diff --git a/diff/fd/example_test.go b/diff/fd/example_test.go index 0a707299..0fe7f156 100644 --- a/diff/fd/example_test.go +++ b/diff/fd/example_test.go @@ -17,14 +17,14 @@ func ExampleDerivative() { return math.Sin(x) } // Compute the first derivative of f at 0 using the default settings. - fmt.Println("f'(0) ≈", fd.Derivative(f, 0, nil)) + fmt.Println("f′(0) ≈", fd.Derivative(f, 0, nil)) // Compute the first derivative of f at 0 using the forward approximation // with a custom step size. df := fd.Derivative(f, 0, &fd.Settings{ Formula: fd.Forward, Step: 1e-3, }) - fmt.Println("f'(0) ≈", df) + fmt.Println("f′(0) ≈", df) f = func(x float64) float64 { return math.Pow(math.Cos(x), 3) @@ -38,12 +38,12 @@ func ExampleDerivative() { OriginKnown: true, OriginValue: f(0), }) - fmt.Println("f''(0) ≈", df) + fmt.Println("f′′(0) ≈", df) // Output: - // f'(0) ≈ 1 - // f'(0) ≈ 0.9999998333333416 - // f''(0) ≈ -2.999999981767587 + // f′(0) ≈ 1 + // f′(0) ≈ 0.9999998333333416 + // f′′(0) ≈ -2.999999981767587 } func ExampleJacobian() { diff --git a/interp/cubic.go b/interp/cubic.go index 647df5f7..755339ee 100644 --- a/interp/cubic.go +++ b/interp/cubic.go @@ -371,7 +371,7 @@ func makeCubicSplineSecondDerivativeEquations(a mat.MutableBanded, b mat.Mutable // NaturalCubic is a piecewise cubic 1-dimensional interpolator with // continuous value, first and second derivatives, which can be fitted to (X, Y) // value pairs without providing derivatives. It uses the boundary conditions -// Y''(left end ) = Y''(right end) = 0. +// Y′′(left end ) = Y′′(right end) = 0. // See e.g. https://www.math.drexel.edu/~tolya/cubicspline.pdf for details. type NaturalCubic struct { cubic PiecewiseCubic @@ -396,7 +396,7 @@ func (nc *NaturalCubic) Fit(xs, ys []float64) error { a := mat.NewTridiag(n, nil, nil, nil) b := mat.NewVecDense(n, nil) makeCubicSplineSecondDerivativeEquations(a, b, xs, ys) - // Add boundary conditions y''(left) = y''(right) = 0: + // Add boundary conditions y′′(left) = y′′(right) = 0: b.SetVec(0, 0) b.SetVec(n-1, 0) a.SetBand(0, 0, 1) @@ -412,7 +412,7 @@ func (nc *NaturalCubic) Fit(xs, ys []float64) error { // ClampedCubic is a piecewise cubic 1-dimensional interpolator with // continuous value, first and second derivatives, which can be fitted to (X, Y) // value pairs without providing derivatives. It uses the boundary conditions -// Y'(left end ) = Y'(right end) = 0. +// Y′(left end ) = Y′(right end) = 0. type ClampedCubic struct { cubic PiecewiseCubic } @@ -436,13 +436,13 @@ func (cc *ClampedCubic) Fit(xs, ys []float64) error { a := mat.NewTridiag(n, nil, nil, nil) b := mat.NewVecDense(n, nil) makeCubicSplineSecondDerivativeEquations(a, b, xs, ys) - // Add boundary conditions y''(left) = y''(right) = 0: - // Condition Y'(left end) = 0: + // Add boundary conditions y′′(left) = y′′(right) = 0: + // Condition Y′(left end) = 0: