Complex Numbers
COMPLEX: Convert to complex type.
CONJ: Compute the complex conjugate.
DCOMPLEX: Convert to double-precision complex type.
IMAGINARY: Compute the imaginary part of a complex value.
REAL_PART: Compute the real part of a complex value.
Correlation Analysis
A_CORRELATE: Compute the autocorrelation.
C_CORRELATE: Compute the cross correlation.
CORRELATE: Compute the linear Pearson correlation.
M_CORRELATE: Compute the multiple correlation coefficient.
P_CORRELATE: Compute the partial correlation coefficient.
R_CORRELATE: Compute the rank correlation.
Curve and Surface Fitting
COMFIT: Fit paired data using a filtering function.
CRVLENGTH: Compute the length of a curve.
CURVEFIT: Fit multivariate data with a user-supplied function.
FUNCT: Evaluate the sum of a Gaussian and a 2nd-order polynomial.
GAUSS2DFIT: Fit a 2D elliptical Gaussian equation to rectilinearly-gridded data.
GAUSSFIT: Fit the sum of a Gaussian and a quadratic.
GRID_TPS: Use thin plate splines to interpolate a set of values over a regular 2D grid.
KRIG2D: Interpolate points to a grid using kriging.
LADFIT: Fit paired data using the least absolute deviation method.
LINFIT: Fit data to a linear model.
LMFIT: Do a non-linear least squares fit.
MIN_CURVE_SURF: Interpolate points with a minimum-curvature or thin-plate-spline surface.
POLY_FIT: Perform a least-squares polynomial fit.
REGRESS: Compute fit using multiple linear regression.
SFIT: Perform a polynomial fit to a surface.
SVDFIT: Multivariate least-squares fit using singular-value decomposition.
TRIGRID: Interpolates data to a regular grid from a triangulation.
Differentiation and Integration
CRVLENGTH: Compute the length of a curve.
DERIV: Perform differentiation using three-point Langrangian interpolation.
DERIVSIG: Compute the standard deviation of a derivative.
INT_2D: Compute the double integral of a bivariate function.
INT_3D: Compute the triple integral of a trivariate function.
INT_TABULATED: Integrate a tabulated set of data.
LSODE: Advance a solution to a system of ordinary differential equations one time-step.
QROMB: Evaluate an integral over a closed interval.
QROMO: Evaluate an integral over an open interval.
QSIMP: Evaluate an integral using Simpson’s rule.
RK4: Solve differential equations using the fourth-order Runge-Kutta method.
Eigenvalues and Eigenvectors
EIGENQL: Compute eigenvalues and eigenvectors of a real, symmetric array.
EIGENVEC: Compute eigenvectors of a real, non-symmetric array.
ELMHES: Reduce a nonsymmetric array to upper Hessenberg form.
HQR: Return all eigenvalues of an upper Hessenberg array.
TRIQL: Determine eigenvalues and eigenvectors of a tridiagonal array.
TRIRED: Reduce a real, symmetric array to tridiagonal form.
Gridding and Interpolation
BILINEAR: Construct an array using bilinear interpolation.
CONGRID: Shrink or expand an array by an arbitrary amount.
GRID_INPUT: Preprocess and sorts two-dimensional scattered data points, and removes duplicate values.
GRID_TPS: Use thin plate splines to interpolate a set of values over a regular 2D grid.
GRID3: Create a 3D dataset from a set of scattered 3D nodes.
GRIDDATA: Interpolate scattered data values and locations sampled on a plane or a sphere to a regular grid.
INTERPOL: Perform linear interpolation on vectors.
INTERPOLATE: Perform linear, bilinear, or trilinear interpolation.
KRIG2D: Interpolate points to a grid using kriging.
MIN_CURVE_SURF: Interpolate points with a minimum-curvature or thin-plate-spline surface.
POLY: Interpolate a surface from polar coordinates to rectangular coordinates.
SPH_SCAT: Perform spherical gridding.
SPL_INIT: Establishe the type of interpolating spline.
SPL_INTERP: Perform cubic spline interpolation.
REBIN: Shrink or expand an array by integral multiples or factors of the original dimensions.
