utl

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 Go to latest Published: Nov 4, 2024 License: BSD-3-Clause Imports: 13 Imported by: 0

README

Gosl. utl. Utilities. Lists. Dictionaries. Simple Numerics

Go Reference

This package implements functions for simplifying numeric calculations such as finding the maximum and minimum of lists (i.e. slices), allocation of deep structures such as slices of slices, and generation of arrays. It also contains functions for sorting quantities and updating dictionaries (i.e. maps).

This package does not aim for high performance linear algebra computations. For that purpose, we have the la package. Nonetheless, utl package is OK for small computations such as for vectors in the 3D space. It also tries to use the best algorithms for sorting that are implemented in the standard Go library and others.

Example of what the functions here can do:

  • Generate lists of integers
  • Generate lists of float64s
  • Cumulative sums
  • Handling tables of float64s
  • Pareto fronts
  • Slices and deep (nested) slices up to the 4th depth
  • Allocate deep slices
  • Serialization of deep slices
  • Sorting
  • Maps and dictionaries
  • Append to maps of slices of float64
  • Find the best square for given size = numberOfRows * numberOfColumns
  • ...

API

Please see the documentation here

Documentation

Overview

Package utl implements functions for simplifying calculations and allocation of structures such as slices and slices of slices. It also contains functions for sorting quantities.

Index

Constants

View Source 
const (
	// SQ2 = sqrt(2) [https://oeis.org/A002193]
	SQ2 = 1.41421356237309504880168872420969807856967187537694807317667974

	// SQ3 = sqrt(3) [https://oeis.org/A002194]
	SQ3 = 1.73205080756887729352744634150587236694280525381038062805580698

	// SQ5 = sqrt(5) [https://oeis.org/A002163]
	SQ5 = 2.23606797749978969640917366873127623544061835961152572427089724

	// SQ6 = sqrt(6) [https://oeis.org/A010464]
	SQ6 = 2.44948974278317809819728407470589139196594748065667012843269257

	// SQ7 = sqrt(7) [https://oeis.org/A010465]
	SQ7 = 2.64575131106459059050161575363926042571025918308245018036833446

	// SQ8 = sqrt(8) [https://oeis.org/A010466]
	SQ8 = 2.82842712474619009760337744841939615713934375075389614635335947
)

Variables

This section is empty.

Functions

func AllFalse 

func AllFalse(values []bool) bool

AllFalse returns true if all values are false

func AllTrue 

func AllTrue(values []bool) bool

AllTrue returns true if all values are true

func Alloc 

func Alloc(m, n int) (mat [][]float64)

Alloc allocates a slice of slices of float64

func ArgMinMax 

func ArgMinMax(v []float64) (imin, imax int)

ArgMinMax finds the indices of min and max arguments

func BestSquare 

func BestSquare(size int) (nrow, ncol int)

BestSquare finds the best square for given size=Nrows * Ncolumns

func BestSquareApprox 

func BestSquareApprox(size int) (nrow, ncol int)

BestSquareApprox finds the best square for given size=Nrows * Ncolumns. Approximate version; i.e. nrow*ncol may not be equal to size

func Clone 

func Clone(a [][]float64) (b [][]float64)

Clone allocates and clones a matrix of float64

func Cross3d 

func Cross3d(w, u, v []float64)

Cross3d computes the cross product of two 3D vectors u and w 

w = u cross v
Note: w must be pre-allocated

func CumSum 

func CumSum(cs, p []float64)

CumSum returns the cumulative sum of the elements in p 

Input:
 p -- values
Output:
 cs -- cumulated sum; pre-allocated with len(cs) == len(p)

func Deep2checkSize 

func Deep2checkSize(n1, n2 int, a [][]float64) bool

Deep2checkSize checks if dimensions of Deep2 slice are correct

func Deep2transpose 

func Deep2transpose(a [][]float64) (aT [][]float64)

Deep2transpose returns the transpose of a deep2 slice

func Deep3GetInfo 

func Deep3GetInfo(I, P []int, S []float64, verbose bool) (nitems, nrows, ncolsTot int, ncols []int)

Deep3GetInfo returns information of serialized array of array of array

func Deep3alloc 

func Deep3alloc(n1, n2, n3 int) (a [][][]float64)

Deep3alloc allocates a slice of slice of slice

func Deep3checkSize 

func Deep3checkSize(n1, n2, n3 int, a [][][]float64) bool

Deep3checkSize checks if dimensions of Deep3 slice are correct

func Deep3set 

func Deep3set(a [][][]float64, v float64)

