forked from p30928647/excelize
This closes #1171, improve the compatibility and added new formula function
ref #65, added new formula function: FINV
This commit is contained in:
parent
354d1696d8
commit
61eb265c29
335
calc.go
335
calc.go
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@ -415,6 +415,7 @@ type formulaFuncs struct {
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// FALSE
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// FIND
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// FINDB
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// FINV
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// FISHER
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// FISHERINV
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// FIXED
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@ -5835,6 +5836,340 @@ func (fn *formulaFuncs) EXPONDIST(argsList *list.List) formulaArg {
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return newNumberFormulaArg(lambda.Number * math.Exp(-lambda.Number*x.Number))
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}
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// d1mach returns double precision real machine constants.
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func d1mach(i int) float64 {
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arr := []float64{
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2.2250738585072014e-308,
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1.7976931348623158e+308,
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1.1102230246251565e-16,
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2.2204460492503131e-16,
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0.301029995663981195,
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}
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if i > len(arr) {
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return 0
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}
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return arr[i-1]
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}
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// chebyshevInit determines the number of terms for the double precision
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// orthogonal series "dos" needed to insure the error is no larger
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// than "eta". Ordinarily eta will be chosen to be one-tenth machine
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// precision.
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func chebyshevInit(nos int, eta float64, dos []float64) int {
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i, e := 0, 0.0
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if nos < 1 {
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return 0
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}
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for ii := 1; ii <= nos; ii++ {
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i = nos - ii
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e += math.Abs(dos[i])
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if e > eta {
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return i
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}
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}
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return i
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}
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// chebyshevEval evaluates the n-term Chebyshev series "a" at "x".
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func chebyshevEval(n int, x float64, a []float64) float64 {
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if n < 1 || n > 1000 || x < -1.1 || x > 1.1 {
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return math.NaN()
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}
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twox, b0, b1, b2 := x*2, 0.0, 0.0, 0.0
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for i := 1; i <= n; i++ {
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b2 = b1
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b1 = b0
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b0 = twox*b1 - b2 + a[n-i]
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}
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return (b0 - b2) * 0.5
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}
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// lgammacor is an implementation for the log(gamma) correction.
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func lgammacor(x float64) float64 {
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algmcs := []float64{
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0.1666389480451863247205729650822, -0.1384948176067563840732986059135e-4,
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0.9810825646924729426157171547487e-8, -0.1809129475572494194263306266719e-10,
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0.6221098041892605227126015543416e-13, -0.3399615005417721944303330599666e-15,
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0.2683181998482698748957538846666e-17, -0.2868042435334643284144622399999e-19,
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0.3962837061046434803679306666666e-21, -0.6831888753985766870111999999999e-23,
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0.1429227355942498147573333333333e-24, -0.3547598158101070547199999999999e-26,
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0.1025680058010470912000000000000e-27, -0.3401102254316748799999999999999e-29,
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0.1276642195630062933333333333333e-30,
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}
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nalgm := chebyshevInit(15, d1mach(3), algmcs)
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xbig := 1.0 / math.Sqrt(d1mach(3))
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xmax := math.Exp(math.Min(math.Log(d1mach(2)/12.0), -math.Log(12.0*d1mach(1))))
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if x < 10.0 {
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return math.NaN()
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} else if x >= xmax {
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return 4.930380657631324e-32
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} else if x < xbig {
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tmp := 10.0 / x
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return chebyshevEval(nalgm, tmp*tmp*2.0-1.0, algmcs) / x
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}
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return 1.0 / (x * 12.0)
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}
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// logrelerr compute the relative error logarithm.