dxL := xs[1] - xs[0] b.SetVec(0, (ys[1]-ys[0])/dxL) a.SetBand(0, 0, dxL/3) a.SetBand(0, 1, dxL/6) - // Condition Y'(right end) = 0: + // Condition Y′(right end) = 0: m := n - 1 dxR := xs[m] - xs[m-1] b.SetVec(m, (ys[m]-ys[m-1])/dxR) diff --git a/mathext/airy.go b/mathext/airy.go index 7b8865f1..d1865a9d 100644 --- a/mathext/airy.go +++ b/mathext/airy.go @@ -8,7 +8,7 @@ import "gonum.org/v1/gonum/mathext/internal/amos" // AiryAi returns the value of the Airy function at z. The Airy function here, // Ai(z), is one of the two linearly independent solutions to -// y'' - y*z = 0. +// y′′ - y*z = 0. // See http://mathworld.wolfram.com/AiryFunctions.html for more detailed information. func AiryAi(z complex128) complex128 { // id specifies the order of the derivative to compute, @@ -23,7 +23,7 @@ func AiryAi(z complex128) complex128 { // AiryAiDeriv returns the value of the derivative of the Airy function at z. The // Airy function here, Ai(z), is one of the two linearly independent solutions to -// y'' - y*z = 0. +// y′′ - y*z = 0. // See http://mathworld.wolfram.com/AiryFunctions.html for more detailed information. func AiryAiDeriv(z complex128) complex128 { // id specifies the order of the derivative to compute, diff --git a/num/hyperdual/hyperdual_example_test.go b/num/hyperdual/hyperdual_example_test.go index 745e711e..1bb9d092 100644 --- a/num/hyperdual/hyperdual_example_test.go +++ b/num/hyperdual/hyperdual_example_test.go @@ -24,12 +24,12 @@ func ExampleNumber_fike() { v := fn(hyperdual.Number{Real: 1.5, E1mag: 1, E2mag: 1}) fmt.Printf("v=%.4f\n", v) - fmt.Printf("fn(1.5)=%.4f\nfn'(1.5)=%.4f\nfn''(1.5)=%.4f\n", v.Real, v.E1mag, v.E1E2mag) + fmt.Printf("fn(1.5)=%.4f\nfn′(1.5)=%.4f\nfn′′(1.5)=%.4f\n", v.Real, v.E1mag, v.E1E2mag) // Output: // // v=(4.4978+4.0534ϵ₁+4.0534ϵ₂+9.4631ϵ₁ϵ₂) // fn(1.5)=4.4978 - // fn'(1.5)=4.0534 - // fn''(1.5)=9.4631 + // fn′(1.5)=4.0534 + // fn′′(1.5)=9.4631 } diff --git a/num/hyperdual/hyperdual_test.go b/num/hyperdual/hyperdual_test.go index 307a839f..d3f27e52 100644 --- a/num/hyperdual/hyperdual_test.go +++ b/num/hyperdual/hyperdual_test.go @@ -301,13 +301,13 @@ func TestHyperdual(t *testing.T) { t.Errorf("unexpected %s(%v): got:%v want:%v", test.name, x, fxHyperdual.Real, fx) } if !same(fxHyperdual.E1mag, dFx, tol) { - t.Errorf("unexpected %s'(%v) (ϵ₁): got:%v want:%v", test.name, x, fxHyperdual.E1mag, dFx) + t.Errorf("unexpected %s′(%v) (ϵ₁): got:%v want:%v", test.name, x, fxHyperdual.E1mag, dFx) } if !same(fxHyperdual.E1mag, fxHyperdual.E2mag, tol) { t.Errorf("mismatched ϵ₁ and ϵ₂ for %s(%v): ϵ₁:%v ϵ₂:%v", test.name, x, fxHyperdual.E1mag, fxHyperdual.E2mag) } if !same(fxHyperdual.E1E2mag, d2Fx, tol) { - t.Errorf("unexpected %s''(%v): got:%v want:%v", test.name, x, fxHyperdual.E1E2mag, d2Fx) + t.Errorf("unexpected %s′′(%v): got:%v want:%v", test.name, x, fxHyperdual.E1E2mag, d2Fx) } } }