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