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ref #65, initial formula functions: GROWTH and TREND

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xuri 2022-04-17 23:49:37 +08:00
parent 6fa950a4f8
commit 0b8965dba9
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2 changed files with 848 additions and 62 deletions
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calc.go
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@ -462,6 +462,7 @@ type formulaFuncs struct {
// GCD
// GEOMEAN
// GESTEP
// GROWTH
// HARMEAN
// HEX2BIN
// HEX2DEC
@ -682,6 +683,7 @@ type formulaFuncs struct {
// TINV
// TODAY
// TRANSPOSE
// TREND
// TRIM
// TRIMMEAN
// TRUE
@ -960,7 +962,11 @@ func (f *File) evalInfixExpFunc(sheet, cell string, token, nextToken efp.Token,
argsStack.Peek().(*list.List).PushBack(arg)
}
} else {
opdStack.Push(efp.Token{TValue: arg.Value(), TType: efp.TokenTypeOperand, TSubType: efp.TokenSubTypeNumber})
val := arg.Value()
if arg.Type == ArgMatrix && len(arg.Matrix) > 0 && len(arg.Matrix[0]) > 0 {
val = arg.Matrix[0][0].Value()
}
opdStack.Push(efp.Token{TValue: val, TType: efp.TokenTypeOperand, TSubType: efp.TokenSubTypeNumber})
}
return nil
}
@ -2015,7 +2021,6 @@ func (fn *formulaFuncs) COMPLEX(argsList *list.List) formulaArg {
// cmplx2str replace complex number string characters.
func cmplx2str(num complex128, suffix string) string {
c := fmt.Sprint(num)
realPart, imagPart := fmt.Sprint(real(num)), fmt.Sprint(imag(num))
isNum, i := isNumeric(realPart)
if isNum && i > 15 {
@ -2025,7 +2030,7 @@ func cmplx2str(num complex128, suffix string) string {
if isNum && i > 15 {
imagPart = roundPrecision(imagPart, -1)
}
c = realPart
c := realPart
if imag(num) > 0 {
c += "+"
}
@ -4073,7 +4078,8 @@ func newFormulaArgMatrix(numMtx [][]float64) (arg [][]formulaArg) {
for r, row := range numMtx {
arg = append(arg, make([]formulaArg, len(row)))
for c, cell := range row {
arg[r][c] = newNumberFormulaArg(cell)
decimal, _ := big.NewFloat(cell).SetPrec(15).Float64()
arg[r][c] = newNumberFormulaArg(decimal)
}
}
return
@ -5819,12 +5825,12 @@ func (fn *formulaFuncs) BETAdotDIST(argsList *list.List) formulaArg {
if a.Number == b.Number {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
fScale := b.Number - a.Number
x.Number = (x.Number - a.Number) / fScale
scale := b.Number - a.Number
x.Number = (x.Number - a.Number) / scale
if cumulative.Number == 1 {
return newNumberFormulaArg(getBetaDist(x.Number, alpha.Number, beta.Number))
}
return newNumberFormulaArg(getBetaDistPDF(x.Number, alpha.Number, beta.Number) / fScale)
return newNumberFormulaArg(getBetaDistPDF(x.Number, alpha.Number, beta.Number) / scale)
}
// BETADIST function calculates the cumulative beta probability density
@ -6665,12 +6671,12 @@ func getLogGamma(fZ float64) float64 {
// getLowRegIGamma returns lower regularized incomplete gamma function.
func getLowRegIGamma(fA, fX float64) float64 {
fLnFactor := fA*math.Log(fX) - fX - getLogGamma(fA)
fFactor := math.Exp(fLnFactor)
lnFactor := fA*math.Log(fX) - fX - getLogGamma(fA)
factor := math.Exp(lnFactor)
if fX > fA+1 {
return 1 - fFactor*getGammaContFraction(fA, fX)
return 1 - factor*getGammaContFraction(fA, fX)
}
return fFactor * getGammaSeries(fA, fX)
return factor * getGammaSeries(fA, fX)
}
// getChiSqDistCDF returns left tail for the Chi-Square distribution.
@ -7610,6 +7616,703 @@ func (fn *formulaFuncs) GEOMEAN(argsList *list.List) formulaArg {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
// getNewMatrix create matrix by given columns and rows.
func getNewMatrix(c, r int) (matrix [][]float64) {
for i := 0; i < c; i++ {
for j := 0; j < r; j++ {
for x := len(matrix); x <= i; x++ {
matrix = append(matrix, []float64{})
}
for y := len(matrix[i]); y <= j; y++ {
matrix[i] = append(matrix[i], 0)
}
matrix[i][j] = 0
}
}
return
}
// approxSub subtract two values, if signs are identical and the values are
// equal, will be returns 0 instead of calculating the subtraction.
func approxSub(a, b float64) float64 {
if ((a < 0 && b < 0) || (a > 0 && b > 0)) && math.Abs(a-b) < 2.22045e-016 {
return 0
}
return a - b
}
// matrixClone return a copy of all elements of the original matrix.
func matrixClone(matrix [][]float64) (cloneMatrix [][]float64) {
for i := 0; i < len(matrix); i++ {
for j := 0; j < len(matrix[i]); j++ {
for x := len(cloneMatrix); x <= i; x++ {
cloneMatrix = append(cloneMatrix, []float64{})
}
for k := len(cloneMatrix[i]); k <= j; k++ {
cloneMatrix[i] = append(cloneMatrix[i], 0)
}
cloneMatrix[i][j] = matrix[i][j]
}
}
return
}
// trendGrowthMatrixInfo defined matrix checking result.
