XLPack function list November 20, 2020 * Subject to change without notice Category VBA routine name (WS function name) Functions V5.4 Lite V5.4 VBA WS Solver VBA WS Solver A3. Real arithmetic A3. Real arithmetic D1num IEEE 754 special numbers (double precision) ALL V IsFinite Determines if finite value (double precision) ALL V IsInf Determines if infinite value (double precision) ALL V IsNan Determines if NaN (not a number) (double precision) ALL V IsNormal Determines if nomal value (double precision) ALL V Signbit Determines if negative value (double precision) ALL V A4. Complex arithmetic A4. Complex arithmetic Creal Real part of complex number ALL Cimag Imaginary part of complex number ALL Cabs Absolute value of complex number ALL Conj Conjugate number ALL Carg Argument of complex number ALL Cproj Projection of complex number on Riemann sphere ALL Cmplx Building complex number ALL Cpolar Building complex number (polar coordinate) ALL Cminus Sign inversion of complex number ALL Cadd Addition of complex numbers ALL Cdadd Addition of complex number and real number ALL Csub Subtraction of complex number from complex number ALL Cdsub Subtraction of real number from complex number ALL Dcsub Subtraction of complex number from real number ALL Cmul Multiplication of complex numbers ALL Cdmul Multiplication of complex number and real number ALL Cdiv Division of complex number by complex number ALL Cddiv Division of complex number by real number ALL Dcdiv Division of real number by complex number ALL Cpow Power of complex number ALL Cdpow Power of a complex number (real order) ALL Cipow Power of a complex number (integer order) ALL C. Elementary and special functions C1. Integer-valued functions Factorial Factorial ALL V C2. Powers, roots, reciprocals Fma (WFma) (x*y)+z ALL ALL V V Hypot (WHypot) sqrt(x^2+y^2) ALL ALL V V Cbrt (WCbrt) Cube root ALL ALL V V Csqrt Complex square root ALL Ccbrt Complex cube root ALL C3. Polynomials Laguerre Laguerre polynomial Ln(x) M3 Alaguerre Associated Laguerre polynomial Lnm(x) M3 Legendre Legendre polynomial Pn(x) M3 Legendred Derivative of Legendre polynomial Pn(x) M3 Alegendre Associated Legendre polynomial Pnm(x) M3 Sharmonic Spherical harmonic Ylm(θ, φ) M3 Sharmonicr Real part of spherical harmonic Ylm(θ, φ) M3 Sharmonici Imaginary part of spherical harmonic Ylm(θ, φ) M3 Hermite Hermite polynomial Hn(x) M3 Chebt Chebyshev polynomial of first kind Tn(x) M3 Chebtd Derivative of Chebyshev polynomial of first kind Tn'(x) M3 Chebu Chebyshev polynomial of second kind Un(x) M3 Chebs Evaluation of Chebyshev series M3 C4. Elementary transcendental functions Expm1 (WExpm1) exp(x)-1 ALL ALL V V Exp2 2^x (base-2 exponent of x) ALL V Log1p (WLog1p) ln(1+x) ALL ALL V V Log2 log2(x) (base-2 logarithm of x) ALL V Log10 log10(x) (base-10 logarithm of x) ALL V Sqrt1pm1 sqrt(1 + x) - 1 ALL Powm1 x^y - 1 ALL Sinpi sin(πx) ALL Cospi cos(πx) ALL Acos arccos(x) ALL V Asin arcsin(x) ALL V Atan2 arctan2(y, x) ALL V Cosh cosh(x) ALL V Sinh sinh(x) ALL V Tanh tanh(x) ALL V Acosh arccosh(x) ALL V Asinh arcsinh(x) ALL V Atanh arctanh(x) ALL V Cexp Complex exp(z) ALL Clog Complex ln(z) ALL Cexpm1 Complex exp(z)-1 ALL Clog1p Complex ln(1+z) ALL Ccos Complex cos(z) ALL Csin Complex sin(z) ALL Ctan Complex tan(z) ALL Cacos Complex arccos(z) ALL Casin Complex arcsin(z) ALL Catan Complex arctan(z) ALL Ccosh Complex cosh(z) ALL Csinh Complex sinh(z) ALL Ctanh Complex tanh(z) ALL Cacosh Complex arcosh(z) ALL Casinh Complex arsinh(z) ALL Catanh Complex artanh(z) ALL Ccot Complex cot(z) ALL C5. Exponential and logarithmic integrals Li (WLi) Logarithmic integral li(x) M3 M3 V V Ei (WEi) Exponential integral Ei(x) M3 M3 V V E1 Exponential integral E1(x) M3 V En (WEn) Exponential integrals En(x) M3 M3 Exint (WEn) Sequences of exponential integrals E(N+k,X) M3% Spenc (WSpenc) Spence's function (dilogarithm function) Li2(x) M3% M3% Spence (WSpence) Spence's function (dilogarithm function) Li2(x) M3 M3 C6. Cosine and sine integrals Ci (WCi) Cosine integral Ci(x) M3 M3 Si (WSi) Sine integral Si(x) M3 M3 Chi (WChi) Hyperbolic cosine integral Chi(x) M3 M3 Shi (WShi) Hyperbolic sine integral Shi(x) M3 M3 C7a. Gamma functions Gamma Gamma function Γ(x) M3 V Gamma1pm1 Gamma function Γ(1+x) - 1 Lngam Logarithm of gamma function ln(Γ(x)) M3 Lngams Logarithm of gamma function ln|Γ(x)| and sign of gamma function Gamr (WGamr) Reciprocal of gamma function 1/Γ(x) M3 M3 Gamratio Ratio of gamma functions Γ(a)/Γ(b) Gamdratio Ratio of gamma functions Γ(a)/Γ(a+δ) Cgamma Gamma function Γ(z) (complex argument) M3 Clngam Logarithm of gamma function ln(Γ(z)) (complex argument) M3 Cgamr Reciprocal of gamma function 1/Γ(z) (complex argument) M3 Poch (WPoch) Pochhammer's symbol (a)x M3 M3 Poch1 (WPoch1) Relative Pochhammer's symbol ((a)x - 1)/x M3 M3 C7b. Beta functions Beta (WBeta) Beta function B(a, b) M3 M3 Lnbeta (WLnbeta) Logarithm of beta function ln(B(a,b)) M3 M3 Cbeta Beta function B(a, b) (complex argument) M3 Clnbeta Logarithm of beta function ln(B(a, b)) (complex argument) M3 C7c. Polygamma functions Psi (WPsi) Digamma (or psi) function ψ(x) M3% M3% V% V% Digamma (WDigamma) Digamma (or psi) function ψ(x) M3 M3 V V Trigamma Trigamma function ψ1(x) M3 Polygamma (WPolygamma) Polygamma function ψn(x) M3 M3 Psifn (Wpsid) Polygamma function ψn(x) (derivatives of psi function ψ(x)) M3% M3% Cpsi Digamma (or psi) function ψ(z) (complex argument) M3% Cdigamma Digamma (or psi) function ψ(z) (complex argument) M3 C7e. Incomplete Gamma functions Gami (WGami) Incomplete gamma function γ(a, x) M3 M3 Gamic (WGamic) Complementary incomplete gamma function Γ(a, x) M3 M3 Gamit (WGamit) Tricomi's incomplete gamma function γ*(a, x) M3 M3 Gammap Normalized incomplete gamma function P(a, x) M3 Gammaq Normalized complementary incomplete gamma function Q(a, x) M3 Gammapi Inverse function of x for normalized incomplete gamma function P(a, x) M3 Gammaqi Inverse function of x for normalized complementary incomplete gamma function Q(a, x) M3 Gammapia Inverse function of a for normalized incomplete gamma function P(a, x) M3 Gammaqia Inverse function of a for normalized complementary incomplete gamma function Q(a, x) M3 Gammapd Derivative of normalized incomplete gamma function P(a, x) M3 C7f. Incomplete Beta functions Betai (WBetai) Normalized incomplete beta function Ix(a, b) M3% M3% Betax Incomplete beta function Bx(a, b) M3 Betaxc Compliment of incomplete beta function 1 - Bx(a, b) M3 Ibeta (WIbeta) Normalized incomplete beta function Ix(a, b) M3 M3 Ibetac Normalized compliment of incomplete beta function 1 - Ix(a, b) M3 Ibetai Normalized incomplete beta function Ix(a, b) inverse for x M3 Ibetaci Normalized compliment of incomplete beta function 1 - Ix(a, b) inverse for x M3 Ibetaia Normalized incomplete beta function Ix(a, b) inverse for a M3 Ibetacia Normalized compliment of incomplete beta function 1 - Ix(a, b) inverse for a M3 Ibetaib Normalized incomplete beta function Ix(a, b) inverse for b M3 Ibetacib Normalized compliment of incomplete beta function 1 - Ix(a, b) inverse for b M3 Ibetad Derivative of normalized incomplete beta function Ix(a, b) M3 C7g. Riemann zeta function Zeta (WZeta) Riemann zeta function ζ(x) M3 M3 C8. Error functions Erf Error function erf(x) M3 V Erfc Complementary error function erfc(x) M3 V Erfi Error function erf(x) inverse M3 Erfci Complementary error function erf(x) inverse M3 Daws (WDaws) Dawson's function F(x) M3% M3% Dawson (WDawson) Dawson's function F(x) M3 M3 Fresc (WFresc) Fresnel integral C(x) M3 M3 Fress (WFress) Fresnel integral S(x) M3 M3 C10a. Bessel functions Besj0 Bessel function of the first kind of order zero J0(x) M3 V Besj1 Bessel function of the first kind of order one J1(x) M3 V Besjn Bessel functions of the first kind of order n Jn(x) M3 Besjnu (WBesj) Bessel function of the first kind of order ν Jν(x) (fractional order) M3 M3 V V Besy0 Bessel function of the second kind of order zero Y0(x) M3 V Besy1 Bessel function of the second kind of order one Y1(x) M3 V Besyn Bessel functions of the second kind of order n Yn(x) M3 Besynu (WBesy) Bessel function of the second kind of order ν Yν(x) (fractional order) M3 M3 V V Besj Sequence of Bessel functions of the first kind Jν(x) (fractional order) M3% Besy Sequence of Bessel functions of the second kind Yν(x) (fractional order) M3% Besjnd Derivative J'n(x) of Bessel function of the first kind of order n Jn(x) M3 Besjnud (WBesjd) Derivative J'ν(x) of Bessel function of the first kind of order ν Jν(x) (fractional order) M3 M3 Besynd Derivative Y'n(x) of modified Bessel functions of the second kind of order n Yn(x) M3 Besynud (WBesyd) Derivative Y'ν(x) of Bessel function of the second kind of order ν Yν(x) (fractional order) M3 M3 Sbesjn Spherical Bessel function of the first kind jn(x) M3 Sbesjnu (WSbesj) Spherical Bessel function of the first kind of order ν jν(x) (fractional order) M3 M3 Sbesyn Spherical Bessel function of the second kind yn(x) M3 Sbesynu (WSbesy) Spherical Bessel function of the second kind of order ν yν(x) (fractional order) M3 M3 Sbesj (WSbesj) Spherical Bessel function of the first kind jν(x) (fractional order) M3% Sbesy (WSbesy) Spherical