Cash Scenario Simulator	Simulates deterministic what-if cash trajectories under configurable collection, disbursement, financing, and macro-stress assumptions.
Cashflow Planning Console	Provides a single operating console for cash flow governance with deterministic KPI cards, multi-week trend context, and legal-entity cash posture indicators aligned to treasury cadence.
Constraint Impact Simulator	Simulates deterministic impact of discrete constraints such as supplier shortages, line downtime, labor deficits, and logistics disruptions on fulfillment and revenue.
Cost Category Diagnostics	Decomposes budget outcomes by category, department, and supplier concentration to identify which spend classes are driving unfavorable plan movement.
Critical Path Projection Panel	Projects deterministic critical path timelines by combining current task progress, dependency readiness, and risk-adjusted duration assumptions.
Demand Capacity Console	Provides a single planning console that aligns demand outlook, available capacity, and service-level risk in one deterministic operating view for weekly execution cadence.
Demand Driver Diagnostics	Decomposes demand changes into explicit drivers such as promotions, pricing, channel mix, and regional seasonality so teams can identify what is materially changing the short-term load on constrained capacity.
Department Commitment Tracker	Tracks department-level budget commitments against approved targets with deterministic visibility into pledge quality, delivery timing, and closure confidence.
Dependency Risk Planner	Converts cross-project dependency exposure into deterministic mitigation plans with quantified schedule risk reduction and owner accountability.
Headcount Variance Monitor	Quantifies deterministic headcount variance from approved plan to current and forecasted staffing, using a bridge that isolates hiring, attrition, transfers, and organizational change effects.
Hiring Scenario Simulator	Simulates deterministic hiring strategies under configurable assumptions for offer acceptance, recruiter throughput, compensation pressure, and onboarding capacity.
Inflow Outflow Diagnostics	Decomposes cash movement into inflow and outflow drivers across customer segments, payment channels, and disbursement classes to expose root causes of cash volatility.
Labor Cost Capacity Planner	Aligns labor cost and workforce capacity decisions in a deterministic planning model that balances staffing mix, productivity assumptions, and budget constraints.
Liquidity Variance Monitor	Tracks liquidity headroom versus plan and policy floors across rolling daily and weekly horizons.
Plan vs Actual Variance	Quantifies budget variance between plan and actuals with a deterministic bridge from baseline assumptions to observed spend outcomes.
Project Action Queue	Consolidates project remediation tasks into a deterministic queue ranked by delivery impact, deadline proximity, and recovery feasibility.
Project Planning Console	Provides a single deterministic command view for project delivery health across schedule, effort, budget, and milestone confidence in one governance-ready surface.
Role Supply-Demand Diagnostics	Breaks workforce pressure into role-by-role supply versus demand detail so planners can pinpoint where shortages are concentrated and whether internal mobility can close the gap.
Run-Rate Projection Panel	Projects year-end budget outcomes from observed run-rate and seasonality assumptions, allowing early intervention before variance becomes non-recoverable.
Runway Projection Panel	Projects deterministic cash runway by combining opening liquidity, expected net burn, and financing availability over monthly horizons.
Scenario Capacity Optimizer	Simulates deterministic what-if scenarios that re-balance demand and capacity using levers such as overtime, subcontracting, line re-sequencing, and allocation policy changes.
Scenario Rebaseline Simulator	Simulates deterministic rebaseline scenarios that adjust scope, sequencing, staffing intensity, and contingency allocation to restore schedule confidence.
Schedule Effort Diagnostics	Decomposes schedule and effort variance into actionable root causes such as scope churn, dependency wait time, staffing shortfall, and rework intensity.
Seasonality Projection Panel	Projects deterministic seasonal demand curves across future periods to expose upcoming load peaks and troughs before they convert into service failure risk.
Skill Gap Projection Panel	Projects deterministic skill supply versus projected skill demand across future periods to identify capability deficits before critical initiatives enter execution.
Staffing Action Queue	Consolidates workforce interventions into a deterministic action queue ranked by delivery impact, skill criticality, and due-date urgency.
What-If Budget Scenarios	Supports deterministic what-if simulation for budget reallocation across departments, categories, and initiatives under policy and capacity constraints.
Workforce Planning Console	Delivers a single deterministic command view for workforce supply, approved demand, open requisitions, and labor-capacity coverage across the planning horizon.
Working Capital Planner	Converts working-capital levers into deterministic cash impact plans across receivables, payables, and inventory with owner-based execution tracking.