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func logrelerr(x float64) float64 {
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alnrcs := []float64{
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0.10378693562743769800686267719098e+1, -0.13364301504908918098766041553133,
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0.19408249135520563357926199374750e-1, -0.30107551127535777690376537776592e-2,
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0.48694614797154850090456366509137e-3, -0.81054881893175356066809943008622e-4,
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0.13778847799559524782938251496059e-4, -0.23802210894358970251369992914935e-5,
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0.41640416213865183476391859901989e-6, -0.73595828378075994984266837031998e-7,
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0.13117611876241674949152294345011e-7, -0.23546709317742425136696092330175e-8,
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0.42522773276034997775638052962567e-9, -0.77190894134840796826108107493300e-10,
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0.14075746481359069909215356472191e-10, -0.25769072058024680627537078627584e-11,
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0.47342406666294421849154395005938e-12, -0.87249012674742641745301263292675e-13,
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0.16124614902740551465739833119115e-13, -0.29875652015665773006710792416815e-14,
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0.55480701209082887983041321697279e-15, -0.10324619158271569595141333961932e-15,
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0.19250239203049851177878503244868e-16, -0.35955073465265150011189707844266e-17,
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0.67264542537876857892194574226773e-18, -0.12602624168735219252082425637546e-18,
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0.23644884408606210044916158955519e-19, -0.44419377050807936898878389179733e-20,
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0.83546594464034259016241293994666e-21, -0.15731559416479562574899253521066e-21,
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0.29653128740247422686154369706666e-22, -0.55949583481815947292156013226666e-23,
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0.10566354268835681048187284138666e-23, -0.19972483680670204548314999466666e-24,
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0.37782977818839361421049855999999e-25, -0.71531586889081740345038165333333e-26,
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0.13552488463674213646502024533333e-26, -0.25694673048487567430079829333333e-27,
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0.48747756066216949076459519999999e-28, -0.92542112530849715321132373333333e-29,
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0.17578597841760239233269760000000e-29, -0.33410026677731010351377066666666e-30,
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0.63533936180236187354180266666666e-31,
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}
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nlnrel := chebyshevInit(43, 0.1*d1mach(3), alnrcs)
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if x <= -1 {
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return math.NaN()
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}
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if math.Abs(x) <= 0.375 {
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return x * (1.0 - x*chebyshevEval(nlnrel, x/0.375, alnrcs))
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}
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return math.Log(x + 1.0)
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}
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// logBeta is an implementation for the log of the beta distribution
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// function.
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func logBeta(a, b float64) float64 {
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corr, p, q := 0.0, a, a
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if b < p {
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p = b
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}
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if b > q {
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q = b
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}
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if p < 0 {
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return math.NaN()
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}
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if p == 0 {
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return math.MaxFloat64
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}
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if p >= 10.0 {
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corr = lgammacor(p) + lgammacor(q) - lgammacor(p+q)
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return math.Log(q)*-0.5 + 0.918938533204672741780329736406 + corr + (p-0.5)*math.Log(p/(p+q)) + q*logrelerr(-p/(p+q))
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}
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if q >= 10 {
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corr = lgammacor(q) - lgammacor(p+q)
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val, _ := math.Lgamma(p)
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return val + corr + p - p*math.Log(p+q) + (q-0.5)*logrelerr(-p/(p+q))
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}
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return math.Log(math.Gamma(p) * (math.Gamma(q) / math.Gamma(p+q)))
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}
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// pbetaRaw is a part of pbeta for the beta distribution.
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func pbetaRaw(alnsml, ans, eps, p, pin, q, sml, x, y float64) float64 {
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if q > 1.0 {
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xb := p*math.Log(y) + q*math.Log(1.0-y) - logBeta(p, q) - math.Log(q)
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ib := int(math.Max(xb/alnsml, 0.0))
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term := math.Exp(xb - float64(ib)*alnsml)
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c := 1.0 / (1.0 - y)
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p1 := q * c / (p + q - 1.0)
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finsum := 0.0
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n := int(q)
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if q == float64(n) {
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n = n - 1
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}
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for i := 1; i <= n; i++ {
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if p1 <= 1 && term/eps <= finsum {
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break
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}
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xi := float64(i)
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term = (q - xi + 1.0) * c * term / (p + q - xi)
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if term > 1.0 {
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ib = ib - 1
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term = term * sml
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}
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if ib == 0 {
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finsum = finsum + term
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}
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}
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ans = ans + finsum
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}
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if y != x || p != pin {
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ans = 1.0 - ans
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}
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ans = math.Max(math.Min(ans, 1.0), 0.0)
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return ans
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}
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// pbeta returns distribution function of the beta distribution.
