// Function for duplicating data structure for quadrature. This helps
// preserve certain data that needs to be reused between different nodes
// at which we need to evaluate the function to be integrated.
func (t *IntegStruct) CopyIntegStruct(s *IntegStruct) {
t.E_mode = s.E_mode
t.E_Fermi = s.E_Fermi
t.mu1 = s.mu1
t.mu2 = s.mu2
t.f1 = s.f1
t.f2 = s.f2
t.f1_prime = s.f1_prime
t.f2_prime = s.f2_prime
t.V_MTJ = s.V_MTJ
t.Temperature = s.Temperature
t.deltaL = s.deltaL
t.deltaR = s.deltaR
t.m_fmL = s.m_fmL
t.m_ox = s.m_ox
t.m_fmR = s.m_fmR
t.t_fmL = s.t_fmL
t.t_fmR = s.t_fmR
t.N_fmL = s.N_fmL
t.N_ox = s.N_ox
t.N_fmR = s.N_fmR
t.BT_Mat_L = s.BT_Mat_L
t.BT_Mat_R = s.BT_Mat_R
t.Hamiltonian = cmplxSparse.SparseCopy(s.Hamiltonian)
t.ECurrFactor = s.ECurrFactor
t.SCurrFactor = s.SCurrFactor
return
}
func testDiagSolver(n int) {
fmt.Println("Initializing Sparse matrix structure\n")
tmp := cmplxSparse.New()
matrixSize := int(2 * n)
fmt.Println("Making sparse ", matrixSize, "x", matrixSize, " Hamiltonian tridiagonal matrix\n")
cmplxSparse.MakeHamTriDiag(n, tmp)
for idx0 := 0; idx0 < matrixSize; idx0++ {
tmp.Data[idx0][2] -= complex(0.0, 5.0)
}
fmt.Println("Accessing matrix elements of Hamiltonian (m,n):")
for idx0 := 0; idx0 < matrixSize; idx0++ {
for idx1 := 0; idx1 < matrixSize; idx1++ {
test := cmplxSparse.AccessMatrix(idx0, idx1, tmp)
fmt.Printf("%f ", test)
}
fmt.Printf("\n")
}
fmt.Printf("\n")
tmp0 := cmplxSparse.SparseCopy(tmp)
cmplxSparse.SparseDiagLU(tmp0)
fmt.Println("Accessing matrix elements of LU (m,n):")
for idx0 := 0; idx0 < matrixSize; idx0++ {
for idx1 := 0; idx1 < matrixSize; idx1++ {
test := cmplxSparse.AccessMatrix(idx0, idx1, tmp0)
fmt.Printf("%f ", test)
}
fmt.Printf("\n")
}
fmt.Printf("\n")
InvBuffer := make([][]complex128, matrixSize)
for idx0 := range InvBuffer {
InvBuffer[idx0] = make([]complex128, matrixSize)
for idx1 := range InvBuffer[idx0] {
InvBuffer[idx0][idx1] = 0.0 + 0.0i
}
}
for idx0 := range InvBuffer {
InvBuffer[idx0][idx0] = 1.0 + 0.0i
BufferMatrix := cmplxSparse.SparseDiagLinearSolver(tmp0, InvBuffer[idx0])
InvBuffer[idx0] = BufferMatrix
}
fmt.Println("Accessing matrix elements of inverse (m,n):")
for idx0 := range InvBuffer {
for idx1 := range InvBuffer[idx0] {
fmt.Printf("%.15g ", InvBuffer[idx0][idx1])
}
fmt.Printf("\n")
}
}
func testLU(n int) {
fmt.Println("Initializing Sparse matrix structure\n")
tmp := cmplxSparse.New()
matrixSize := int(2 * n)
fmt.Println("Making sparse ", matrixSize, "x", matrixSize, " Hamiltonian tridiagonal matrix\n")
cmplxSparse.MakeHamTriDiag(n, tmp)
for idx0 := 0; idx0 < matrixSize; idx0++ {
tmp.Data[idx0][2] -= complex(0.0, 5.0)
}
LU_mat := cmplxSparse.SparseCopy(tmp)
cmplxSparse.SparseDiagLU(LU_mat)
fmt.Println("Accessing matrix elements (m,n):")
for idx0 := 0; idx0 < matrixSize; idx0++ {
for idx1 := 0; idx1 < matrixSize; idx1++ {
test := cmplxSparse.AccessMatrix(idx0, idx1, LU_mat)
fmt.Printf("%f ", test)
}
fmt.Printf("\n")
}
fmt.Println("\n")
}
// This function is called during quadrature integration over energies.