Risk Compliance

Tool	Description
Audit Follow-Up Queue	Centralizes all active follow-up actions from internal audit findings into a deterministic, prioritized execution queue that supports daily coordination and weekly escalation review.
Closure Variance Monitor	Tracks deterministic variance between planned and actual closure outcomes for internal audit findings, with explicit linkage to due dates, evidence sufficiency, and residual risk reduction.
Committee Effectiveness Tracker	Tracks deterministic committee effectiveness outcomes across participation, decision throughput, action closure, and documentation quality dimensions.
Compliance Control Hub	Serves as the canonical executive summary for compliance controls with deterministic snapshots of control inventory, ownership coverage, testing outcomes, and evidence completeness by framework and business process.
Compliance Variance Monitor	Tracks deterministic variance between committed compliance plans and actual delivery performance across control testing, issue closure, evidence collection, and policy attestation milestones.
Control Effectiveness Analyzer	Evaluates control health across design adequacy, operating performance, test outcomes, and issue recurrence with deterministic scoring at control and process levels.
Control Gap Diagnostics	Decomposes compliance control gaps into deterministic drivers across frameworks, obligations, process steps, and operating entities so teams can isolate root causes behind weak control coverage and recurring assurance findings.
Control Maturity Analyzer	Assesses deterministic cyber control maturity across design, implementation, operating effectiveness, and evidence sustainability to identify where control stacks remain fragile despite policy compliance claims.
Cyber Risk Command Center	Provides the canonical operating view for cyber risk management with deterministic visibility into current exposure, unresolved vulnerabilities, overdue patch obligations, and open security actions.
Decision Latency Analyzer	Measures deterministic governance decision-cycle performance from submission through committee review and formal resolution.
Enterprise Risk Register	Provides the canonical enterprise risk register with deterministic scoring for impact, likelihood, control maturity, and residual risk to support board and committee governance cycles.
Escalation Compliance Audit	Audits deterministic escalation records against governance protocol requirements, including trigger criteria, notification timelines, approval authority, and closure evidence standards.
Finding Theme Diagnostics	Decomposes internal audit findings into deterministic themes, sub-themes, and root-cause drivers so teams can identify systemic control breakdowns rather than treating each finding as an isolated event.
Governance Action Queue	Centralizes deterministic governance actions into a ranked execution queue so teams can triage policy, committee, and escalation follow-up tasks by urgency, governance impact, and dependency readiness.
Governance Control Board	Provides the canonical operating view for enterprise governance with deterministic visibility into active policies, adherence posture, committee obligations, and unresolved governance exceptions.
Incident Impact Tracker	Tracks deterministic business impact of cyber incidents across detection-to-recovery stages, including service disruption, customer effect, regulatory exposure, and cost accumulation.
Internal Audit Command Center	Provides the canonical operating view for the internal audit function with deterministic visibility into audit plan progress, active engagements, open findings, and closure risk.
Issue Severity Heatmap	Maps internal audit issue severity concentration across control domains and business entities using deterministic severity and exposure scoring to surface where aggregate assurance risk is accumulating.
Mitigation Variance Monitor	Monitors mitigation initiative execution against approved plan with deterministic tracking of milestone adherence, spend-to-plan, and realized residual-risk reduction for each high-priority risk theme.
Oversight Variance Monitor	Tracks deterministic variance between planned governance oversight commitments and actual completion outcomes across committee deliverables, policy attestations, escalation handling, and decision documentation timeliness.
Owner Timeliness Analyzer	Evaluates deterministic closure timeliness performance for remediation owners to identify consistent delivery strengths, chronic delays, and escalation hotspots.
Patch Variance Monitor	Tracks deterministic variance between committed patch plans and actual deployment outcomes, with explicit linkage to risk reduction objectives, maintenance windows, and SLA obligations.
Policy Adherence Diagnostics	Decomposes policy adherence into deterministic drivers across policy families, business units, attestation cycles, and control evidence quality so governance teams can isolate where non-adherence originates.
Policy Coverage Analyzer	Analyzes deterministic policy coverage by mapping policy clauses to implemented controls, evidence artifacts, and ownership accountability across regulatory frameworks.
Remediation Action Queue	Provides a deterministic, prioritized queue of remediation actions tied to open findings, control deficiencies, and policy exceptions.
Repeat Finding Tracker	Tracks deterministic recurrence of previously reported findings to identify persistent control weaknesses that survive one or more remediation cycles.
Risk Action Queue	Centralizes open risk actions into a deterministic queue ranked by residual exposure, due-date pressure, and control dependency criticality for daily execution management.
Risk Exposure Diagnostics	Decomposes enterprise risk exposure into deterministic contributors by business unit, geography, risk type, and control environment maturity so teams can isolate concentrated risk pockets.
Risk Heatmap Explorer	Visualizes enterprise risks on a deterministic impact-likelihood heatmap with overlays for residual score, control strength, and mitigation status to support prioritization and escalation decisions.
Risk Scenario Simulator	Simulates deterministic enterprise risk outcomes under configurable macro, operational, and control-disruption assumptions to quantify potential exposure range and resilience capacity.
Security Action Queue	Centralizes deterministic security action routing so vulnerability, detection, hardening, and incident follow-up tasks can be prioritized by risk, urgency, and dependency readiness.
Threat Surface Explorer	Maps deterministic threat surface exposure across internet-facing assets, identity trust paths, cloud entry points, and third-party connections so teams can understand where structural attack opportunity is expanding faster than control coverage.
Vulnerability Exposure Diagnostics	Decomposes vulnerability exposure into deterministic drivers across asset criticality, exploit availability, internet reachability, and compensating control strength so teams can isolate where technical debt creates disproportionate business risk.

