// Function to obtain complex conjugate (dagger operation) of
// sparse matrix stored in diagonal form
func SparseDiagDagger(s *SparseMat) *SparseMat {
// Initiaize variables for indexing purposes
matSize := len(s.Data)
numDiags := len(s.Data[0])
mainDiagIdx := (numDiags - 1) / 2
// Initialize output variable
t := SparseCopy(s)
for idx0 := 0; idx0 < matSize; idx0++ {
// Complex conjugate main diagonal
t.Data[idx0][mainDiagIdx] = cmplx.Conj(t.Data[idx0][mainDiagIdx])
// When there are more than one diagonal stored, and if we are not in the top left most entry,
// we will need to swap rows and columns, and complex conjugate those entries as well.
if (idx0 > 1) && (mainDiagIdx > 0) {
loopIdx := mainDiagIdx
if idx0 < loopIdx {
loopIdx = idx0
}
for idx1 := 1; idx1 < loopIdx; idx1++ {
// Swap row and columns, and conjugate those entries
t.Data[idx0][mainDiagIdx-idx1], t.Data[idx0-idx1][mainDiagIdx+idx1] = cmplx.Conj(t.Data[idx0-idx1][mainDiagIdx+idx1]), cmplx.Conj(t.Data[idx0][mainDiagIdx-idx1])
}
}
}
return t
}
func (a *matrix) choleskyDecomp() *matrix {
l := like(a)
// Cholesky-Banachiewicz algorithm
for r, rxc0 := 0, 0; r < a.stride; r++ {
// calculate elements along row, up to diagonal
x := rxc0
for c, cxc0 := 0, 0; c < r; c++ {
sum := a.ele[x]
for k := 0; k < c; k++ {
sum -= l.ele[rxc0+k] * cmplx.Conj(l.ele[cxc0+k])
}
l.ele[x] = sum / l.ele[cxc0+c]
x++
cxc0 += a.stride
}
// calcualate diagonal element
sum := a.ele[x]
for k := 0; k < r; k++ {
sum -= l.ele[rxc0+k] * cmplx.Conj(l.ele[rxc0+k])
}
l.ele[x] = cmplx.Sqrt(sum)
rxc0 += a.stride
}
return l
}
// Function to compute basis transformation matrix
func BasisTransform(th, phi float64) *[2][2]complex128 {
BTMatrix := new([2][2]complex128)
th_2, phi_2 := 0.5*th, 0.5*phi
csn := cmplx.Cos(complex(th_2, 0.0)) * cmplx.Exp(complex(0.0, -1.0*phi_2))
sn := cmplx.Sin(complex(th_2, 0.0)) * cmplx.Exp(complex(0.0, phi_2))
BTMatrix[0][0] = cmplx.Conj(csn)
BTMatrix[0][1] = cmplx.Conj(sn)
BTMatrix[1][0] = complex(-1.0, 0.0) * sn
BTMatrix[1][1] = csn
return BTMatrix
}
func XCorrFFT(x1, x2 []float64, circular bool) []float64 {
// zero padding.
