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linalg.cpp File Reference

Source code for most of the DenseVector<T> and DenseMatrix<T> methods, where T = double or T = std::complex<double>. Also some miscellaneous stuff. More...

#include "linalg.h"
#include "linalg/shortclawrap.h"

Include dependency graph for linalg.cpp:


Functions

const complex I (0, 1)
 Definition of the imaginary identity, I (declared in linalg.h).
void ThrowError (char *errstring, bool fatal)
 A routine for easily printing an error string, and aborting if necessary.
void Profile (char *methodname, int p1, int p2, double p3)
 Prints methodname, p1, p2, and p3 to "profile.log".
std::istream & eatwhite (std::istream &input)
 Fast-forward a stream pointer past all whitespace. Used by FlexibleTable.
template<>
void Copy (DenseVector< complex > &dest, const DenseVector< complex > &src)
 Copies one DenseVector<complex> into another. Uses BLAS if possible.
template<>
void Copy (DenseVector< double > &dest, const DenseVector< double > &src)
 Copy one DenseVector<double> into another. Uses BLAS if possible.
template<>
void Add (DenseVector< complex > &result, const DenseVector< complex > &v1, const DenseVector< complex > &v2, complex scale)
 Adds a scalar multiple of one DenseVector<complex> to another, and stores the result in another. Uses BLAS if possible.
template<>
void Add (DenseVector< double > &result, const DenseVector< double > &v1, const DenseVector< double > &v2, double scale)
 Adds a scalar multiple of one DenseVector<double> to another, storing the result in a third. Uses BLAS if possible.
template<>
void AddTo (DenseVector< complex > &result, const DenseVector< complex > &v, complex scale)
 Adds a scalar multiple of one DenseVector<complex> to another. Uses BLAS if possible.
template<>
void AddTo (DenseVector< double > &result, const DenseVector< double > &v, double scale)
 Adds a scalar multiple of one DenseVector<double> to another in place. Uses BLAS if possible.
template<>
void Multiply (DenseVector< complex > &result, const DenseVector< complex > &v, complex scalar)
 Scales a DenseVector<complex> by a scalar, storing the result in another. Uses BLAS if possible.
template<>
void Multiply (DenseVector< double > &result, const DenseVector< double > &v, double scalar)
 Scales one DenseVector<double> by a scalar, storing the result in another. Uses BLAS if possible.
template<>
void MultiplyBy (DenseVector< complex > &result, complex scalar)
 Scales a DenseVector<complex> by a scalar in place. Uses BLAS if possible.
template<>
void MultiplyBy (DenseVector< double > &result, double scalar)
 Scales a DenseVector<double> by a scalar in place. Uses BLAS if possible.
template<>
double dot (const DenseVector< double > &v1, const DenseVector< double > &v2)
 Computes the dot product between two DenseVector<double> objects. Uses BLAS if possible.
template<>
complex dot (const DenseVector< complex > &v1, const DenseVector< complex > &v2)
 Computes the dot product between two DenseVector<complex> objects. Uses BLAS if possible.
template<>
double c_dot (const DenseVector< double > &v1, const DenseVector< double > &v2)
 Computes the conjugate dot product between two DenseVector<double> objects. Uses BLAS if possible.
template<>
complex c_dot (const DenseVector< complex > &v1, const DenseVector< complex > &v2)
 Computes the conjugate dot product between two DenseVector<complex> objects. Uses BLAS if possible.
DenseVector< complex > & Randomize (DenseVector< complex > &v)
 Assigns a Gaussian random vector (all real and imaginary components are independent, univariate Gaussian random numbers).
DenseVector< double > RealPart (const DenseVector< complex > &v)
 Returns a DenseVector<double> containing the real part of the argument.
DenseVector< double > ImaginaryPart (const DenseVector< complex > &v)
 Returns a DenseVector<double> containing the imaginary part of the argument.
DenseVector< double > & Randomize (DenseVector< double > &v)
 Assigns a Gaussian random vector (all components are independent, univariate Gaussian random numbers).
DenseMatrix< double > RealPart (const DenseMatrix< complex > &m)
 Returns a DenseMatrix<double> containing the real part of the argument.