Status Scorecards

Tool	Description
Adoption & Engagement Scorecard	Provides a focused scorecard for end-to-end adoption and engagement performance across activation funnel stages, feature depth, and repeat-use stability.
Attrition Risk Brief	Produces a concise attrition risk brief with segment-level risk concentrations, top predicted drivers, and intervention recommendations by owner.
Board Metric Briefing	Structures board-level metrics into three zones: growth, resilience, and execution, each with current performance, quarter-over-quarter delta, and commentary cues.
Budget Attainment Board	Displays budget attainment as a board-style grid with rows by department and columns for spend, revenue, headcount cost, and discretionary programs.
Capacity Bottleneck Brief	Summarizes the highest-impact bottlenecks across lines, stations, and support resources with explicit quantification of lost throughput and queue accumulation.
Cash & Margin Scorecard	Combines margin quality and cash realization signals into a compact scorecard with side-by-side cards for gross margin, contribution margin, operating cash flow margin, and cash conversion ratio.
Downtime Impact Panel	Quantifies the operational and service impact of planned and unplanned downtime across critical assets, translating stoppage minutes into lost output, delayed orders, and cost exposure.
Engagement Signal Rollup	Consolidates engagement signals from pulse surveys, participation behavior, manager effectiveness indicators, and wellbeing flags into a single rollup.
Executive KPI Cockpit	Presents a single-screen executive cockpit with a top KPI ribbon (revenue, gross margin, EBITDA, NPS, on-time delivery), a trend panel for the last 8 periods, and a status grid grouped by business pillar.
Expense Efficiency Brief	Summarizes expense efficiency through a structured brief that compares spend levels against output indicators such as revenue, customers served, and project throughput.
Feature Goal Attainment	Organizes feature initiatives by objective and release train, pairing goal definitions with measured outcome attainment and confidence in sustained impact.
Finance Alert Digest	Aggregates finance-specific exceptions into a daily digest covering cash floor breaches, overdue receivables spikes, margin drops, and budget overrun alerts.
Finance KPI Cockpit	Presents a one-screen finance control tower with headline tiles for revenue, gross margin, operating expense ratio, free cash flow, and net working capital days.
Forecast Confidence Panel	Provides a confidence-centered forecast panel that scores forecast quality across revenue, margin, cash flow, and expense lines using bias and accuracy diagnostics.
Headcount Capacity Scorecard	Provides a focused scorecard for workforce capacity using side-by-side views of approved positions, filled positions, vacancy load, and critical-role coverage.
Hiring Velocity Panel	Tracks end-to-end hiring execution across requisition aging, stage conversion, time-to-fill, and offer acceptance quality in a single operational panel.
Initiative Health Rollup	Aggregates major strategic initiatives into a unified health rollup, blending schedule confidence, budget burn, risk load, and dependency exposure.
KPI Alert Digest	Provides an alert-centric dashboard that aggregates breached KPI thresholds, trend-break anomalies, and stale owner updates into a single digest.
Operations KPI Cockpit	Presents an operations control-tower view that consolidates throughput, first-pass yield, schedule adherence, service level attainment, and unplanned downtime into a single, scan-first cockpit.
Ops Alert Digest	Consolidates operational exceptions into a daily digest covering throughput shortfalls, quality excursions, downtime spikes, and service-level breaches.
People Alert Digest	Aggregates people-related exceptions into a daily digest covering attrition spikes, hiring SLA breaches, engagement drops, policy compliance gaps, and manager-risk anomalies.
People KPI Cockpit	Presents a single-screen workforce cockpit with headline tiles for total headcount, regrettable attrition, hiring plan attainment, engagement index, and manager span-of-control stability.
Product Alert Digest	Aggregates product-related alert events into a daily digest covering adoption drops, engagement anomalies, reliability regressions, and conversion deterioration.
Product KPI Cockpit	Presents a single-screen product cockpit that consolidates active adoption, engagement depth, release reliability, trial-to-paid conversion, and retained revenue influence into one scan-first view.
Quarterly Variance Brief	Summarizes quarter-level performance variance against plan, forecast, and prior-year comparables with explicit driver decomposition.
Release Impact Rollup	Synthesizes release-level outcomes into a rollup that compares expected impact versus observed impact across adoption lift, engagement quality, reliability side effects, and monetization contribution.
Reliability Health Board	Tracks reliability health using a board layout that combines service availability, incident burden, defect escape, and mean time to recovery by product surface.
Retention Health Brief	Delivers a concise retention brief that combines gross retention, net retention influence, churn-risk concentration, and save-program effectiveness.
Service Level Board	Tracks service-level attainment across order-to-delivery and case-resolution commitments, with explicit segmentation by channel, region, and customer tier.
Shift Performance Rollup	Aggregates shift-level performance across safety, quality, throughput, and adherence dimensions to provide a consistent view of crew execution quality.
Strategic Goal Scorecard	Organizes strategic goals by pillar and objective, pairing lagging outcomes with leading milestone indicators in one scorecard.
Talent Health Board	Tracks talent health using a board layout that combines capability depth, internal mobility, succession coverage, and performance distribution indicators.
Target Commitment Tracker	Tracks committed targets by owner, period, and confidence, highlighting where commitments repeatedly miss delivery windows.
Throughput & Utilization Scorecard	Provides a focused scorecard for line throughput and asset utilization, combining achieved output, planned capacity, and utilization dispersion by line, shift, and product family.
Working Capital Watch	Focuses on the three working-capital levers (DSO, DPO, DIO) with a composite cash-cycle indicator and directional signal badges.

Interactive

Area

Tool	Description
Area Chart	Interactive area chart based on Observable Plot’s area-chart gallery example, plotting stock closing price by date with an area fill and overlaid line.
Area Chart with Missing Data	Interactive area chart adapted from Observable Plot’s plot-area-chart-missing-data gallery example, showing a weekly closing-price series with missing values at the beginning of the timeline.
Area Chart with Gradient Fill	Interactive area chart adapted from Observable Plot’s area-chart-with-gradient example, showing weekly closing prices over time with a gradient-filled area under the series and a line overlay for trend clarity.
Area + Line Custom Mark	Interactive area-and-line chart adapted from Observable Plot’s plot-arealiney-custom-mark gallery example, implemented as a custom composite mark that combines a zero baseline rule, an area fill, and a line over weekly closing prices.
Burndown Chart	Interactive burndown chart adapted from Observable Plot’s plot-burndown-chart gallery example, showing daily open issues as a stacked area where each issue contributes to every day from creation until close (or the selected burn date).
Difference Chart	Interactive difference chart adapted from Observable Plot’s plot-difference-chart gallery example, comparing monthly temperatures between New York and San Francisco and shading the gap between the two series.
Faceted Area Chart	Interactive faceted area chart adapted from Observable Plot’s plot-faceted-areas example, showing monthly unemployment trends as small-multiple area panels split by industry.
Horizon Chart of Unemployment by Industry	Interactive horizon chart adapted from Observable Plot’s plot-unemployment-horizon-chart gallery example, showing monthly unemployment trends as faceted horizon bands for multiple industries.
Urban Traffic Horizon Bands	Interactive horizon chart adapted from Observable Plot’s plot-horizon gallery example, showing hourly vehicles-per-hour patterns as faceted horizon bands across multiple transit routes.
Normalized Stack: Music Revenue Mix	Interactive normalized stacked area chart adapted from Observable Plot’s plot-normalized-stack gallery example, showing each format’s share of annual music revenue so every year sums to 100%.
Population Pyramid by Marital Status	Interactive population pyramid adapted from Observable Plot’s plot-population-pyramid gallery example, showing mirrored male and female age distributions where male values render on the left and female values on the right.
Proportion Plot Across Workforce Measures	Interactive proportion plot adapted from Observable Plot’s plot-proportion-plot gallery example, using stacked flowing areas to show how age-group shares change across four measures: population, labor force, employed, and full-time workers.
Ribbon Chart: U.S. Recorded Music Revenue	Interactive ribbon-style stacked area chart adapted from Observable Plot’s plot-ribbon-chart gallery example, showing annual U.S.
Stacked Area Unemployment Trends	Interactive stacked area chart adapted from Observable Plot’s plot-stacked-area-chart gallery example, showing monthly unemployment levels by industry as stacked layers over time.
Variable Fill Area	Interactive area chart adapted from Observable Plot’s plot-variable-fill-area gallery example, showing weekly closing price over time with area fill intensity mapped to a selected metric.
Wiggle Streamgraph by Stack Offset	Interactive streamgraph adapted from Observable Plot’s plot-stack-offset gallery example, using stacked area layers for music-format revenue over time and exposing stack offset behavior directly in the UI.

