ACCR_INT_MAT Function on page 515—Evaluates the interest which has accrued on a security that pays interest at maturity.

ACCR_INT_PER Function on page 516—Evaluates the interest which has accrued on a security that pays interest periodically.

AIRY_AI Function on page 475—Evaluates the Airy function.

AIRY_BI Function on page 477—Evaluates the Airy function of the second kind.

BESSI Function on page 458—Evaluates a modified Bessel function of the first kind with real order and real or complex parameters.

BESSI_EXP Function on page 465—Evaluates the exponentially scaled modified Bessel function of the first kind of orders zero and one.

BESSJ Function on page 460—Evaluates a Bessel function of the first kind with real order and real or complex parameters.

BESSK Function on page 462—Evaluates a modified Bessel function of the second kind with real order and real or complex parameters.

BESSK_EXP Function on page 466—Evaluates the exponentially scaled modified Bessel function of the third kind of orders zero and one.

BESSY Function on page 463—Evaluates a Bessel function of the second kind with real order and real or complex parameters.

BETA Function on page 450—Evaluates the real beta function B(x,y).

BETACDF Function on page 618—Evaluates the beta probability distribution function.

BETAI Function on page 453—Evaluates the real incomplete beta function.

BINOMIALCDF Function on page 619—Evaluates the binomial distribution function.

BINORMALCDF Function on page 605—Evaluates the bivariate normal distribution function.

BOND_EQV_YIELD Function on page 519—Evaluates the bond-equivalent yield of a Treasury bill.

BSINTERP Function on page 117—Computes a one- or two-dimensional spline interpolant.

BSKNOTS Function on page 125—Computes the knots for a spline interpolant.

BSLSQ Function on page 140—Computes a one- or two-dimensional, least-squares spline approximation.

CHFAC Procedure on page 30—Computes the Cholesky factor, L, of a real or complex symmetric positive definite matrix A, such that A = LLT.

CHISQCDF Function on page 607—Evaluates the chi-squared distribution function. Using a keyword, the inverse of the chi-squared distribution can be evaluated.

CHISQTEST Function on page 561—Chi-squared goodness-of-fit test

CHNNDFAC Procedure on page 44—Computes the Cholesky factorization of the real matrix A such that A = RTR = LLT.

CHNNDSOL Function on page 41—Solves a real symmetric nonnegative definite system of linear equations Ax = b. Computes the solution to Ax = b given the Cholesky factor.

CHSOL Function on page 26—Solves a symmetric positive definite system of real or complex linear equations Ax = b.

CMAST_ERR_PRINT Procedure on page 646—Sets options for error printing in Math and Stat options.

CMAST_ERR_STOP Function on page 645—Sets options for error recovery in Math and Stat options.

CMAST_ERR_TRANS Function on page 646—Informational Error codes for routine

CONLSQ Function on page 149—Computes a least-squares constrained spline approximation.

CONSTANT Function on page 630—Returns the value of various mathematical and physical constants.

CONVEXITY Function on page 520—Evaluates the convexity for a security.

CONVOL1D Function on page 356—Computes the discrete convolution of two one dimensional arrays.

CORR1D Function on page 359—Compute the discrete correlation of two one-dimensional arrays.

COUPON_DAYS Function on page 522—Evaluates the number of days in the coupon period containing the settlement date.

COUPON_DNC Function on page 527—Evaluates the number of days starting with the settlement date and ending with the next coupon date.

COUPON_NCD Function on page 542—Evaluates the first coupon date which follows the settlement date.

COUPON_NUM Function on page 524—Evaluates the number of coupons payable between the settlement date and the maturity date.

COUPON_PCD Function on page 543—Evaluates the coupon date which immediately precedes the settlement date.

CSINTERP Function on page 108—Computes a cubic spline interpolant, specifying various endpoint conditions. The default interpolant satisfies the not-a-knot condition.

CSSHAPE Function on page 113—Computes a shape-preserving cubic spline.