Bessel function of the second kind yν(x) (fractional order) M3% Cbesh Sequence of Hankel functions Hν(m)(z) (fractional order) (complex argument) M3 Cbesj Sequence of Bessel functions of the first kind Jν(z) (fractional order) (complex argument) M3 Cbesy Sequence of Bessel functions of the second kind Yν(z) (fractional order) (complex argument) M3 C10b. Modified Bessel functions Besi0 Modified Bessel function of the first kind of order zero I0(x) M3 V Besi1 Modified Bessel function of the first kind of order one I1(x) M3 V Besin Modified Bessel function of the first kind of order n In(x) M3 Besinu (WBesi) Modified Bessel function of the first kind of order ν Iν(x) (fractional order) M3 M3 V V Besk0 Modified Bessel function of the second kind of order zero K0(x) M3 V Besk1 Modified Bessel function of the second kind of order one K1(x) M3 V Beskn Modified Bessel function of the second kind of order n Kn(x) M3 Besknu (WBesk) Modified Bessel function of the second kind of order ν Kν(x) (fractional order) M3 M3 V V Besi Sequence of modified Bessel functions of the first kind Iν(x) (fractional order) M3% Besk Sequence of modified Bessel functions of the second kind Kν(x) (fractional order) M3% Besind Derivative I'n(x) of modified Bessel function of the first kind of order n In(x) M3 Besinud (WBesid) Derivative I'ν(x) of modified Bessel function of the first kind of order ν Iν(x) (fractional order) M3 M3 Besknd Derivative K'n(x) of modified Bessel functions of the second kind of order n Kn(x) M3 Besknud (WBeskd) Derivative K'ν(x) of modified Bessel function of the second kind of order ν Kν(x) (fractional order) M3 M3 Sbesin Modified spherical Bessel function of the first kind in(x) M3 Sbesinu (WSbesi) Modified spherical Bessel function of the first kind of order ν iν(x) (fractional order) M3 M3 Sbeskn Modified spherical Bessel function of the second kind kn(x) M3 Sbesknu (WSbesk) Modified spherical Bessel function of the second kind of order ν kν(x) (fractional order) M3 M3 Sbesi (WSbesi) Modified spherical Bessel function of the first kind iν(x) (fractional order) M3% Sbesk (WSbesk) Modified spherical Bessel function of the second kind kν(x) (fractional order) M3% Cbesi Sequence of modified Bessel functions of the first kind Iν(z) (fractional order) (complex argument) M3 Cbesk Sequence of modified Bessel functions of the second kind Kν(z) (fractional order) (complex argument) M3 C10d. Airy functions Airyai (WAiryai) Airy function Ai(x) M3 M3 Airybi (WAirybi) Airy function Bi(x) M3 M3 Airyaid (WAiryaid) Derivative Ai'(x) of Airy function Ai(x) M3 M3 Airybid (WAirybid) Derivative Bi'(x) of Airy function Bi(x) M3 M3 Airy (WAiry) Airy function Ai(x) or its derivative Ai'(x) M3% M3% Biry (WBiry) Airy function Bi(x) or its derivative Bi'(x) M3% M3% Cairy Airy function Ai(x) or its derivative Ai'(z) (complex argument) M3 Cbiry Airy function Bi(x) or its derivative Bi'(z) (complex argument) M3 C11. Hypergeometric functions Hyp1f1 Hypergeometric function 1F1(a; b; z) (Kummer's function M(a, b, z)) M3 Lhyp1f1 Logarithm of hypergeometric function ln|1F1(a; b; z)| M3 Hyp1f1r Regularized hypergeometric functions 1F1(a; b; z)/Γ(b) M3 Chu Confluent hypergeometric function U(a,b,x) M3 Hyp2f1 Hypergeometric function 2F1(a1, a2; b; z) (Gaussian hypergeometric function) M3 Hyp0f1 Hypergeometric function 0F1(; b; z) M3 Hyp1f0 Hypergeometric function 1F0(a; z) M3 Hyp2f0 Hypergeometric function 2F0(a1, a2; z) M3 C13. Jacobi elliptic functions Jelli Jacobi elliptic functions sn(u, k), cn(u,k), dn(u, k) M3 Jsn (WJsn) Jacobi elliptic functions sn(u, k) M3 M3 Jcn (WJcn) Jacobi elliptic functions cn(u, k) M3 M3 Jdn (WJdn) Jacobi elliptic functions dn(u, k) M3 M3 Jns Jacobi elliptic functions ns(u, k) M3 Jnc Jacobi elliptic functions nc(u, k) M3 Jnd Jacobi elliptic functions nd(u, k) M3 Jsc Jacobi elliptic functions sc(u, k) M3 Jsd Jacobi elliptic functions sd(u, k) M3 Jdc Jacobi elliptic functions dc(u, k) M3 Jds Jacobi elliptic functions ds(u, k) M3 Jcs Jacobi elliptic functions cs(u, k) M3 Jcd Jacobi elliptic functions cd(u, k) M3 C14. Elliptic Integrals Celli1 (WCelli1) Complete elliptic integral of the first kind K(k) M3 M3 V V Celli2 (WCelli2) Complete elliptic integral of the second kind E(k) M3 M3 V V Celli3 (WCelli3) Complete elliptic integral of the third kind P(n, k) M3 M3 V V Elli1 (WElli1) Incomplete elliptic integral of the first kind F(phi, k) M3 M3 Elli2 (WElli2) Incomplete elliptic integral of the second kind E(phi, k) M3 M3 Elli3 (WElli3) Incomplete elliptic integral of the third kind P(phi, n, k) M3 M3 Rc (WRc) Carlson form of elliptic integral RC(x, y) M3 M3 Rd (WRd) Carlson form of elliptic integral RD(x, y, z) M3 M3 Rg (WRg) Carlson form of elliptic integral RG(x, y, z) M3 M3 Rf (WRf) Carlson form of elliptic integral RF(x, y, z) M3 M3 Rj (WRj) Carlson form of elliptic integral RJ(x, y, z, p) M3 M3 Jzeta Jacobi zeta function Z(φ, k) M3 C19. Other special functions Dconst (WDconst) Numerical quantities ALL ALL V V D. Linear algebra D1. Elementary vector and matrix operations D1a. Elementary vector operations: BLAS1 Daxpy y <- ax + y M1 Dcopy y <- x M1 Ddot x^T * y M1 Drotg Constructs Givens plane rotation M1 Drotmg Constructs modified Givens plane rotation M1 Drot Applies Givens plane rotation M1 Drotm Applies modified Givens plane rotation M1 Dscal x <- ax M1 Dswap y <-> x M1 Dasum | X | (1-norm) M1 Dnrm2 ||X||2 (2-norm of vector) M1 Zaxpy y <- ax + y (complex vector) M2 Zcopy y <- x (complex vector) M2 Zdotu x^T * y (complex vector) M2 Zdotc x^H * y (complex vector) M2 Zrotg Constructs Givens plane rotation (complex vector) M2 Zrot Applies Givens plane rotation (complex vector) M2 Zdrot Applies Givens plane rotation (complex vector) M2 Zdscal x <- ax (complex vector) M2 Zscal x <- ax (complex vector) (a is real number) M2 Zswap y <-> x (complex vector) M2 Dzasum |Re(x)|+|Im(x)| (1-norm) (complex vector) M2 Dznrm2 ||x||2 (2-norm) (complex vector) M2 D1a. Elementary vector operations: BLAS2 Dgemv y <- αAx+βy or y <- αA^Tx+βy M1 Dgbmv y <- αAx+βy or y <- αA^Tx+βy (band matrix) M1 Dsymv y <- αAx+βy (symmetric matrix) M1 Dsbmv y <- αAx+βy (symmetric band matrix) M1 Dspmv y <- αAx+βy (symmetric matrix) (packed form) M1 Dtrmv x <- Op(A)x (Op(A) = A or A^T) (triangular matrix) M1 Dtbmv x <- Op(A)x (Op(A) = A or A^T) (triangular band matrix) M1 Dtpmv x <- Op(A)x (Op(A) = A or A^T) (triangular matrix) (packed form) M1 Dtrsv Solution of Op(A)x = b (Op(A) = A or A^T) (triangular matrix) M1 Dtbsv Solution of Op(A)x = b (Op(A) = A or A^T) (triangular band matrix) M1 Dtpsv Solution of Op(A)x = b (Op(A) = A or A^T) (triangular matrix) (packed form) M1 Dger A <- αxy^T + A M1 Dsyr A <- αxx^T + A (symmetric matrix) M1 Dspr A <- αxx^T + A (symmetric matrix) (packed form) M1 Dsyr2 A <- αxy^T + αyx^T + A (symmetric matrix) M1 Dspr2 A <- αxy^T + αyx^T + A (symmetric matrix) (packed form) M1 Zgemv y <- αOp(A)x+βy (Op(A) = A, A^T or A^H) (complex matrix) M2 Zgbmv y <- αOp(A)x+βy (Op(A) = A, A^T or A^H) (complex band matrix) M2 Zhemv y <- αAx+βy (Hermitian matrix) M2 Zhbmv y <- αAx+βy (Hermitian band matrix) M2 Zhpmv y <- αAx+βy (Hermitian matrix) (packed form) M2 Zsymv y <- αAx+βy (complex symmetric matrix) M2 Zsbmv y <- αAx+βy (complex symmetric band matrix) M2 Zspmv y <- αAx+βy (complex symmetric matrix) (packed form) M2 Ztrmv x <- Op(A)x (Op(A) = A, A^T or A^H) (complex triangular matrix) M2 Ztbmv x <- Op(A)x (Op(A) = A, A^T or A^H) (complex triangular band matrix) M2 Ztpmv x <- Op(A)x (Op(A) = A, A^T or A^H) (complex triangular matrix) (packed form) M2 Ztrsv Solution of Op(A)x = b (Op(A) = A, A^T or A^H) (complex triangular matrix) M2 Ztbsv Solution of Op(A)x = b (Op(A) = A, A^T or A^H) (complex triangular band matrix) M2 Ztpsv Solution of Op(A)x = b  (Op(A) = A, A^T or A^H) (complex triangular matrix) (packed form) M2 Zgeru A <- αxy^T + A (complex matrix) M2 Zgerc A <- αxy^H + A (complex matrix) M2 Zher A <- αxx^H + A (Hermitian matrix) M2 Zhpr A <- αxx^H + A (Hermitian matrix) (packed form) M2 Zsyr A <- αxx^T + A (complex symmetric matrix) M2 Zspr A <- αxx^T + A (complex symmetric matrix) (packed form) M2 Zher2 A <- αxy^H + conjg(α)yx^H + A (Hermitian matrix) M2 Zhpr2 A <- αxy^H + conjg(α)yx^H + A (Hermitian matrix) (packed form) M2 Zsyr2 A <- αxy^T + αyx^T + A (complex symmetric matrix) M2 Zspr2 A <- αxy^T + αyx^T + A (complex symmetric matrix) (packed form) M2 D1b. Elementary matrix operations: BLAS3 Dgemm C <- αOp(A)Op(B) + βC (Op(X) = X, X^T) M1 Dsymm C <- αAB + βC or αBA + βC M1 Dtrmm B <- αOp(A)B or αBOp(A) (Op(A) = A or A^T) (triangular matrix) M1 Dtrsm Solution of Op(A)X = αB or XOp(A) = αB (Op(A) = A or A^T) M1 Dsyrk C <- αAA^T + βC or αA^TA + βC M1 Dsyr2k C <- αAB^T + αBA^T + βC or αA^TB + αB^TA + βC M1 Zgemm C <- αOp(A)Op(B) + βC (Op(X) = X, X^T or X^H) (complex matrix) M2 Zsymm C <- αAB + βC or αBA + βC (complex symmetric matrix) M2 Zhemm C <- αAB + βC or αBA + βC (Hermitian matrix) M2 Ztrmm B <- αOp(A)B or αBOp(A) (Op(A) = A, A^T or A^H) (complex triangular matrix) M2 Ztrsm Solution of Op(A)X = αB or XOp(A) = αB (Op(A) = A, A^T or A^H) (complex triangular matrix) M2 Zsyrk C <- αAA^T + βC or αA^TA + βC (complex