Arrow Link Vector

Tool	Description
Arc Diagram	A network arc diagram visualizing relationships in a JavaScript ecosystem (25 nodes across 7 groups: Frontend Frameworks, Server Frameworks, Build Tools, Compilers, Testing, Visualization, Styling).
Arrow Variation Chart	An arrow variation chart showing changes in population and income inequality across 25 US metro areas from 1980 to 2015.
Barley Trellis Plot with Arrows	A trellis (small multiples) chart showing year-over-year barley yield changes across 6 Minnesota trial sites (University Farm, Waseca, Morris, Crookston, Grand Rapids, Duluth) and 10 barley varieties.
Difference Arrows	A difference arrows chart showing the gender participation gap across 25 Olympic sports.
Finite State Machine	A directed graph visualization of a finite state machine (Markov chain) with three states (A, B, C) arranged in a circle.
Phases of the Moon	A lunar calendar visualization showing the phases of the moon for any given year, in the style of Irwin Glusker.

Bar

Tool	Description
Bar and Tick	Interactive bar-and-tick chart based on Observable Plot’s bar-and-tick gallery example, using deterministic English letter frequency data with bars and overlaid tick marks on a percent-scaled y-axis.
State Population Change Diverging Bars	Interactive diverging horizontal bar chart based on Observable Plot’s state population change example, showing percent change from 2010 to 2019 for seeded U.S.
Diverging Stacked Likert Bars	Interactive diverging stacked bar chart based on Observable Plot’s diverging stacked bar gallery example, using deterministic survey responses grouped by question and Likert response category.
Faceted Lollipop by State	Interactive faceted lollipop chart based on Observable Plot’s faceted lollipop gallery example, using deterministic state-by-year population rows with state, year, and population columns.
Grouped Bar Chart by State and Age Group	Interactive grouped bar chart based on Observable Plot’s grouped bar gallery example, using faceted state panels (fx) and age-group categories on each panel with population on the y-axis.
Olympians Grouped Bar Chart	Interactive grouped bar chart based on Observable Plot’s olympians grouped bar gallery example, faceting by sport (fx) and grouping bars by sex on the x-axis.
Horizontal Bar Chart	Interactive horizontal bar chart based on Observable Plot’s horizontal bar gallery example, using English letter frequencies on a top-oriented percent axis with grid lines.
Horizontal Bars with a Label	Interactive horizontal bar chart based on Observable Plot’s horizontal-bar-with-label gallery example, using deterministic company market-value data in billions.
Horizontal Stacked Bars	Interactive horizontal stacked bar chart based on Observable Plot’s horizontal stacked bars gallery example, using deterministic congressional-style records with party, gender, chamber, and region dimensions.
Lollipop Chart	Interactive lollipop chart based on Observable Plot’s lollipop gallery example, using deterministic English letter frequency data with Plot.ruleX stems and Plot.dot heads on a percent-scaled y-axis.
Ordinal Time Bar Chart	Interactive quarterly bar chart based on Observable Plot’s ordinal bar chart example, using deterministic labor-market style data with quarter, vacancies, and applications columns.
Single Stacked Percentage Bar	Interactive single stacked percentage bar based on Observable Plot’s stacked percentages gallery example, using deterministic English letter-frequency data where all segments compose one 100% horizontal bar.
Single Stacked Bar by Olympian Sport Share	Interactive single stacked horizontal bar based on Observable Plot’s single stacked bar example, using deterministic olympian sport participation counts converted into share of total athletes.
Stacked Bars by Island and Species	Interactive stacked bar chart based on Observable Plot’s stacked bars gallery example, showing deterministic penguin island data with species-specific stacked segments.
Crimean War Stacked Bars by Cause	Interactive stacked monthly bar chart based on Observable Plot’s Crimean War barY example, using deterministic long-form data with date, cause, and deaths columns.
Stacked Vertical Histogram	Interactive vertical histogram based on Observable Plot’s stacked olympians histogram example, using deterministic athlete records with weight, sex, sport, and athlete name fields.
Stacked Waffles by Weight and Sex	Interactive faceted waffle chart based on Observable Plot’s stacked waffles gallery example, using deterministic athlete rows with weight, sex, and sport fields.
Survey Waffle	Interactive waffle chart based on Observable Plot’s survey waffle gallery example, using deterministic survey question rows with baseline yes counts from a 120-person survey.
Temporal Bar Chart	Interactive temporal bar chart based on Observable Plot’s temporal bar chart example, using deterministic daily weather-style records with date, wind, temperature, and precipitation columns.
Vertical Bar Chart	Interactive vertical bar chart inspired by Observable Plot’s vertical bar gallery example, using English letter frequencies on a percent-scaled y-axis with a zero baseline rule.
Vertical Bars with Rotated Labels	Interactive vertical bar chart based on Observable Plot’s rotated-label bars gallery example, showing deterministic brand market values with long category names on the x-axis.