CSSMOOTH Function on page 155—Computes a smooth cubic spline approximation to noisy data by using cross-validation to estimate the smoothing parameter or by directly choosing the smoothing parameter.

CUM_INTR Function on page 485—Evaluates the cumulative interest paid between two periods.

CUM_PRINC Function on page 486—Evaluates the cumulative principal paid between two periods.

DATETODAYS Function on page 629—Computes the number of days from January 1, 1900, to the given date.

DAYSTODATE Procedure on page 628—Gives the date corresponding to the number of days since January 1, 1900.

DEA_PETZOLD_GEAR Procedure on page 250—Solves a first order differential-algebraic system of equations, g(t, y, y') = 0, using the Petzold-Gear BDF method.

DEPREC_AMORDEGRC Function on page 528—Evaluates the depreciation for each accounting period. During the evaluation of the function a depreciation coefficient based on the asset life is applied.

DEPREC_AMORLINC Function on page 530—Evaluates the depreciation for each accounting period.

DEPRECIATION_DB Function on page 487—Evaluates the depreciation of an asset using the fixed-declining balance method.

DEPRECIATION_DDB Function on page 489—Evaluates the depreciation of an asset using the double-declining balance method.

DEPRECIATION_SLN Function on page 491—Evaluates the depreciation of an asset using the straight-line method.

DEPRECIATION_SYD Function on page 492—Evaluates the depreciation of an asset using the sum-of-years digits method.

DEPRECIATION_VDB Function on page 493—Evaluates the depreciation of an asset for any given period using the variable-declining balance method.

EIG Function on page 90—Numerical differentiation using three-point Lagrangian

DISCOUNT_PR Function on page 531—Evaluates the price of a security sold for less than its face value.

DISCOUNT_RT Function on page 533—Evaluates the interest rate implied when a security is sold for less than its value at maturity in lieu of interest payments.

DISCOUNT_YLD Function on page 535—Evaluates the annual yield of a discounted security.

DOLLAR_DECIMAL Function on page 495—Converts a fractional price to a decimal price.

DOLLAR_FRACTION Function on page 496—Converts a decimal price to a fractional price.

DURATION Function on page 536—Evaluates the annual duration of a security where the security has periodic interest payments.

DURATION_MAC Function on page 540—Evaluates the modified Macauley duration of a security.

EFFECTIVE_RATE Function on page 497—Evaluates the effective annual interest rate.

EIG Function on page 90—Computes the eigenexpansion of a real or complex matrix A. If the matrix is known to be symmetric or Hermitian, a keyword can be used to trigger more efficient algorithms.

EIGSYMGEN Function on page 94—Computes the generalized eigenexpansion of a system Ax = λBx. The matrices A and B are real and symmetric, and B is positive definite.

ELE Function on page 468—Evaluates the complete elliptic integral of the second kind E(x).

ELK Function on page 467—Evaluates the complete elliptic integral of the kind K(x).

ELRC Function on page 473—Evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.

ELRD Function on page 470—Evaluates Carlson’s elliptic integral of the second kind RD(x, y, z).

ELRF Function on page 469—Evaluates Carlson’s elliptic integral of the first kind RF(x, y, z).

ELRJ Function on page 471—Evaluates Carlson’s elliptic integral of the third kind RJ(x, y, z, r).

ERF Function on page 444—Evaluates the real error function erf ( x ). Using a keyword, the inverse error function erf-1(x) can be evaluated.

ERFC Function on page 447—Evaluates the real complementary error function erf(x). Using a keyword, the inverse complementary error function erf-1(x) can be evaluated.

ERFCE Function on page 444—Evaluates the exponentially scaled complementary error function.

ERFE Function on page 446—Evaluates a scaled function related to ERFC(z).

FAURE_INIT Function on page 595—Initializes the structure used for computing a shuffled Faure sequence.

FAURE_NEXT_PT Function on page 598—Generates a shuffled Faure sequence.