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func pbeta(x, pin, qin float64) (ans float64) {
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eps := d1mach(3)
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alneps := math.Log(eps)
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sml := d1mach(1)
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alnsml := math.Log(sml)
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y := x
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p := pin
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q := qin
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if p/(p+q) < x {
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y = 1.0 - y
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p = qin
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q = pin
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}
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if (p+q)*y/(p+1.0) < eps {
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xb := p*math.Log(math.Max(y, sml)) - math.Log(p) - logBeta(p, q)
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if xb > alnsml && y != 0.0 {
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ans = math.Exp(xb)
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}
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if y != x || p != pin {
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ans = 1.0 - ans
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}
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} else {
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ps := q - math.Floor(q)
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if ps == 0.0 {
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ps = 1.0
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}
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xb := p*math.Log(y) - logBeta(ps, p) - math.Log(p)
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if xb >= alnsml {
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ans = math.Exp(xb)
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term := ans * p
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if ps != 1.0 {
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n := int(math.Max(alneps/math.Log(y), 4.0))
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for i := 1; i <= n; i++ {
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xi := float64(i)
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term = term * (xi - ps) * y / xi
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ans = ans + term/(p+xi)
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}
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}
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}
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ans = pbetaRaw(alnsml, ans, eps, p, pin, q, sml, x, y)
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}
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return ans
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}
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// betainvProbIterator is a part of betainv for the inverse of the beta function.
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func betainvProbIterator(alpha1, alpha3, beta1, beta2, beta3, logbeta, lower, maxCumulative, prob1, prob2, upper float64, needSwap bool) float64 {
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var i, j, prev, prop4 float64
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j = 1
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for prob := 0; prob < 1000; prob++ {
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prop3 := pbeta(beta3, alpha1, beta1)
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prop3 = (prop3 - prob1) * math.Exp(logbeta+prob2*math.Log(beta3)+beta2*math.Log(1.0-beta3))
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if prop3*prop4 <= 0 {
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prev = math.Max(math.Abs(j), maxCumulative)
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}
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h := 1.0
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for iteratorCount := 0; iteratorCount < 1000; iteratorCount++ {
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j = h * prop3
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if math.Abs(j) < prev {
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i = beta3 - j
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if i >= 0 && i <= 1.0 {
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if prev <= alpha3 {
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return beta3
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}
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if math.Abs(prop3) <= alpha3 {
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return beta3
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}
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if i != 0 && i != 1.0 {
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break
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}
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}
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}
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h /= 3.0
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}
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if i == beta3 {
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return beta3
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}
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beta3, prop4 = i, prop3
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}
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return beta3
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}
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// betainv is an implementation for the quantile of the beta distribution.