Cell

Tool	Description
Auto Mark Heatmap Explorer	Visualizes deterministic seeded athlete records with weight on the x-axis and height on the y-axis, using color to represent local density as a heatmap.
Auto Mark Heatmap by Weight and Sex	Recreates the Observable Plot auto-mark heatmap 2 pattern by plotting athlete weight on the x-axis and sex on the y-axis, with color encoding binned count density.
Calendar Activity Heatmap	Recreates the Observable Plot calendar example as a faceted year-by-year calendar heatmap where x is week-of-year and y is weekday, with each cell encoding a deterministic daily activity value.
Correlation Heatmap Explorer	Displays a pairwise correlation matrix across six deterministic seeded numeric fields (Demand, Temperature, Humidity, Wind, Solar, Price), with variables shown on both axes and color encoding Pearson correlation from -1 to 1.
Continuous Dimensions Heatmap	Recreates the Observable Plot continuous dimensions heatmap style by binning two quantitative dimensions: carat on the x-axis and price on the y-axis.
Seattle Temperature Temporal Heatmap	Recreates the Observable Plot Seattle temperature heatmap pattern using a calendar-like grid where day-of-month is on the x-axis and month is on the y-axis.
Simplified Dow Jones Calendar	Recreates the Observable Plot Dow Jones simplified calendar by faceting each year into horizontal calendar strips, encoding week-of-year on x and weekday on y with cell color representing daily percentage change in close.
Simpsons IMDb Ratings Heatmap	Recreates the Observable Plot Simpsons ratings example as a season-by-episode heatmap with season on the top x-axis, episode index on the y-axis, and cell color encoding IMDb rating.
Sorted Heatmap of Traffic by Hour	Shows a heatmap of traffic volume by hour (x-axis) and location (y-axis), where each cell color encodes an aggregated traffic metric.

Contour Density

Tool	Description
Blurred Contours	Geomagnetic field anomalies over Southern California visualized using Observable Plot’s contour mark with blur interpolation, based on the Plot blurred contours example.
Water Vapor Contour Map	Global precipitable water vapor visualized as filled contours on a geographic projection, based on the Observable Plot contours-projection example.
Faceted Density	Faceted density contour plot of penguin morphometric measurements, based on the Observable Plot density-faceted example.
Diamond Density (Stroke)	Density contour plot of diamonds showing carat vs price relationship, based on the Observable Plot density-stroke example.
Faceted Function Contour	A 2×2 grid of contour plots where each cell visualizes fill = fx(x) × fy(y), faceted by combinations of trigonometric (sin, cos) and linear functions.
Filled Contours	Volcanic elevation data rendered as filled contour bands, based on the Observable Plot filled contours example.
Function Contour Plot	Visualizes mathematical functions as filled contour maps using Observable Plot’s contour mark.
IGRF90 Contours	International Geomagnetic Reference Field (1990) total intensity contours over Southern California, based on the Observable Plot IGRF90 contours example.
Olympians Density	Density contour plot of Olympic athletes showing height (cm) vs.
One-Dimensional Density	Old Faithful geyser data visualized as layered one-dimensional density contours with individual data points, based on the Observable Plot one-dimensional density example.
Point Cloud Density	Old Faithful geyser eruption data visualized as a two-layer density estimation over a point cloud, based on the Observable Plot point-cloud-density example.
Stroked Contours	Elevation contour lines of the Maunga Whau volcano rendered as stroke-only contours (no fill), based on the Observable Plot stroked contours example.
Walmart Store Density	Kernel density estimation of Walmart store locations across the continental United States, based on the Observable Plot walmart-density example.

Delaunay Voronoi

Tool	Description
Centroid Voronoi	Displays a Voronoi tessellation computed from the centroids of all US counties, using Observable Plot’s centroid transform on GeoJSON county features loaded from the us-atlas CDN.
Delaunay Hull	Displays a Delaunay mesh triangulation with convex hulls overlaid, using Palmer Penguins data.
Delaunay Links	Displays a Delaunay triangulation link chart using Palmer Penguins data.
Planar vs Spherical Voronoi	Compares planar (Euclidean) and spherical (geodesic) Voronoi tessellations of 50 world airports on various map projections.
Voronoi Map	Displays a Voronoi tessellation of US state capitals on an azimuthal projection, showing each capital’s nearest-neighbor geographic region.
Voronoi Scatterplot	Displays a Voronoi tessellation scatterplot using Palmer Penguins data.
Walmart Store Voronoi	Displays a Voronoi mesh of Walmart store locations across the United States on a geographic projection, showing the territory nearest to each store.