Deep3set sets deep slice of slice of slice with v values

func Deep4alloc 

func Deep4alloc(n1, n2, n3, n4 int) (a [][][][]float64)

Deep4alloc allocates a slice of slice of slice of slice

func Deep4set 

func Deep4set(a [][][][]float64, v float64)

Deep4set sets deep slice of slice of slice of slice with v values

func DeserializeDeep2 

func DeserializeDeep2(v []float64, m, n int) (a [][]float64)

DeserializeDeep2 converts a column-major array to a matrix

func DeserializeDeep3 

func DeserializeDeep3(I, P []int, S []float64, debug bool) (A [][][]float64)

DeserializeDeep3 deserializes an array of array of array in column-compressed format

func Digits 

func Digits(maxint int) (ndigits int, format string)

Digits returns the nubmer of digits

func Dot3d 

func Dot3d(u, v []float64) (s float64)

Dot3d returns the dot product between two 3D vectors

func DurSum 

func DurSum(v []time.Duration) (seconds float64)

DurSum sums all seconds in v 

NOTE: this is not efficient and should be used for small slices only

func Expon 

func Expon(val float64) (ndigits int)

Expon returns the exponent

func Fill 

func Fill(s []float64, val float64)

Fill fills a slice of float64

func FlipCoin 

func FlipCoin(p float64) bool

FlipCoin generates a Bernoulli variable; throw a coin with probability p

func FromFloat64s 

func FromFloat64s(a []float64) (b []int)

FromFloat64s returns a new slice of int from a slice of float64

func FromInts 

func FromInts(a []int) (b []float64)

FromInts returns a new slice of float64 from a slice of ints

func FromString 

func FromString(s string) (r []float64)

FromString splits a string with numbers separeted by spaces into float64

func FromStrings 

func FromStrings(s []string) (v []float64)

FromStrings converts a slice of strings to a slice of float64

func GetColumn 

func GetColumn(j int, v [][]float64) (x []float64)

GetColumn returns the column of a matrix of float64

func GetCopy 

func GetCopy(in []float64) (out []float64)

GetCopy gets a copy of slice of float64

func GetITout 

func GetITout(allOutputTimes, timeStationsOut []float64, tol float64) (I []int, T []float64)

GetITout returns indices and output times 

Input:
  all_output_times  -- array with all output times. ex: [0,0.1,0.2,0.22,0.3,0.4]
  time_stations_out -- time stations for output: ex: [0,0.2,0.4]
  tol               -- tolerance to compare times
Output:
  iout -- indices of times in all_output_times
  tout -- times corresponding to iout
Notes:
  use -1 in all_output_times to enforce output of last timestep

func GetMapped 

func GetMapped(X []float64, filter func(x float64) float64) (Y []float64)

GetMapped returns a new slice such that: Y[i] = filter(X[i])

func GetMapped2 

func GetMapped2(X [][]float64, filter func(x float64) float64) (Y [][]float64)

GetMapped2 returns a new slice of slice such that: Y[i][j] = filter(X[i][j]) 

NOTE: each row in X may have different number of columns; i.e. len(X[0]) may be != len(X[1])

func GetReversed 

func GetReversed(in []float64) (out []float64)

GetReversed return a copy with reversed items

func GetSorted 

func GetSorted(A []float64) (sortedA []float64)

GetSorted returns a sorted (increasing) copy of 'A'

func GetStrides 

func GetStrides(nTotal, nReq int) (I []int)

GetStrides returns nReq indices from 0 (inclusive) to nTotal (inclusive) 

Input:
  nTotal -- total number of intices
  nReq -- required indices
Example:
  GetStrides(2001, 5) => [0 400 800 1200 1600 2000 2001]

NOTE: GetStrides will always include nTotal as the last item in I

func GtPenalty 

func GtPenalty(x, b, penaltyM float64) float64

GtPenalty implements a 'greater than' penalty function where x must be greater than b; otherwise the error is magnified

func GtePenalty 

func GtePenalty(x, b, penaltyM float64) float64

GtePenalty implements a 'greater than or equal' penalty function where x must be greater than b or equal to be; otherwise the error is magnified

func Iabs 

func Iabs(a int) int

Iabs performs the absolute operation with ints

func Imax 

func Imax(a, b int) int

Imax returns the maximum between two integers

func Imin 

func Imin(a, b int) int

Imin returns the minimum between two integers

func IntAddScalar 

func IntAddScalar(a []int, s int) (res []int)