ftlength := len(x1)
if !circular {
length := len(x1) * 2
var i uint32 = 1
for ftlength < length {
ftlength = 1 << i
i++
}
}
datax1 := make([]complex128, ftlength)
datax2 := make([]complex128, ftlength)
for i := 0; i < len(x1); i++ {
datax1[i] = complex(x2[i%len(x2)], 0)
datax2[i] = complex(x1[i%len(x1)], 0)
}
v1 := fft.FFT(datax1)
v2 := fft.FFT(datax2)
temp := []complex128{}
for i := 0; i < len(v1); i++ {
v := v1[i] * cmplx.Conj(v2[i])
temp = append(temp, v)
}
v3 := fft.IFFT(temp)
res := []float64{}
for i := 0; i < len(x1); i++ {
res = append(res, real(v3[i]))
}
return res
}
func (a *triangleMat) Set(i, j int, x complex128) {
if otherTri(i, j, a.Tri) {
i, j = j, i
x = cmplx.Conj(x)
}
a.Set(i, j, x)
}
func (this *Matrix) parallel_Traspose(i0, i1, j0, j1 int, res *Matrix, done chan<- bool, conjugate bool) {
di := i1 - i0
dj := j1 - j0
done2 := make(chan bool, THRESHOLD)
if di >= dj && di >= THRESHOLD && runtime.NumGoroutine() < maxGoRoutines {
mi := i0 + di/2
go this.parallel_Traspose(i0, mi, j0, j1, res, done2, conjugate)
this.parallel_Traspose(mi, i1, j0, j1, res, done2, conjugate)
<-done2
<-done2
} else if dj >= THRESHOLD && runtime.NumGoroutine() < maxGoRoutines {
mj := j0 + dj/2
go this.parallel_Traspose(i0, i1, j0, mj, res, done2, conjugate)
this.parallel_Traspose(i0, i1, mj, i1, res, done2, conjugate)
<-done2
<-done2
} else {
if !conjugate {
for i := i0; i <= i1; i++ {
for j := j0; j <= j1; j++ {
res.SetValue(j, i, this.GetValue(i, j))
}
}
} else {
for i := i0; i <= i1; i++ {
for j := j0; j <= j1; j++ {
res.SetValue(j, i, cmplx.Conj(this.GetValue(i, j)))
}
}
}
}
done <- true
}
func (self *ComplexV) VmulConj(b *ComplexV) *ComplexV {
r := Zeros(len(*self))
for k, a := range *self {
(*r)[k] = a * cmplx.Conj((*b)[k])
}
return r
}
func (self *ComplexV) Conj() *ComplexV {
r := Zeros(len(*self))
for k, a := range *self {
(*r)[k] = cmplx.Conj(a)
}
return r
}
func ZdotcInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128) {
for i := 0; i < int(n); i++ {
sum += y[iy] * cmplx.Conj(x[ix])
ix += incX
iy += incY
}
return
}
// ci <- k conj(ai) bi
func scaleMul(c *fftw.Array2, k complex128, a, b *fftw.Array2) {
m, n := a.Dims()
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
ax := cmplx.Conj(a.At(i, j))
bx := b.At(i, j)
c.Set(i, j, k*ax*bx)
}
}
}
// Creates a conjugated copy of the matrix.
func Conj(a Const) *Mat {
m, n := a.Dims()
b := New(m, n)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
b.Set(i, j, cmplx.Conj(a.At(i, j)))
}
}
return b
}
// ci <- ci + conj(ai) bi
func addMul(c *fftw.Array2, a, b *fftw.Array2) {
m, n := a.Dims()
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
ax := cmplx.Conj(a.At(i, j))
bx := b.At(i, j)
cx := c.At(i, j)
c.Set(i, j, cx+ax*bx)
}
}
}
// implementation of Trans method
func (v *vectorComplex) Trans() {
if v.Type() == ColVector {
v.vectorType = RowVector
} else {
v.vectorType = ColVector
}
for i := 0; i < v.Dim(); i++ {
v.elements[i] = cmplx.Conj(v.elements[i])
}
}
func (a *triangleMat) At(i, j int) complex128 {
swap := otherTri(i, j, a.Tri)
if swap {
i, j = j, i
}
x := a.Mat.At(i, j)
if swap {
x = cmplx.Conj(x)
}
return x
}
func main() {
a := 1 + 1i
b := 3.14159 + 1.25i
fmt.Println("a: ", a)
fmt.Println("b: ", b)
fmt.Println("a + b: ", a+b)
fmt.Println("a * b: ", a*b)
fmt.Println("-a: ", -a)
fmt.Println("1 / a: ", 1/a)
fmt.Println("a̅: ", cmplx.Conj(a))
}
// Calc tests whether c is in the Mandelbrot set.
// return 0 if c is in the set,
// otherwise return i (> 0) where i is number of trials
// when absolute value of z exceed by 2.
func Calc(c complex128, limit int) (int, complex128) {
z := c
for i := 1; i <= limit; i++ {
if real(z*cmplx.Conj(z)) > 4 {
return i, z
}
z *= z
z += c
}
return 0, z
}
func (cdma *CDMA) DeSpread(InCH gocomm.Complex128Channel, OutCH gocomm.Complex128Channel) {
despcode := vlib.Conj(cdma.SpreadSequence)
var result complex128
for i := 0; i < len(despcode); i++ {
rxchips := (<-InCH).Ch
result += rxchips * cmplx.Conj(despcode[i])
}
var chdataOut gocomm.SComplex128Obj
chdataOut.Ch = result
OutCH <- chdataOut
}
// 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
}
func (self *ComplexV) FindMax() (inx int, a float64) {
a = 0.
