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all: run gofmt and generate all packages

Browse Source 
Changes made in dsp/fourier/internal/fftpack break the formatting used
there, so these are reverted. There will be complaints in CI.

[git-generate]
gofmt -w .
go generate gonum.org/v1/gonum/blas
go generate gonum.org/v1/gonum/blas/gonum
go generate gonum.org/v1/gonum/unit
go generate gonum.org/v1/gonum/unit/constant
go generate gonum.org/v1/gonum/graph/formats/dot
go generate gonum.org/v1/gonum/graph/formats/rdf
go generate gonum.org/v1/gonum/stat/card

git checkout -- dsp/fourier/internal/fftpack
This commit is contained in:
Dan Kortschak
2022-08-05 20:57:59 +09:30
parent fee5019b48
commit 5f0141ca4c
308 changed files with 5004 additions and 3064 deletions
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259
optimize/functions/functions.go
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@@ -14,15 +14,16 @@ import (
// Beale implements the Beale's function.
//
// Standard starting points:
// Easy: [1, 1]
// Hard: [1, 4]
//
// Easy: [1, 1]
// Hard: [1, 4]
//
// References:
// - Beale, E.: On an Iterative Method for Finding a Local Minimum of a
// Function of More than One Variable. Technical Report 25, Statistical
// Techniques Research Group, Princeton University (1958)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Beale, E.: On an Iterative Method for Finding a Local Minimum of a
// Function of More than One Variable. Technical Report 25, Statistical
// Techniques Research Group, Princeton University (1958)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type Beale struct{}
func (Beale) Func(x []float64) float64 {
@@ -92,11 +93,13 @@ func (Beale) Minima() []Minimum {
// BiggsEXP2 implements the Biggs' EXP2 function.
//
// Standard starting point:
// [1, 2]
//
// [1, 2]
//
// Reference:
// Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
// of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
//
// Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
// of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
type BiggsEXP2 struct{}
func (BiggsEXP2) Func(x []float64) (sum float64) {
@@ -150,11 +153,13 @@ func (BiggsEXP2) Minima() []Minimum {
// BiggsEXP3 implements the Biggs' EXP3 function.
//
// Standard starting point:
// [1, 2, 1]
//
// [1, 2, 1]
//
// Reference:
// Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
// of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
//
// Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
// of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
type BiggsEXP3 struct{}
func (BiggsEXP3) Func(x []float64) (sum float64) {
@@ -210,11 +215,13 @@ func (BiggsEXP3) Minima() []Minimum {
// BiggsEXP4 implements the Biggs' EXP4 function.
//
// Standard starting point:
// [1, 2, 1, 1]
//
// [1, 2, 1, 1]
//
// Reference:
// Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
// of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
//
// Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
// of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
type BiggsEXP4 struct{}
func (BiggsEXP4) Func(x []float64) (sum float64) {
@@ -272,11 +279,13 @@ func (BiggsEXP4) Minima() []Minimum {
// BiggsEXP5 implements the Biggs' EXP5 function.
//
// Standard starting point:
// [1, 2, 1, 1, 1]
//
// [1, 2, 1, 1, 1]
//
// Reference:
// Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
// of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
//
// Biggs, M.C.: Minimization algorithms making use of non-quadratic properties
// of the objective function. IMA J Appl Math 8 (1971), 315-327; doi:10.1093/imamat/8.3.315
type BiggsEXP5 struct{}
func (BiggsEXP5) Func(x []float64) (sum float64) {
@@ -336,14 +345,15 @@ func (BiggsEXP5) Minima() []Minimum {
// BiggsEXP6 implements the Biggs' EXP6 function.
//
// Standard starting point:
// [1, 2, 1, 1, 1, 1]
//
// [1, 2, 1, 1, 1, 1]
//
// References:
// - Biggs, M.C.: Minimization algorithms making use of non-quadratic
// properties of the objective function. IMA J Appl Math 8 (1971), 315-327;
// doi:10.1093/imamat/8.3.315
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Biggs, M.C.: Minimization algorithms making use of non-quadratic
// properties of the objective function. IMA J Appl Math 8 (1971), 315-327;
// doi:10.1093/imamat/8.3.315
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type BiggsEXP6 struct{}
func (BiggsEXP6) Func(x []float64) (sum float64) {
@@ -417,13 +427,14 @@ func (BiggsEXP6) Minima() []Minimum {
// Box3D implements the Box' three-dimensional function.