type trendGrowthMatrixInfo struct {
trendType, nCX, nCY, nRX, nRY, M, N int
mtxX, mtxY [][]float64
}
// prepareTrendGrowthMtxX is a part of implementation of the trend growth prepare.
func prepareTrendGrowthMtxX(mtxX [][]float64) [][]float64 {
var mtx [][]float64
for i := 0; i < len(mtxX); i++ {
for j := 0; j < len(mtxX[i]); j++ {
if mtxX[i][j] == 0 {
return nil
}
for x := len(mtx); x <= j; x++ {
mtx = append(mtx, []float64{})
}
for y := len(mtx[j]); y <= i; y++ {
mtx[j] = append(mtx[j], 0)
}
mtx[j][i] = mtxX[i][j]
}
}
return mtx
}
// prepareTrendGrowthMtxY is a part of implementation of the trend growth prepare.
func prepareTrendGrowthMtxY(bLOG bool, mtxY [][]float64) [][]float64 {
var mtx [][]float64
for i := 0; i < len(mtxY); i++ {
for j := 0; j < len(mtxY[i]); j++ {
if mtxY[i][j] == 0 {
return nil
}
for x := len(mtx); x <= j; x++ {
mtx = append(mtx, []float64{})
}
for y := len(mtx[j]); y <= i; y++ {
mtx[j] = append(mtx[j], 0)
}
mtx[j][i] = mtxY[i][j]
}
}
if bLOG {
var pNewY [][]float64
for i := 0; i < len(mtxY); i++ {
for j := 0; j < len(mtxY[i]); j++ {
fVal := mtxY[i][j]
if fVal <= 0 {
return nil
}
for x := len(pNewY); x <= j; x++ {
pNewY = append(pNewY, []float64{})
}
for y := len(pNewY[j]); y <= i; y++ {
pNewY[j] = append(pNewY[j], 0)
}
pNewY[j][i] = math.Log(fVal)
}
}
mtx = pNewY
}
return mtx
}
// prepareTrendGrowth check and return the result.
func prepareTrendGrowth(bLOG bool, mtxX, mtxY [][]float64) (*trendGrowthMatrixInfo, formulaArg) {
var nCX, nRX, M, N, trendType int
nRY, nCY := len(mtxY), len(mtxY[0])
cntY := nCY * nRY
newY := prepareTrendGrowthMtxY(bLOG, mtxY)
if newY == nil {
return nil, newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
var newX [][]float64
if len(mtxX) != 0 {
nRX, nCX = len(mtxX), len(mtxX[0])
if newX = prepareTrendGrowthMtxX(mtxX); newX == nil {
return nil, newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
if nCX == nCY && nRX == nRY {
trendType, M, N = 1, 1, cntY // simple regression
} else if nCY != 1 && nRY != 1 {
return nil, newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
} else if nCY == 1 {
if nRX != nRY {
return nil, newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
}
trendType, M, N = 2, nCX, nRY
} else if nCX != nCY {
return nil, newErrorFormulaArg(formulaErrorREF, formulaErrorREF)
} else {
trendType, M, N = 3, nRX, nCY
}
} else {
newX = getNewMatrix(nCY, nRY)
nCX, nRX = nCY, nRY
num := 1.0
for i := 0; i < nRY; i++ {
for j := 0; j < nCY; j++ {
newX[j][i] = num
num++
}
}
trendType, M, N = 1, 1, cntY
}
return &trendGrowthMatrixInfo{
trendType: trendType,
nCX: nCX,
nCY: nCY,
nRX: nRX,
nRY: nRY,
M: M,
N: N,
mtxX: newX,
mtxY: newY,
}, newEmptyFormulaArg()
}
// calcPosition calculate position for matrix by given index.
func calcPosition(mtx [][]float64, idx int) (row, col int) {
rowSize := len(mtx[0])
col = idx
if rowSize > 1 {
col = idx / rowSize
}
row = idx - col*rowSize
return
}
// getDouble returns float64 data type value in the matrix by given index.
func getDouble(mtx [][]float64, idx int) float64 {
row, col := calcPosition(mtx, idx)
return mtx[col][row]
}
// putDouble set a float64 data type value in the matrix by given index.
func putDouble(mtx [][]float64, idx int, val float64) {
row, col := calcPosition(mtx, idx)
mtx[col][row] = val
}
// calcMeanOverAll returns mean of the given matrix by over all element.
func calcMeanOverAll(mtx [][]float64, n int) float64 {
var sum float64
for i := 0; i < len(mtx); i++ {
for j := 0; j < len(mtx[i]); j++ {
sum += mtx[i][j]
}
}
return sum / float64(n)
}
// calcSumProduct returns uses the matrices as vectors of length M over all
// element.
func calcSumProduct(mtxA, mtxB [][]float64, m int) float64 {
sum := 0.0
for i := 0; i < m; i++ {
sum += getDouble(mtxA, i) * getDouble(mtxB, i)
}
return sum
}
// calcColumnMeans calculates means of the columns of matrix.
func calcColumnMeans(mtxX, mtxRes [][]float64, c, r int) {
for i := 0; i < c; i++ {
var sum float64
for k := 0; k < r; k++ {
sum += mtxX[i][k]
}
putDouble(mtxRes, i, sum/float64(r))
}
return
}
// calcColumnsDelta calculates subtract of the columns of matrix.