inx = 0
for k, x := range *self {
p := x * cmplx.Conj(x)
if real(p) > a {
a = real(p)
inx = k
}
}
return inx, a
}
func ComplexRoots(f []complex128, p0 complex128, p1 complex128, p2 complex128, e float64) complex128 {
k := 0 + 0i
m := cmplx.Sqrt((HornerItCmplx(f, p2)) * cmplx.Conj(HornerItCmplx(f, p2)))
n := cmplx.Sqrt((HornerItCmplx(f, p2))*cmplx.Conj(HornerItCmplx(f, p2))) - cmplx.Sqrt((HornerItCmplx(f, k))*cmplx.Conj(HornerItCmplx(f, k)))
var mr, nr float64
mr, nr = real(m), real(n)
j := 1
for (mr > e || math.Abs(nr) > e) && j < 1000*len(f) {
A := ((p1-p2)*(HornerItCmplx(f, p0)-HornerItCmplx(f, p2)) - (p0-p1)*(HornerItCmplx(f, p1)-HornerItCmplx(f, p2))) / ((p0 - p2) * (p1 - p2) * (p0 - p1))
B := ((cmplx.Pow(p0-p2, 2))*(HornerItCmplx(f, p1)-HornerItCmplx(f, p2)) - (cmplx.Pow(p1-p2, 2))*(HornerItCmplx(f, p0)-HornerItCmplx(f, p2))) / ((p0 - p2) * (p1 - p2) * (p0 - p1))
C := HornerItCmplx(f, p2)
div1 := cmplx.Sqrt((B + cmplx.Sqrt(cmplx.Pow(B, 2)-4*A*C)) * cmplx.Conj(B+cmplx.Sqrt(cmplx.Pow(B, 2)-4*A*C)))
div2 := cmplx.Sqrt((B - cmplx.Sqrt(cmplx.Pow(B, 2)-4*A*C)) * (cmplx.Conj(B - cmplx.Sqrt(cmplx.Pow(B, 2)-4*A*C))))
var div1r, div2r float64
div1r, div2r = real(div1), real(div2)
var D complex128
if div1r > div2r {
D = (B + cmplx.Sqrt(cmplx.Pow(B, 2)-4*A*C))
} else {
D = (B - cmplx.Sqrt(cmplx.Pow(B, 2)-4*A*C))
}
p3 := p2 - ((2 * C) / D)
k = p2
p2, p1, p0 = p3, p2, p1
m := cmplx.Sqrt((HornerItCmplx(f, p2)) * cmplx.Conj(HornerItCmplx(f, p2)))
n := cmplx.Sqrt((HornerItCmplx(f, p2))*cmplx.Conj(HornerItCmplx(f, p2))) - cmplx.Sqrt((HornerItCmplx(f, k))*cmplx.Conj(HornerItCmplx(f, k)))
mr, nr = real(m), real(n)
j++
}
return p2
}
// Returns an error if the matrix is not Hermitian.
// Assumes that matrix is square.
func errNonHerm(a Const) error {
n, _ := a.Dims()
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
ij, ji := a.At(i, j), a.At(j, i)
want, got := ij, cmplx.Conj(ji)
if !(eqEpsAbs(want, got, EpsHermAbs) || eqEpsRel(want, got, EpsHermRel)) {
return fmt.Errorf("not Hermitian: at %d, %d: upper %g, lower %g", i, j, ij, ji)
}
}
}
return nil
}
// isLeftEigenvectorOf returns whether the vector yRe+i*yIm, where i is the
// imaginary unit, is the left eigenvector of A corresponding to the eigenvalue
// lambda.
//
// A left eigenvector corresponding to a complex eigenvalue λ is a complex
// non-zero vector y such that
// y^H A = λ y^H,
// which is equivalent for real A to
// A^T y = conj(λ) y,
func isLeftEigenvectorOf(a blas64.General, yRe, yIm []float64, lambda complex128, tol float64) bool {
if a.Rows != a.Cols {
panic("matrix not square")
}
if imag(lambda) != 0 && yIm == nil {
// Complex eigenvalue of a real matrix cannot have a real
// eigenvector.
return false
}
n := a.Rows
// Compute A^T real(y) and store the result into yReAns.
yReAns := make([]float64, n)
blas64.Gemv(blas.Trans, 1, a, blas64.Vector{1, yRe}, 0, blas64.Vector{1, yReAns})
if imag(lambda) == 0 && yIm == nil {
// Real eigenvalue and eigenvector.
