Excel Lambda functions for numerical analyses

EXNAL

/* ROOTS OF FUNCTIONS */
BISEC = LAMBDA(f, lbound, ubound, [prec],
    LET(
        c, (lbound + ubound) / 2,
        fl, f(lbound), fu, f(ubound), fc, f(c),
        IF(
            ABS(fc) < MAX(prec, 1E-15),
            c,
            IF(
                SIGN(fl) = SIGN(fc),
                BISEC(f, c, ubound, prec),
                BISEC(f, lbound, c, prec)
            )
        )
    )
);

FALSEPOS = LAMBDA(f, lbound, ubound, [prec],
    LET(
        fl, f(lbound), fu, f(ubound),
        c, ubound - fu * (lbound - ubound) / (fl - fu),
        fc, f(c),
        IF(
            ABS(fc) <= MAX(prec, 0.000001),
            c,
            IF(
                SIGN(fl) = SIGN(fc),
                FALSEPOS(f, c, ubound, prec),
                FALSEPOS(f, lbound, c, prec)
            )
        )
    )
);

NR = LAMBDA(f, x0, [prec],
    LET(
        fx, f(x0),
        IF(
            ABS(fx) <= MAX(prec, 0.000001),
            x0,
            LET(
                xr, x0 - fx / DF(f)(x0),
                NR(f, xr, prec)
            )
        )
    )
);

/* LINEAR ALGEBRAIC EQUATIONS */
LINSOLVE = LAMBDA(_coefmat, _constmat, MMULT(MINVERSE(_coefmat), _constmat));

/* CURVE FITTING */
POLEST = LAMBDA(listY, listX, n, LINEST(listY, POWER(listX, TRANSPOSE(SEQUENCE(n, 1, 1, 1)))));

CPOLINT = LAMBDA(x, coeffs,
    LET(
        n, COUNT(coeffs),
        MMULT(
            POWER(x, TRANSPOSE(SEQUENCE(n, 1, n - 1, -1))) * coeffs,
            SEQUENCE(n, 1, 1, 0)
        )
    )
);

DPOLINT = LAMBDA(listY, listX, n, x,
    MMULT(
        POWER(x, TRANSPOSE(SEQUENCE(n + 1, 1, n, -1))) * POLEST(listY, listX, n),
        SEQUENCE(n + 1, 1, 1, 0)
    )
);

/* NUMERICAL DIFFERENTATION */
DF = LAMBDA(f,
    LAMBDA(x,
        LET(
            dx, 0.00001,
            (f(x + dx) - f(x - dx)) / (2 * dx)
        )
    )
);

/* EXTREMA */
LOCALEXT = LAMBDA(f, lbound, ubound,
    LET(
        extx, BISEC(DF(f), lbound, ubound, 0.00001),
        exty, f(extx),
        MAKEARRAY(1, 2, LAMBDA(ir, ic, CHOOSE(ic, extx, exty)))
    )
);