IntAddScalar adds a scalar to all values in a slice of integers

func IntAlloc 

func IntAlloc(m, n int) (mat [][]int)

IntAlloc allocates a matrix of integers

func IntBoolMapSort 

func IntBoolMapSort(m map[int]bool) (sortedKeys []int)

IntBoolMapSort returns sorted keys of map[int]bool

func IntClone 

func IntClone(a [][]int) (b [][]int)

IntClone allocates and clones a matrix of integers

func IntCopy 

func IntCopy(in []int) (out []int)

IntCopy returns a copy of slice of ints

func IntFill 

func IntFill(s []int, val int)

IntFill fills a slice of integers

func IntFilter 

func IntFilter(a []int, out func(idx int) bool) (res []int)

IntFilter filters out components in slice 

NOTE: this function is not efficient and should be used with small slices only

func IntGetSorted 

func IntGetSorted(A []int) (sortedA []int)

IntGetSorted returns a sorted (increasing) copy of 'A'

func IntIndexSmall 

func IntIndexSmall(a []int, val int) int

IntIndexSmall finds the index of an item in a slice of ints 

NOTE: this function is not efficient and should be used with small slices only; say smaller than 20

func IntIntsMapAppend 

func IntIntsMapAppend(m map[int][]int, key int, item int)

IntIntsMapAppend appends a new item to a map of slice. 

Note: this function creates a new slice in the map if key is not found.

func IntMinMax 

func IntMinMax(v []int) (mi, ma int)

IntMinMax returns the maximum and minimum elements in v 

NOTE: this is not efficient and should be used for small slices only

func IntNegOut 

func IntNegOut(a []int) (res []int)

IntNegOut filters out negative components in slice 

NOTE: this function is not efficient and should be used with small slices only

func IntPy 

func IntPy(a []int) (res string)

IntPy returns a Python string representing a slice of integers

func IntRange 

func IntRange(n int) (res []int)

IntRange generates a slice of integers from 0 to n-1

func IntRange2 

func IntRange2(start, stop int) []int

IntRange2 generates slice of integers from start to stop (but not stop)

func IntRange3 

func IntRange3(start, stop, step int) (res []int)

IntRange3 generates a slice of integers from start to stop (but not stop), afer each 'step'

func IntSort3 

func IntSort3(a, b, c *int)

IntSort3 sorts 3 values in ascending order

func IntSort4 

func IntSort4(a, b, c, d *int)

IntSort4 sort four values in ascending order

func IntUnique 

func IntUnique(slices ...[]int) (res []int)

IntUnique returns a unique and sorted slice of integers

func IntVals 

func IntVals(n int, val int) (s []int)

IntVals allocates a slice of integers with size==n, filled with val

func IsPowerOfTwo 

func IsPowerOfTwo(n int) bool

IsPowerOfTwo checks if n is power of 2; i.e. 2⁰, 2¹, 2², 2³, 2⁴, ...

func L2norm 

func L2norm(p, q []float64) (dist float64)

L2norm returns the Euclidean distance between p and q

func LinSpace 

func LinSpace(start, stop float64, num int) (res []float64)

LinSpace returns evenly spaced numbers over a specified closed interval.

func LinSpaceOpen 

func LinSpaceOpen(start, stop float64, num int) (res []float64)

LinSpaceOpen returns evenly spaced numbers over a specified open interval.

func Max 

func Max(a, b float64) float64

Max returns the maximum between two float point numbers

func MeshGrid2d 

func MeshGrid2d(xmin, xmax, ymin, ymax float64, nx, ny int) (X, Y [][]float64)

MeshGrid2d creates a grid with x-y coordinates 

X, Y -- [ny][nx]

func MeshGrid2dF 

func MeshGrid2dF(xmin, xmax, ymin, ymax float64, nx, ny int, f func(x, y float64) float64) (X, Y, Z [][]float64)

MeshGrid2dF creates a grid with x-y coordinates and evaluates z=f(x,y) 

X, Y, Z -- [ny][nx]

func MeshGrid2dFG 

func MeshGrid2dFG(xmin, xmax, ymin, ymax float64, nx, ny int, fg func(x, y float64) (z, u, v float64)) (X, Y, Z, U, V [][]float64)