func (s *IntegStruct) NEGF_EnergyIntegFunc(EnergyValue float64) *[]float64 {
// Initialize the return value
t := make([]float64, 4)
// Get t0 on left and right of Hamiltonian matrix
MatrixSize := len(s.Hamiltonian.Data)
MaxDiagIdx := len(s.Hamiltonian.Data[0])
MainDiagIdx := (MaxDiagIdx - 1) / 2
// Adjust Hamiltonian with sigma1 to obtain the inverse of Green's function matrix
InvGMatrix := cmplxSparse.SparseCopy(s.Hamiltonian)
// Adjust main diagonal with the energy value of interest
for idx0 := 0; idx0 < MatrixSize; idx0++ {
InvGMatrix.Data[idx0][MainDiagIdx] += complex(EnergyValue, utils.Zplus)
}
// Store f1*gam1 and f2*gam2. Note that these matrices are non-zero at the top
// left and bottom right, respectively. Hence, it is sufficient to store them
// as just 2 x 2 matrices.
f1gam1, f2gam2 := new([2][2]complex128), new([2][2]complex128)
f1, f2 := cmplxSparse.FermiEnergy(EnergyValue, s.mu1, s.Temperature), cmplxSparse.FermiEnergy(EnergyValue, s.mu2, s.Temperature)
// Calculate f1*gam1 first and store in a buffer
SelfEnergyBuffer := cmplxSparse.SelfEnergyEntries(EnergyValue, s.E_mode, 0.0, s.deltaL, s.V_MTJ, s.t_fmL, s.BT_Mat_L)
f1gam1[0][0] = complex(0.0, f1) * (SelfEnergyBuffer[0][0] - cmplx.Conj(SelfEnergyBuffer[0][0]))
f1gam1[0][1] = complex(0.0, f1) * (SelfEnergyBuffer[0][1] - cmplx.Conj(SelfEnergyBuffer[1][0]))
f1gam1[1][0] = complex(0.0, f1) * (SelfEnergyBuffer[1][0] - cmplx.Conj(SelfEnergyBuffer[0][1]))
f1gam1[1][1] = complex(0.0, f1) * (SelfEnergyBuffer[1][1] - cmplx.Conj(SelfEnergyBuffer[1][1]))
InvGMatrix.Data[0][MainDiagIdx] -= SelfEnergyBuffer[0][0]
InvGMatrix.Data[0][MainDiagIdx+1] -= SelfEnergyBuffer[0][1]
InvGMatrix.Data[1][MainDiagIdx-1] -= SelfEnergyBuffer[1][0]
InvGMatrix.Data[1][MainDiagIdx] -= SelfEnergyBuffer[1][1]
// Calculate f2*gam2 next and store in a buffer
SelfEnergyBuffer = cmplxSparse.SelfEnergyEntries(EnergyValue, s.E_mode, 0.0, s.deltaR, -1.0*s.V_MTJ, s.t_fmR, s.BT_Mat_R)
f2gam2[0][0] = complex(0.0, f2) * (SelfEnergyBuffer[0][0] - cmplx.Conj(SelfEnergyBuffer[0][0]))
f2gam2[0][1] = complex(0.0, f2) * (SelfEnergyBuffer[0][1] - cmplx.Conj(SelfEnergyBuffer[1][0]))
f2gam2[1][0] = complex(0.0, f2) * (SelfEnergyBuffer[1][0] - cmplx.Conj(SelfEnergyBuffer[0][1]))
f2gam2[1][1] = complex(0.0, f2) * (SelfEnergyBuffer[1][1] - cmplx.Conj(SelfEnergyBuffer[1][1]))
// Adjust Hamiltonian with sigma2 to obtain the inverse of Green's function matrix
InvGMatrix.Data[MatrixSize-2][MainDiagIdx] -= SelfEnergyBuffer[0][0]
InvGMatrix.Data[MatrixSize-2][MainDiagIdx+1] -= SelfEnergyBuffer[0][1]
InvGMatrix.Data[MatrixSize-1][MainDiagIdx-1] -= SelfEnergyBuffer[1][0]
InvGMatrix.Data[MatrixSize-1][MainDiagIdx] -= SelfEnergyBuffer[1][1]
// Calculate Green's Function matrix
GMatrix := cmplxSparse.CalcGreensFunc(InvGMatrix)
// Calculate Gn = G * (f1*gam1 + f2*gam2) * (G^+)...