func calcColumnsDelta(mtx, columnMeans [][]float64, c, r int) {
for i := 0; i < c; i++ {
for k := 0; k < r; k++ {
mtx[i][k] = approxSub(mtx[i][k], getDouble(columnMeans, i))
}
}
}
// calcSign returns sign by given value, no mathematical signum, but used to
// switch between adding and subtracting.
func calcSign(val float64) float64 {
if val > 0 {
return 1
}
return -1
}
// calcColsMaximumNorm is a special version for use within QR
// decomposition. Maximum norm of column index c starting in row index r;
// matrix A has count n rows.
func calcColsMaximumNorm(mtxA [][]float64, c, r, n int) float64 {
var norm float64
for row := r; row < n; row++ {
if norm < math.Abs(mtxA[c][row]) {
norm = math.Abs(mtxA[c][row])
}
}
return norm
}
// calcFastMult returns multiply n x m matrix A with m x l matrix B to n x l matrix R.
func calcFastMult(mtxA, mtxB, mtxR [][]float64, n, m, l int) {
var sum float64
for row := 0; row < n; row++ {
for col := 0; col < l; col++ {
sum = 0.0
for k := 0; k < m; k++ {
sum += mtxA[k][row] * mtxB[col][k]
}
mtxR[col][row] = sum
}
}
}
// calcRowsEuclideanNorm is a special version for use within QR
// decomposition. Euclidean norm of column index c starting in row index r;
// matrix a has count n rows.
func calcRowsEuclideanNorm(mtxA [][]float64, c, r, n int) float64 {
var norm float64
for row := r; row < n; row++ {
norm += mtxA[c][row] * mtxA[c][row]
}
return math.Sqrt(norm)
}
// calcRowsSumProduct is a special version for use within QR decomposition.
// <A(a);B(b)> starting in row index r;
// a and b are indices of columns, matrices A and B have count n rows.
func calcRowsSumProduct(mtxA [][]float64, a int, mtxB [][]float64, b, r, n int) float64 {
var result float64
for row := r; row < n; row++ {
result += mtxA[a][row] * mtxB[b][row]
}
return result
}
// calcSolveWithUpperRightTriangle solve for X in R*X=S using back substitution.
func calcSolveWithUpperRightTriangle(mtxA [][]float64, vecR []float64, mtxS [][]float64, k int, bIsTransposed bool) {
var row int
for rowp1 := k; rowp1 > 0; rowp1-- {
row = rowp1 - 1
sum := getDouble(mtxS, row)
for col := rowp1; col < k; col++ {
if bIsTransposed {
sum -= mtxA[row][col] * getDouble(mtxS, col)
} else {
sum -= mtxA[col][row] * getDouble(mtxS, col)
}
}
putDouble(mtxS, row, sum/vecR[row])
}
}
// calcRowQRDecomposition calculates a QR decomposition with Householder
// reflection.
func calcRowQRDecomposition(mtxA [][]float64, vecR []float64, k, n int) bool {
for col := 0; col < k; col++ {
scale := calcColsMaximumNorm(mtxA, col, col, n)
if scale == 0 {
return false
}
for row := col; row < n; row++ {
mtxA[col][row] = mtxA[col][row] / scale
}
euclid := calcRowsEuclideanNorm(mtxA, col, col, n)
factor := 1.0 / euclid / (euclid + math.Abs(mtxA[col][col]))
signum := calcSign(mtxA[col][col])
mtxA[col][col] = mtxA[col][col] + signum*euclid
vecR[col] = -signum * scale * euclid
// apply Householder transformation to A
for c := col + 1; c < k; c++ {
sum := calcRowsSumProduct(mtxA, col, mtxA, c, col, n)
for row := col; row < n; row++ {
mtxA[c][row] = mtxA[c][row] - sum*factor*mtxA[col][row]
}
}
}
return true
}
// calcApplyColsHouseholderTransformation transposed matrices A and Y.
func calcApplyColsHouseholderTransformation(mtxA [][]float64, r int, mtxY [][]float64, n int) {
denominator := calcColsSumProduct(mtxA, r, mtxA, r, r, n)
numerator := calcColsSumProduct(mtxA, r, mtxY, 0, r, n)
factor := 2 * (numerator / denominator)
for col := r; col < n; col++ {
putDouble(mtxY, col, getDouble(mtxY, col)-factor*mtxA[col][r])
}
}
// calcRowMeans calculates means of the rows of matrix.
func calcRowMeans(mtxX, mtxRes [][]float64, c, r int) {
for k := 0; k < r; k++ {
var fSum float64
for i := 0; i < c; i++ {
fSum += mtxX[i][k]
}
mtxRes[k][0] = fSum / float64(c)
}
}
// calcRowsDelta calculates subtract of the rows of matrix.
func calcRowsDelta(mtx, rowMeans [][]float64, c, r int) {
for k := 0; k < r; k++ {
for i := 0; i < c; i++ {
mtx[i][k] = approxSub(mtx[i][k], rowMeans[k][0])
}
}
}
// calcColumnMaximumNorm returns maximum norm of row index R starting in col
// index C; matrix A has count N columns.
func calcColumnMaximumNorm(mtxA [][]float64, r, c, n int) float64 {
var norm float64
for col := c; col < n; col++ {
if norm < math.Abs(mtxA[col][r]) {
norm = math.Abs(mtxA[col][r])
}
}
return norm
}
// calcColsEuclideanNorm returns euclidean norm of row index R starting in
// column index C; matrix A has count N columns.