// Compute λy and store the result into lambday.
lambday := make([]float64, n)
floats.AddScaled(lambday, real(lambda), yRe)
if floats.Distance(yReAns, lambday, math.Inf(1)) > tol {
return false
}
return true
}
// Complex eigenvector, and real or complex eigenvalue.
// Compute A^T imag(y) and store the result into yImAns.
yImAns := make([]float64, n)
blas64.Gemv(blas.Trans, 1, a, blas64.Vector{1, yIm}, 0, blas64.Vector{1, yImAns})
// Compute conj(λ)y and store the result into lambday.
lambda = cmplx.Conj(lambda)
lambday := make([]complex128, n)
for i := range lambday {
lambday[i] = lambda * complex(yRe[i], yIm[i])
}
for i, v := range lambday {
ay := complex(yReAns[i], yImAns[i])
if cmplx.Abs(v-ay) > tol {
return false
}
}
return true
}
func main() {
f := 3.2e5
display(f)
x := -7.3 - 8.9i
display(x)
y := complex64(-18.3 + 8.9i)
display(y)
z := complex(f, 13.2)
display(z)
display(real(y))
display(imag(z))
display(cmplx.Conj(z))
display(cmplx.Inf())
display(cmplx.NaN())
display(cmplx.Sqrt(z))
}
// implementation of Trans method
func (m *matrixComplex) Trans() {
transMatrixNumCols := m.numRows
transMatrixNumRows := m.numCols
transMatrixElements := make([][]complex128, transMatrixNumRows)
for i := 0; i < len(transMatrixElements); i++ {
transMatrixElements[i] = make([]complex128, transMatrixNumCols)
}
for i := 0; i < transMatrixNumRows; i++ {
for j := 0; j < transMatrixNumCols; j++ {
transMatrixElements[i][j] = cmplx.Conj(m.Get(j, i))
}
}
m.numRows = transMatrixNumRows
m.numCols = transMatrixNumCols
m.elements = transMatrixElements
}
// return a ConjugateTraspose
func (this *Matrix) ConjugateTraspose() *Matrix {
if this.m == 1 || this.n == 1 {
c := this.Copy()
t := c.m
c.m = c.n
c.n = t
c = c.Apply(
func(a complex128) complex128 {
return cmplx.Conj(a)
})
return c
}
out := NullMatrixP(this.n, this.m)
done := make(chan bool)
go this.parallel_Traspose(1, this.m, 1, this.n, out, done, true)
<-done
return out
}
// Function for calculating the self-energy matrices
func SelfEnergyEntries(currEnergy, modeEnergy, delta0, delta1, potential float64, t0 complex128, BT_Mat *[2][2]complex128) *[2][2]complex128 {
s := new([2][2]complex128)
SumEnergy := complex(currEnergy-modeEnergy+0.5*potential-delta0, utils.Zplus)
SumEnergy /= complex(-2.0, 0.0) * t0
SumEnergy += complex(1.0, 0.0)
sig_uu := complex(-1.0, 0.0) * t0 * cmplx.Exp(1.0i*cmplx.Acos(SumEnergy))
SumEnergy = complex(currEnergy-modeEnergy+0.5*potential-delta1, utils.Zplus)
SumEnergy /= complex(-2.0, 0.0) * t0
SumEnergy += complex(1.0, 0.0)
sig_dd := complex(-1.0, 0.0) * t0 * cmplx.Exp(1.0i*cmplx.Acos(SumEnergy))
s[0][0] = cmplx.Conj(BT_Mat[0][0])*sig_uu*BT_Mat[0][0] + cmplx.Conj(BT_Mat[1][0])*sig_dd*BT_Mat[1][0]
s[0][1] = cmplx.Conj(BT_Mat[0][0])*sig_uu*BT_Mat[0][1] + cmplx.Conj(BT_Mat[1][0])*sig_dd*BT_Mat[1][1]
s[1][0] = cmplx.Conj(BT_Mat[0][1])*sig_uu*BT_Mat[0][0] + cmplx.Conj(BT_Mat[1][1])*sig_dd*BT_Mat[1][0]
s[1][1] = cmplx.Conj(BT_Mat[0][1])*sig_uu*BT_Mat[0][1] + cmplx.Conj(BT_Mat[1][1])*sig_dd*BT_Mat[1][1]
return s
}
// Given a buffer length, symbol length and a binary bitstring, compute the
// frequency domain of the preamble for later use.