symmetric matrix) M2 Zherk C <- αAA^H + βC or αA^HA + βC (Hermitian matrix) M2 Zsyr2k C <- αAB^T + αBA^T + βC or αA^TB + αB^TA + βC (complex symmetric matrix) M2 Zher2k C <- αAB^H + conjg(α)BA^H + βC or αA^HB + conjg(α)B^HA + βC (Hermitian matrix) M2 D1b. Elementary matrix operations: norm of matrix Dlange Norm of matrix (general matrix) M1 V Dlangb Norm of matrix (band matrix) M1 Dlangt Norm of matrix (tridiagonal matrix) M1 Dlansy Norm of matrix (symmetric matrix) M1 V Dlansb Norm of matrix (symmetric band matrix) M1 Dlansp Norm of matrix (symmetric matrix) (packed form) M1 Dlanst Norm of matrix (symmetric tridiagonal matrix) M1 Dlantr Norm of matrix (trapezoidal or triangular matrix) M1 Zlange Norm of matrix (complex matrix) M2 Zlangb Norm of matrix (complex band matrix) M2 Zlangt Norm of matrix (complex tridiagonal matrix) M2 Zlansy Norm of matrix (complex symmetric matrix) M2 Zlansb Norm of matrix (complex symmetric band matrix) M2 Zlansp Norm of matrix (complex symmetric matrix) (packed form) M2 Zlanhe Norm of matrix (Hermitian matrix) M2 Zlanhb Norm of matrix (Hermitian band matrix) M2 Zlanhp Norm of matrix (Hermitian matrix) (packed form) M2 Zlanht Norm of matrix (Hermitian tridiagonal matrix) M2 Zlantr Norm of matrix (complex trapezoidal or triangular matrix) M2 D2. Solution of systems of linear equations D2a. Solution of systems of linear equations (general matrices) Dgesv (WDgesv) Solution of system of linear equations Ax = b M1 M1 V V Dgetrf LU factorization of coefficient matrix M1 Dgetrs Solution of LU factorized system of linear equations M1 Dgetri Inverse matrix M1 Dgesvx Solution of system of linear equations Ax = b (expert driver) M1 Dgecon Condition number of matrix M1 V Dsgesv Solution of system of linear equations Ax = b (mixed precision with iterative refinement) M1 Dgbsv (WDgbsv) Solution of system of linear equations Ax = b (band matrix) M1 M1 Dgbtrf LU factorization of coefficient matrix (band matrix) M1 Dgbtrs Solution of LU factorized system of linear equations (band matrix) M1 Dgbsvx Solution of system of linear equations Ax = b (band matrix) (expert driver) M1 Dgbcon Condition number of matrix (band matrix) M1 Dgtsv (WDgtsv) Solution of system of linear equations Ax = b (tridiagonal matrix) M1 M1 Dgttrf LU factorization of coefficient matrix (tridiagonal matrix) M1 Dgttrs Solution of LU factorized system of linear equations (tridiagonal matrix) M1 Dgtsvx Solution of system of linear equations Ax = b (tridiagonal matrix) (expert driver) M1 Dgtcon Condition number of matrix (tridiagonal matrix) M1 D2a3. Solution of systems of linear equations (triangular matrices) Dtrtrs (WDtrtrs) Solution of system of linear equations Ax = b (triangular matrix) M1 M1 Dtrtri Inverse matrix (triangular matrix) M1 Dtrcon Condition number of matrix (triangular matrix) M1 Dtptrs Solution of system of linear equations Ax = b (triangular matrix) (packed form) M1 Dtptri Inverse matrix (triangular matrix) (packed form) M1 Dtpcon Condition number of matrix (triangular matrix) (packed form) M1 Dtbtrs Solution of system of linear equations Ax = b (triangular band matrix) M1 Dtbcon Condition number of matrix (triangular band matrix) M1 D2b1a. Solution of systems of linear equations (symmetric matrices) Dsysv (WDsysv) Solution of system of linear equations Ax = b (symmetric matrix) M1 M1 Dsytrf UDU^T or LDL^T factorization of coefficient matrix (symmetric matrix) M1 Dsytrs Solution of UDU^T or LDL^T factorized system of linear equations (symmetric matrix) M1 Dsytri Inverse matrix (symmetric matrix) M1 Dsysvx Solution of system of linear equations Ax = b (symmetric matrix) (expert driver) M1 Dsycon Condition number of matrix (symmetric matrix) M1 Dspsv Solution of system of linear equations Ax = b (symmetric matrix) (packed form) M1 Dsptrf UDU^T or LDL^T factorization of coefficient matrix (symmetric matrix) (packed form) M1 Dsptrs Solution of UDU^T or LDL^T factorized system of linear equations (symmetric matrix) (packed form) M1 Dsptri Inverse matrix (symmetric matrix) (packed form) M1 Dspsvx Solution of system of linear equations Ax = b (symmetric matrix) (packed form) (expert driver) M1 Dspcon Condition number of matrix (symmetric matrix) (packed form) M1 D2b1b. Solution of systems of linear equations (symmetric positive definite matrices) Dposv (WDposv) Solution of system of linear equations Ax = b (symmetric positive definite matrix) M1 M1 V V Dpotrf Cholesky factorization of coefficient matrix (symmetric positive definite matrix) M1 Dpotrs Solution of Cholesky factorized system of linear equations (symmetric positive definite matrix) M1 Dpotri Inverse matrix (symmetric positive definite matrix) M1 Dposvx Solution of system of linear equations Ax = b (symmetric positive definite matrix) (expert driver) M1 Dpocon Condition number of matrix (symmetric positive definite matrix) M1 V Dsposv Solution of system of linear equations Ax = b (symmetric positive definite matrix) (mixed precision with iterative refinement) M1 Dppsv Solution of system of linear equations Ax = b (symmetric positive definite matrix) (packed form) M1 Dpptrf Cholesky factorization of coefficient matrix (symmetric positive definite matrix) (packed form) M1 Dpptrs Solution of Cholesky factorized system of linear equations (symmetric positive definite matrix) (packed form) M1 Dpptri Inverse matrix (symmetric positive definite matrix) (packed form) M1 Dppsvx Solution of system of linear equations Ax = b (symmetric positive definite matrix) (packed form) (expert driver) M1 Dppcon Condition number of matrix (symmetric positive definite matrix) (packed form) M1 D2b2. Solution of systems of linear equations (symmetric positive definite banded matrices) Dpbsv (WDpbsv) Solution of system of linear equations Ax = b (symmetric positive definite band matrix) M1 M1 Dpbtrf Cholesky factorization of coefficient matrix (symmetric positive definite band matrix) M1 Dpbtrs Solution of Cholesky factorized system of linear equations (symmetric positive definite band matrix) M1 Dpbsvx Solution of system of linear equations Ax = b (symmetric positive definite band matrix) (expert driver) M1 Dpbcon Condition number of matrix (symmetric positive definite band matrix) M1 Dptsv (WDptsv) Solution of system of linear equations Ax = b (symmetric positive definite tridiagonal matrix) M1 M1 Dpttrf LDL^T factorization of coefficient matrix (symmetric positive definite tridiagonal matrix) M1 Dpttrs Solution of LDL^T factorized system of linear equations (symmetric positive definite tridiagonal matrix) M1 Dptsvx Solution of system of linear equations Ax = b (symmetric positive definite tridiagonal matrix) (expert driver) M1 Dptcon Condition number of matrix (symmetric positive definite tridiagonal matrix) M1 D2c. Solution of systems of linear equations (general complex matrices) Zgesv (WZgesv(2)) Solution of system of linear equations Ax = b (complex matrix) M2 M2 Zgetrf LU factorization of coefficient matrix (complex matrix) M2 Zgetrs Solution of LU factorized system of linear equations (complex matrix) M2 Zgetri Inverse matrix (complex matrix) M2 Zgesvx Solution of system of linear equations Ax = b (complex matrix) (expert driver) M2 Zgecon Condition number of matrix (complex matrix) M2 Zcgesv Solution of system of linear equations Ax = b (mixed precision with iterative refinement) (complex matrix) M2 Zgbsv (WZgbsv(2)) Solution of system of linear equations Ax = b (complex band matrix) M2 M2 Zgbtrf LU factorization of coefficient matrix (complex band matrix) M2 Zgbtrs Solution of LU factorized system of linear equations (complex band matrix) M2 Zgbsvx Solution of system of linear equations Ax = b (complex band matrix) (expert driver) M2 Zgbcon Condition number of matrix (complex band matrix) M2 Zgtsv (WZgtsv(2)) Solution of system of linear equations Ax = b (complex tridiagonal matrix) M2 M2 Zgttrf LU factorization of coefficient matrix (complex tridiagonal matrix) M2 Zgttrs Solution of LU factorized system of linear equations (complex tridiagonal matrix) M2 Zgtsvx Solution of system of linear equations Ax = b (complex tridiagonal matrix) (expert driver) M2 Zgtcon Condition number of matrix (complex tridiagonal matrix) M2 Zsysv (WZsysv(2)) Solution of system of linear equations Ax = b (complex symmetric matrix) M2 M2 Zsytrf UDU^H or LDL^H factorization of coefficient matrix (complex symmetric matrix) M2 Zsytrs Solution of UDU^H or LDL^H factorized system of linear equations (complex symmetric matrix) M2 Zsytri Inverse matrix (complex symmetric matrix) M2 Zsysvx Solution of system of linear equations Ax = b (complex symmetric matrix) (expert driver) M2 Zsycon Condition number of matrix (complex symmetric matrix) M2 Zspsv Solution of system of linear equations Ax = b (complex symmetric matrix) (packed form) M2 Zsptrf UDU^H or LDL^H factorization of coefficient matrix (complex symmetric matrix) (packed form) M2 Zsptrs Solution of UDU^H or LDL^H factorized system of linear equations (complex symmetric matrix) (packed form) M2 Zsptri Inverse matrix (complex symmetric matrix) (packed form) M2 Zspsvx Solution of system of linear equations Ax = b (complex symmetric matrix) (packed