Dot

Tool	Description
Anscombe’s Quartet Explorer	Interactive faceted scatterplot based on Observable Plot’s Anscombe’s quartet example, using Plot.frame, Plot.line, and Plot.dot marks over the canonical quartet dataset.
Beeswarm Dodge of Car Metrics	Interactive dodged beeswarm chart inspired by Observable Plot’s cars dodge example, drawing car records as Plot.dotX marks with Plot.dodgeY so overlapping values stack into a readable swarm.
Centroid Dot Explorer	Interactive map-style dot chart inspired by Observable Plot’s centroid-dot example, overlaying Plot.geoCentroid and Plot.centroid markers on seeded region polygons in an Albers USA projection.
Diverging Color Scatterplot	Interactive scatterplot of yearly global surface temperature anomalies with a diverging BuRd color scale centered around zero.
Dot Heatmap of Athlete Size	Interactive dot heatmap based on Observable Plot’s dot-heatmap gallery example, binning athlete weight on the x-axis and height on the y-axis.
Dot-Bin Weight Histogram	Interactive dot-bin histogram based on Observable Plot’s dot-bins gallery example, using athlete weight values binned across the x-axis with dot radius proportional to count in each bin.
Dot Sort Bubble Map	Interactive bubble map inspired by Observable Plot’s dot-sort gallery example, plotting seeded U.S.
Faceted Dodge Penguins	Interactive faceted dodge chart based on Observable Plot’s plot-dodge-penguins example, drawing penguin records as Plot.dot marks with Plot.dodgeX and faceting by species or island.
Olympians Hexbin Heatmap	Interactive hexbin heatmap based on Observable Plot’s olympians-hexbin gallery example, aggregating athlete weight on the x-axis and height on the y-axis into hexbin cells.
Ordinal Scatterplot	Interactive categorical scatterplot based on Observable Plot’s ordinal-scatterplot gallery example, where bubble size encodes the number of penguin records at each category intersection.
Proportional Symbol Scatterplot	Interactive stock-move scatterplot modeled on Observable Plot’s proportional-symbol example, with x-position as daily percent change and y-position as log-scaled daily trading volume.
Quantile-Quantile Plot	Interactive QQ plot inspired by Observable Plot’s qq-plot example, comparing two selected sample batches by plotting matched quantiles against each other.
Penguin Measurement Scatterplot	Interactive scatterplot of penguin measurements with selectable X and Y numeric fields and adjustable point radius.
Scatterplot with Color	Interactive color scatterplot inspired by Observable Plot’s gallery example, plotting penguin measurements with species encoded by color.
Scatterplot with Interactive Tips	Interactive athlete scatterplot based on Observable Plot’s interactive tips example, plotting weight on the x-axis and height on the y-axis with sex encoded by color.
Scatterplot with Ordinal Dimension	Interactive penguin scatterplot based on Observable Plot’s ordinal-dimension gallery example, plotting a numeric measure on the x-axis against an ordinal category on the y-axis.
Sized Hexbin Heatmap	Interactive sized-hexbin chart based on Observable Plot’s hexbin-binWidth gallery example, plotting athlete weight on the x-axis and height on the y-axis.
Stacked Dots by Age and Gender	Interactive mirrored stacked-dot chart inspired by Observable Plot’s stacked-dots example, using member age on the x-axis and stacking count above/below zero by gender.
Symbol Channel Scatterplot	Interactive penguin scatterplot modeled on Observable Plot’s symbol-channel example, encoding one categorical field by marker symbol and another by color.
Wealth & Health of Nations	Interactive bubble scatterplot based on Observable Plot’s wealth-health-nations example, plotting income per person on a logarithmic x-axis against life expectancy on the y-axis.

Geo

Tool	Description
US Map — Albers USA Projection	An interactive map of the United States using the Albers USA composite projection, inspired by the Observable Plot Albers USA projection example.
Bivariate Choropleth Map	An interactive bivariate choropleth map of the United States inspired by the Observable Plot bivariate choropleth example.
US County Choropleth Map	An interactive choropleth map of the United States showing county-level data, inspired by the Observable Plot choropleth example.
Earthquake Globe	An interactive earthquake globe inspired by the Observable Plot earthquake globe example.
Election Wind Map	An interactive election wind map of the United States inspired by the Observable Plot election wind map example.
Floor Plan	An interactive architectural floor plan rendered using Plot.geo with an identity projection, inspired by the Observable Plot floor plan example.
GeoTIFF Contours	An interactive filled contour visualization of global geographic data fields, inspired by the Observable Plot GeoTIFF contours example.
Hexbin Map	An interactive hexbin map of the United States inspired by the Observable Plot hexbin map example.
Store Expansion Map — Small Multiples	An interactive small-multiples geographic map inspired by the Observable Plot map small multiples example.
Polar Projection Explorer	An interactive azimuthal map projection explorer inspired by the Observable Plot polar projection example.
Shockwave Distance Rings	An interactive geographic visualization of concentric distance rings radiating from a geological epicenter, inspired by the Observable Plot shockwave example showing the Hunga Tonga eruption.
US Population Spike Map	An interactive spike map of the United States showing county-level population as vertical spikes, inspired by the Observable Plot spike map example.
US State Centroids	An interactive map of the United States showing centroid dots at the geographic center of each state, inspired by the Observable Plot state centroids example.
US Counties by First Letter	An interactive map of the United States showing county centroids filtered by the starting letter of the county name, inspired by the Observable Plot “V counties” example.
Wind Map	An interactive wind vector field visualization inspired by the Observable Plot wind map example.
World Map Projections	An interactive world map projection explorer inspired by the Observable Plot world projections example.

Image

Tool	Description
Background Image Scatterplot	Interactive scatterplot inspired by Observable Plot’s background-image gallery example, plotting penguin culmen length (x) and culmen depth (y) on top of a selectable Wikimedia-hosted background image.
Default Image Scatterplot	Interactive adaptation of Observable Plot’s plot-image-scatterplot-2 gallery example, using Plot.image to map Wikimedia-hosted presidential portraits across total favorable (x) and total unfavorable (y) opinion percentages.
Image Dodge Timeline	Interactive adaptation of Observable Plot’s image-dodge gallery example, plotting Wikimedia-hosted U.S.
Olympic Medal Image Plot	Interactive adaptation of the Observable Plot image-medals example pattern, using Plot.image to place Wikimedia-hosted country flag images on a time-versus-medal chart.
Presidential Favorability Image Scatterplot	Interactive adaptation of Observable Plot’s image-scatterplot example, using Plot.image to position Wikimedia-hosted U.S.