func NewPreambleDetector(n uint, symbolLength float64, bits string) (pd PreambleDetector) {
// Plan forward and reverse transforms.
pd.forward = fftw.NewHCDFT1D(n, nil, nil, fftw.Forward, fftw.InPlace, fftw.Measure)
pd.Real = pd.forward.Real
pd.Complex = pd.forward.Complex
pd.backward = fftw.NewHCDFT1D(n, pd.Real, pd.Complex, fftw.Backward, fftw.PreAlloc, fftw.Measure)
// Zero out input array.
for i := range pd.Real {
pd.Real[i] = 0
}
// Generate the preamble basis function.
for idx, bit := range bits {
// Must account for rounding error.
sIdx := idx << 1
lower := intRound(float64(sIdx) * symbolLength)
upper := intRound(float64(sIdx+1) * symbolLength)
for i := 0; i < upper-lower; i++ {
if bit == '1' {
pd.Real[lower+i] = 1.0
pd.Real[upper+i] = -1.0
} else {
pd.Real[lower+i] = -1.0
pd.Real[upper+i] = 1.0
}
}
}
// Transform the preamble basis function.
pd.forward.Execute()
// Create the preamble template and store conjugated DFT result.
pd.template = make([]complex128, len(pd.Complex))
copy(pd.template, pd.Complex)
for i := range pd.template {
pd.template[i] = cmplx.Conj(pd.template[i])
}
return
}
func (f FFTW) XCorr(x1, x2 []float64) []float64 {
var v1, v2, temp []complex128
var rs []float64
v1 = f.foward.ExecuteNewArray(x2)
v2 = f.foward.ExecuteNewArray(x1)
for i := 0; i < len(v1); i++ {
v := v1[i] * cmplx.Conj(v2[i])
temp = append(temp, v)
}
rs = f.backward.ExecuteNewArray(temp)
totl := len(f.backward.Real)
res := []float64{}
for i := 0; i < len(x1); i++ {
res = append(res, rs[i]/float64(totl))
}
return res
}
func (k *CQKernel) ProcessInverse(cv []complex128) []complex128 {
// matrix multiply by conjugate transpose of m_kernel. This is
// actually the original kernel as calculated, we just stored the
// conjugate-transpose of the kernel because we expect to be doing
// more forward transforms than inverse ones.
if len(k.kernel.data) == 0 {
panic("Whoops - return empty array? is this even possible?")
}
ncols := k.Properties.binsPerOctave * k.Properties.atomsPerFrame
nrows := k.Properties.fftSize
rv := make([]complex128, nrows, nrows)
for j := 0; j < ncols; j++ {
i0 := k.kernel.origin[j]
i1 := i0 + len(k.kernel.data[j])
for i := i0; i < i1; i++ {
rv[i] += cv[j] * cmplx.Conj(k.kernel.data[j][i-i0])
}
}
return rv
}
func (cqi *CQInverse) processOctaveColumn(octave int, column []complex128) {
// 3. For each taller column, take the product with the inverse CQ
// kernel (which is the conjugate of the forward kernel) and
// perform an inverse FFT
bpo := cqi.kernel.Properties.binsPerOctave
apf := cqi.kernel.Properties.atomsPerFrame
fftSize := cqi.kernel.Properties.fftSize
if len(column) != bpo*apf {
fmt.Printf("Error: column in octave %d has size %d, required = %d * %d = %d\n",
octave, len(column), bpo, apf, bpo*apf)
panic("Invalid argument to inverse processOctaveColumn")
}
transformed := cqi.kernel.ProcessInverse(column)
// For inverse real transforms, force symmetric conjugate representation first.
for i := fftSize/2 + 1; i < fftSize; i++ {
transformed[i] = cmplx.Conj(transformed[fftSize-i])
}
inverse := fft.IFFT(transformed)
cqi.overlapAddAndResample(octave, realParts(inverse))
}