// Since f1*gam1 and f2*gam2 are sparse matrices, we do not need to do a full matrix multiplication
// Calculate the non-zero portion of (f1*gam1 + f2*gam2) * (G^+) and store in RearMultBuffer:
// i.e. First two rows of the product are obtained from f1*gam1*(G^+) and are stored as the first
// two rows of RearMultBuffer. The last two rows of the product are obtained from f1*gam2*(G^+) and
// are stored as the last two rows of RearMultBuffer.
RearMultBuffer := make([][]complex128, 4)
RearIdx0, RearIdx1 := MatrixSize-2, MatrixSize-1
// Initialize buffer storage
for idx0 := 0; idx0 < 4; idx0++ {
RearMultBuffer[idx0] = make([]complex128, MatrixSize)
}
// Calculate each row of RearMultBuffer
for idx0 := 0; idx0 < MatrixSize; idx0++ {
RearMultBuffer[0][idx0] = f1gam1[0][0]*cmplx.Conj(GMatrix[idx0][0]) + f1gam1[0][1]*cmplx.Conj(GMatrix[idx0][1])
RearMultBuffer[1][idx0] = f1gam1[1][0]*cmplx.Conj(GMatrix[idx0][0]) + f1gam1[1][1]*cmplx.Conj(GMatrix[idx0][1])
if (idx0 > 1) && (idx0 < RearIdx0) {
RearMultBuffer[2][idx0] = f2gam2[0][0]*cmplx.Conj(GMatrix[idx0][2]) + f2gam2[0][1]*cmplx.Conj(GMatrix[idx0][3])
RearMultBuffer[3][idx0] = f2gam2[1][0]*cmplx.Conj(GMatrix[idx0][2]) + f2gam2[1][1]*cmplx.Conj(GMatrix[idx0][3])
} else {
RearMultBuffer[2][idx0] = f2gam2[0][0]*cmplx.Conj(GMatrix[idx0][RearIdx0]) + f2gam2[0][1]*cmplx.Conj(GMatrix[idx0][RearIdx1])
RearMultBuffer[3][idx0] = f2gam2[1][0]*cmplx.Conj(GMatrix[idx0][RearIdx0]) + f2gam2[1][1]*cmplx.Conj(GMatrix[idx0][RearIdx1])
}
}
// Finally, compute the required entries of Gn.
GnF, GnR := new([2][2]complex128), new([2][2]complex128)
GnF[0][0], GnF[0][1], GnF[1][0], GnF[1][1] = 0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+0.0i
GnR[0][0], GnR[0][1], GnR[1][0], GnR[1][1] = 0.0+0.0i, 0.0+0.0i, 0.0+0.0i, 0.0+0.0i
PtIdx0 := 2*s.N_fmL + 1
PtIdx1, PtIdx2, PtIdx3 := PtIdx0-1, PtIdx0+1, PtIdx0+2
// GMatrix is actually the transpose of G. Due to the nature of (f1*gam1 + f2*gam2)
// the entries of G that we need are:
// 1. The first two rows.
// 2. The first two columns.
// 3. The last two rows.
// 4. The last two columns.
// Scanning the first index of GMatrix scans through the columns of G.
// The second index of GMatrix selects the row.
for idx0 := 0; idx0 < 4; idx0++ {
if idx0 < 2 {
// When multiplication involves first two rows of RearMultBuffer,
// we need to access first two columns of G.
GnF[0][0] += GMatrix[idx0][PtIdx1] * RearMultBuffer[idx0][PtIdx2]
GnF[0][1] += GMatrix[idx0][PtIdx1] * RearMultBuffer[idx0][PtIdx3]
GnF[1][0] += GMatrix[idx0][PtIdx0] * RearMultBuffer[idx0][PtIdx2]
GnF[1][1] += GMatrix[idx0][PtIdx0] * RearMultBuffer[idx0][PtIdx3]
GnR[0][0] += GMatrix[idx0][PtIdx2] * RearMultBuffer[idx0][PtIdx1]
GnR[0][1] += GMatrix[idx0][PtIdx2] * RearMultBuffer[idx0][PtIdx0]
GnR[1][0] += GMatrix[idx0][PtIdx3] * RearMultBuffer[idx0][PtIdx1]
GnR[1][1] += GMatrix[idx0][PtIdx3] * RearMultBuffer[idx0][PtIdx0]
} else {
// When multiplication involves last two rows of RearMultBuffer,
// we need to access last two columns of G.