SPLINE: Perform cubic spline interpolation.
SPLINE_P: Perform parametric cubic spline interpolation.
TRI_SURF: Interpolate gridded set of points with a smooth quintic surface.
TRIANGULATE: Construct the Delaunay triangulation of a planar set of points.
TRIGRID: Interpolate data to a regular grid from a triangulation.
VALUE_LOCATE: Find the intervals within a vector that bracket a set of search values.
VORONOI: Compute the Voronoi polygon given the Delaunay triangulation.
Hypothesis Testing
CTI_TEST: Perform the chi-square goodness-of-fit test.
FV_TEST: Perform the F-variance test.
KW_TEST: Perform the Kruskal-Wallis H-test.
LNP_TEST: Compute the Lomb Normalized Periodogram.
MD_TEST: Perform the Median Delta test.
R_TEST: Run tests for randomness.
RS_TEST: Perform the Wilcoxon Rank-Sum test.
S_TEST: Perform the Sign test.
TM_TEST: Perform t-means test.
XSQ_TEST: Compute the Chi-square goodness-of-fit test.
LAPACK Routines
LA_CHOLDC: Compute the Cholesky factorization of an n-by-n symmetric positive-definite array.
LA_CHOLMPROVE: Use Cholesky factorization to improve the solution to a system of linear equations.
LA_CHOLSOL: Used in conjunction with LA_CHOLDC to solve a set of linear equations.
LA_DETERM: Use LU decomposition to compute the determinant of a square array.
LA_EIGENPROBLEM: Use the QR algorithm to compute eigenvalues and eigenvectors.
LA_EIGENQL: Compute selected eigenvalues and eigenvectors.
LA_EIGENVEC: Use the QR algorithm to compute all or some eigenvectors.
LA_ELMHES: Reduce a real nonsymmetric or complex array to upper Hessenberg from.
LA_GM_LINEAR_MODEL: Used to solve a general Gauss-Markov linear model problem.
LA_HQR: Use the multishift QR algorithm to compute eigenvalues.
LA_INVERT: Use LU decomposition to compute the inverse of a square array.
LA_LEAST_SQUARE_EQUALITY: Used to solve linear least-squares problems.
LA_LEAST_SQUARES: Used to solve linear least-squares problems.
LA_LINEAR_EQUATION: Use LU decomposition to sole a system of linear equations.
LA_LUDC: Compute the LU decomposition of an array.
LA_LUMPROVE: Use LU decomposition to improve the solution to a system of linear equations.
LA_LUSOL: Used in conjunction with LA_LUDC to solve a set of linear equations.
LA_SVD: Compute the singular value decomposition of an array.
LA_TRIDC: Compute the LU decomposition of a tridiagonal array.
LA_TRIMPROVE: Improve the solution to a system of linear equations with a tridiagonal array.
LA_TRIQL: Use the QL and QR variants of the implicitly-shifted QR algorithm to compute eigenvalues and eigenvectors.
LA_TRIRED: Reduce a real symmetric or complex Hermitian array to real tridiagonal from.
LA_TRISOL: Used in conjunction with LA_TRIDC to solve a set of linear equations.
Linear Systems
CHOLDC: Construct the Cholesky decomposition of a matrix.
CHOLSOL: Solve a set of linear equations (use with CHOLDC).
COND: Compute the condition number of a square matrix.
CRAMER: Solve a system of linear equations using Cramer’s rule.
CROSSP: Compute vector cross product.
DETERM: Compute the determinant of a square matrix.
GS_ITER: Solve a linear system using Gauss-Seidel iteration.
IDENTITY: Return an identity array.
INVERT: Compute the inverse of a square array.
LINBCG: Solve a set of sparse linear equations using the iterative biconjugate gradient method.
LU_COMPLEX: Solve complex linear system using LU decomposition.
LUDC: Replace an array with the LU decomposition.
LUMPROVE: Use LU decomposition to iteratively improve an approximate solution.
LUSOL: Solve a set of linear equations. Use with LUDC.
NORM: Compute Euclidean norm of vector or Infinity norm of array.
SVDC: Compute Singular Value Decomposition of an array.