FCDF Function on page 611—Evaluates the F distribution function. Using a keyword, the inverse of the F distribution function can be evaluated.

FCN_DERIV Function on page 220—Computes the first, second, or third derivative of a user-supplied function.

FCNLSQ Function on page 137—Computes a least-squares fit using user-supplied functions.

FEYNMAN_KAC Function on page 293—Solves the generalized Feynman-Kac PDE on a rectangular grid using a finite element Galerkin method.

FEYNMAN_KAC_EVALUATE Function on page 334—Computes the value of a Hermite quintic spline or the value of one of its derivatives.

FFTCOMP Function on page 345—Computes discrete Fourier transform of a real or complex sequence. Using keywords, a real-to-complex transform or two-dimensional complex Fourier transform can be computed.

FFTINIT Function on page 354—Computes parameters for a one-dimensional FFT to be used in function FFTCOMP with keyword Init_Params.

FMIN Function on page 384—Finds the minimum point of a smooth function f (x) of a single variable using function evaluations and, optionally, through both function evaluations and first derivative evaluations.

FMINV Function on page 394—Minimizes a function f(x) of n variables using a quasi-Newton method.

FREQTABLE Function on page 565—Tallies observations into a one-way frequency table

FRESNEL_COSINE Function on page 474—Evaluates cosine Fresnel integral.

FRESNEL_SINE Function on page 474—Evaluates sine Fresnel integral.

FUTURE_VAL_SCHD Function on page 499—Evaluates the future value of an initial principal taking into consideration a schedule of compound interest rates.

FUTURE_VALUE Function on page 498—Evaluates the future value of an investment.

GAMMA Function on page 454—Evaluates the real gamma function Γ(x).

GAMMACDF Function on page 616—Evaluates the gamma distribution function.

GAMMAI Function on page 456—Evaluates the incomplete gamma function γ(a,x).

GENEIG Procedure on page 96—Computes the generalized eigenexpansion of a system Ax = λBx.

GQUAD Procedure on page 217—Computes a Gauss, Gauss-Radau, or Gauss-Lobatto quadrature rule with various classical weight functions.

HERMITE Function on page 478—Evaluates Hermite polynomials.

HYPERGEOCDF Function on page 621—Evaluates the hypergeometric distribution function.

INT_PAYMENT Function on page 500—Evaluates the interest payment for an investment for a given period.

INT_RATE_ANNUITY Function on page 501—Evaluates the interest rate per period of an annuity.

INT_RATE_RETURN Function on page 502—Evaluates the internal rate of return for a schedule of cash flows.

INT_RATE_SCHD Function on page 504—Evaluates the internal rate of return for a schedule of cash flows. It is not necessary that the cash flows be periodic.

INT_RATE_SEC Function on page 538—Evaluates the interest rate of a fully invested security.

RBFIMSCL Procedure on page 182—Linear interpolation of vectors

INTFCN Function on page 192—Integrates a user-supplied function using different combinations of keywords and parameters.

INTFCN_QMC Function on page 215—Integrates a function on a hyper-rectangle using a quasi-Monte Carlo method.

INTFCNHYPER Function on page 213—Integrates a function on a hyper-rectangle.

INV Function on page 17—Computes the inverse of a real or complex, square matrix.

KELVIN_BEI0 Function on page 480—Evaluates the Kelvin function of the first kind, bei, of order zero.

KELVIN_BER0 Function on page 479—Evaluates the Kelvin function of the first kind, ber, of order zero.

KELVIN_KEI0 Function on page 482—Evaluates the Kelvin function of the second kind, kei, of order zero.

KELVIN_KER0 Function on page 481—Evaluates the Kelvin function of the second kind, ker, of order zero.

LAPLACE_INV Function on page 361—Computes the inverse Laplace transform of a complex function.

LEGENDRE Function on page 483—Evaluates the associated Legendre functions.