MeshGrid2dFG creates a grid with x-y coordinates and evaluates (z,u,v)=fg(x,y) 

X, Y, Z, U, V -- [ny][nx]

func MeshGrid2dV 

func MeshGrid2dV(xVals, yVals []float64) (X, Y [][]float64)

MeshGrid2dV creates a grid with x-y coordinates given x and y values 

X, Y -- [len(yVals)][len(xVals)]

func Min 

func Min(a, b float64) float64

Min returns the minimum between two float point numbers

func MinMax 

func MinMax(v []float64) (mi, ma float64)

MinMax returns the maximum and minimum elements in v 

NOTE: this is not efficient and should be used for small slices only

func NonlinSpace 

func NonlinSpace(xa, xb float64, N int, R float64, symmetric bool) (x []float64)

NonlinSpace generates N points such that the ratio between the last segment (or the middle segment) to the first one is equal to a given constant R. 

The ratio between the last (or middle largest) segment to the first one is:

    ΔxL   = Δx0 ⋅ R

The ratio between successive segments is

             k-1
    Δx[k] = α    ⋅ Δx[0]

Unsymmetricc case:

  |--|-------|------------|-----------------|
   Δx0                            ΔxL

Symmetric case with odd number of spacings:

  |---|--------|---------------|--------|---|
   Δx0                ΔxL                Δx0

Symmetric case with even number of spacings:

  |---|----------------|----------------|---|
   Δx0       ΔxL               ΔxL       Δx0

func Ones 

func Ones(n int) (res []float64)

Ones generates a slice of float64 with ones

func ParetoFront 

func ParetoFront(Ovs [][]float64) (front []int)

ParetoFront computes the Pareto optimal front 

Input:
 Ovs -- [nsamples][ndim] objective values
Output:
 front -- indices of pareto front
Note: this function is slow for large sets

func ParetoMin 

func ParetoMin(u, v []float64) (uDominates, vDominates bool)

ParetoMin compares two vectors using Pareto's optimal criterion 

Note: minimum dominates (is better)

func ParetoMinProb 

func ParetoMinProb(u, v []float64, φ float64) (uDominates bool)

ParetoMinProb compares two vectors using Pareto's optimal criterion φ ∃ [0,1] is a scaling factor that helps v win even if it's not smaller. If φ==0, deterministic analysis is carried out. If φ==1, probabilistic analysis is carried out. As φ → 1, v "gets more help". 

Note: (1) minimum dominates (is better)
      (2) v dominates if !uDominates

func PrintDeep3 

func PrintDeep3(name string, A [][][]float64)

PrintDeep3 prints an array of array of array

func PrintDeep4 

func PrintDeep4(name string, A [][][][]float64, format string)

PrintDeep4 prints an array of array of array

func PrintMemStat 

func PrintMemStat(msg string)

PrintMemStat prints memory statistics

func ProbContestSmall 

func ProbContestSmall(u, v, φ float64) float64

ProbContestSmall computes the probability for a contest between u and v where u wins if it's the smaller value. φ ∃ [0,1] is a scaling factor that helps v win even if it's not smaller. If φ==0, deterministic analysis is carried out. If φ==1, probabilistic analysis is carried out. As φ → 1, v "gets more help".

func Prof 

func Prof(mem, silent bool) func()

Prof runs either CPU profiling or MEM profiling 

INPUT:
  mem    -- memory profiling instead of CPU profiling
  silent -- hide messages

OUTPUT:
  returns a "stop()" function to be called before exiting
  output files are saved to "/tmp/gosl/cpu.pprof"; or
                            "/tmp/gosl/mem.pprof"
Run analysis with:
    go tool pprof <binary-goes-here> /tmp/gosl/cpu.pprof
or
    go tool pprof <binary-goes-here> /tmp/gosl/mem.pprof

Example of use (notice the last parentheses):

     func main() {
        defer utl.Prof(false, false)()
        ...
     }

func ProfCPU 

func ProfCPU(dirout, filename string, silent bool) func()

ProfCPU activates CPU profiling 

OUTPUT: returns a "stop()" function to be called before exiting

Example of use (notice the last parentheses):

     func main() {
        defer ProfCPU("/tmp", "cpu.pprof", true)()
        ...
     }

Run analysis with:
    go tool pprof <binary-goes-here> /tmp/cpu.pprof

func ProfMEM 

func ProfMEM(dirout, filename string, silent bool) func()