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func betainv(probability, alpha, beta, lower, upper float64) float64 {
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minCumulative, maxCumulative := 1.0e-300, 3.0e-308
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lowerBound, upperBound := maxCumulative, 1.0-2.22e-16
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needSwap := false
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var alpha1, alpha2, beta1, beta2, beta3, prob1, x, y float64
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if probability <= 0.5 {
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prob1, alpha1, beta1 = probability, alpha, beta
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} else {
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prob1, alpha1, beta1, needSwap = 1.0-probability, beta, alpha, true
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}
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logbeta := logBeta(alpha, beta)
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prob2 := math.Sqrt(-math.Log(prob1 * prob1))
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prob3 := prob2 - (prob2*0.27061+2.3075)/(prob2*(prob2*0.04481+0.99229)+1)
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if alpha1 > 1 && beta1 > 1 {
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alpha2, beta2, prob2 = 1/(alpha1+alpha1-1), 1/(beta1+beta1-1), (prob3*prob3-3)/6
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x = 2 / (alpha2 + beta2)
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y = prob3*math.Sqrt(x+prob2)/x - (beta2-alpha2)*(prob2+5/6.0-2/(x*3))
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beta3 = alpha1 / (alpha1 + beta1*math.Exp(y+y))
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} else {
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beta2, prob2 = 1/(beta1*9), beta1+beta1
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beta2 = prob2 * math.Pow(1-beta2+prob3*math.Sqrt(beta2), 3)
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if beta2 <= 0 {
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beta3 = 1 - math.Exp((math.Log((1-prob1)*beta1)+logbeta)/beta1)
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} else {
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beta2 = (prob2 + alpha1*4 - 2) / beta2
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if beta2 <= 1 {
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beta3 = math.Exp((logbeta + math.Log(alpha1*prob1)) / alpha1)
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} else {
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beta3 = 1 - 2/(beta2+1)
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}
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}
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}
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beta2, prob2 = 1-beta1, 1-alpha1
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if beta3 < lowerBound {
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beta3 = lowerBound
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} else if beta3 > upperBound {
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beta3 = upperBound
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}
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alpha3 := math.Max(minCumulative, math.Pow(10.0, -13.0-2.5/(alpha1*alpha1)-0.5/(prob1*prob1)))
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beta3 = betainvProbIterator(alpha1, alpha3, beta1, beta2, beta3, logbeta, lower, maxCumulative, prob1, prob2, upper, needSwap)
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if needSwap {
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beta3 = 1.0 - beta3
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}
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return (upper-lower)*beta3 + lower
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}
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// FINV function calculates the inverse of the (right-tailed) F Probability
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// Distribution for a supplied probability. The syntax of the function is:
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//
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// FINV(probability,deg_freedom1,deg_freedom2)
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//
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func (fn *formulaFuncs) FINV(argsList *list.List) formulaArg {
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if argsList.Len() != 3 {
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return newErrorFormulaArg(formulaErrorVALUE, "FINV requires 3 arguments")
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}
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var probability, d1, d2 formulaArg
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if probability = argsList.Front().Value.(formulaArg).ToNumber(); probability.Type != ArgNumber {
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return probability
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}
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if d1 = argsList.Front().Next().Value.(formulaArg).ToNumber(); d1.Type != ArgNumber {
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return d1
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}
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if d2 = argsList.Back().Value.(formulaArg).ToNumber(); d2.Type != ArgNumber {
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return d2
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}
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if probability.Number <= 0 || probability.Number > 1 {
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return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
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}
