Dual

Dual number for automatic differentation

Constructors

this this(Dual!R d)
this(R re)
this(Rr re, Rd du): Construct a dual number with the specified real and dual parts. In the case where a single argument is passed that is not a dual number, the imaginary part of the result will be zero.

Members

Functions

opAssign Dual opAssign(R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opAssign Dual opAssign(Dual!R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinary Dual!(CommonType!(T, R)) opBinary(Dual!R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinary Dual!(CommonType!(T, R)) opBinary(Dual!R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinary Dual!(CommonType!(T, R)) opBinary(Dual!R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinary Dual!(CommonType!(T, R)) opBinary(R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinary Dual!(CommonType!(T, R)) opBinary(R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinary Dual!T opBinary(R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinaryRight Dual!(CommonType!(T, R)) opBinaryRight(R lhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinaryRight Dual!(CommonType!(T, R)) opBinaryRight(R lhs): Undocumented in source. Be warned that the author may not have intended to support it.
opBinaryRight Dual!(CommonType!(T, R)) opBinaryRight(R lhs): Undocumented in source. Be warned that the author may not have intended to support it.
opCmp int opCmp(Dual!R z): Undocumented in source. Be warned that the author may not have intended to support it.
opCmp int opCmp(R r): Undocumented in source. Be warned that the author may not have intended to support it.
opEquals bool opEquals(Dual!R z): Undocumented in source. Be warned that the author may not have intended to support it.
opEquals bool opEquals(R r): Undocumented in source. Be warned that the author may not have intended to support it.
opOpAssign Dual opOpAssign(D rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opOpAssign Dual opOpAssign(R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opOpAssign Dual opOpAssign(R rhs): Undocumented in source. Be warned that the author may not have intended to support it.
opUnary Dual opUnary(): Undocumented in source. Be warned that the author may not have intended to support it.
toString string toString()
void toString(Writer w, FormatSpec!Char formatSpec): Converts the dual number to a string representation. The second form of this function is usually not called directly; instead, it is used via std.string.format, as shown in the examples below. Supported format characters are 'e', 'f', 'g', 'a', and 's'. See the std.format and std.string.format documentation for more information.

Variables

du T du;: The dual part
re T re;: The real part

To calculate the derivate of a function, set the dual part of the variable by which you want to derive to 1. Other dual numbers should have dual part of 0. Then just calculate the function like you would with normal numbers. The real part is always identically to the result with normal numbers. After the calculation the dual part holds the derivate of the function.

import std.math;
// f(x) = x⁵ f'(x) = 5x⁴ for x = 2
const x = Dual!double(2.0, 1.0);
auto f2 = x^^5;
assert(approxEqual(f2.re, 2.0^^5));
assert(approxEqual(f2.du, 5.0 * 2.0^^4));

// f(x) = 3x² f'(x) = 6x for x = 2
f2 = 3.0 * x * x;
assert(approxEqual(f2.re, 3.0 * 2.0 * 2.0));
assert(approxEqual(f2.du, 6.0 * 2.0));

// f(x) = 3/(1-x) f'(x) = 3/(1-x)^2 for x = 2
f2 = 3.0/(1.0 - x);
assert(approxEqual(f2.re, -3.0));
assert(approxEqual(f2.du, 3.0));

// f(x) = 3exp(2x), f'(x) = 6exp(2x) for x = 2
f2 = 3 * exp(2 * x);
assert(approxEqual(f2.re, 3 * std.math.exp(4.0)));
assert(approxEqual(f2.du, 6 * std.math.exp(4.0)));

Dual

Constructors

Members

Functions

Variables

Examples

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