SVSOL: Solve a set of linear equations using back-substitution.
TRACE: Compute the trace of an array.
TRISOL: Solve a tridiagonal systems of linear equations.
Mathematical Error Assessment
CHECK_MATH: Return and clear accumulated math errors.
FINITE: Determine if a value is finite.
MACHAR: Return machine-specific parameters for floating-point arithmetic.
Miscellaneous Math Routines
ABS: Compute the absolute value.
CEIL: Compute the closest integer greater than or equal to X.
CIR_3PNT: Compute the radius and center of a circle, given 3 points.
COMPLEXROUND: Round a complex array.
DIAG_MATRIX: Construct a diagonal matrix from an input vector, or if given a matrix, then extracts a diagonal vector.
DIST: Create an array with each element proportional to its frequency.
EXP: Compute the natural exponential function of given expression.
FLOOR: Compute the closest integer less than or equal to argument.
IDLUNIT: Perform unit conversions and dimensional analysis.
IMAGINARY: Compute the imaginary part of a complex value.
ISHFT: Perform integer bit shift.
LEEFILT: Perform the Lee filter algorithm on an image array.
MATRIX_MULTIPLY: Calculate the matrix-multiply operator (#) of two (possibly transposed) arrays.
MATRIX_POWER: Compute the product of a matrix with itself.
PNT_LINE: Compute the perpendicular distance between a point and a line.
POLY_AREA: Compute the area of a polygon given the coordinates of its vertices.
PRIMES: Compute prime numbers.
PRODUCT: Compute the product of elements within an array.
ROUND: Compute the integer closest to its argument.
SIGNUM: Compute the sign (-1, 0, +1).
SPH_4PNT: Return center and radius of a sphere given 4 points.
SQRT: Compute the square root.
TOTAL: Sum of the elements of an array.
VOIGT: Calculate the intensity of atomic absorption line profiles.
Multivariate Analysis
CLUST_WTS: Compute cluster weights of an array for cluster analysis.
CLUSTER: Perform cluster analysis.
CLUSTER_TREE: Compute the hierarchical clustering for a set of m items in an n-dimensional space.
CTI_TEST: Perform the chi-square goodness-of-fit test.
DENDRO_PLOT: Draw a two-dimensional dendrite plot on the Direct Graphics device.
DENDROGRAM: Construct a dendrogram and returns a set of vertices and connectivity.
DISTANCE_MEASURE: Compute the pairwise distance between a set of items or observations.
KW_TEST: Perform the Kruskal-Wallis H-test.
M_CORRELATE: Compute the multiple correlation coefficient.
P_CORRELATE: Compute the partial correlation coefficient.
PCOMP: Compute the principal components and derived variables.
STANDARDIZE: Compute standardized variables.
Nonlinear Equations
BROYDEN: Solve nonlinear equations using Broyden’s method.
FX_ROOT: Compute real and complex roots of a univariate nonlinear function using an optimal Müller’s method.
FZ_ROOTS: Find the roots of a complex polynomial using Laguerre’s method.
NEWTON: Solve nonlinear equations using Newton’s method.
Optimization
AMOEBA: Minimize a function using downhill simplex method.
CONSTRAINED_MIN: Minimize a function using Generalized Reduced Gradient Method.
DFPMIN: Minimize a function using Davidon-Fletcher-Powell method.
POWELL: Minimize a function using the Powell method.
SIMPLEX: Use the simplex method to solve linear programming problems.
Probability
BINOMIAL: Compute the binomial distribution function.
CHISQR_CVF: Compute the cutoff value in a Chi-square distribution.
CHISQR_PDF: Compute the Chi-square distribution function.
F_CVF: Compute the cutoff value in an F distribution.
F_PDF: Compute the F distribution function.
GAUSS_CVF: Compute the cutoff value in Gaussian distribution.
GAUSS_PDF: Compute the Gaussian distribution function.
GAUSSINT: Compute the integral of the Gaussian probability function.
T_CVF: Compute the cutoff value in a Student’s t distribution.
T_PDF: Compute Student's t distribution.
Sparse Arrays
Note: SPRSIN must be used to convert to sparse storage format before the other routines can be used.
