Data commit

Task/Conjugate-transpose/Go/conjugate-transpose.go

@@ -0,0 +1,112 @@
+package main
+
+import (
+    "fmt"
+    "math"
+    "math/cmplx"
+)
+
+// a type to represent matrices
+type matrix struct {
+    ele  []complex128
+    cols int
+}
+
+// conjugate transpose, implemented here as a method on the matrix type.
+func (m *matrix) conjTranspose() *matrix {
+    r := &matrix{make([]complex128, len(m.ele)), len(m.ele) / m.cols}
+    rx := 0
+    for _, e := range m.ele {
+        r.ele[rx] = cmplx.Conj(e)
+        rx += r.cols
+        if rx >= len(r.ele) {
+            rx -= len(r.ele) - 1
+        }
+    }
+    return r
+}
+
+// program to demonstrate capabilites on example matricies
+func main() {
+    show("h", matrixFromRows([][]complex128{
+        {3, 2 + 1i},
+        {2 - 1i, 1}}))
+
+    show("n", matrixFromRows([][]complex128{
+        {1, 1, 0},
+        {0, 1, 1},
+        {1, 0, 1}}))
+
+    show("u", matrixFromRows([][]complex128{
+        {math.Sqrt2 / 2, math.Sqrt2 / 2, 0},
+        {math.Sqrt2 / -2i, math.Sqrt2 / 2i, 0},
+        {0, 0, 1i}}))
+}
+
+func show(name string, m *matrix) {
+    m.print(name)
+    ct := m.conjTranspose()
+    ct.print(name + "_ct")
+
+    fmt.Println("Hermitian:", m.equal(ct, 1e-14))
+
+    mct := m.mult(ct)
+    ctm := ct.mult(m)
+    fmt.Println("Normal:", mct.equal(ctm, 1e-14))
+
+    i := eye(m.cols)
+    fmt.Println("Unitary:", mct.equal(i, 1e-14) && ctm.equal(i, 1e-14))
+}
+
+// two constructors
+func matrixFromRows(rows [][]complex128) *matrix {
+    m := &matrix{make([]complex128, len(rows)*len(rows[0])), len(rows[0])}
+    for rx, row := range rows {
+        copy(m.ele[rx*m.cols:(rx+1)*m.cols], row)
+    }
+    return m
+}
+
+func eye(n int) *matrix {
+    r := &matrix{make([]complex128, n*n), n}
+    n++
+    for x := 0; x < len(r.ele); x += n {
+        r.ele[x] = 1
+    }
+    return r
+}
+
+// print method outputs matrix to stdout
+func (m *matrix) print(heading string) {
+    fmt.Print("\n", heading, "\n")
+    for e := 0; e < len(m.ele); e += m.cols {
+        fmt.Printf("%6.3f ", m.ele[e:e+m.cols])
+        fmt.Println()
+    }
+}
+
+// equal method uses ε to allow for floating point error.
+func (a *matrix) equal(b *matrix, ε float64) bool {
+    for x, aEle := range a.ele {
+        if math.Abs(real(aEle)-real(b.ele[x])) > math.Abs(real(aEle))*ε ||
+            math.Abs(imag(aEle)-imag(b.ele[x])) > math.Abs(imag(aEle))*ε {
+            return false
+        }
+    }
+    return true
+}
+
+// mult method taken from matrix multiply task
+func (m1 *matrix) mult(m2 *matrix) (m3 *matrix) {
+    m3 = &matrix{make([]complex128, (len(m1.ele)/m1.cols)*m2.cols), m2.cols}
+    for m1c0, m3x := 0, 0; m1c0 < len(m1.ele); m1c0 += m1.cols {
+        for m2r0 := 0; m2r0 < m2.cols; m2r0++ {
+            for m1x, m2x := m1c0, m2r0; m2x < len(m2.ele); m2x += m2.cols {
+                m3.ele[m3x] += m1.ele[m1x] * m2.ele[m2x]
+                m1x++
+            }
+            m3x++
+        }
+    }
+    return m3
+}