form) (expert driver) M2 Zspcon Condition number of matrix (complex symmetric matrix) (packed form) M2 D2c3. Solution of systems of linear equations (triangular complex matrices) Ztrtrs (WZtrtrs(2)) Solution of system of linear equations Ax = b (complex triangular matrix) M2 M2 Ztrtri Inverse matrix (complex triangular matrix) M2 Ztrcon Condition number of matrix (complex triangular matrix) M2 Ztptrs Solution of system of linear equations Ax = b (complex triangular matrix) (packed form) M2 Ztptri Inverse matrix (complex triangular matrix) (packed form) M2 Ztpcon Condition number of matrix (complex triangular matrix) (packed form) M2 Ztbtrs Solution of system of linear equations Ax = b (complex triangular band matrix) M2 Ztbcon Condition number of matrix (complex triangular band matrix) M2 D2d1a. Solution of systems of linear equations (Hermitian matrices) Zhesv (WZhesv(2)) Solution of system of linear equations Ax = b (Hermitian matrix) M2 M2 Zhetrf UDU^H or LDL^H factorization of coefficient matrix (Hermitian matrix) M2 Zhetrs Solution of UDU^H or LDL^H factorized system of linear equations (Hermitian matrix) M2 Zhetri Inverse matrix (Hermitian matrix) M2 Zhesvx Solution of system of linear equations Ax = b (Hermitian matrix) (expert driver) M2 Zhecon Condition number of matrix (Hermitian matrix) M2 Zhpsv Solution of system of linear equations Ax = b (Hermitian matrix) (packed form) M2 Zhptrf UDU^H or LDL^H factorization of coefficient matrix (Hermitian matrix) (packed form) M2 Zhptrs Solution of UDU^H or LDL^H factorized system of linear equations (Hermitian matrix) (packed form) M2 Zhptri Inverse matrix (Hermitian matrix) (packed form) M2 Zhpsvx Solution of system of linear equations Ax = b (Hermitian matrix) (packed form) (expert driver) M2 Zhpcon Condition number of matrix (Hermitian matrix) (packed form) M2 D2d1b. Solution of systems of linear equations (positive definite Hermitian matrices) Zposv (WZposv(2)) Solution of system of linear equations Ax = b (Hermitian positive definite matrix) M2 M2 Zpotrf Cholesky factorization of coefficient matrix (Hermitian positive definite matrix) M2 Zpotrs Solution of Cholesky factorized system of linear equations (Hermitian positive definite matrix) M2 Zpotri Inverse matrix (Hermitian positive definite matrix) M2 Zposvx Solution of system of linear equations Ax = b (Hermitian positive definite matrix) (expert driver) M2 Zpocon Condition number of matrix (Hermitian positive definite matrix) M2 Zcposv Solution of system of linear equations Ax = b (Hermitian positive definite matrix) (mixed precision with iterative refinement) M2 Zppsv Solution of system of linear equations Ax = b (Hermitian positive definite matrix) (packed form) M2 Zpptrf Cholesky factorization of coefficient matrix (Hermitian positive definite matrix) (packed form) M2 Zpptrs Solution of Cholesky factorized system of linear equations (Hermitian positive definite matrix) (packed form) M2 Zpptri Inverse matrix (Hermitian positive definite matrix) (packed form) M2 Zppsvx Solution of system of linear equations Ax = b (Hermitian positive definite matrix) (packed form) (expert driver) M2 Zppcon Condition number of matrix (Hermitian positive definite matrix) (packed form) M2 D2d2. Solution of systems of linear equations (positive definite banded Hermitian matrices) Zpbsv (WZpbsv(2)) Solution of system of linear equations Ax = b (Hermitian positive definite band matrix) M2 M2 Zpbtrf Cholesky factorization of coefficient matrix (Hermitian positive definite band matrix) M2 Zpbtrs Solution of Cholesky factorized system of linear equations (Hermitian positive definite band matrix) M2 Zpbsvx Solution of system of linear equations Ax = b (Hermitian positive definite band matrix) (expert driver) M2 Zpbcon Condition number of matrix (Hermitian positive definite band matrix) M2 Zptsv (WZptsv(2)) Solution of system of linear equations Ax = b (Hermitian positive definite tridiagonal matrix) M2 M2 Zpttrf LDL^H factorization of coefficient matrix (Hermitian positive definite tridiagonal matrix) M2 Zpttrs Solution of LDL^H factorized system of linear equations (Hermitian positive definite tridiagonal matrix) M2 Zptsvx Solution of system of linear equations Ax = b (Hermitian positive definite tridiagonal matrix) (expert driver) M2 Zptcon Condition number of matrix (Hermitian positive definite tridiagonal matrix) M2 D4. Eigenvalues and eigenvectors D4a1. Ordinary eigenvalue problems (symmetric matrices) Dsyev (WDsyev) Eigenvalues and eigenvectors (symmetric matrix) M1 M1 V V Dsyevx Eigenvalues and eigenvectors (symmetric matrix) (expert driver) M1 Dspev Eigenvalues and eigenvectors (symmetric matrix) (packed form) M1 Dspevx Eigenvalues and eigenvectors (symmetric matrix) (packed form) (expert driver) M1 Dsbev (WDsbev) Eigenvalues and eigenvectors (symmetric band matrix) M1 M1 Dsbevx Eigenvalues and eigenvectors (symmetric band matrix) (expert driver) M1 Dstev (WDstev) Eigenvalues and eigenvectors (symmetric tridiagonal matrix) M1 M1 Dstevx Eigenvalues and eigenvectors (symmetric tridiagonal matrix) (expert driver) M1 Ddisna Condition numbers for the eigenvectors M1 D4a2. Ordinary eigenvalue problems (general matrices) Dgeev (WDgeev) Eigenvalues and eigenvectors M1 M1 Dgeevx Eigenvalues and eigenvectors (expert driver) M1 Dgees Schur decomposition M1 Dgees_r Schur decomposition (reverse communication version) M1 Dgeesx Schur decomposition (expert driver) M1 Dgeesx_r Schur decomposition (expert driver) (reverse communication version) M1 D4a3. Ordinary eigenvalue problems (Hermitian matrices) Zheev (WZheev(2)) Eigenvalues and eigenvectors (Hermitian matrix) M2 M2 Zheevx Eigenvalues and eigenvectors (Hermitian matrix) (expert driver) M2 Zhpev Eigenvalues and eigenvectors (Hermitian matrix) (packed form) M2 Zhpevx Eigenvalues and eigenvectors (Hermitian matrix) (packed form) (expert driver) M2 Zhbev (WZhbev(2)) Eigenvalues and eigenvectors (Hermitian band matrix) M2 M2 Zhbevx Eigenvalues and eigenvectors (Hermitian band matrix) (expert driver) M2 D4a4. Ordinary eigenvalue problems (general complex matrices) Zgeev (WZgeev(2)) Eigenvalues and eigenvectors (complex matrix) M2 M2 Zgeevx Eigenvalues and eigenvectors (complex matrix) (expert driver) M2 Zgees Schur decomposition (complex matrix) M2 Zgees_r Schur decomposition (complex matrix) (reverse communication version) M2 Zgeesx Schur decomposition (complex matrix) (expert driver) M2 Zgeesx_r Schur decomposition (complex matrix) (expert driver) (reverse communication version) M2 D4b1. Generalized eigenvalue problems (symmetric matrices) Dsygv (WDsygv) Generalized eigenvalue problem (symmetric matrix) M1 M1 Dsygvx Generalized eigenvalue problem (symmetric matrix) (expert driver) M1 Dspgv Generalized eigenvalue problem (symmetric matrix) (packed form) M1 Dspgvx Generalized eigenvalue problem (symmetric matrix) (packed form) (expert driver) M1 Dsbgv (WDsbgv) Generalized eigenvalue problem (symmetric band matrix) M1 M1 Dsbgvx Generalized eigenvalue problem (expert driver) (symmetric band matrix) M1 D4b2. Generalized eigenvalue problems (general matrices) Dggev (WDggev) Generalized eigenvalue problem M1 M1 Dggevx Generalized eigenvalue problem (expert driver) M1 Dgges Generalized Schur decomposition M1 Dgges_r Generalized Schur decomposition (reverse communication version) M1 Dggesx Generalized Schur decomposition (expert driver) M1 Dggesx_r Generalized Schur decomposition (expert driver) (reverse communication version) M1 D4b3. Generalized eigenvalue problems (Hermitian matrices) Zhegv (WZhegv(2)) Generalized eigenvalue problem (Hermitian matrix) M2 M2 Zhegvx Generalized eigenvalue problem (Hermitian matrix) (expert driver) M2 Zhpgv Generalized eigenvalue problem (Hermitian matrix) (packed form) M2 Zhpgvx Generalized eigenvalue problem (Hermitian matrix) (expert driver) (packed form) M2 Zhbgv (WZhbgv(2)) Generalized eigenvalue problem (Hermitian band matrix) M2 M2 Zhbgvx Generalized eigenvalue problem (Hermitian band matrix) (expert driver) M2 D4b4. Generalized eigenvalue problems (general complex matrices) Zggev (WZggev(2)) Generalized eigenvalue problem (complex matrix) M2 M2 Zggevx Generalized eigenvalue problem (complex matrix) (expert driver) M2 Zgges Generalized Schur decomposition (complex matrix) M2 Zgges_r Generalized Schur decomposition (complex matrix) (reverse communication version) M2 Zggesx Generalized Schur decomposition (complex matrix) (expert driver) M2 Zggesx_r Generalized Schur decomposition (complex matrix) (expert driver) (reverse communication version) M2 D5. QR factorization D5. QR factorization Dgeqp3 QR factorization with pivoting M1 Dgeqrf QR factorization M1 Dorgqr Generates matrix Q of QR factorization M1 Dormqr Multiplies matrix Q of QR factorization M1 Dgelqf LQ factorization M1 Dorglq Generates matrix Q of LQ factorization M1 Dormlq Multiplies matrix Q of LQ factorization M1 Zgeqp3 QR factorization with pivoting (complex matrix) M2 Zgeqrf QR factorization (complex matrix) M2 Zungqr Generates matrix Q of QR factorization (complex matrix) M2 Zunmqr Multiplies matrix Q of QR factorization (complex matrix) M2 Zgelqf LQ factorization (complex