LINEAR_PROGRAMMING Function on page 406—Minimizes the Euclidean scalar product <c,x> on Rn, for fixed c, linear constraints bl ≤ Ax ≤ bu, and bounds xl ≤ x ≤ xu.

LINPROG Function on page 415—Solves a linear programming problem using the revised simplex algorithm.

LNBETA Function on page 452—Evaluates the logarithm of the real beta function ln β(x,y).

LNGAMMA Function on page 455—Evaluates the llogarithm of the absolute value of the gamma function log Γ(x).

LUFAC Procedure on page 23—Computes the LU factorization of a real or complex matrix.

LUSOL Function on page 18—Solves a general system of real or complex linear equations Ax = b.

MACHINE Function on page 634—Returns information describing the computer’s arithmetic.

MATRIX_NORM Function on page 641—Computes various norms of a rectangular matrix, a matrix stored in band format, and a matrix stored in coordinate format.

MATURITY_REC Function on page 548—Evaluates the amount one receives when a fully invested security reaches the maturity date.

MINCONGEN Function on page 421—Minimizes a general objective function subject to linear equality/inequality constraints.

MIN_UNCON_GOLDEN Function on page 390—(Univariate Function) Finds the minimum point of a nonsmooth function of a single variable using the golden section search method.

MOD_INTERN_RATE Function on page 505—Evaluates the modified internal rate of return for a schedule of periodic cash flows.

NANFINDER Procedure on page 639—Finds all instances of nan, inf, -inf in an array.

NET_PRES_VALUE Function on page 506—Evaluates the net present value of a stream of unequal periodic cash flows, which are subject to a given discount rate.

NLINLSQ Function on page 400—Solves a nonlinear least-squares problem using a modified Levenberg-Marquardt algorithm.

NOMINAL_RATE Function on page 508—Evaluates the nominal annual interest rate.

NONLINPROG Function on page 427—Solves a general nonlinear programming problem using the successive quadratic programming (QP) algorithm.

NORM Function on page 640—Computes various norms of a vector or the difference of two vectors.

NORMALCDF Function on page 603—Evaluates the standard normal (Gaussian) distribution function. Using a keyword, the inverse of the standard normal (Gaussian) distribution can be evaluated.

NUM_PERIODS Function on page 509—Evaluates the number of periods for an investment for which periodic and constant payments are made and the interest rate is constant.

ODE Function—Solves an initial value problem, which is possibly stiff, using the Adams-Gear methods for ordinary differential equations. Using keywords, the Runge-Kutta-Verner fifth-order and sixth-order method can be used if the problem is known not to be stiff.

ODEBV Function—Solves a general system of ordinary differential equations.

PAYMENT Function on page 510—Evaluates the periodic payment for an investment.

PDE_1D_MG Procedure on page 262—Solves a system of partial differential equations.

PDE_MOL Function on page 279—Solves a system of partial differential equations of the form ut = f(x, t, u, ux, uxx) using the method of lines. The solution is represented with cubic Hermite polynomials.

POISSON2D Function on page 337—Solves Poisson’s or Helmholtz’s equation on a two-dimensional rectangle using a fast Poisson solver based on the HODIE finite-difference scheme on a uniform mesh.

POISSONCDF Function on page 622—Evaluates the Poisson distribution function.

POLYEVAL Function on page 166—Evaluates a polynomial in n variables.

POLYFITN Function on page 168—Fits a polynomial to some n dimensional data.

PRES_VAL_SCHD Function on page 512—Evaluates the present value for a schedule of cash flows. It is not necessary that the cash flows be periodic.

PRESENT_VALUE Function on page 511—Evaluates the net present value of a stream of equal periodic cash flows, which are subject to a given discount rate.

PRICE_MATURITY Function on page 547—Evaluates the price, per $100 face value, of a security that pays interest at maturity.

PRICE_PERIODIC Function on page 545—Evaluates the price, per $100 face value, of a security that pays periodic interest.