//
// Standard starting point:
// [0, 10, 20]
//
// [0, 10, 20]
//
// References:
// - Box, M.J.: A comparison of several current optimization methods, and the
// use of transformations in constrained problems. Comput J 9 (1966), 67-77
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Box, M.J.: A comparison of several current optimization methods, and the
// use of transformations in constrained problems. Comput J 9 (1966), 67-77
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type Box3D struct{}
func (Box3D) Func(x []float64) (sum float64) {
@@ -485,11 +496,14 @@ func (Box3D) Minima() []Minimum {
// BraninHoo implements the Branin-Hoo function. BraninHoo is a 2-dimensional
// test function with three global minima. It is typically evaluated in the domain
// x_0 ∈ [-5, 10], x_1 ∈ [0, 15].
// f(x) = (x_1 - (5.1/(4π^2))*x_0^2 + (5/π)*x_0 - 6)^2 + 10*(1-1/(8π))cos(x_0) + 10
//
// f(x) = (x_1 - (5.1/(4π^2))*x_0^2 + (5/π)*x_0 - 6)^2 + 10*(1-1/(8π))cos(x_0) + 10
//
// It has a minimum value of 0.397887 at x^* = {(-π, 12.275), (π, 2.275), (9.424778, 2.475)}
//
// Reference:
// https://www.sfu.ca/~ssurjano/branin.html (obtained June 2017)
//
// https://www.sfu.ca/~ssurjano/branin.html (obtained June 2017)
type BraninHoo struct{}
func (BraninHoo) Func(x []float64) float64 {
@@ -525,11 +539,12 @@ func (BraninHoo) Minima() []Minimum {
// BrownBadlyScaled implements the Brown's badly scaled function.
//
// Standard starting point:
// [1, 1]
//
// [1, 1]
//
// References:
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type BrownBadlyScaled struct{}
func (BrownBadlyScaled) Func(x []float64) float64 {
@@ -587,14 +602,15 @@ func (BrownBadlyScaled) Minima() []Minimum {
// BrownAndDennis implements the Brown and Dennis function.
//
// Standard starting point:
// [25, 5, -5, -1]
//
// [25, 5, -5, -1]
//
// References:
// - Brown, K.M., Dennis, J.E.: New computational algorithms for minimizing a
// sum of squares of nonlinear functions. Research Report Number 71-6, Yale
// University (1971)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Brown, K.M., Dennis, J.E.: New computational algorithms for minimizing a
// sum of squares of nonlinear functions. Research Report Number 71-6, Yale
// University (1971)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type BrownAndDennis struct{}
func (BrownAndDennis) Func(x []float64) (sum float64) {
@@ -689,14 +705,15 @@ func (BrownAndDennis) Minima() []Minimum {
// Its Hessian matrix is singular at the minimizer.
//
// Standard starting point:
// [3, -1, 0, 3, 3, -1, 0, 3, ..., 3, -1, 0, 3]
//
// [3, -1, 0, 3, 3, -1, 0, 3, ..., 3, -1, 0, 3]
//
// References:
// - Spedicato E.: Computational experience with quasi-Newton algorithms for
// minimization problems of moderatly large size. Towards Global
// Optimization 2 (1978), 209-219
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Spedicato E.: Computational experience with quasi-Newton algorithms for
// minimization problems of moderatly large size. Towards Global
// Optimization 2 (1978), 209-219
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type ExtendedPowellSingular struct{}
func (ExtendedPowellSingular) Func(x []float64) (sum float64) {
@@ -762,13 +779,14 @@ func (ExtendedPowellSingular) Minima() []Minimum {
// function.
//
// Standard starting point:
// Easy: [-1.2, 1, -1.2, 1, ...]
// Hard: any point far from the minimum
//
// Easy: [-1.2, 1, -1.2, 1, ...]
// Hard: any point far from the minimum
//
// References:
// - Rosenbrock, H.H.: An Automatic Method for Finding the Greatest or Least
// Value of a Function. Computer J 3 (1960), 175-184
// - http://en.wikipedia.org/wiki/Rosenbrock_function
// - Rosenbrock, H.H.: An Automatic Method for Finding the Greatest or Least
// Value of a Function. Computer J 3 (1960), 175-184
// - http://en.wikipedia.org/wiki/Rosenbrock_function
type ExtendedRosenbrock struct{}
func (ExtendedRosenbrock) Func(x []float64) (sum float64) {
@@ -858,11 +876,13 @@ func (ExtendedRosenbrock) Minima() []Minimum {
// caused by the finite floating point precision.