ProfMEM activates memory profiling 

OUTPUT: returns a "stop()" function to be called before exiting

Example of use (notice the last parentheses):

     func main() {
        defer ProfMEM("/tmp", "mem.pprof", true)()
        ...
     }

Run analysis with:
    go tool pprof <binary-goes-here> /tmp/mem.pprof

func Qsort 

func Qsort(arr []float64)

Qsort sort an array arr[0..n-1] into ascending numerical order using the Quicksort algorithm. arr is replaced on output by its sorted rearrangement. Normally, the optional argument m should be omitted, but if it is set to a positive value, then only the first m elements of arr are sorted. Implementation from [1] 

Reference:
[1] Press WH, Teukolsky SA, Vetterling WT, Fnannery BP (2007) Numerical Recipes: The Art of
    Scientific Computing. Third Edition. Cambridge University Press. 1235p.

func Qsort2 

func Qsort2(arr, brr []float64)

Qsort2 sorts an array arr[0..n-1] into ascending order using Quicksort, while making the corresponding rearrangment of the array brr[0..n-1]. Implementation from [1] 

Reference:
[1] Press WH, Teukolsky SA, Vetterling WT, Fnannery BP (2007) Numerical Recipes: The Art of
    Scientific Computing. Third Edition. Cambridge University Press. 1235p.

func Scaling 

func Scaling(s, x []float64, ds, tol float64, reverse, useinds bool) (xmin, xmax float64)

Scaling computes a scaled version of the input slice with results in [0.0, 1.0] 

Input:
 x       -- values
 ds      -- δs value to be added to all 's' values
 tol     -- tolerance for capturing xmax ≅ xmin
 reverse -- compute reverse series;
            i.e. 's' decreases from 1 to 0 while x goes from xmin to xmax
 useinds -- if (xmax-xmin)<tol, use indices to generate the 's' slice;
            otherwise, 's' will be filled with δs + zeros
Ouptut:
 s          -- scaled series; pre--allocated with len(s) == len(x)
 xmin, xmax -- min(x) and max(x)

func SerializeDeep2 

func SerializeDeep2(a [][]float64) (v []float64)

SerializeDeep2 converts a matrix into a column-major array

func SerializeDeep3 

func SerializeDeep3(A [][][]float64) (I, P []int, S []float64)

SerializeDeep3 serializes an array of array of array in column-compressed format

func Sort3 

func Sort3(a, b, c *float64)

Sort3 sorts 3 values in ascending order

func Sort3Desc 

func Sort3Desc(a, b, c *float64)

Sort3Desc sorts 3 values in descending order

func Sort4 

func Sort4(a, b, c, d *float64)

Sort4 sort four values in ascending order

func SortQuadruples 

func SortQuadruples(i []int, x, y, z []float64, by string) (I []int, X, Y, Z []float64)

SortQuadruples sorts i, x, y, and z by "i", "x", "y", or "z" 

Note: either i, x, y, or z can be nil; i.e. at least one of them must be non nil

func StrAlloc 

func StrAlloc(m, n int) (mat [][]string)

StrAlloc allocates a matrix of strings

func StrBoolMapSort 

func StrBoolMapSort(m map[string]bool) (sortedKeys []string)

StrBoolMapSort returns sorted keys of map[string]bool

func StrBoolMapSortSplit 

func StrBoolMapSortSplit(m map[string]bool) (sortedKeys []string, sortedVals []bool)

StrBoolMapSortSplit returns sorted keys of map[string]bool and sorted values

func StrFltMapSort 

func StrFltMapSort(m map[string]float64) (sortedKeys []string)

StrFltMapSort returns sorted keys of map[string]float64

func StrFltMapSortSplit 

func StrFltMapSortSplit(m map[string]float64) (sortedKeys []string, sortedVals []float64)

StrFltMapSortSplit returns sorted keys of map[string]float64 and sorted values

func StrFltsMapAppend 

func StrFltsMapAppend(m map[string][]float64, key string, item float64)

StrFltsMapAppend appends a new item to a map of slice. 

Note: this function creates a new slice in the map if key is not found.

func StrIndexSmall 

func StrIndexSmall(a []string, val string) int

StrIndexSmall finds the index of an item in a slice of strings 

NOTE: this function is not efficient and should be used with small slices only; say smaller than 20

func StrIntMapSort 

func StrIntMapSort(m map[string]int) (sortedKeys []string)

StrIntMapSort returns sorted keys of map[string]int

func StrIntMapSortSplit 

func StrIntMapSortSplit(m map[string]int) (sortedKeys []string, sortedVals []int)

StrIntMapSortSplit returns sorted keys of map[string]int and sorted values

func StrIntsMapAppend 

func StrIntsMapAppend(m map[string][]int, key string, item int)

StrIntsMapAppend appends a new item to a map of slice. 