func calcColsEuclideanNorm(mtxA [][]float64, r, c, n int) float64 {
var norm float64
for col := c; col < n; col++ {
norm += (mtxA[col][r]) * (mtxA[col][r])
}
return math.Sqrt(norm)
}
// calcColsSumProduct returns sum product for given matrix.
func calcColsSumProduct(mtxA [][]float64, a int, mtxB [][]float64, b, c, n int) float64 {
var result float64
for col := c; col < n; col++ {
result += mtxA[col][a] * mtxB[col][b]
}
return result
}
// calcColQRDecomposition same with transposed matrix A, N is count of
// columns, k count of rows.
func calcColQRDecomposition(mtxA [][]float64, vecR []float64, k, n int) bool {
var sum float64
for row := 0; row < k; row++ {
// calculate vector u of the householder transformation
scale := calcColumnMaximumNorm(mtxA, row, row, n)
if scale == 0 {
return false
}
for col := row; col < n; col++ {
mtxA[col][row] = mtxA[col][row] / scale
}
euclid := calcColsEuclideanNorm(mtxA, row, row, n)
factor := 1 / euclid / (euclid + math.Abs(mtxA[row][row]))
signum := calcSign(mtxA[row][row])
mtxA[row][row] = mtxA[row][row] + signum*euclid
vecR[row] = -signum * scale * euclid
// apply Householder transformation to A
for r := row + 1; r < k; r++ {
sum = calcColsSumProduct(mtxA, row, mtxA, r, row, n)
for col := row; col < n; col++ {
mtxA[col][r] = mtxA[col][r] - sum*factor*mtxA[col][row]
}
}
}
return true
}
// calcApplyRowsHouseholderTransformation applies a Householder transformation to a
// column vector Y with is given as Nx1 Matrix. The vector u, from which the
// Householder transformation is built, is the column part in matrix A, with
// column index c, starting with row index c. A is the result of the QR
// decomposition as obtained from calcRowQRDecomposition.
func calcApplyRowsHouseholderTransformation(mtxA [][]float64, c int, mtxY [][]float64, n int) {
denominator := calcRowsSumProduct(mtxA, c, mtxA, c, c, n)
numerator := calcRowsSumProduct(mtxA, c, mtxY, 0, c, n)
factor := 2 * (numerator / denominator)
for row := c; row < n; row++ {
putDouble(mtxY, row, getDouble(mtxY, row)-factor*mtxA[c][row])
}
}
// calcTrendGrowthSimpleRegression calculate simple regression for the calcTrendGrowth.
func calcTrendGrowthSimpleRegression(bConstant, bGrowth bool, mtxY, mtxX, newX, mtxRes [][]float64, meanY float64, N int) {
var meanX float64
if bConstant {
meanX = calcMeanOverAll(mtxX, N)
for i := 0; i < len(mtxX); i++ {
for j := 0; j < len(mtxX[i]); j++ {
mtxX[i][j] = approxSub(mtxX[i][j], meanX)
}
}
}
sumXY := calcSumProduct(mtxX, mtxY, N)
sumX2 := calcSumProduct(mtxX, mtxX, N)
slope := sumXY / sumX2
var help float64
var intercept float64
if bConstant {
intercept = meanY - slope*meanX
for i := 0; i < len(mtxRes); i++ {
for j := 0; j < len(mtxRes[i]); j++ {
help = newX[i][j]*slope + intercept
if bGrowth {
mtxRes[i][j] = math.Exp(help)
} else {
mtxRes[i][j] = help
}
}
}
} else {
for i := 0; i < len(mtxRes); i++ {
for j := 0; j < len(mtxRes[i]); j++ {
help = newX[i][j] * slope
if bGrowth {
mtxRes[i][j] = math.Exp(help)
} else {
mtxRes[i][j] = help
}
}
}
}
}
// calcTrendGrowthMultipleRegressionPart1 calculate multiple regression for the
// calcTrendGrowth.
func calcTrendGrowthMultipleRegressionPart1(bConstant, bGrowth bool, mtxY, mtxX, newX, mtxRes [][]float64, meanY float64, RXN, K, N int) {
vecR := make([]float64, N) // for QR decomposition
means := getNewMatrix(K, 1) // mean of each column
slopes := getNewMatrix(1, K) // from b1 to bK
if len(means) == 0 || len(slopes) == 0 {
return
}
if bConstant {
calcColumnMeans(mtxX, means, K, N)
calcColumnsDelta(mtxX, means, K, N)
}
if !calcRowQRDecomposition(mtxX, vecR, K, N) {
return
}
// Later on we will divide by elements of vecR, so make sure that they aren't zero.
bIsSingular := false
for row := 0; row < K && !bIsSingular; row++ {
bIsSingular = bIsSingular || vecR[row] == 0
}
if bIsSingular {
return
}
for col := 0; col < K; col++ {
calcApplyRowsHouseholderTransformation(mtxX, col, mtxY, N)
}
for col := 0; col < K; col++ {
putDouble(slopes, col, getDouble(mtxY, col))
}
calcSolveWithUpperRightTriangle(mtxX, vecR, slopes, K, false)
// Fill result matrix
calcFastMult(newX, slopes, mtxRes, RXN, K, 1)
if bConstant {
intercept := meanY - calcSumProduct(means, slopes, K)
for row := 0; row < RXN; row++ {
mtxRes[0][row] = mtxRes[0][row] + intercept
}
}
if bGrowth {
for i := 0; i < RXN; i++ {
putDouble(mtxRes, i, math.Exp(getDouble(mtxRes, i)))
}
}
}
// calcTrendGrowthMultipleRegressionPart2 calculate multiple regression for the
// calcTrendGrowth.
