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 nonlinear equations
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, integration
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 integral equations
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 transforms
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, probability
L6. Random number generation
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 routines
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.