Interaction

Tool	Description
Color Crosshair	An interactive scatterplot demonstrating Observable Plot’s color crosshair feature, inspired by the Plot color crosshair gallery example.
Crosshair Explorer	An interactive scatterplot demonstrating Observable Plot’s crosshair mark.
CrosshairX Explorer	An interactive line chart demonstrating Observable Plot’s crosshairX mark, inspired by the Plot crosshairX gallery example.
Tips with Additional Channels	An interactive scatterplot demonstrating Observable Plot’s channels option for adding extra data fields to tooltips without mapping them to visual encodings, inspired by the Plot tips with additional channels gallery example.
Tips with Longer Text	An interactive scatterplot demonstrating Observable Plot’s tip mark with longer, paragraph-length text content, inspired by the Observable Plot tips with longer text gallery example.
Line Chart with Interactive Tip	An interactive line chart inspired by the Observable Plot line chart with interactive tip example.
Map & Tips	An interactive US map demonstrating Observable Plot’s tip mark with geographic centroid positioning, inspired by the Plot maps tips gallery example.
Multi-Series Line Chart with Interactive Tips	An interactive multi-series line chart inspired by the Observable Plot multi-series line chart with interactive tips example.
One-Dimensional Crosshair	An interactive one-dimensional distribution chart inspired by the Observable Plot one-dimensional crosshair example.
One-Dimensional Pointing	An interactive histogram inspired by the Observable Plot one-dimensional pointing example.
Pointer Modes: X, Y, and XY	An interactive line chart demonstrating Observable Plot’s three pointer modes (pointerX, pointerY, and pointer/XY), inspired by the Plot pointer modes gallery example.
Pointer Target Position	An interactive stock price line chart demonstrating Observable Plot’s pointer target position concept, inspired by the Plot pointer target position gallery example.
Pointer Transform Explorer	An interactive scatterplot demonstrating Observable Plot’s pointer transform, inspired by the Plot pointer transform gallery example.
Static Annotations	An interactive line chart with static text annotations, inspired by the Observable Plot static annotations gallery example.
Tip Format	An interactive scatterplot demonstrating Observable Plot’s tip format option, inspired by the Plot tip format gallery example.
Tips with Paired Channels	An interactive histogram demonstrating Observable Plot’s tip behavior with paired channels (x1/x2 from binX, y1/y2 from stackY), inspired by the Plot tips paired channels gallery example.

Line

Tool	Description
Bollinger Band Pulse	Interactive Bollinger bands chart modeled after the Observable Plot bollinger-bands gallery example, using deterministic daily close values stored in a bf-backed table.
Connected Scatterplot Explorer	Interactive connected scatterplot inspired by the Observable Plot connected-scatterplot example, using deterministic yearly driving-versus-gasoline seed data in a bf-backed table.
Indexed Stock Performance Chart	Interactive line chart modeled after the Observable Plot index chart pattern, using deterministic monthly close prices for AAPL, AMZN, GOOG, and IBM in a bf-backed table.
Labeled Multi-Line Stock Chart	Interactive multi-series stock close chart inspired by the Observable labeled multi-line example, using deterministic bf seed data for AAPL, AMZN, GOOG, and IBM over monthly dates.
Simple Line Chart Explorer	Interactive single-series line chart of stock closing price by date using deterministic seed data in a bf table.
Line Chart Percent Change Explorer	Interactive single-series percent-change line chart modeled after the Observable Plot line-chart-percent-change example, using deterministic monthly closing prices in a bf-backed seed table.
Crimean War Line Chart With Markers	Interactive multi-series line chart inspired by the Observable line-chart-with-markers example, using deterministic monthly Crimean-war-style deaths data in a bf-backed table with wide cause columns that are pivoted to long-form in-app.
Line Chart With Gaps Explorer	Interactive time-series line chart inspired by the Observable line-chart-with-gaps example, using deterministic monthly closing values from 2024 through 2025 stored in a bf-backed seed table.
Sparse Line Aggregation Explorer	Interactive line chart inspired by the Observable Plot sparse-line example, using deterministic timestamped observations stored in a bf-backed seed table.
Marey’s Trains Stringline Explorer	Interactive stringline chart inspired by the Observable Plot Marey’s trains example, using deterministic bf-backed Caltrain-style seed data with station names, route distance, train identifier, direction, service class (normal, limited, bullet), schedule type (weekday/weekend), and formatted time strings.
Temperature Anomaly Moving Average Explorer	Interactive line chart inspired by the Observable Plot moving-average example, using deterministic monthly temperature anomaly values stored in a bf-backed table.
Metro Unemployment Multi-Line Chart	Interactive multi-series line chart of monthly unemployment rates using deterministic seed data stored in a bf table.
Non-Temporal Line Chart Explorer	Interactive non-temporal line chart modeled after the Observable Plot non-temporal line example, using deterministic stage-profile seed data in a bf-backed table with numeric distance, elevation, and gradient columns.
Phone Feature Radar Chart	Interactive radar chart inspired by the Observable Plot radar-chart gallery example, implemented with a polar-style azimuthal projection, concentric guide rings, radial axis links, and closed polygon outlines for each phone model.
Faceted Radar Chart Small Multiples	Interactive faceted radar chart inspired by the Observable Plot radar-chart-faceted gallery example, using deterministic bf-backed vehicle profile seed data with six metrics (Price, Efficiency, Performance, Safety, Comfort, and Cargo) normalized per metric and rendered as one radar panel per vehicle.
Random Walk Drift Explorer	Interactive random walk line chart inspired by the Observable Plot random-walk example, using deterministic seeded step increments stored in a bf-backed table.
Government Receipts Slope Chart	Interactive slope chart inspired by the Observable Plot slope-chart gallery example, using deterministic bf-backed country data for government receipts (% of GDP) at two time points (1970 and 2020).
Cancer Survival Rates Slope Chart	Interactive slope-style cancer survival chart inspired by the Observable Plot cancer-survival-rates example, using deterministic bf-backed seed data with four categorical follow-up horizons (5 Year, 10 Year, 15 Year, 20 Year) for multiple cancer types.