Note: this function creates a new slice in the map if key is not found.

func StrVals 

func StrVals(n int, val string) (s []string)

StrVals allocates a slice of strings with size==n, filled with val

func Sum 

func Sum(v []float64) (sum float64)

Sum sums all items in v 

NOTE: this is not efficient and should be used for small slices only

func Swap 

func Swap(a, b *float64)

Swap swaps two float64 numbers

func ToStrings 

func ToStrings(v []float64, format string) (s []string)

ToStrings converts a slice of float64 to a slice of strings

func Vals 

func Vals(n int, v float64) (res []float64)

Vals generates a slice of float64 filled with v

Types

type List 

type List struct {
	Vals [][]float64 // values
}

List implements a tabular list with variable number of columns 

Example:
  Vals = [][]float64{
           {0.0},
           {1.0, 1.1, 1.2, 1.3},
           {2.0, 2.1},
           {3.0, 3.1, 3.2},
         }

func (*List) Append 

func (o *List) Append(rowidx int, value float64)

Append appends items to List

type Observable 

type Observable struct {
	// contains filtered or unexported fields
}

Observable indicates that an object is observable; i.e. it has a list of interested observers

func (*Observable) AddObserver 

func (o *Observable) AddObserver(obs Observer)

AddObserver adds an object to the list of interested observers

func (*Observable) NotifyUpdate 

func (o *Observable) NotifyUpdate()

NotifyUpdate notifies observers of updates

type Observer 

type Observer interface {
	Update() // the data observed by this observer is being update
}

Observer is an interface to objects that need to observe something

type OutFcnType 

type OutFcnType func(u []float64, t float64)

OutFcnType is a function that sets the "u" array with an output @ time "t"

type Outputter 

type Outputter struct {
	Dt     float64     // time step
	DtOut  float64     // time step for output
	Tmax   float64     // final time (eventually increased to accommodate all time steps)
	Nsteps int         // number of time steps
	Every  int         // increment to output after every time step
	Tidx   int         // the index of the time step for the next output
	Nmax   int         // max number of outputs
	Idx    int         // index in the output arrays for the next output == num.outputs in the end
	T      []float64   // saved t values len = Nmax
	U      [][]float64 // saved u values @ t. [Nmax][nu]
	Fcn    OutFcnType  // function to process output. may be nil
}

Outputter helps with the output of (numerical) results 

The time loop can be something like:
  t := 0.0
  for tidx := 0; tidx < outper.Nsteps; tidx++ {
      t += outper.Dt
      ... // do something
      outper.MaybeNow(tidx, t)
  }

func NewOutputter 

func NewOutputter(dt, dtOut, tmax float64, nu int, outFcn OutFcnType) (o *Outputter)

NewOutputter creates a new Outputter 

dt     -- time step
dtOut  -- time step for output
tmax   -- final time (of simulation)
outFcn -- callback function to perform output (may be nil)
NOTE: a first output will be processed if outFcn != nil

func (*Outputter) MaybeNow 

func (o *Outputter) MaybeNow(tidx int, t float64)

MaybeNow process the output if tidx == NextIdxT

type P 

type P struct {

	// input
	N      string  `json:"n"`      // name of parameter
	V      float64 `json:"v"`      // value of parameter
	Min    float64 `json:"min"`    // min value
	Max    float64 `json:"max"`    // max value
	S      float64 `json:"s"`      // standard deviation
	D      string  `json:"d"`      // probability distribution type
	U      string  `json:"u"`      // unit (not verified)
	Adj    int     `json:"adj"`    // adjustable: unique ID (greater than zero)
	Dep    int     `json:"dep"`    // depends on "adj"
	Extra  string  `json:"extra"`  // extra data
	Inact  bool    `json:"inact"`  // parameter is inactive in optimization
	SetDef bool    `json:"setdef"` // tells model to use a default value

	// connected parameter
	Other *P // dependency: connected parameter

	// function
	Func func(t float64, x []float64) // a function y=f(t,x)
	// contains filtered or unexported fields
}

P holds numeric parameters defined by a name N and a value V.