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if d1.Number < 1 || d1.Number >= math.Pow10(10) {
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return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
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}
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if d2.Number < 1 || d2.Number >= math.Pow10(10) {
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return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
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}
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return newNumberFormulaArg((1/betainv(1.0-(1.0-probability.Number), d2.Number/2, d1.Number/2, 0, 1) - 1.0) * (d2.Number / d1.Number))
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}
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// NORMdotDIST function calculates the Normal Probability Density Function or
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// the Cumulative Normal Distribution. Function for a supplied set of
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// parameters. The syntax of the function is:
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48
calc_test.go
48
calc_test.go
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@ -851,6 +851,14 @@ func TestCalcCellValue(t *testing.T) {
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"=EXPONDIST(0.5,1,TRUE)": "0.393469340287367",
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"=EXPONDIST(0.5,1,FALSE)": "0.606530659712633",
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"=EXPONDIST(2,1,TRUE)": "0.864664716763387",
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// FINV
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"=FINV(0.2,1,2)": "3.55555555555555",
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"=FINV(0.6,1,2)": "0.380952380952381",
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"=FINV(0.6,2,2)": "0.666666666666667",
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"=FINV(0.6,4,4)": "0.763454070045235",
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"=FINV(0.5,4,8)": "0.914645355977072",
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"=FINV(0.1,79,86)": "1.32646097270444",
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"=FINV(1,40,5)": "0",
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// NORM.DIST
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"=NORM.DIST(0.8,1,0.3,TRUE)": "0.252492537546923",
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"=NORM.DIST(50,40,20,FALSE)": "0.017603266338215",
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@ -2359,6 +2367,14 @@ func TestCalcCellValue(t *testing.T) {
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"=EXPONDIST(0,1,\"\")": "strconv.ParseBool: parsing \"\": invalid syntax",
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"=EXPONDIST(-1,1,TRUE)": "#NUM!",
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"=EXPONDIST(1,0,TRUE)": "#NUM!",
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// FINV
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"=FINV()": "FINV requires 3 arguments",
|
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"=FINV(\"\",1,2)": "strconv.ParseFloat: parsing \"\": invalid syntax",
|
||||
"=FINV(0.2,\"\",2)": "strconv.ParseFloat: parsing \"\": invalid syntax",
|
||||
"=FINV(0.2,1,\"\")": "strconv.ParseFloat: parsing \"\": invalid syntax",
|
||||
"=FINV(0,1,2)": "#NUM!",
|
||||
"=FINV(0.2,0.5,2)": "#NUM!",
|
||||
"=FINV(0.2,1,0.5)": "#NUM!",
|
||||
// NORM.DIST
|
||||
"=NORM.DIST()": "NORM.DIST requires 4 arguments",
|
||||
// NORMDIST
|
||||
|
|
@ -4220,6 +4236,38 @@ func TestGetYearDays(t *testing.T) {
|
|||
}
|
||||
}
|
||||
|
||||
func TestCalcD1mach(t *testing.T) {
|
||||
assert.Equal(t, 0.0, d1mach(6))
|
||||
}
|
||||
|
||||
func TestCalcChebyshevInit(t *testing.T) {
|
||||
assert.Equal(t, 0, chebyshevInit(0, 0, nil))
|
||||
assert.Equal(t, 0, chebyshevInit(1, 0, []float64{0}))
|
||||
}
|
||||
|
||||
func TestCalcChebyshevEval(t *testing.T) {
|
||||
assert.True(t, math.IsNaN(chebyshevEval(0, 0, nil)))
|
||||
}
|
||||
|
||||
func TestCalcLgammacor(t *testing.T) {
|
||||
assert.True(t, math.IsNaN(lgammacor(9)))
|
||||
assert.Equal(t, 4.930380657631324e-32, lgammacor(3.7451940309632633e+306))
|
||||
assert.Equal(t, 8.333333333333334e-10, lgammacor(10e+07))
|
||||
}
|
||||
|
||||
func TestCalcLgammaerr(t *testing.T) {
|
||||
assert.True(t, math.IsNaN(logrelerr(-2)))
|
||||
}
|
||||
|
||||
func TestCalcLogBeta(t *testing.T) {
|
||||
assert.True(t, math.IsNaN(logBeta(-1, -1)))
|
||||
assert.Equal(t, math.MaxFloat64, logBeta(0, 0))
|
||||
}
|
||||
|
||||
func TestCalcBetainvProbIterator(t *testing.T) {
|
||||
assert.Equal(t, 1.0, betainvProbIterator(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, true))
|
||||
}
|
||||
|
||||
func TestNestedFunctionsWithOperators(t *testing.T) {
|
||||
f := NewFile()
|
||||
formulaList := map[string]string{
|
||||
|
|
|
|||
|
|
@ -39,10 +39,10 @@ type xlsxWorkbook struct {
|
|||
Conformance string `xml:"conformance,attr,omitempty"`
|
||||
FileVersion *xlsxFileVersion `xml:"fileVersion"`
|
||||
FileSharing *xlsxExtLst `xml:"fileSharing"`
|
||||
AlternateContent *xlsxAlternateContent `xml:"mc:AlternateContent"`
|
||||
DecodeAlternateContent *xlsxInnerXML `xml:"http://schemas.openxmlformats.org/markup-compatibility/2006 AlternateContent"`
|
||||
WorkbookPr *xlsxWorkbookPr `xml:"workbookPr"`
|
||||
WorkbookProtection *xlsxWorkbookProtection `xml:"workbookProtection"`
|
||||
AlternateContent *xlsxAlternateContent `xml:"mc:AlternateContent"`
|
||||
DecodeAlternateContent *xlsxInnerXML `xml:"http://schemas.openxmlformats.org/markup-compatibility/2006 AlternateContent"`
|
||||
BookViews *xlsxBookViews `xml:"bookViews"`
|
||||
Sheets xlsxSheets `xml:"sheets"`
|
||||
FunctionGroups *xlsxExtLst `xml:"functionGroups"`
|
||||
|
|
|
|||
Loading…
Reference in New Issue