func calcTrendGrowthMultipleRegressionPart2(bConstant, bGrowth bool, mtxY, mtxX, newX, mtxRes [][]float64, meanY float64, nCXN, K, N int) {
vecR := make([]float64, N) // for QR decomposition
means := getNewMatrix(K, 1) // mean of each row
slopes := getNewMatrix(K, 1) // row from b1 to bK
if len(means) == 0 || len(slopes) == 0 {
return
}
if bConstant {
calcRowMeans(mtxX, means, N, K)
calcRowsDelta(mtxX, means, N, K)
}
if !calcColQRDecomposition(mtxX, vecR, K, N) {
return
}
// later on we will divide by elements of vecR, so make sure that they aren't zero
bIsSingular := false
for row := 0; row < K && !bIsSingular; row++ {
bIsSingular = bIsSingular || vecR[row] == 0
}
if bIsSingular {
return
}
for row := 0; row < K; row++ {
calcApplyColsHouseholderTransformation(mtxX, row, mtxY, N)
}
for col := 0; col < K; col++ {
putDouble(slopes, col, getDouble(mtxY, col))
}
calcSolveWithUpperRightTriangle(mtxX, vecR, slopes, K, true)
// fill result matrix
calcFastMult(slopes, newX, mtxRes, 1, K, nCXN)
if bConstant {
fIntercept := meanY - calcSumProduct(means, slopes, K)
for col := 0; col < nCXN; col++ {
mtxRes[col][0] = mtxRes[col][0] + fIntercept
}
}
if bGrowth {
for i := 0; i < nCXN; i++ {
putDouble(mtxRes, i, math.Exp(getDouble(mtxRes, i)))
}
}
}
// calcTrendGrowthRegression is a part of implementation of the calcTrendGrowth.
func calcTrendGrowthRegression(bConstant, bGrowth bool, trendType, nCXN, nRXN, K, N int, mtxY, mtxX, newX, mtxRes [][]float64) {
if len(mtxRes) == 0 {
return
}
var meanY float64
if bConstant {
copyX, copyY := matrixClone(mtxX), matrixClone(mtxY)
mtxX, mtxY = copyX, copyY
meanY = calcMeanOverAll(mtxY, N)
for i := 0; i < len(mtxY); i++ {
for j := 0; j < len(mtxY[i]); j++ {
mtxY[i][j] = approxSub(mtxY[i][j], meanY)
}
}
}
switch trendType {
case 1:
calcTrendGrowthSimpleRegression(bConstant, bGrowth, mtxY, mtxX, newX, mtxRes, meanY, N)
break
case 2:
calcTrendGrowthMultipleRegressionPart1(bConstant, bGrowth, mtxY, mtxX, newX, mtxRes, meanY, nRXN, K, N)
break
default:
calcTrendGrowthMultipleRegressionPart2(bConstant, bGrowth, mtxY, mtxX, newX, mtxRes, meanY, nCXN, K, N)
}
}
// calcTrendGrowth returns values along a predicted exponential trend.
func calcTrendGrowth(mtxY, mtxX, newX [][]float64, bConstant, bGrowth bool) ([][]float64, formulaArg) {
getMatrixParams, errArg := prepareTrendGrowth(bGrowth, mtxX, mtxY)
if errArg.Type != ArgEmpty {
return nil, errArg
}
trendType := getMatrixParams.trendType
nCX := getMatrixParams.nCX
nRX := getMatrixParams.nRX
K := getMatrixParams.M
N := getMatrixParams.N
mtxX = getMatrixParams.mtxX
mtxY = getMatrixParams.mtxY
// checking if data samples are enough
if (bConstant && (N < K+1)) || (!bConstant && (N < K)) || (N < 1) || (K < 1) {
return nil, errArg
}
// set the default newX if necessary
nCXN, nRXN := nCX, nRX
if len(newX) == 0 {
newX = matrixClone(mtxX) // mtxX will be changed to X-meanX
} else {
nRXN, nCXN = len(newX[0]), len(newX)
if (trendType == 2 && K != nCXN) || (trendType == 3 && K != nRXN) {
return nil, errArg
}
}
var mtxRes [][]float64
switch trendType {
case 1:
mtxRes = getNewMatrix(nCXN, nRXN)
break
case 2:
mtxRes = getNewMatrix(1, nRXN)
break
default:
mtxRes = getNewMatrix(nCXN, 1)
}
calcTrendGrowthRegression(bConstant, bGrowth, trendType, nCXN, nRXN, K, N, mtxY, mtxX, newX, mtxRes)
return mtxRes, errArg
}
// trendGrowth is an implementation of the formula functions GROWTH and TREND.