P is convenient to store the range of allowed values in Min and Max, and other information such as standard deviation S, probability distribution type D, among others.

Dependent variables may be connected to P using Connect so when Set is called, the dependendt variable is updated as well.

Other parameters can be linked to this one via the Other data member and Func may be useful to compute y=f(t,x)

func (*P) Connect 

func (o *P) Connect(V *float64)

Connect connects parameter to variable

func (*P) Set 

func (o *P) Set(V float64)

Set sets parameter, including connected variables

type Params 

type Params []*P

Params holds many parameters 

A set of Params can be initialized as follows:

  var params Params
  params = []*P{
      {N: "klx", V: 1.0},
      {N: "kly", V: 2.0},
      {N: "klz", V: 3.0},
  }

Alternatively, see NewParams function

func NewParams 

func NewParams(pp ...interface{}) (o Params)

NewParams returns a set of parameters 

This is an alternative to initializing Params by setting slice items

A set of Params can be initialized as follows:

  params := NewParams(
      &P{N: "P1", V: 1},
      &P{N: "P2", V: 2},
      &P{N: "P3", V: 3},
  )

Alternatively, you may set slice components directly (see Params definition)

func (*Params) CheckAndGetValues 

func (o *Params) CheckAndGetValues(names []string) (values []float64)

CheckAndGetValues check min/max limits and return values. Will panic if values are outside corresponding min/max range. Will also panic if a parameter name is not found.

func (*Params) CheckAndSetVariables 

func (o *Params) CheckAndSetVariables(names []string, variables []*float64)

CheckAndSetVariables get parameter values and check limits defined in Min and Max Will panic if values are outside corresponding Min/Max range. Will also panic if a parameter name is not found.

func (*Params) CheckLimits 

func (o *Params) CheckLimits()

CheckLimits check limits of variables given in Min/Max Will panic if values are outside corresponding Min/Max range.

func (*Params) Connect 

func (o *Params) Connect(V *float64, name, caller string) (errorMessage string)

Connect connects parameter

func (*Params) ConnectSet 

func (o *Params) ConnectSet(V []*float64, names []string, caller string) (errorMessage string)

ConnectSet connects set of parameters

func (*Params) ConnectSetOpt 

func (o *Params) ConnectSetOpt(V []*float64, names []string, optional []bool, caller string) (errorMessage string)

ConnectSetOpt connects set of parameters with some being optional

func (*Params) Find 

func (o *Params) Find(name string) *P

Find finds a parameter by name 

Note: returns nil if not found

func (*Params) GetBool 

func (o *Params) GetBool(name string) bool

GetBool reads Boolean parameter or Panic Returns true if P[name] > 0; otherwise returns false Will panic if name does not exist in parameters set

func (*Params) GetBoolOrDefault 

func (o *Params) GetBoolOrDefault(name string, defaultValue bool) bool

GetBoolOrDefault reads Boolean parameter or returns default value Returns true if P[name] > 0; otherwise returns false Will return defaultValue if name does not exist in parameters set

func (*Params) GetIntOrDefault 

func (o *Params) GetIntOrDefault(name string, defaultInt int) int

GetIntOrDefault reads parameter or returns default value Will return defaultInt if name does not exist in parameters set

func (*Params) GetValue 

func (o *Params) GetValue(name string) float64

GetValue reads parameter or Panic Will panic if name does not exist in parameters set

func (*Params) GetValueOrDefault 

func (o *Params) GetValueOrDefault(name string, defaultValue float64) float64

GetValueOrDefault reads parameter or returns default value Will return defaultValue if name does not exist in parameters set

func (*Params) GetValues 

func (o *Params) GetValues(names []string) (values []float64, found []bool)

GetValues get parameter values

func (*Params) SetBool 

func (o *Params) SetBool(name string, value float64)

SetBool sets Boolean parameter or Panic Sets +1==true if value > 0; otherwise sets -1==false Will panic if name does not exist in parameters set

func (*Params) SetValue 

func (o *Params) SetValue(name string, value float64)

SetValue sets parameter or Panic Will panic if name does not exist in parameters set

func (Params) String 

func (o Params) String() (l string)

String returns a summary of parameters

type Quadruple 

type Quadruple struct {
	I int
	X float64
	Y float64
	Z float64
}

Quadruple helps to sort a quadruple of 1 int and 3 float64s

type Quadruples 

type Quadruples []*Quadruple

Quadruples helps to sort quadruples

func BuildQuadruples 

func BuildQuadruples(i []int, x, y, z []float64) (q Quadruples)

