Notebooks · lib/cas/derivs

The derivative table, as the CAS reads it

Generated from lib/cas/rules/derivatives.toml by viv cas derivs; edit the TOML file and run viv cas derivs > lib/cas/derivs.viv. grad.rs reads the same file (lang/viv/src/derivs.rs), so the reverse-mode gradient and the CAS's diff use one derivative for each head.

CAS_DERIV_ADJ[i] is the adjoint of CAS_DERIV_HEAD[i] in g, u and y; the CAS reads it with g = 1, which is the derivative of head(u) with respect to u. The test here reads every adjoint; lib/cas/calculus's test holds each derivative to a central difference at the table's points.

Used with import cas.derivs.

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[1]lines 17–31

from cas.parse import cas
from cas.store import cas_isfail

CAS_DERIV_ID = ["diff.exp", "diff.log", "diff.ln", "diff.sqrt", "diff.sin", "diff.cos", "diff.tan", "diff.tanh", "diff.sinh", "diff.cosh", "diff.asin", "diff.acos", "diff.atan", "diff.erf"]
CAS_DERIV_HEAD = ["exp", "log", "ln", "sqrt", "sin", "cos", "tan", "tanh", "sinh", "cosh", "asin", "acos", "atan", "erf"]
CAS_DERIV_ADJ = ["g * y", "g / u", "g / u", "g / (2 * y)", "g * cos(u)", "-(g * sin(u))", "g * (1 + y * y)", "g * (1 - y * y)", "g * cosh(u)", "g * sinh(u)", "g / sqrt(1 - u * u)", "-(g / sqrt(1 - u * u))", "g / (1 + u * u)", "g * (2 / sqrt(pi) * exp(-(u * u)))"]
# the points each row is tested at: the row, and x
CAS_DERIV_AT_RULE = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13]
CAS_DERIV_AT_X = [-1.5, 0.25, 2.0, 0.3, 1.0, 4.5, 0.3, 1.0, 4.5, 0.3, 1.0, 4.5, -1.5, 0.25, 2.0, -1.5, 0.25, 2.0, -1.2, 0.25, 1.0, -1.5, 0.25, 2.0, -1.5, 0.25, 2.0, -1.5, 0.25, 2.0, -0.7, 0.25, 0.9, -0.7, 0.25, 0.9, -1.5, 0.25, 2.0, -1.5, 0.25, 2.0]

test "every adjoint in the table reads as an expression in g, u and y" {
    for i to len(CAS_DERIV_ADJ) {
        assert_true(not cas_isfail(cas(CAS_DERIV_ADJ[i])))
    }
}

from cas.parse import cas
from cas.store import cas_isfail

CAS_DERIV_ID = ["diff.exp", "diff.log", "diff.ln", "diff.sqrt", "diff.sin", "diff.cos", "diff.tan", "diff.tanh", "diff.sinh", "diff.cosh", "diff.asin", "diff.acos", "diff.atan", "diff.erf"]
CAS_DERIV_HEAD = ["exp", "log", "ln", "sqrt", "sin", "cos", "tan", "tanh", "sinh", "cosh", "asin", "acos", "atan", "erf"]
CAS_DERIV_ADJ = ["g * y", "g / u", "g / u", "g / (2 * y)", "g * cos(u)", "-(g * sin(u))", "g * (1 + y * y)", "g * (1 - y * y)", "g * cosh(u)", "g * sinh(u)", "g / sqrt(1 - u * u)", "-(g / sqrt(1 - u * u))", "g / (1 + u * u)", "g * (2 / sqrt(pi) * exp(-(u * u)))"]
# the points each row is tested at: the row, and x
CAS_DERIV_AT_RULE = [0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13]
CAS_DERIV_AT_X = [-1.5, 0.25, 2.0, 0.3, 1.0, 4.5, 0.3, 1.0, 4.5, 0.3, 1.0, 4.5, -1.5, 0.25, 2.0, -1.5, 0.25, 2.0, -1.2, 0.25, 1.0, -1.5, 0.25, 2.0, -1.5, 0.25, 2.0, -1.5, 0.25, 2.0, -0.7, 0.25, 0.9, -0.7, 0.25, 0.9, -1.5, 0.25, 2.0, -1.5, 0.25, 2.0]

test "every adjoint in the table reads as an expression in g, u and y" {
    for i to len(CAS_DERIV_ADJ) {
        assert_true(not cas_isfail(cas(CAS_DERIV_ADJ[i])))
    }
}