Raster

Tool	Description
Mandelbrot Set Explorer	Interactive fractal visualization of the Mandelbrot set using Observable Plot’s raster mark with a computed fill function.
Projected Raster — Water Vapor	Global precipitable water vapor visualization rendered as a projected raster using Observable Plot’s raster mark.
Volcano Raster	Topographic heatmap of a volcanic surface rendered with Observable Plot’s raster mark.

Rect

Tool	Description
Band Chart with Rule	Displays monthly temperature ranges as vertical rule bands where each mark spans from minimum temperature (y1) to maximum temperature (y2) at a date on the x-axis, matching the Observable Plot band-chart-with-rule pattern and including a horizontal zero-temperature baseline.
Binned Box Plot of Diamond Prices	Displays diamond price distributions as box plots grouped into carat bins, following the Observable Plot binned box pattern by applying fx interval binning to the carat field and plotting price on the y-axis.
California COVID-19 Disparities Bullet Graph	Displays a faceted bullet-graph style comparison by race and age using two horizontal bars per row: a gray background bar for population share and a colored foreground bar for COVID-19 case share, mirroring the Observable Plot bullet graph gallery composition.
Candlestick Price Explorer	Displays daily OHLC price movement using the Observable Plot candlestick pattern: one ruleX mark for each session’s low-to-high wick and a second thick ruleX mark for the open-to-close body, colored by direction (down, flat, up).
County Bounding Boxes Explorer	Displays deterministic county-style geographic bounding rectangles as rect marks projected with Albers USA, following the Observable Plot county boxes pattern of drawing [x1, y1, x2, y2] coordinate bounds.
Cumulative Histogram Explorer	Displays athlete weight data as a cumulative histogram using Plot rectY with Plot.binX and the cumulative setting, following the Observable Plot cumulative histogram gallery pattern.
Cumulative Distribution of Poverty	Displays a cumulative poverty distribution as stacked rectangles using country population on the x-axis and the share of people living below a poverty threshold on the y-axis, matching the Observable Plot rectY + stackX gallery pattern.
Impact of Vaccines by State and Year	Displays disease case intensity as a state-by-year rectangular timeline, matching the Observable Plot vaccine-impact pattern where each state row is segmented by yearly intervals and colored by cases per 100,000 people.
Marimekko Revenue Mix by Market and Segment	Displays a Marimekko chart where each market occupies horizontal width proportional to total revenue, and each segment fills vertical share within that market, following the Observable Plot marimekko rect composition pattern.
Normal Histogram Explorer	Displays a histogram of deterministic near-normal sample values using Plot rectY with binning on the x-axis, along with an overlaid normal reference curve derived from the sample mean and standard deviation.
Overlapping Histograms	Compares deterministic male and female athlete weight distributions as overlapping histograms using Plot rectY with Plot.binX, closely following the Observable Plot overlapping histogram gallery pattern.
Percentogram Explorer	Displays deterministic numeric observations as a percentogram using Plot rectY with percentile-derived thresholds, so each bin contains an equal share of points while bin widths vary with the data distribution.
Pre-binned Histogram Explorer	Displays a pre-binned histogram using Plot rectY with explicit lower and upper bin boundaries (x0/x1) and precomputed frequencies, following the Observable Plot pre-binned histogram gallery pattern.
Crimean War Deaths by Cause	Displays monthly deaths from the Crimean War as stacked rectangular marks with one segment per cause (Disease, Wounds, Other), following the Plot rectY gallery pattern with monthly intervals.
Global Warming Stripes	Shows annual temperature anomaly values as contiguous yearly stripes, using one horizontal strip where each year is encoded by a diverging color from cooler to warmer anomalies.

Rule Tick

Tool	Description
Population Barcode Chart	A barcode-style chart showing US state population distributions by age group, inspired by the Observable Plot barcode example.
Germany Traffic Patterns	A sorted-groups tick chart showing hourly vehicle counts at 12 German highway counting stations, inspired by the Observable Plot sorted-groups example.
Band Chart with Rule	A temperature band chart showing daily min/max temperature ranges for a full year of synthetic weather data.
Bar & Tick Chart	A letter frequency chart combining translucent bars with tick marks to show exact values, inspired by the Observable Plot bar-and-tick example.
Candlestick Chart	An OHLC candlestick chart displaying ~65 days of synthetic stock price data.

Text

Tool	Description
Hexbin Text for Athlete Height and Weight	Interactive adaptation of Observable Plot’s hexbin-text example, plotting seeded athlete body metrics on weight (x) and height (y) axes.
US State Labels Explorer	Interactive adaptation of Observable Plot’s plot-state-labels example, showing U.S.
Caltrain Stem-and-Leaf Schedule	Interactive adaptation of Observable Plot’s caltrain-schedule example, plotting deterministic Caltrain-like departures as text leaves around an hourly stem.
IPO Text Dodge Timeline	Interactive adaptation of Observable Plot’s text-dodge example, plotting seeded IPO events by date and market capitalization.
Text Spiral Explorer	Interactive adaptation of Observable Plot’s plot-text-spiral example, plotting seeded spiral coordinates generated from deterministic index-based math.
This Is Just To Say — Interactive Text Layout	Interactive adaptation of Observable Plot’s this-is-just-to-say example, rendering William Carlos Williams’s poem lines as Plot.text marks inside a framed chart.
Voronoi Labels for Airport Points	Interactive adaptation of Observable Plot’s voronoi-labels example, plotting seeded U.S.

Tree

Tool	Description
Cluster Dendrogram	A cluster dendrogram of biological taxonomy data (Kingdom → Phylum → Class → Order → Family → Genus → Species) rendered using Observable Plot’s cluster mark.
Indented Tree Diagram	An indented tree diagram of a project file system hierarchy rendered using Observable Plot’s tree mark with a custom indented layout.
Tree Tidy Layout	A hierarchical tree diagram of the Flare visualization toolkit rendered using Observable Plot’s tree mark with the Reingold–Tilford “tidy” algorithm.