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ampsci
c++ program for high-precision atomic structure calculations of single-valence systems
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#include <SpinorMatrix.hpp>
Public Member Functions | |
| SpinorMatrix (std::size_t i0, std::size_t stride, std::size_t size, bool incl_g, std::shared_ptr< const Grid > rgrid) | |
| T & | ff (std::size_t i, std::size_t j) |
| direct access to matrix elements | |
| T & | fg (std::size_t i, std::size_t j) |
| T & | gf (std::size_t i, std::size_t j) |
| T & | gg (std::size_t i, std::size_t j) |
| const T | ff (std::size_t i, std::size_t j) const |
| const T | fg (std::size_t i, std::size_t j) const |
| const T | gf (std::size_t i, std::size_t j) const |
| const T | gg (std::size_t i, std::size_t j) const |
| const LinAlg::Matrix< T > & | ff () const |
| direct access to matrix's | |
| const LinAlg::Matrix< T > & | fg () const |
| const LinAlg::Matrix< T > & | gf () const |
| const LinAlg::Matrix< T > & | gg () const |
| LinAlg::Matrix< T > & | ff () |
| LinAlg::Matrix< T > & | fg () |
| LinAlg::Matrix< T > & | gf () |
| LinAlg::Matrix< T > & | gg () |
| std::size_t | size () const |
| std::size_t | g_size () const |
| bool | includes_g () const |
| std::size_t | i0 () const |
| std::size_t | stride () const |
| void | zero () |
| Sets all matrix elements to zero. | |
| SpinorMatrix< T > & | drop_g () |
| Kills g parts of spinor matrix, in place! | |
| SpinorMatrix< T > & | create_g () |
| Creates g parts of spinor matrix - will have value 0. | |
| SpinorMatrix< T > & | operator+= (const SpinorMatrix< T > &rhs) |
| Matrix adition +,-. | |
| SpinorMatrix< T > & | operator-= (const SpinorMatrix< T > &rhs) |
| Matrix adition +,-. | |
| SpinorMatrix< T > & | operator*= (const T x) |
| Scalar multiplication. | |
| SpinorMatrix< T > & | operator+= (T aI) |
| Adition of identity: Matrix<T> += T : T assumed to be *Identity! | |
| SpinorMatrix< T > & | operator-= (T aI) |
| Adition of identity: Matrix<T> -= T : T assumed to be *Identity! | |
| SpinorMatrix< T > & | mult_elements_by (const SpinorMatrix< T > &rhs) |
| Multiply elements (in place): Gij -> Gij*Bij. | |
| SpinorMatrix< T > & | mult_elements_by (const RadialMatrix< T > &rhs) |
| Multiply elements (in place): Gij -> Gij*Bij. | |
| SpinorMatrix< T > | conj () const |
| Returns conjugate of matrix. | |
| SpinorMatrix< double > | real () const |
| Returns real part of complex matrix (changes type; returns a real matrix) | |
| SpinorMatrix< double > | imag () const |
| Returns imag part of complex matrix (changes type; returns a real matrix) | |
| SpinorMatrix< std::complex< double > > | complex () const |
| Converts a real to complex matrix (changes type; returns a complex matrix) | |
| SpinorMatrix< T > & | invert_in_place () |
| Inversion (in place) | |
| SpinorMatrix< T > | inverse () const |
| Returns inverse of matrix; original matrix unchanged. | |
| SpinorMatrix< T > & | drj_in_place () |
| Multiplies by drj: Q_ij -> Q_ij*dr_j, in place. | |
| SpinorMatrix< T > & | dri_in_place () |
| Multiplies by dri: Q_ij -> Q_ij*dr_i, in place. | |
| SpinorMatrix< T > | drj () const |
| Multiplies by drj: Q_ij -> Q_ij*dr_j. Returns new matrix (orig unchanged) | |
| SpinorMatrix< T > | dri () const |
| Multiplies by dri: Q_ij -> Q_ij*dr_i. Returns new matrix (orig unchanged) | |
| double | dr (std::size_t sub_index) const |
| returns dr at position along sub grid | |
| std::size_t | index_to_fullgrid (std::size_t i) const |
| Converts an index on the sub-grid to the full grid. | |
| void | add (const DiracSpinor &ket, const DiracSpinor &bra, T k=T(1.0)) |
| Adds k*|ket><bra| to matrix (used for building Green's functions) | |
| DiracSpinor | operator* (const DiracSpinor &Fn) const |
| Action of SpinorMatrix operator on DiracSpinor. Inludes Integration: G*F = Int[G(r,r')*F(r') dr'] = sum_j G_ij*F_j*drdu_j*du. | |
Friends | |
| SpinorMatrix< T > | operator+ (SpinorMatrix< T > lhs, const SpinorMatrix< T > &rhs) |
| Matrix adition +,-. | |
| SpinorMatrix< T > | operator- (SpinorMatrix< T > lhs, const SpinorMatrix< T > &rhs) |
| Matrix adition +,-. | |
| SpinorMatrix< T > | operator* (const T x, SpinorMatrix< T > rhs) |
| Scalar multiplication. | |
| SpinorMatrix< T > | operator+ (SpinorMatrix< T > M, T aI) |
| Adition of identity: Matrix<T> + T : T assumed to be *Identity! | |
| SpinorMatrix< T > | operator- (SpinorMatrix< T > M, T aI) |
| Adition of identity: Matrix<T> - T : T assumed to be *Identity! | |
| SpinorMatrix< T > | operator* (const SpinorMatrix< T > &a, const SpinorMatrix< T > &b) |
| Matrix multplication: C=A*B := Cij = \sum_k Aik*Bkj. Note: integration measure not included: call .drj() first to include it! | |
| SpinorMatrix< T > | mult_elements (SpinorMatrix< T > lhs, const SpinorMatrix< T > &rhs) |
| Multiply elements (new matrix): Gij = Aij*Bij. | |
| SpinorMatrix< T > | mult_elements (SpinorMatrix< T > lhs, const RadialMatrix< T > &rhs) |
| Multiply elements (new matrix): Gij = Aij*Bij. | |
| SpinorMatrix< T > | mult_elements (const RadialMatrix< T > &rhs, SpinorMatrix< T > lhs) |
| Multiply elements (new matrix): Gij = Aij*Bij. | |
| std::ostream & | operator<< (std::ostream &os, const SpinorMatrix< T > &a) |
Defines SpinorMatrix, Radial Dirac Spinor matrix. Designed to store Greens-function like operators: |Fa><Fb| (where Fa, Fb are radial Dirac spinors), as a radial matrix. The matrix is stored on a sub-grid (between r0 and rmax), with a specified stride.
SpinorMatrix is a 2*2 matrix in spinor space {ff, fg, gf, gg} - the g blocks are small and are optional. Each block is an N*N radial matrix, where N is a subset of the number of points along the full radial grid. May store doubles or complex doubles.
SpinorMatrix = {ff fg} {gf gg} SpinorMatrix * F = {ff fg} * (f) {gf gg} (g) = (ff(r,r')*f(r') + fg(r,r')*g(r')) (gf(r,r')*f(r') + gg(r,r')*g(r'))
Note: Careful to distinguish SpinorMatrix multiplication/integration: G1 * G2 = Int G1(ra,rb)*G2(rb,rc) = Sum_j G1(i,j)*G2(j,k)
G1.drj() * G2 = Int G1(ra,rb)*G2(rb,rc)*dr_b = Sum_j G1(i,j)*G2(j,k)*drdu_j*du = G1 * G2.dri()
While almost always symmetric, this doesn't assume that.
1.9.8