func (fn *formulaFuncs) trendGrowth(name string, argsList *list.List) formulaArg {
if argsList.Len() < 1 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s requires at least 1 argument", name))
}
if argsList.Len() > 4 {
return newErrorFormulaArg(formulaErrorVALUE, fmt.Sprintf("%s allows at most 4 arguments", name))
}
var knowY, knowX, newX [][]float64
var errArg formulaArg
constArg := newBoolFormulaArg(true)
knowY, errArg = newNumberMatrix(argsList.Front().Value.(formulaArg), false)
if errArg.Type == ArgError {
return errArg
}
if argsList.Len() > 1 {
knowX, errArg = newNumberMatrix(argsList.Front().Next().Value.(formulaArg), false)
if errArg.Type == ArgError {
return errArg
}
}
if argsList.Len() > 2 {
newX, errArg = newNumberMatrix(argsList.Front().Next().Next().Value.(formulaArg), false)
if errArg.Type == ArgError {
return errArg
}
}
if argsList.Len() > 3 {
if constArg = argsList.Back().Value.(formulaArg).ToBool(); constArg.Type != ArgNumber {
return constArg
}
}
var mtxNewX [][]float64
for i := 0; i < len(newX); i++ {
for j := 0; j < len(newX[i]); j++ {
for x := len(mtxNewX); x <= j; x++ {
mtxNewX = append(mtxNewX, []float64{})
}
for k := len(mtxNewX[j]); k <= i; k++ {
mtxNewX[j] = append(mtxNewX[j], 0)
}
mtxNewX[j][i] = newX[i][j]
}
}
mtx, errArg := calcTrendGrowth(knowY, knowX, mtxNewX, constArg.Number == 1, name == "GROWTH")
if errArg.Type != ArgEmpty {
return errArg
}
return newMatrixFormulaArg(newFormulaArgMatrix(mtx))
}
// GROWTH function calculates the exponential growth curve through a given set
// of y-values and (optionally), one or more sets of x-values. The function
// then extends the curve to calculate additional y-values for a further
// supplied set of new x-values. The syntax of the function is:
//
// GROWTH(known_y's,[known_x's],[new_x's],[const])
//
func (fn *formulaFuncs) GROWTH(argsList *list.List) formulaArg {
return fn.trendGrowth("GROWTH", argsList)
}
// HARMEAN function calculates the harmonic mean of a supplied set of values.
// The syntax of the function is:
//
@ -9652,92 +10355,98 @@ func (fn *formulaFuncs) TINV(argsList *list.List) formulaArg {
return fn.TdotINVdot2T(argsList)
}
// TREND function calculates the linear trend line through a given set of
// y-values and (optionally), a given set of x-values. The function then
// extends the linear trendline to calculate additional y-values for a further
// supplied set of new x-values. The syntax of the function is:
//
// TREND(known_y's,[known_x's],[new_x's],[const])
//
func (fn *formulaFuncs) TREND(argsList *list.List) formulaArg {
return fn.trendGrowth("TREND", argsList)
}
// tTest calculates the probability associated with the Student's T Test.
func tTest(bTemplin bool, pMat1, pMat2 [][]formulaArg, nC1, nC2, nR1, nR2 int, fT, fF float64) (float64, float64, bool) {
var fCount1, fCount2, fSum1, fSumSqr1, fSum2, fSumSqr2 float64
func tTest(bTemplin bool, mtx1, mtx2 [][]formulaArg, c1, c2, r1, r2 int, fT, fF float64) (float64, float64, bool) {
var cnt1, cnt2, sum1, sumSqr1, sum2, sumSqr2 float64
var fVal formulaArg
for i := 0; i < nC1; i++ {
for j := 0; j < nR1; j++ {
fVal = pMat1[i][j].ToNumber()
for i := 0; i < c1; i++ {
for j := 0; j < r1; j++ {
fVal = mtx1[i][j].ToNumber()
if fVal.Type == ArgNumber {
fSum1 += fVal.Number
fSumSqr1 += fVal.Number * fVal.Number
fCount1++
sum1 += fVal.Number
sumSqr1 += fVal.Number * fVal.Number
cnt1++
}
}
}
for i := 0; i < nC2; i++ {
for j := 0; j < nR2; j++ {
fVal = pMat2[i][j].ToNumber()
for i := 0; i < c2; i++ {
for j := 0; j < r2; j++ {
fVal = mtx2[i][j].ToNumber()
if fVal.Type == ArgNumber {
fSum2 += fVal.Number
fSumSqr2 += fVal.Number * fVal.Number
fCount2++
sum2 += fVal.Number
sumSqr2 += fVal.Number * fVal.Number
cnt2++
}
}
}
if fCount1 < 2.0 || fCount2 < 2.0 {
if cnt1 < 2.0 || cnt2 < 2.0 {
return 0, 0, false
}
if bTemplin {
fS1 := (fSumSqr1 - fSum1*fSum1/fCount1) / (fCount1 - 1) / fCount1
fS2 := (fSumSqr2 - fSum2*fSum2/fCount2) / (fCount2 - 1) / fCount2
fS1 := (sumSqr1 - sum1*sum1/cnt1) / (cnt1 - 1) / cnt1
fS2 := (sumSqr2 - sum2*sum2/cnt2) / (cnt2 - 1) / cnt2
if fS1+fS2 == 0 {
return 0, 0, false
}
c := fS1 / (fS1 + fS2)
fT = math.Abs(fSum1/fCount1-fSum2/fCount2) / math.Sqrt(fS1+fS2)
fF = 1 / (c*c/(fCount1-1) + (1-c)*(1-c)/(fCount2-1))
fT = math.Abs(sum1/cnt1-sum2/cnt2) / math.Sqrt(fS1+fS2)
fF = 1 / (c*c/(cnt1-1) + (1-c)*(1-c)/(cnt2-1))
return fT, fF, true
}
fS1 := (fSumSqr1 - fSum1*fSum1/fCount1) / (fCount1 - 1)
fS2 := (fSumSqr2 - fSum2*fSum2/fCount2) / (fCount2 - 1)
fT = math.Abs(fSum1/fCount1-fSum2/fCount2) / math.Sqrt((fCount1-1)*fS1+(fCount2-1)*fS2) * math.Sqrt(fCount1*fCount2*(fCount1+fCount2-2)/(fCount1+fCount2))
fF = fCount1 + fCount2 - 2
fS1 := (sumSqr1 - sum1*sum1/cnt1) / (cnt1 - 1)
fS2 := (sumSqr2 - sum2*sum2/cnt2) / (cnt2 - 1)
fT = math.Abs(sum1/cnt1-sum2/cnt2) / math.Sqrt((cnt1-1)*fS1+(cnt2-1)*fS2) * math.Sqrt(cnt1*cnt2*(cnt1+cnt2-2)/(cnt1+cnt2))
fF = cnt1 + cnt2 - 2
return fT, fF, true
}
// tTest is an implementation of the formula function TTEST.