PRINC_PAYMENT Function on page 513—Evaluates the payment on the principal for a specified period.

QRFAC Procedure on page 35—Computes the QR factorization of a real matrix A.

QRSOL Function on page 31—Solves a real linear least-squares problem Ax = b.

QUADPROG Function on page 418—Solves a quadratic programming (QP) problem subject to linear equality or inequality constraints.

RADBE Function on page 181—Evaluates a radial-basis fit computed by RADBF.

RADBF Function on page 172—Computes an approximation to scattered data in Rn for n ≥ 2 using radial-basis functions.

RANDOM Function on page 577—Generates pseudorandom numbers

RANDOMOPT Procedure on page 573—Control of the random number seed and uniform (0,1) generator.

RANKS Function on page 568—Ranks, normal scores, or exponential scores.

RBFIMSCL Procedure on page 182—Multiscale radial basis interpolation for n-dimensional data.

SCAT2DINTERP Function on page 169—Computes a smooth bivariate interpolant to scattered data that is locally a quintic polynomial in two variables.

SETTLEMENT_DB Function on page 525—Evaluates the number of days starting with the beginning of the coupon period and ending with the settlement date.

SMOOTHDATA1D Function on page 162—Smooth one-dimensional data by error detection.

SP_BDFAC Procedure on page 62—Compute the LU factorization of a matrix stored in band storage mode.

SP_BDPDFAC Function on page 73—Compute the RTR Cholesky factorization of symmetric positive definite matrix, A, in band symmetric storage mode.

SP_BDPDSOL Function on page 71—Solve a symmetric positive definite system of linear equations Ax = b in band symmetric storage mode.

SP_BDSOL Function on page 60—Solve a general band system of linear equations Ax = b.

SP_CG Function on page 78—Solve a real symmetric definite linear system using a conjugate gradient method. Using keywords, a preconditioner can be supplied.

SP_GMRES Function on page 75—Solve a linear system Ax = b using the restarted generalized minimum residual (GMRES) method.

SP_LUFAC Function on page 55—Compute an LU factorization of a sparse matrix stored in either coordinate format or CSC format.

SP_LUSOL Function on page 50—Solve a sparse system of linear equations Ax = b.

SP_MVMUL Function on page 81—Compute a matrix-vector product involving sparse matrix and a dense vector.

SP_PDFAC Function on page 68—Solve a sparse symmetric positive definite system of linear equations Ax = b.

SP_PDSOL Function on page 64—Solve a sparse symmetric positive definite system of linear equations Ax = b.

SPINTEG Function on page 134—Computes the integral of a one- or two-dimensional spline.

SPVALUE Function on page 129—Computes values of a spline or values of one of its derivatives.

SVDCOMP Function on page 38—Computes the singular value decomposition (SVD), A=USVT, of a real or complex rectangular matrix A. An estimate of the rank of A also can be computed.

TBILL_PRICE Function on page 550—Evaluates the price per $100 face value of a Treasury bill.

TBILL_YIELD Function on page 551—Evaluates the yield of a Treasury bill.

TCDF Function on page 613—Evaluates the Student’s t distribution function.

WgSplineTool Procedure on page 158—Widget-based interface

YEAR_FRACTION Function on page 553—Evaluates the fraction of a year represented by the number of whole days between two dates.

YIELD_MATURITY Function on page 554—Evaluates the annual yield of a security that pays interest at maturity.

YIELD_PERIODIC Function on page 556—Evaluates the yield of a security that pays periodic interest.

ZEROFCN Function on page 375—Finds the real zeros of a real function using Müller’s method.

ZEROPOLY Function on page 368—Finds the zeros of a polynomial with real or complex coefficients using the companion matrix method or, optionally, the Jenkins-Traub, three-stage algorithm.

ZEROS_FUNCTION Function on page 370—Finds the real zeros of a real, continuous, univariate function.

ZEROSYS Function on page 378—Solves a system of n nonlinear equations using a modified Powell hybrid algorithm.