targIdx := MatrixSize - 4
GnF[0][0] += GMatrix[targIdx+idx0][PtIdx1] * RearMultBuffer[idx0][PtIdx2]
GnF[0][1] += GMatrix[targIdx+idx0][PtIdx1] * RearMultBuffer[idx0][PtIdx3]
GnF[1][0] += GMatrix[targIdx+idx0][PtIdx0] * RearMultBuffer[idx0][PtIdx2]
GnF[1][1] += GMatrix[targIdx+idx0][PtIdx0] * RearMultBuffer[idx0][PtIdx3]
GnR[0][0] += GMatrix[targIdx+idx0][PtIdx2] * RearMultBuffer[idx0][PtIdx1]
GnR[0][1] += GMatrix[targIdx+idx0][PtIdx2] * RearMultBuffer[idx0][PtIdx0]
GnR[1][0] += GMatrix[targIdx+idx0][PtIdx3] * RearMultBuffer[idx0][PtIdx1]
GnR[1][1] += GMatrix[targIdx+idx0][PtIdx3] * RearMultBuffer[idx0][PtIdx0]
}
}
// We know the Hamiltonian is stored in diagonal format. Extract the wanted values of Hamiltonian
// and multiply accordingly to GnF and GnR.
HamF, HamR, MatrixBuffer := new([2][2]complex128), new([2][2]complex128), new([2][2]complex128)
HamR[0][1] = -1.0 * s.Hamiltonian.Data[PtIdx2][MainDiagIdx-1]
HamR[0][0] = -1.0 * s.Hamiltonian.Data[PtIdx2][MainDiagIdx-2]
HamR[1][1] = -1.0 * s.Hamiltonian.Data[PtIdx3][MainDiagIdx-2]
HamF[1][0] = -1.0 * s.Hamiltonian.Data[PtIdx0][MainDiagIdx+1]
HamF[0][0] = -1.0 * s.Hamiltonian.Data[PtIdx1][MainDiagIdx+2]
HamF[1][1] = -1.0 * s.Hamiltonian.Data[PtIdx0][MainDiagIdx+2]
if MaxDiagIdx > 6 {
HamR[1][0] = -1.0 * s.Hamiltonian.Data[PtIdx3][MainDiagIdx-3]
HamF[0][1] = -1.0 * s.Hamiltonian.Data[PtIdx1][MainDiagIdx+3]
} else {
HamR[1][0] = 0.0 + 0.0i
HamF[0][1] = 0.0 + 0.0i
}
// Calculate term from H*Gn - Gn*H;
MatrixBuffer[0][0] = 1.0i * (HamR[0][0]*GnF[0][0] + HamR[0][1]*GnF[1][0] - GnR[0][0]*HamF[0][0] - GnR[0][1]*HamF[1][0])
MatrixBuffer[0][1] = 1.0i * (HamR[0][0]*GnF[0][1] + HamR[0][1]*GnF[1][1] - GnR[0][0]*HamF[0][1] - GnR[0][1]*HamF[1][1])
MatrixBuffer[1][0] = 1.0i * (HamR[1][0]*GnF[0][0] + HamR[1][1]*GnF[1][0] - GnR[1][0]*HamF[0][0] - GnR[1][1]*HamF[1][0])
MatrixBuffer[1][1] = 1.0i * (HamR[1][0]*GnF[0][1] + HamR[1][1]*GnF[1][1] - GnR[1][0]*HamF[0][1] - GnR[1][1]*HamF[1][1])
// Calculate current density, and components of spin current
t[0] = -1.0 * real(MatrixBuffer[0][0]+MatrixBuffer[1][1]) // Charge current density
t[1] = real(MatrixBuffer[1][0] + MatrixBuffer[0][1])
t[2] = real(1.0i*MatrixBuffer[0][1] - 1.0i*MatrixBuffer[1][0])
t[3] = real(MatrixBuffer[0][0] - MatrixBuffer[1][1]) // z-component of spin current density
// Return result
return &t
}
