func indexCheck(c, A, b *base.Matrix) (m, n int) {
// Check matrix rows and columns.
m1, n1 := A.Size() // numRows, numCols
m2, _ := b.Size()
_, n2 := c.Size()
if m1 == m2 && n1 == n2 {
if m1 < n1 {
m = m1
n = n1
} else {
return 0, -1
}
} else {
return 0, -2
}
return m, n
}
func Simplex(c, A, b *base.Matrix) (z float64, x base.Vector, iB []int, iN []int, err error) {
// Check matrix rows and columns.
m, n := indexCheck(c, A, b)
switch n {
case -1:
return 0, nil, nil, nil, ErrorIllegalIndex
case -2:
return 0, nil, nil, nil, ErrorDimensionMismatch
}
// Prepare index list for creating matrices in each iteration.
index := make([]int, n, n)
for i := 1; i <= n; i++ {
index[i-1] = i
}
iB = index[n-m : n]
iN = index[0 : n-m]
// Define variables specified in Simplex algorithm.
var X, Z, cB, cN, B, N *base.Matrix
var k, l int
var σmax, βmin float64
// For starting the iteration.
k = -1
for k != 0 {
// Initialize matrices.
X = base.MakeZero(n, 1)
cB = c.GetCols(iB)
cN = c.GetCols(iN)
B = A.GetCols(iB)
N = A.GetCols(iN)
// Compute intermidiate matrices for algorithm.
Binv, _ := B.Inverse()
T1, _ := base.Product(cB, Binv, N)
Sigma, _ := base.Subtract(cN, T1)
σ := Sigma.Vector
// Find the biggest σ for judgement.
k = 0
σmax = 0
for i, s := range σ {
if s > σmax {
σmax = s
k = i + 1
}
}
if k == 0 {
// If there is no σ positive, the iteration stop and optimization reaches.
d, _ := base.Multiply(Binv, b)
X.SetRows(iB, d)
Z, _ = base.Product(cB, Binv, b)
x = X.Vector
z = Z.Get(1, 1)
continue
} else {
// If there is at least one σ positive, looking for varialbe to exchange.
ak := N.GetCol(k)
a, _ := base.Multiply(Binv, ak)
d, _ := base.Multiply(Binv, b)
// This is for find a positive β for later comparison.
avec := a.Vector
dvec := d.Vector
for i, ai := range avec {
if ai > 0 {
βmin = dvec[i] / ai
l = i + 1
break
}
}
// Find the smallest β which corresponding to the variable to exchange.
for i := 0; i < m; i++ {
β := dvec[i] / avec[i]
if avec[i] > 0 && β < βmin {
βmin = β
l = i + 1
}
}
// Exchange varialbes, controlled by indices.
iB[l-1], iN[k-1] = iN[k-1], iB[l-1]
}
}
return z, x, iB, iN, nil
}