matrix) M2 Zunglq Generates matrix Q of LQ factorization (complex matrix) M2 Zunmlq Multiplies matrix Q of LQ factorization (complex matrix) M2 D6. Singular value decomposition D6. Singular value decomposition (SVD) Dgesvd (WDgesvd) Singular value decomposition (SVD) M1 M1 Dgesvdx Singular value decomposition (SVD) (expert driver) M1 Dgesvj Singular value decomposition (SVD) (Jacobi SVD algorithm) M1 Dgejsv Singular value decomposition (SVD) (preconditioned Jacobi SVD algorithm) M1 Dggsvd3 (WDggsvd3) Generalized singular value decomposition (GSVD) M1 M1 Zgesvd (WZgedvs(2)) Singular value decomposition (SVD) (complex matrix) M2 M2 Zgesvdx Singular value decomposition (SVD) (complex matrix) (expert driver) M2 Zgesvj Singular value decomposition (SVD) (Jacobi SVD algorithm) (complex matrix) M2 Zgejsv Singular value decomposition (SVD) (preconditioned Jacobi SVD algorithm) (complex matrix) M2 Zggsvd3(WZggsvd3(2)) Generalized singular value decomposition (GSVD) (complex matrix) M2 M2 D9. Overdetermined or underdetermined systems of linear equations D9a. Overdetermined or underdetermined systems of linear equations (unconstrained) Dgels (WDgels) Full rank overdetermined or underdetermined linear systems M1 M1 V V Dgelsy (WDgelsy) Overdetermined or underdetermined linear systems (orthogonal factorization) M1 M1 Dgelss (WDgelss) Overdetermined or underdetermined linear systems (SVD) M1 M1 Zgels (WZgels(2)) Full rank overdetermined or underdetermined linear systems (complex matrix) M2 M2 Zgelsy (WZgelsy(2)) Overdetermined or underdetermined linear systems (orthogonal factorization) (complex matrix) M2 M2 Zgelss (WZgelss(2)) Overdetermined or underdetermined linear systems (SVD) (complex matrix) M2 M2 Dgecov Variance-covariance matrix of LLS factorized by Dgels M1 V Dgecovy Variance-covariance matrix of LLS factorized by Dgelsy M1 Dgecovs Variance-covariance matrix of LLS factorized by Dgelss M1 Zgecov Variance-covariance matrix of LLS factorized by Zgels (complex matrix) M2 Zgecovy Variance-covariance matrix of LLS factorized by Zgelsy (complex matrix) M2 Zgecovs Variance-covariance matrix of LLS factorized by Zgelss (complex matrix) M2 D9b. Overdetermined or underdetermined systems of linear equations (constrained) Dgglse (WDgglse) Linear equality-constrained least squares (LSE) problem M1 M1 Dggglm (WDggglm) General Gauss-Markov linear model (GLM) problem M1 M1 Zgglse (WZgglse(2)) Linear equality-constrained least squares (LSE) problem (complex matrix) M2 M2 Zggglm (WZggglm(2)) General Gauss-Markov linear model (GLM) problem (complex matrix) M2 M2 E. Interpolation E. Interpolation (polynomial interpolation) Polint Polynomial interpolation M4 Polyvl Value of polynomial and derivatives M4 Polcof Coefficients of polynomial interpolation M4 Fitlag Iterative Lagrange interpolation M4 E. Interpolation (piecewise cubic Hermite interpolation / cubic spline interpolation) Pchim Piecewise cubic Hermite interpolation (default boundary conditions) M4 Pchic Piecewise cubic Hermite interpolation M4 Pchse (WPchse) Piecewise cubic spline interpolation ("not a not" condition) M4 M4 V V Pchsp Piecewise cubic spline interpolation M4 Pchfe (WPchfe) Evaluation of function values for piecewise cubic Hermite (or cubic spline) interpolation M4 M4 V V Pchfd Evaluation of function and derivative values for piecewise cubic Hermite (or cubic spline) interpolation M4 Chfev Cubic Hermite function values M4 Chfdv Cubic Hermite function and derivative values M4 Pchbs Piecewise cubic Hermite to B-spline conversion M4 Pchcm Monotonicity check for piecewise cubic Hermite function M4 E. Interpolation (B-spline interpolation) Bint4 B-representation of cubic spline interpolation M4 Bintk B-representation of k-th order spline interpolation M4 Bvalue Evaluation of function or derivative value for B-representation of B-spline M4 Ppvalu Evaluation of function or derivative value for PP (piecewise polynomial) form of B-spline M4 Bsplpp B-representation to PP (piecewise polynomial) form of B-spline conversion M4 Bsplvn Compute the value of B-spline basis functions M4 Bsplvd Compute the value and the derivatives of B-spline basis functions M4 Bspldr Construct a divided difference table from B-representation for derivative calculation by Bsplev M4 Bsplev Evaluation of function and derivative values for B-representation of B-spline M4 Interv Compute Ileft for the input to Bsplvn and Bsplvd M4 Banfac LU factorization of banded coefficient matrix of system of linear equations (support routine for Bint4 and Bintk) M4 Banslv Solution of LU factorized system of linear equations  (support routine for Bint4 and Bintk) M4 E3a3. Quadrature involving fitted functions Pchia (WPchia) Integral of piecewise cubic Hermite / cubic spline function M4 M4 V V Pchid Integral of piecewise cubic Hermite / cubic spline function (over an interval whoes endpoints are data points) M4 Bsqad Integral of B-representation of B-spline M4 Bfqad Integral of product of arbitrary function and B-representation of B-spline M4 Bfqad_r Integral of product of arbitrary function and B-representation of B-spline (reverse communication version) M4 Ppqad Integral of PP (piecewise polynomial) form of B-spline M4 Pfqad Integral of product of arbitrary function and PP (piecewise polynomial) form of B-spline M4 Pfqad_r Integral of product of arbitrary function and PP (piecewise polynomial) form of B-spline (reverse communication version) M4 F. Solution of nonl F1a. Roots of polynomials F1a. Roots of polynomials Cpzero (WCpzero(2)) Roots of a polynomial (complex coefficients) (Netwon method) M3 M3 Rpzero Roots of a polynomial (real coefficients) (Netwon method) M3 Rpzero2 (WRpzero2) Roots of a polynomial (real coefficients) (Netwon method) (Complex type is not used) M3 M3 V V Cpqr79 (WCpqr79(2)) Roots of a polynomial (complex coefficients) (by computing the eigenvalues of the companion matrix) M3 M3 Rpqr79 Roots of a polynomial (real coefficients) (by computing the eigenvalues of the companion matrix) M3 Dka (WDka(2)) Roots of a polynomial (complex coefficients) (Durand-Kerner-Aberth (DKA) method) M3 M3 F1b. Solution of single general nonlinear equation F1b. Solution of single general nonlinear equation Dfzero Zero of the general nonlinear function M3 M3 V V Dfzero_r Zero of the general nonlinear function (reverse communication version) M3 V F2. Solution of a system of nonlinear equations F2. Solution of a system of nonlinear equations Hybrj Solution of a system of nonlinear equations by Powell hybrid method M3 Hybrj_r Solution of a system of nonlinear equations by Powell hybrid method (reverse communication version) M3 Hybrj1 Solution of a system of nonlinear equations by Powell hybrid method (simple driver) M3 M3 Hybrj1_r Solution of a system of nonlinear equations by Powell hybrid method (simple driver) (reverse communication version) M3 Hybrd Solution of a system of nonlinear equations by Powell hybrid method (Jacobian not required) M3 Hybrd_r Solution of a system of nonlinear equations by Powell hybrid method (Jacobian not required) (reverse communication version) M3 Hybrd1 Solution of a system of nonlinear equations by Powell hybrid method (Jacobian not required) (simple driver) M3 M3 V V Hybrd1_r Solution of a system of nonlinear equations by Powell hybrid method (Jacobian not required) (simple driver) (reverse communication version) M3 V Chkder Checks the gradient calculation (for Hybrj and Hybrj1) M3 Sos Solution of a system of nonlinear equations (Brown's method) M3 M3 Sos_r Solution of a system of nonlinear equations (Brown's method) (reverse communication version) M3 G. Optimization G1a. Unconstrained optimization of a general univariate function G1a. Unconstrained optimization of a general univariate function Dfmin Minimum of a single variable general nonlinear function M3 M3 V V Dfmin_r Minimum of a single variable general nonlinear function (reverse communication version) M3 V G1b. Unconstrained optimization of a general multivariate function G1b. Unconstrained optimization of a general multivariate function Optif9 Minimum of a multivariable nonlinear function (quasi-Newton method or trust region method) M3 Optif9_r Minimum of a multivariable nonlinear function (quasi-Newton method or trust region method) (reverse communication version) M3 Optif0 Minimum of a multivariable nonlinear function (quasi-Newton method) (simple driver) M3 M3 V V Optif0_r Minimum of a multivariable nonlinear function (quasi-Newton method) (simple driver) (reverse communication version) M3 V Mng Minimum of a multivariable nonlinear function (trust region method) M3 M3 Mng_r Minimum of a multivariable nonlinear function (trust region method) (reverse communication version) M3 Mnf Minimum of a multivariable nonlinear function (trust region method) (gradient computed by finite differences) M3 M3 Mnf_r Minimum of a multivariable nonlinear function (trust region method) (gradient computed by finite differences) (reverse communication version) M3 Mnh Minimum of a multivariable nonlinear function (trust region method) (gradient and Hessian computed analytically) M3 Mnh_r Minimum of a multivariable nonlinear function (trust region method) (gradient and Hessian computed analytically) (reverse communication version) M3 Subplex Minimum of a multivariable nonlinear function (subspace-searching simplex method) M3 M3 Subplex_r Minimum of a multivariable nonlinear function (subspace-searching simplex method) (reverse communication version) M3 G2. Constrained optimization of a general multivariate function G2. Constrained optimization of a general multivariate function Mngb Minimization of multivariate function (trust region method) (simply bounded) M3 Mngb_r Minimization of multivariate function (trust region method) (simply bounded) (reverse communication version) M3 Mnfb Minimization of multivariate function (trust region method) (simply bounded) (gradient computed by finite differences) M3 Mnfb_r Minimization of multivariate function (trust region method) (simply bounded) (gradient computed by finite differences) (reverse communication version) M3 Mnhb Minimization of multivariate function (trust region method) (simply bounded) (gradient and Hessian computed analytically) M3 Mnhb_r Minimization of multivariate function (trust region method) (simply bounded) (gradient and Hessian computed analytically) (reverse communication version) M3 H. Differentiation, H2. Quadrature H2a1a. 1-D finite interval quadrature (user-defined integrand function) H2a1a. 1-D finite interval quadrature (fixed number of points) Qk15 Finite interval quadrature (15-point Gauss-Kronrod rule) M4 V Qk15_r Finite interval quadrature (15-point Gauss-Kronrod rule) (reverse communication version) M4 V Qk21 Finite interval quadrature (21-point Gauss-Kronrod rule) M4 Qk21_r Finite interval quadrature (21-point Gauss-Kronrod rule) (reverse communication version) M4 Qk31 Finite interval quadrature (31-point Gauss-Kronrod rule) M4 Qk31_r Finite interval quadrature (31-point Gauss-Kronrod rule) (reverse communication version) M4 Qk41 Finite interval quadrature (41-point Gauss-Kronrod rule) M4 Qk41_r Finite interval quadrature (41-point Gauss-Kronrod rule) (reverse communication version) M4 Qk51 Finite interval quadrature (51-point Gauss-Kronrod rule) M4 Qk51_r Finite interval quadrature (51-point Gauss-Kronrod rule) (reverse communication version) M4 Qk61 Finite interval quadrature (61-point Gauss-Kronrod rule) M4 Qk61_r Finite interval quadrature (61-point Gauss-Kronrod rule) (reverse communication version) M4 H2a1a. 1-D finite interval quadrature (automatic quadrature) Qng Finite interval automatic quadrature (21/43/87-point Gauss-Kronrod rule) M4 Qng_r Finite interval automatic quadrature (21/43/87-point Gauss-Kronrod rule) (reverse communication version) M4 Qag Finite interval adaptive quadrature (15/21/31/41/51/61-point Gauss-Kronrod rule) M4 M4 V V Qag_r Finite interval adaptive quadrature (15/21/31/41/51/61-point Gauss-Kronrod rule) (reverse communication version) M4 V Qags Finite interval adaptive quadrature with sigularities (21-point Gauss-Kronrod rule) M4 M4 Qags_r Finite interval adaptive quadrature with sigularities (21-point Gauss-Kronrod rule) (reverse communication version) M4 Defin Finite interval automatic quadrature (double exponential (DE) formula) M4 M4 Defin_r Finite interval automatic quadrature (double exponential (DE) formula) (reverse communication version) M4 H2a1b. 1-D finite interval quadrature (tabulated integrand) H2a1b. 1-D finite interval quadrature (tabulated integrand) Avint (WAvint) Finite interval quadrature for a function with tabulated data (approximation with overlapping parabolas) M4 M4 H2a2a. 1-D finite interval quadrature (special integrand) (user-defined integrand function) H2a2a. 1-D finite interval quadrature (special integrand) Qagp Finite interval adaptive quadrature with known singular points (21-point Gauss-Kronrod rule) M4 Qagp_r Finite interval adaptive quadrature with known singular points (21-point Gauss-Kronrod rule) (reverse communication version) M4 Qawc Finite interval adaptive quadrature for Cauchy principal values (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) M4 M4 Qawc_r Finite interval adaptive quadrature for Cauchy principal values (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) (reverse communication version) M4 Qaws Finite interval adaptive quadrature for singular functions (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) M4 M4 Qaws_r Finite interval adaptive quadrature for singular functions (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) (reverse communication version) M4 Qawo Finite interval adaptive quadrature for oscillatory functions (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) M4 M4 Qawo_r Finite interval adaptive quadrature for oscillatory functions (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) (reverse communication version) M4 H2a3a. 1-D semi-infinite interval quadrature (user-defined integrand function) H2a3a. 1-D semi-infinite interval quadrature Qk15i Semi-infinite/infinite interval quadrature (15-point Gauss-Kronrod rule) M4 Qk15i_r Semi-infinite/infinite interval quadrature (15-point Gauss-Kronrod rule) (reverse communication version) M4 Qagi Semi-infinite/infinite interval adaptive quadrature (15-point Gauss-Kronrod rule) M4 M4 V V Qagi_r Semi-infinite/infinite interval adaptive quadrature (15-point Gauss-Kronrod rule) (reverse communication version) M4 V Qawf Semi-infinite interval adaptive quadrature for Fourier integrals (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) M4 M4 Qawf_r Semi-infinite interval adaptive quadrature for Fourier integrals (25-point Clenshaw-Curtis and 15-point Gauss-Kronrod rule) (reverse communication version) M4 Dehint Semi-infinite interval automatic quadrature (double exponential (DE) formula) M4 M4 Dehint_r Semi-infinite interval automatic quadrature (double exponential (DE) formula) (reverse communication version) M4 Deoint Semi-infinite interval automatic quadrature for Fourier integrals (double exponential (DE) formula) M4 M4 Deoint_r Semi-infinite interval automatic quadrature for Fourier integrals (double exponential (DE) formula) (reverse communication version) M4 H2a4. 1-D infinite interval quadrature (user-defined integrand function) H2a4. 1-D infinite interval quadrature Deiint Infinite interval automatic quadrature (double exponential (DE) formula) M4 M4 Deiint_r Infinite interval automatic quadrature (double exponential (DE) formula) (reverse communication version) M4 I. Differential and i I1. Ordinary differential equations I1a1. Initial value problem of ordinary differential equations (for non-stiff problem) Derkf Initial value problem of ordinary differential equations (5(4)-th order Runge-Kutta-Fehlberg method) M4 M4 V V Derkf_r Initial value problem of ordinary differential equations (5(4)-th order Runge-Kutta-Fehlberg method) (reverse communication version) M4 V DerkfInt Initial value problem of ordinary differential equations (5(4)-th order Runge-Kutta-Fehlberg method) (interpolation for dense output) M4 V Dopri5 Initial value problem of ordinary differential equations (5(4)-th order Dorman-Prince method) M4 M4 Contd5 Initial value problem of ordinary differential equations (5(4)-th order Dorman-Prince method) (interpolation for dense output) Dopri5_r Initial value problem of ordinary differential equations (5(4)-th order Dorman-Prince method) (reverse communication version) M4 Contd5_r Initial value problem of ordinary differential equations (5(4)-th order Dorman-Prince method) (reverse communication version) (interpolation for dense output) Dverk Initial value problem of ordinary differential equations (6(5)-th order Runge-Kutta-Verner method) M4 Dverk_r Initial value problem of ordinary differential equations (6(5)-th order Runge-Kutta-Verner method) (reverse communication version) M4 DverkInt Initial value problem of ordinary differential equations (6(5)-th order Runge-Kutta-Verner method) (interpolation for dense output) M4 Dop853 Initial value problem of ordinary differential equations (8(5,3)-th order Dorman-Prince method) M4 M4 Contd8 Initial value problem of ordinary differential equations (8(5,3)-th order Dorman-Prince method) (interpolation for dense output) M4 Dop853_r Initial value problem of ordinary differential equations (8(5,3)-th order Dorman-Prince method) (reverse communication version) M4 Contd8_r Initial value problem of ordinary differential equations (8(5,3)-th order Dorman-Prince method) (reverse communication version) (interpolation for dense output) M4 Deabm Initial value problem of ordinary differential equations (1~12-th order Adams-Bashforth-Moulton predictor-corrector method) M4 M4 Deabm_r Initial value problem of ordinary differential equations (1~12-th order Adams-Bashforth-Moulton predictor-corrector method) (reverse communication version) M4 Odex Initial value problem of ordinary differential equations (extrapolation method (GBS algorithm)) M4 Contx1 Initial value problem of ordinary differential equations (extrapolation method (GBS algorithm)) (interpolation for dense output) M4 Odex_r Initial value problem of ordinary differential equations (extrapolation method (GBS algorithm)) (reverse communication version) M4 Contx1_r Initial