//
// Standard starting point:
// [0.4, 1, 0]
//
// [0.4, 1, 0]
//
// Reference:
// More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization
// software. ACM Trans Math Softw 7 (1981), 17-41
//
// More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization
// software. ACM Trans Math Softw 7 (1981), 17-41
type Gaussian struct{}
func (Gaussian) y(i int) (yi float64) {
@@ -939,14 +959,15 @@ func (Gaussian) Minima() []Minimum {
// GulfResearchAndDevelopment implements the Gulf Research and Development function.
//
// Standard starting point:
// [5, 2.5, 0.15]
//
// [5, 2.5, 0.15]
//
// References:
// - Cox, R.A.: Comparison of the performance of seven optimization algorithms
// on twelve unconstrained minimization problems. Ref. 1335CNO4, Gulf
// Research and Development Company, Pittsburg (1969)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Cox, R.A.: Comparison of the performance of seven optimization algorithms
// on twelve unconstrained minimization problems. Ref. 1335CNO4, Gulf
// Research and Development Company, Pittsburg (1969)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type GulfResearchAndDevelopment struct{}
func (GulfResearchAndDevelopment) Func(x []float64) (sum float64) {
@@ -1016,13 +1037,14 @@ func (GulfResearchAndDevelopment) Minima() []Minimum {
// Function is not defined at x[0] = 0.
//
// Standard starting point:
// [-1, 0, 0]
//
// [-1, 0, 0]
//
// References:
// - Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for
// minimization. Comput J 6 (1963), 163-168
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for
// minimization. Comput J 6 (1963), 163-168
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type HelicalValley struct{}
func (HelicalValley) Func(x []float64) float64 {
@@ -1098,14 +1120,15 @@ func (Linear) Grad(grad, x []float64) []float64 {
// PenaltyI implements the first penalty function by Gill, Murray and Pitfield.
//
// Standard starting point:
// [1, ..., n]
//
// [1, ..., n]
//
// References:
// - Gill, P.E., Murray, W., Pitfield, R.A.: The implementation of two revised
// quasi-Newton algorithms for unconstrained optimization. Report NAC 11,
// National Phys Lab (1972), 82-83
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Gill, P.E., Murray, W., Pitfield, R.A.: The implementation of two revised
// quasi-Newton algorithms for unconstrained optimization. Report NAC 11,
// National Phys Lab (1972), 82-83
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type PenaltyI struct{}
func (PenaltyI) Func(x []float64) (sum float64) {
@@ -1156,14 +1179,15 @@ func (PenaltyI) Minima() []Minimum {
// PenaltyII implements the second penalty function by Gill, Murray and Pitfield.
//
// Standard starting point:
// [0.5, ..., 0.5]
//
// [0.5, ..., 0.5]
//
// References:
// - Gill, P.E., Murray, W., Pitfield, R.A.: The implementation of two revised
// quasi-Newton algorithms for unconstrained optimization. Report NAC 11,
// National Phys Lab (1972), 82-83
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Gill, P.E., Murray, W., Pitfield, R.A.: The implementation of two revised
// quasi-Newton algorithms for unconstrained optimization. Report NAC 11,
// National Phys Lab (1972), 82-83
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type PenaltyII struct{}
func (PenaltyII) Func(x []float64) (sum float64) {
@@ -1236,14 +1260,15 @@ func (PenaltyII) Minima() []Minimum {
// that gives f(x) ≅ 1e-13.
//
// Standard starting point:
// [0, 1]
//
// [0, 1]
//
// References:
// - Powell, M.J.D.: A Hybrid Method for Nonlinear Equations. Numerical
// Methods for Nonlinear Algebraic Equations, P. Rabinowitz (ed.), Gordon
// and Breach (1970)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Powell, M.J.D.: A Hybrid Method for Nonlinear Equations. Numerical
// Methods for Nonlinear Algebraic Equations, P. Rabinowitz (ed.), Gordon
// and Breach (1970)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type PowellBadlyScaled struct{}
func (PowellBadlyScaled) Func(x []float64) float64 {
@@ -1304,14 +1329,15 @@ func (PowellBadlyScaled) Minima() []Minimum {
// Trigonometric implements the trigonometric function.