FULSTR: Restore a sparse matrix to full storage mode.
LINBCG: Solve a set of sparse linear equations using the iterative biconjugate gradient method.
READ_SPR: Read a row-indexed sparse matrix from a file.
SPRSAB: Perform matrix multiplication on sparse matrices.
SPRSAX: Multiply a sparse matrix by a vector.
SPRSIN: Convert a matrix to row-index sparse matrix.
SPRSTP: Construct the transpose of a sparse matrix.
WRITE_SPR: Write a row-indexed sparse array structure to a file.
Special Math Functions
BESELI: Compute the I Bessel function of order N.
BESELJ: Compute the J Bessel function of order N.
BESELK: Compute the K Bessel function of order N.
BESELY: Compute the Y Bessel function of order N.
BETA: Compute the beta function.
ERF: Compute the error function.
ERFC: Compute the complementary error function.
ERFCX: Compute the scaled complementary error function.
EXPINT: Compute the exponential integral.
GAMMA: Compute the gamma function.
IBETA: Compute the incomplete beta function.
IGAMMA: Compute the incomplete gamma function.
LAGUERRE: Compute the associated Laguerre polynomial.
LAMBERTW: Compute the Lambert W function.
LEGENDRE: Compute the associated Legendre polynomial.
LNGAMMA: Compute the logarithm of the gamma function.
POLY: Evaluate the polynomial function of a variable.
SPHER_HARM: Compute the spherical harmonic function.
Statistical Tools
FACTORIAL: Compute the factorial function.
HIST_2D: Compute the histogram of two variables.
HISTOGRAM: Compute the density function of an array.
KURTOSIS: Compute the statistical kurtosis.
MAX: Returns the largest value (and optionally its position) of an array.
MEAN: Compute the mean.
MEANABSDEV: Compute the mean absolute deviation.
MEDIAN: Returns the median value of an array or applies a median filter.
MIN: Returns the smallest value (and optionally its position) of an array.
MOMENT: Compute mean, variance, skewness, and kurtosis.
RANDOMN: Return normally-distributed pseudo-random numbers.
RANDOMU: Return pseudo-random numbers in one of several different distributions.
RANKS: Compute magnitude-based ranks.
RUNNING_STATS: Computes the mean and variance in a stable way for large datasets.
SKEWNESS: Compute the statistical skewness of an n-element vector.
STDDEV: Compute the standard deviation.
TOTAL: Sums of the elements of an array.
VARIANCE: Compute the statistical variance.
Time-Series Analysis
A_CORRELATE: Compute autocorrelation.
C_CORRELATE: Compute cross correlation.
SMOOTH: Smooth with a boxcar average.
TS_COEF: Compute the coefficients for autoregressive time-series.
TS_DIFF: Compute the forward differences of a time-series.
TS_FCAST: Compute future or past values of stationary time-series.
TS_SMOOTH: Compute moving averages of a time-series.
Transcendental Functions
ACOS: Compute the arc-cosine.
ALOG: Compute the natural logarithm.
ALOG2: Compute the logarithm to the base 2.
ALOG10: Compute the logarithm to the base 10.
ASIN: Compute the arc-sine.
ATAN: Compute the arc-tangent.
COS: Compute the cosine.
COSH: Compute the hyperbolic cosine.
EXP: Compute the natural exponential function of a given expression.
SIN: Compute the trigonometric sine.
SINH: Compute the hyperbolic sine.
TAN: Compute the tangent.
TANH: Compute the hyperbolic tangent.
Transforms
BLK_CON: Convolve input signal with impulse-response sequence.
CHEBYSHEV: Compute the forward or reverse Chebyshev polynomial expansion.
CONVOL: Convolve two vectors or arrays.
FFT: Compute the Fast Fourier Transform of an array.
HILBERT: Construct the Hilbert transform.
HOUGH: Compute the Hough transform of a two-dimensional image.
RADON: Compute the Radon transform of a two-dimensional image.
WTN: Compute the wavelet transform.
WV_CWT: Compute the continuous wavelet transform.
WV_DWT: Compute the discrete wavelet transform.
WV_PWT: Compute the partial wavelet transform.