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. |