func (fn *formulaFuncs) tTest(pMat1, pMat2 [][]formulaArg, fTails, fTyp float64) formulaArg {
func (fn *formulaFuncs) tTest(mtx1, mtx2 [][]formulaArg, fTails, fTyp float64) formulaArg {
var fT, fF float64
nC1 := len(pMat1)
nC2 := len(pMat2)
nR1 := len(pMat1[0])
nR2 := len(pMat2[0])
ok := true
c1, c2, r1, r2, ok := len(mtx1), len(mtx2), len(mtx1[0]), len(mtx2[0]), true
if fTyp == 1 {
if nC1 != nC2 || nR1 != nR2 {
if c1 != c2 || r1 != r2 {
return newErrorFormulaArg(formulaErrorNA, formulaErrorNA)
}
var fCount, fSum1, fSum2, fSumSqrD float64
var cnt, sum1, sum2, sumSqrD float64
var fVal1, fVal2 formulaArg
for i := 0; i < nC1; i++ {
for j := 0; j < nR1; j++ {
fVal1 = pMat1[i][j].ToNumber()
fVal2 = pMat2[i][j].ToNumber()
for i := 0; i < c1; i++ {
for j := 0; j < r1; j++ {
fVal1, fVal2 = mtx1[i][j].ToNumber(), mtx2[i][j].ToNumber()
if fVal1.Type != ArgNumber || fVal2.Type != ArgNumber {
continue
}
fSum1 += fVal1.Number
fSum2 += fVal2.Number
fSumSqrD += (fVal1.Number - fVal2.Number) * (fVal1.Number - fVal2.Number)
fCount++
sum1 += fVal1.Number
sum2 += fVal2.Number
sumSqrD += (fVal1.Number - fVal2.Number) * (fVal1.Number - fVal2.Number)
cnt++
}
}
if fCount < 1 {
if cnt < 1 {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)
}
fSumD := fSum1 - fSum2
fDivider := fCount*fSumSqrD - fSumD*fSumD
if fDivider == 0 {
sumD := sum1 - sum2
divider := cnt*sumSqrD - sumD*sumD
if divider == 0 {
return newErrorFormulaArg(formulaErrorDIV, formulaErrorDIV)
}
fT = math.Abs(fSumD) * math.Sqrt((fCount-1)/fDivider)
fF = fCount - 1
fT = math.Abs(sumD) * math.Sqrt((cnt-1)/divider)
fF = cnt - 1
} else if fTyp == 2 {
fT, fF, ok = tTest(false, pMat1, pMat2, nC1, nC2, nR1, nR2, fT, fF)
fT, fF, ok = tTest(false, mtx1, mtx2, c1, c2, r1, r2, fT, fF)
} else {
fT, fF, ok = tTest(true, pMat1, pMat2, nC1, nC2, nR1, nR2, fT, fF)
fT, fF, ok = tTest(true, mtx1, mtx2, c1, c2, r1, r2, fT, fF)
}
if !ok {
return newErrorFormulaArg(formulaErrorNUM, formulaErrorNUM)

85
calc_test.go
View File

@ -572,9 +572,9 @@ func TestCalcCellValue(t *testing.T) {
"=IMPRODUCT(COMPLEX(5,2),COMPLEX(0,1))": "-2+5i",
"=IMPRODUCT(A1:C1)": "4",
// MINVERSE
"=MINVERSE(A1:B2)": "",
"=MINVERSE(A1:B2)": "-0",
// MMULT
"=MMULT(A4:A4,A4:A4)": "",
"=MMULT(A4:A4,A4:A4)": "0",
// MOD
"=MOD(6,4)": "2",
"=MOD(6,3)": "0",
@ -597,7 +597,7 @@ func TestCalcCellValue(t *testing.T) {
`=MULTINOMIAL("",3,1,2,5)`: "27720",
"=MULTINOMIAL(MULTINOMIAL(1))": "1",
// _xlfn.MUNIT
"=_xlfn.MUNIT(4)": "",
"=_xlfn.MUNIT(4)": "1",
// ODD
"=ODD(22)": "23",
"=ODD(1.22)": "3",
@ -4444,6 +4444,83 @@ func TestCalcFORMULATEXT(t *testing.T) {
}
}
func TestCalcGROWTHandTREND(t *testing.T) {
cellData := [][]interface{}{
{"known_x's", "known_y's", 0, -1},
{1, 10, 1},
{2, 20, 1},
{3, 40},
{4, 80},
{},
{"new_x's", "new_y's"},
{5},
{6},
{7},
}
f := prepareCalcData(cellData)
formulaList := map[string]string{
"=GROWTH(A2:B2)": "1",
"=GROWTH(B2:B5,A2:A5,A8:A10)": "160",