value problem of ordinary differential equations (extrapolation method (GBS algorithm)) (reverse communication version) (interpolation for dense output) M4 Doprin Initial value problem of ordinary differential equations (extrapolation method) (for second order differential equations) M4 Doprin_r Initial value problem of ordinary differential equations (extrapolation method) (for second order differential equations) (reverse communication version) M4 Odex2 Initial value problem of ordinary differential equations (extrapolation method) (for second order differential equations) M4 Contx2 Initial value problem of ordinary differential equations (extrapolation method) (for second order differential equations) (interpolation for dense output) M4 Odex2_r Initial value problem of ordinary differential equations (extrapolation method) (for second order differential equations) (reverse communication version) M4 Contx2_r Initial value problem of ordinary differential equations (extrapolation method) (for second order differential equations) (reverse communication version) (interpolation for dense output) M4 Retard Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method) M4 Ylag Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method) (interpolation for back-values of solution) M4 Retard_r Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method) (reverse communication version) M4 Ylag_r Initial value problem of delay differential equations (5(4)-th order Dorman-Prince method) (reverse communication version) (interpolation for back-values of solution) M4 I1a2. Initial value problem of ordinary differential equations (for stiff problem) Debdf Initial value problem of ordinary differential equations (1~5-th order backward differentiation formula (BDF)) M4 M4 Debdf_r Initial value problem of ordinary differential equations (1~5-th order backward differentiation formula (BDF)) (reverse communication version) M4 Radau5 Initial value problem of ordinary differential equations (5-th order implicit Runge-Kutta method (Radau IIA)) M4 Contr5 Initial value problem of ordinary differential equations (5-th order implicit Runge-Kutta method (Radau IIA)) (interpolation for dense output) M4 Radau5_r Initial value problem of ordinary differential equations (5-th order implicit Runge-Kutta method (Radau IIA)) (reverse communication version) M4 Contr5_r Initial value problem of ordinary differential equations (5-th order implicit Runge-Kutta method (Radau IIA)) (reverse communication version) (interpolation for dense output) M4 Radaup Initial value problem of ordinary differential equations (5, 9, 13-th order implicit Runge-Kutta method (Radau IIA)) M4 Contrp Initial value problem of ordinary differential equations (5, 9, 13-th order implicit Runge-Kutta method (Radau IIA)) (interpolation for dense output) M4 Radaup_r Initial value problem of ordinary differential equations (5, 9, 13-th order implicit Runge-Kutta method (Radau IIA)) (reverse communication version) M4 Contrp_r Initial value problem of ordinary differential equations (5, 9, 13-th order implicit Runge-Kutta method (Radau IIA)) (reverse communication version) (interpolation for dense output) M4 Radau Initial value problem of ordinary differential equations (variable (5, 9, 13-th) order implicit Runge-Kutta method (Radau IIA)) M4 M4 Contra Initial value problem of ordinary differential equations (variable (5, 9, 13-th) order implicit Runge-Kutta method (Radau IIA)) (interpolation for dense output) M4 Radau_r Initial value problem of ordinary differential equations (variable (5, 9, 13-th) order implicit Runge-Kutta method (Radau IIA)) (reverse communication version) M4 Contra_r Initial value problem of ordinary differential equations (variable (5, 9, 13-th) order implicit Runge-Kutta method (Radau IIA)) (reverse communication version) (interpolation for dense output) M4 Rodas Initial value problem of ordinary differential equations (4(3)-th order Rosenbrock method) M4 Contro Initial value problem of ordinary differential equations (4(3)-th order Rosenbrock method) (interpolation for dense output) M4 Rodas_r Initial value problem of ordinary differential equations (4(3)-th order Rosenbrock method) (reverse communication version) M4 Contro_r Initial value problem of ordinary differential equations (4(3)-th order Rosenbrock method) (reverse communication version) (interpolation for dense output) M4 Seulex Initial value problem of ordinary differential equations (extrapolation method based on the linearly implicit Euler method) M4 Contex Initial value problem of ordinary differential equations (extrapolation method based on the linearly implicit Euler method) (interpolation for dense output) M4 Seulex_r Initial value problem of ordinary differential equations (extrapolation method based on the linearly implicit Euler method) (reverse communication version) M4 Contex_r Initial value problem of ordinary differential equations (extrapolation method based on the linearly implicit Euler method) (reverse communication version) (interpolation for dense output) M4 Dassl Solution of differential algebraic equation (DAE) (1~5-th order backward differentiation formula (BDF)) M4 Dassl_r Solution of differential algebraic equation (DAE) (1~5-th order backward differentiation formula (BDF)) (reverse communication version) M4 J. Integral transfor J1. Fast Fourier transform (FFT) J1a1. One-dimensional real fast Fourier transforms Rfft1f (WRfft1f) One-dimensional real Fourier transform M3 M3 V V Rfft1b (WRfft1b) One-dimensional real Fourier backward transform M3 M3 V V Rfft1i Initialization of work data for Rfft1f and Rfft1b M3 V Rfftmf One-dimensional real Fourier transform (multiple sequences) M3 Rfftmb One-dimensional real Fourier backward transform (multiple sequences) M3 Rfftmi Initialization of work data for Rfftmf and Rfftmb M3 J1a2. One-dimensional complex fast Fourier transforms Cfft1f (WCfft1f(2)) One-dimensional complex Fourier transform M3 M3 Cfft1b (WCfft1b(2)) One-dimensional complex Fourier backward transform M3 M3 Cfft1i Initialization of work data for Cfft1f and Cfft1b M3 Cfftmf One-dimensional complex Fourier transform (multiple sequences) M3 Cfftmb One-dimensional complex Fourier backward transform (multiple sequences) M3 Cfftmi Initialization of work data for Cfftmf and Cfftmb M3 J1a3. One-dimensional trigonometric fast Fourier transforms Sint1f (WSint1f) One-dimensional real sine transform M3 M3 Sint1b (WSint1b) One-dimensional real sine backward transform M3 M3 Sint1i Initialization of work data for Sint1f and Sint1b M3 Sintmf One-dimensional real sine transform (multiple sequences) M3 Sintmb One-dimensional real sine backward transform (multiple sequences) M3 Sintmi Initialization of work data for Sintmf and Sintmb M3 Cost1f (WCost1f) One-dimensional real cosine transform M3 M3 Cost1b (WCost1b) One-dimensional real cosine backward transform M3 M3 Cost1i Initialization of work data for Cost1f and Cost1b M3 Costmf One-dimensional real cosine transform (multiple sequences) M3 Costmb One-dimensional real cosine backward transform (multiple sequences) M3 Costmi Initialization of work data for Costmf and Costmb M3 J1a3. One-dimensional quarter trigonometric fast Fourier transforms Sinq1f One-dimensional real quarter sine transform M3 Sinq1b One-dimensional real quarter sine backward transform M3 Sinq1i Initialization of work data for Sinq1f and Sinq1b M3 Sinqmf One-dimensional real quarter sine transform (multiple sequences) M3 Sinqmb One-dimensional real quarter sine backward transform (multiple sequences) M3 Sinqmi Initialization of work data for Sinqmf and Sinqmb M3 Cosq1f One-dimensional real quarter cosine transform M3 Cosq1b One-dimensional real quarter cosine backward transform M3 Cosq1i Initialization of work data for Cosq1f and Cosq1b M3 Cosqmf One-dimensional real quarter cosine transform (multiple sequences) M3 Cosqmb One-dimensional real quarter cosine backward transform (multiple sequences) M3 Cosqmi Initialization of work data for Cosqmf and Cosqmb M3 J1b. Multidimensional fast Fourier transforms Rfft2f Two-dimensional real Fourier transform M3 Rfft2b Two-dimensional real Fourier backward transform M3 Rfft2i Initialization of work data for Rfft2f and Rfft2b M3 Rfft2c Full complex data of two-dimensional Fourier transform obtained by Rfft2f M3 Cfft2f Two-dimensional complex Fourier transform M3 Cfft2b Two-dimensional complex Fourier backward transform M3 Cfft2i Initialization of work data for Cfft2f and Cfft2b M3 K. Approximation K1. Least squares approximation K1b1. Nonlinear least squares approximation Lmder Nonlinear least squares approximation (Levenberg-Marquardt method) M3 Lmder_r Nonlinear least squares approximation (Levenberg-Marquardt method) (reverse communication version) M3 Lmder1 Nonlinear least squares approximation (Levenberg-Marquardt method) (simple driver) M3 M3 Lmder1_r Nonlinear least squares approximation (Levenberg-Marquardt method) (simple driver) (reverse communication version) M3 Lmstr Nonlinear least squares approximation (Levenberg-Marquardt method) (limited storage version) M3 Lmstr_r Nonlinear least squares approximation (Levenberg-Marquardt method) (limited storage version) (reverse communication version) M3 Lmstr1 Nonlinear least squares approximation (Levenberg-Marquardt method) (limited storage version) (simple driver) M3 Lmstr1_r Nonlinear least squares approximation (Levenberg-Marquardt method) (limited storage version) (simple driver) (reverse communication version) M3 Lmdif Nonlinear least squares approximation (Levenberg-Marquardt method) (Jacobian not required) M3 Lmdif_r Nonlinear least squares approximation (Levenberg-Marquardt method) (Jacobian not required) (reverse communication version) M3 Lmdif1 Nonlinear least squares approximation (Levenberg-Marquardt method) (Jacobian not required) (simple driver) M3 M3 V V Lmdif1_r Nonlinear least squares approximation (Levenberg-Marquardt method) (Jacobian not required) (simple driver) (reverse communication version) M3 V Chkder Checks the gradient calculation (for Lmder, Lmder1, Lmstr and Lmstr1) (same as F2.) M3 Covar Variance covariance matrix calculation for Lmder, Lmder1, Lmstr, Lmstr1 and Lmdif) M3 N2g Nonlinear least squares approximation (Levenberg-Marquardt method) M3 M3 N2g_r Nonlinear least squares approximation (Levenberg-Marquardt method) (reverse communication version) M3 N2g1 Nonlinear least squares approximation (Levenberg-Marquardt method) (simple driver) M3 N2g1_r Nonlinear least squares approximation (Levenberg-Marquardt method) (simple driver) (reverse communication version) M3 N2f Nonlinear least squares approximation (adaptive algorithm) (Jacobian not required) M3 M3 N2f_r Nonlinear least squares approximation (adaptive algorithm) (Jacobian not required) (reverse communication version) M3 N2f1 Nonlinear least squares approximation (adaptive algorithm) (Jacobian not required) (simple driver) M3 N2f1_r Nonlinear least squares approximation (adaptive algorithm) (Jacobian not required) (simple driver) (reverse communication version) M3 N2p Nonlinear least squares approximation (adaptive algorithm) (limited storage version) M3 N2p_r Nonlinear least squares approximation (adaptive algorithm) (limited storage version) (reverse communication version) M3 K1b2. Constrained nonlinear least squares approximation N2gb Nonlinear least squares approximation (adaptive algorithm) (simply bounded) M3 N2gb_r Nonlinear least squares approximation (adaptive algorithm) (simply bounded) (reverse communication version) M3 N2fb Nonlinear least squares approximation (adaptive algorithm) (simply bounded) (Jacobian not required) M3 N2fb_r Nonlinear least squares approximation (adaptive algorithm) (simply bounded) (Jacobian not required) (reverse communication version) M3 N2pb Nonlinear least squares approximation (adaptive algorithm) (simply bounded) (limited storage version) M3 N2pb_r Nonlinear least squares approximation (adaptive algorithm) (simply bounded) (limited storage version) (reverse communication version) M3 L. Statistics, proba L6. Random numb L6a21. Uniform random numbers L6a21. Uniform random numbers (Mersenne-Twister) InitGenrand Initialization with seed for random number generator (Mersenne Twister) M4 V InitByArray Initialization with array of integers for random number generator (Mersenne Twister) M4 GenrandInt32 Unsigned 32 bit integer random number (Mersenne Twister) M4 V GenrandInt31 Unsigned 31 bit integer random number (Mersenne Twister) M4 V GenrandReal1 32 bit real random number in [0,1] (Mersenne Twister) M4 GenrandReal2 32 bit real random number in [0,1) (Mersenne Twister) M4 GenrandReal3 32 bit real random number in (0,1) (Mersenne Twister) M4 GenrandReal53 53 bit real random number in [0,1) (Mersenne Twister) M4 V InitGenrand64 Initialization of random number generator (64 bit Mersenne Twister) M4# InitByArray64 Initialization with array of integers for random number generator (64 bit Mersenne Twister) M4# Genrand64Int64 Unsigned 64 bit integer random number (64 bit Mersenne Twister) M4# Genrand64Int63 Unsigned 63 bit integer random number (64 bit Mersenne Twister) M4# Genrand64Real1 Double precision real random number in [0, 1] (64 bit Mersenne Twister) M4# Genrand64Real2 Double precision real random number in [0, 1) (64 bit Mersenne Twister) M4# Genrand64Real3 Double precision real random number in (0, 1) (64 bit Mersenne Twister) M4# L6a21. Uniform random numbers (Lagged Fibonacci method) RanStart Initialization for integer random number generator (Lagged Fibonacci method) M4 RanArray Unsigned 30 bit integer random numbers (Lagged Fibonacci method) M4 RanArrNext Unsigned 30 bit integer random number (Lagged Fibonacci method) M4 RanfStart Initialization for real random number generator (Lagged Fibonacci method) M4 RanfArray 53 bit real random numbers in [0,1) (Lagged Fibonacci method) M4 RanfArrNext 53 bit real random number in [0,1) (Lagged Fibonacci method) M4 L6a21. Uniform random numbers (Linear congruential method) Srand48 Initialization with 32-bit seed for Drand48, Lrand48 and Mrand48 (Linear congruential method) M4 Seed48 Initialization with 48-bit seed for Drand48, Lrand48 and Mrand48 (Linear congruential method) M4 Lcong48 Set up parameters for random number generators (Linear congruential method) M4 Drand48 48 bit real random number in [0,1) (Linear congruential method) M4 Erand48 48 bit real random number in [0,1) (Linear congruential method) M4 Lrand48 Unsigned 31 bit integer random number (Linear congruential method) M4 Nrand48 Unsigned 31 bit integer random number (Linear congruential method) M4 Mrand48 Signed 32 bit integer random number (Linear congruential method) M4 Jrand48 Signed 32 bit integer random number (Linear congruential method) M4 L6a14. Normal random numbers L6a14. Normal random numbers GenrandNorm 53 bit real normal random number (Ahrens-Dieter method) (Mersenne Twister) RanfArrNextNorm 53 bit real normal random number (Ahrens-Dieter method) (Lagged Fibonacci method) Drand48Norm 48 bit real normal random number (Ahrens-Dieter method) (Linear congruential method) GenrandNorm 53 bit real normal random number (Ziggurat method) (Mersenne Twister) M4 RanfArrNextNorm 53 bit real normal random number (Ziggurat method) (Lagged Fibonacci method) M4 Drand48Norm 48 bit real normal random number (Ziggurat method) (Linear congruential method) M4 L6a5. Exponential random numbers L6a5. Exponential random numbers GenrandExp 53 bit real exponential random number (Ahrens-Dieter method) (Mersenne Twister) RanfArrNextExp 53 bit real exponential random number (Ahrens-Dieter method) (Lagged Fibonacci method) Drand48Exp 48 bit real exponential random number (Ahrens-Dieter method) (Linear congruential method) GenrandExp 53 bit real exponential random number (Ziggurat method) (Mersenne Twister) M4 RanfArrNextExp 53 bit real exponential random number (Ziggurat method) (Lagged Fibonacci method) M4 Drand48Exp 48 bit real exponential random number (Ziggurat method) (Linear congruential method) M4 L6a7. Gamma random numbers L6a7. Gamma random numbers. GenrandGam 53 bit real gamma random number (Squeeze method of Marsaglia and Tsang) (Mersenne Twister) M4 RanfArrNextGam 53 bit real gamma random number (Squeeze method of Marsaglia and Tsang) (Lagged Fibonacci method) M4 Drand48Gam 48 bit real gamma random number (Squeeze method of Marsaglia and Tsang) (Linear congruential method) M4 R. Service routine R1. Machine-dependent constants R1. Machine-dependent constants Dlamch Machine parameters (double precision floating-point arithmetic) ALL V D1mach Machine parameters (double precision floating-point arithmetic) ALL Slamch Machine parameters (single precision floating-point arithmetic) ALL R1mach Machine parameters (single precision floating-point arithmetic) ALL I1mach Machine parameters (integer machine dependent constants) ALL Z. Others Z1. Test matrix generation Z1. Test matrix generation Dlatms Generates random matrices with specified singular values or symmetric random matrices with specified eigenvalues M1 Dlatmt Generates random matrices with specified singular values or symmetric random matrices with specified eigenvalues (with specified rank of matrix) M1 Dlatme Generates random non-symmetric square matrices with specified eigenvalues M1 Dlatmr Generates random matrices with specified diagonal elements M1 Zlatms Generates random matrices with specified singular values or symmetric random matrices with specified eigenvalues (complex matrix) M2 Zlatmt Generates random matrices with specified singular values or symmetric random matrices with specified eigenvalues (with specified rank of matrix) (complex matrix) M2 Zlatme Generates random non-symmetric square matrices with specified eigenvalues (complex matrix) M2 Zlatmr Generates random matrices with specified diagonal elements (complex matrix) M2 Note 1 - Divided into the following four modules: M1: Linear computation(real), M2: Linear computation(complex), M3: Special functions, nonlinear computation, M4: Interpolation, differential/integral equations, random numbers, ALL: Available in all modules. Note 2 - Changes: %(Blue)Tentative compatibility routines (to be removed), (Green)New routines, (Orange)Program internally changed or feature added. Note 3 - #: Does not work on 32 bit Excel.