//
// Standard starting point:
// [1/dim, ..., 1/dim]
//
// [1/dim, ..., 1/dim]
//
// References:
// - Spedicato E.: Computational experience with quasi-Newton algorithms for
// minimization problems of moderatly large size. Towards Global
// Optimization 2 (1978), 209-219
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Spedicato E.: Computational experience with quasi-Newton algorithms for
// minimization problems of moderatly large size. Towards Global
// Optimization 2 (1978), 209-219
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type Trigonometric struct{}
func (Trigonometric) Func(x []float64) (sum float64) {
@@ -1374,11 +1400,13 @@ func (Trigonometric) Minima() []Minimum {
// VariablyDimensioned implements a variably dimensioned function.
//
// Standard starting point:
// [..., (dim-i)/dim, ...], i=1,...,dim
//
// [..., (dim-i)/dim, ...], i=1,...,dim
//
// References:
// More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization
// software. ACM Trans Math Softw 7 (1981), 17-41
//
// More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization
// software. ACM Trans Math Softw 7 (1981), 17-41
type VariablyDimensioned struct{}
func (VariablyDimensioned) Func(x []float64) (sum float64) {
@@ -1447,13 +1475,14 @@ func (VariablyDimensioned) Minima() []Minimum {
// of minimizing the function is very ill conditioned.
//
// Standard starting point:
// [0, ..., 0]
//
// [0, ..., 0]
//
// References:
// - Kowalik, J.S., Osborne, M.R.: Methods for Unconstrained Optimization
// Problems. Elsevier North-Holland, New York, 1968
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Kowalik, J.S., Osborne, M.R.: Methods for Unconstrained Optimization
// Problems. Elsevier North-Holland, New York, 1968
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type Watson struct{}
func (Watson) Func(x []float64) (sum float64) {
@@ -1597,13 +1626,14 @@ func (Watson) Minima() []Minimum {
// Wood implements the Wood's function.
//
// Standard starting point:
// [-3, -1, -3, -1]
//
// [-3, -1, -3, -1]
//
// References:
// - Colville, A.R.: A comparative study of nonlinear programming codes.
// Report 320-2949, IBM New York Scientific Center (1968)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
// - Colville, A.R.: A comparative study of nonlinear programming codes.
// Report 320-2949, IBM New York Scientific Center (1968)
// - More, J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained
// optimization software. ACM Trans Math Softw 7 (1981), 17-41
type Wood struct{}
func (Wood) Func(x []float64) (sum float64) {
@@ -1674,8 +1704,9 @@ func (Wood) Minima() []Minimum {
// of the minimizer which is located at x=sqrt(2).
//
// References:
// More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
// ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.1)
//
// More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
// ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.1)
type ConcaveRight struct{}
func (ConcaveRight) Func(x []float64) float64 {
@@ -1700,8 +1731,9 @@ func (ConcaveRight) Grad(grad, x []float64) {
// the minimizer which is located at x=399/250=1.596.
//
// References:
// More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
// ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.2)
//
// More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
// ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.2)
type ConcaveLeft struct{}
func (ConcaveLeft) Func(x []float64) float64 {
@@ -1729,8 +1761,9 @@ func (ConcaveLeft) Grad(grad, x []float64) {
// on the derivative is unreliable due to the oscillations.
//
// References:
// More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
// ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.3)
//
// More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
// ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.3)
type Plassmann struct {
L float64 // Number of oscillations for |x-1| ≥ Beta.
Beta float64 // Size of the derivative at zero, f'(0) = -Beta.
@@ -1783,10 +1816,10 @@ func (f Plassmann) Grad(grad, x []float64) {
// the parameter values.
//
// References:
// - More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
// ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.4)
// - Yanai, H., Ozawa, M., and Kaneko, S.: Interpolation methods in one dimensional
// optimization. Computing 27 (1981), 155–163
// - More, J.J., and Thuente, D.J.: Line Search Algorithms with Guaranteed Sufficient Decrease.
// ACM Transactions on Mathematical Software 20(3) (1994), 286–307, eq. (5.4)
// - Yanai, H., Ozawa, M., and Kaneko, S.: Interpolation methods in one dimensional
// optimization. Computing 27 (1981), 155–163
type YanaiOzawaKaneko struct {
Beta1 float64
Beta2 float64