"=GROWTH(B2:B5,A2:A5,A8:A10,FALSE)": "467.84375",
"=GROWTH(A4:A5,A2:B3,A8:A10,FALSE)": "",
"=GROWTH(A3:A5,A2:B4,A2:B3)": "2",
"=GROWTH(A4:A5,A2:B3)": "",
"=GROWTH(A2:B2,A2:B3)": "",
"=GROWTH(A2:B2,A2:B3,A2:B3,FALSE)": "1.28399658203125",
"=GROWTH(A2:B2,A4:B5,A4:B5,FALSE)": "1",
"=GROWTH(A3:C3,A2:C3,A2:B3)": "2",
"=TREND(A2:B2)": "1",
"=TREND(B2:B5,A2:A5,A8:A10)": "95",
"=TREND(B2:B5,A2:A5,A8:A10,FALSE)": "81.66796875",
"=TREND(A4:A5,A2:B3,A8:A10,FALSE)": "",
"=TREND(A4:A5,A2:B3,A2:B3,FALSE)": "1.5",
"=TREND(A3:A5,A2:B4,A2:B3)": "2",
"=TREND(A4:A5,A2:B3)": "",
"=TREND(A2:B2,A2:B3)": "",
"=TREND(A2:B2,A2:B3,A2:B3,FALSE)": "1",
"=TREND(A2:B2,A4:B5,A4:B5,FALSE)": "1",
"=TREND(A3:C3,A2:C3,A2:B3)": "2",
}
for formula, expected := range formulaList {
assert.NoError(t, f.SetCellFormula("Sheet1", "C1", formula))
result, err := f.CalcCellValue("Sheet1", "C1")
assert.NoError(t, err, formula)
assert.Equal(t, expected, result, formula)
}
calcError := map[string]string{
"=GROWTH()": "GROWTH requires at least 1 argument",
"=GROWTH(B2:B5,A2:A5,A8:A10,TRUE,0)": "GROWTH allows at most 4 arguments",
"=GROWTH(A1:B1,A2:A5,A8:A10,TRUE)": "strconv.ParseFloat: parsing \"known_x's\": invalid syntax",
"=GROWTH(B2:B5,A1:B1,A8:A10,TRUE)": "strconv.ParseFloat: parsing \"known_x's\": invalid syntax",
"=GROWTH(B2:B5,A2:A5,A1:B1,TRUE)": "strconv.ParseFloat: parsing \"known_x's\": invalid syntax",
"=GROWTH(B2:B5,A2:A5,A8:A10,\"\")": "strconv.ParseBool: parsing \"\": invalid syntax",
"=GROWTH(A2:B3,A4:B4)": "#REF!",
"=GROWTH(A4:B4,A2:A2)": "#REF!",
"=GROWTH(A2:A2,A4:A5)": "#REF!",
"=GROWTH(C1:C1,A2:A3)": "#NUM!",
"=GROWTH(D1:D1,A2:A3)": "#NUM!",
"=GROWTH(A2:A3,C1:C1)": "#NUM!",
"=TREND()": "TREND requires at least 1 argument",
"=TREND(B2:B5,A2:A5,A8:A10,TRUE,0)": "TREND allows at most 4 arguments",
"=TREND(A1:B1,A2:A5,A8:A10,TRUE)": "strconv.ParseFloat: parsing \"known_x's\": invalid syntax",
"=TREND(B2:B5,A1:B1,A8:A10,TRUE)": "strconv.ParseFloat: parsing \"known_x's\": invalid syntax",
"=TREND(B2:B5,A2:A5,A1:B1,TRUE)": "strconv.ParseFloat: parsing \"known_x's\": invalid syntax",
"=TREND(B2:B5,A2:A5,A8:A10,\"\")": "strconv.ParseBool: parsing \"\": invalid syntax",
"=TREND(A2:B3,A4:B4)": "#REF!",
"=TREND(A4:B4,A2:A2)": "#REF!",
"=TREND(A2:A2,A4:A5)": "#REF!",
"=TREND(C1:C1,A2:A3)": "#NUM!",
"=TREND(D1:D1,A2:A3)": "#REF!",
"=TREND(A2:A3,C1:C1)": "#NUM!",
}
for formula, expected := range calcError {
assert.NoError(t, f.SetCellFormula("Sheet1", "C1", formula))
result, err := f.CalcCellValue("Sheet1", "C1")
assert.EqualError(t, err, expected, formula)
assert.Equal(t, "", result, formula)
}
}
func TestCalcHLOOKUP(t *testing.T) {
cellData := [][]interface{}{
{"Example Result Table"},
@ -4953,7 +5030,7 @@ func TestCalcMODE(t *testing.T) {
formulaList := map[string]string{
"=MODE(A1:A10)": "3",
"=MODE(B1:B6)": "2",
"=MODE.MULT(A1:A10)": "",
"=MODE.MULT(A1:A10)": "3",
"=MODE.SNGL(A1:A10)": "3",
"=MODE.SNGL(B1:B6)": "2",
}