BuildQuadruples initialize Quadruples with i, x, y, and z 

Note: i, x, y, or z can be nil; but at least one of them must be non nil

func (Quadruples) I 

func (o Quadruples) I() (i []int)

I returns the 'i' in quadruples

func (Quadruples) Len 

func (o Quadruples) Len() int

Len returns the length of Quadruples

func (Quadruples) String 

func (o Quadruples) String() string

String returns the string representation of Quadruples

func (Quadruples) Swap 

func (o Quadruples) Swap(i, j int)

Swap swaps two quadruples

func (Quadruples) X 

func (o Quadruples) X() (x []float64)

X returns the 'x' in quadruples

func (Quadruples) Y 

func (o Quadruples) Y() (y []float64)

Y returns the 'y' in quadruples

func (Quadruples) Z 

func (o Quadruples) Z() (z []float64)

Z returns the 'z' in quadruples

type QuadruplesByI 

type QuadruplesByI struct{ Quadruples }

QuadruplesByI defines struct to sort Quadruples by I

func (QuadruplesByI) Less 

func (o QuadruplesByI) Less(i, j int) bool

Less compares two QuadruplesI

type QuadruplesByX 

type QuadruplesByX struct{ Quadruples }

QuadruplesByX defines struct to sort Quadruples by X

func (QuadruplesByX) Less 

func (o QuadruplesByX) Less(i, j int) bool

Less compares two QuadruplesX

type QuadruplesByY 

type QuadruplesByY struct{ Quadruples }

QuadruplesByY Sort Quadruples by Y

func (QuadruplesByY) Less 

func (o QuadruplesByY) Less(i, j int) bool

Less compares two QuadruplesY

type QuadruplesByZ 

type QuadruplesByZ struct{ Quadruples }

QuadruplesByZ defines struct to Sort Quadruples by Z

func (QuadruplesByZ) Less 

func (o QuadruplesByZ) Less(i, j int) bool

Less compares two QuadruplesZ

type SerialList 

type SerialList struct {
	Vals []float64 // values
	Ptrs []int     // pointers
}

SerialList implements a tabular list with variable number of columns using a serial representation 

Example:
    0.0
    1.0  1.1  1.2  1.3
    2.0  2.1
    3.0  3.1  3.2
becomes:
           (0)   (1)    2    3    4   (5)    6   (7)    8    9   (10)
    Vals = 0.0 | 1.0  1.1  1.2  1.3 | 2.0  2.1 | 3.0  3.1  3.2 |
    Ptrs = 0 1 5 7 10
Notes:
    len(Ptrs) = nrows + 1
    Ptrs[len(Ptrs)-1] = len(Vals)

func (*SerialList) Append 

func (o *SerialList) Append(startRow bool, value float64)

Append appends item to SerialList

func (SerialList) Print 

func (o SerialList) Print(fmt string)

Print prints the double-serial-list

type Sorter 

type Sorter struct {
	Index []int
}

Sorter builds an index list to sort arrays of any type. 

Reference:
[1] Press WH, Teukolsky SA, Vetterling WT, Fnannery BP (2007) Numerical Recipes: The Art of
    Scientific Computing. Third Edition. Cambridge University Press. 1235p.

func (*Sorter) GetSorted 

func (o *Sorter) GetSorted(a []float64) (b []float64)

GetSorted returns a copy of array 'a' sorted according to the previously built index. NOTE: the copy may be smaller if the index was built with a smaller set

func (*Sorter) GetSortedI 

func (o *Sorter) GetSortedI(a []int) (b []int)

GetSortedI returns a copy of array 'a' sorted according to the previously built index. NOTE: the copy may be smaller if the index was built with a smaller set

func (*Sorter) Init 

func (o *Sorter) Init(n int, less func(i, j int) bool)

Init builds an index indx[0..n-1] to sort an array a[0..n-1] such that a[indx[j]] is in ascending order for j=0,1,...,n-1. 

Input:
  n    -- number of items in the array to be sorted. n must be ≤ len(a)
  less -- a function that returns true if a[i] < a[j]
Reference:
[1] Press WH, Teukolsky SA, Vetterling WT, Fnannery BP (2007) Numerical Recipes: The Art of
    Scientific Computing. Third Edition. Cambridge University Press. 1235p.

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