DenseMatrix< double > ImaginaryPart (const DenseMatrix< complex > &m)
 Returns a DenseMatrix<double> containing the imaginary part of the argument.
bool internalEigenFactor (DenseMatrix< complex > *matrix, DenseMatrix< complex > *L_ev, DenseMatrix< complex > *R_ev, DenseVector< complex > *evals)
 Private (internal) routine that interfaces to LAPACK complex eigenfactoring routines.
bool internalEigenFactor (DenseMatrix< double > *matrix, DenseMatrix< complex > *L_ev, DenseMatrix< complex > *R_ev, DenseVector< complex > *evals)
 Private (internal) routine that interfaces to LAPACK double eigenfactoring routines.
bool internalSymmetricEigenFactor (DenseMatrix< double > *matrix, DenseMatrix< double > *ev, DenseVector< double > *evals)
 Private (internal) routine that interfaces to LAPACK Hermitian-complex eigenfactoring routines.
bool internalHermitianEigenFactor (DenseMatrix< complex > *matrix, DenseMatrix< complex > *ev, DenseVector< double > *evals)
 Private (internal) routine that interfaces to LAPACK symmetric-double eigenfactoring routines.
bool EigenFactorSymmetric (DenseMatrix< double > &matrix, DenseMatrix< double > &ev, DenseVector< double > &evals)
 Computes the eigenvalues and eigenvectors of a symmetric real matrix.
bool EigenValuesSymmetric (DenseMatrix< double > &matrix, DenseVector< double > &evals)
bool EigenFactorHermitian (DenseMatrix< complex > &matrix, DenseMatrix< complex > &ev, DenseVector< double > &evals)
 Computes the eigenvalues and eigenvectors of a Hermitian complex matrix.
bool EigenValuesHermitian (DenseMatrix< complex > &matrix, DenseVector< double > &evals)
 Computes the eigenvalues (only) of a Hermitian complex matrix.
bool CholeskyFactor (DenseMatrix< double > &M, bool UpperTriangle)
 Computes the Cholesky factorization of a symmetric positive definite matrix in place.
bool CholeskyFactor (DenseMatrix< complex > &M, bool UpperTriangle)
 Computes the Cholesky factorization of a Hermitian positive definite matrix in place.
template<>
void Copy (DenseMatrix< double > &dest, const DenseMatrix< double > &src)
 Copies one DenseMatrix<double> into another. Uses BLAS if possible.
template<>
void Copy (DenseMatrix< complex > &dest, const DenseMatrix< complex > &src)
 Copies one DenseMatrix<complex> into another. Uses BLAS if possible.
template<>
void Add (DenseMatrix< complex > &result, const DenseMatrix< complex > &m1, const DenseMatrix< complex > &m2, complex scale)
 Adds a scalar multiple of one DenseMatrix<complex> to another, storing the result in a third. Uses BLAS if possible.
template<>
void Add (DenseMatrix< double > &result, const DenseMatrix< double > &m1, const DenseMatrix< double > &m2, double scale)
 Adds a scalar multiple of one DenseMatrix<double> to another, storing the result in a third. Uses BLAS if possible.
template<>
void AddTo (DenseMatrix< complex > &result, const DenseMatrix< complex > &m, complex scale)
 Adds a scalar multiple of one DenseMatrix<complex> to another in place. Uses BLAS if possible.
template<>
void AddTo (DenseMatrix< double > &result, const DenseMatrix< double > &m, double scale)
 Adds a scalar multiple of one DenseMatrix<double> to another in place. Uses BLAS if possible.
template<>
void Multiply (DenseMatrix< double > &result, const DenseMatrix< double > &m1, const DenseMatrix< double > &m2)
 Multiplies one DenseMatrix<double> by another, storing the result in a third. Uses BLAS if possible.
template<>
void Multiply (DenseMatrix< complex > &result, const DenseMatrix< complex > &m1, const DenseMatrix< complex > &m2)
 Multiplies one DenseMatrix<complex> by another, storing the result in a third. Uses BLAS if possible.
template<>
void Multiply (DenseMatrix< complex > &result, const DenseMatrix< complex > &m, complex scalar)
 Scales a DenseMatrix<complex> by a scalar, storing the result in another. Uses BLAS if possible.
template<>
void Multiply (DenseMatrix< double > &result, const DenseMatrix< double > &m, double scalar)
 Scales a DenseMatrix<double> by a scalar, storing the result in another. Uses BLAS if possible.
template<>
void MultiplyBy (DenseMatrix< complex > &result, complex scalar)
 Scales a DenseMatrix<complex> by a scalar in place. Uses BLAS if possible.
template<>
void MultiplyBy (DenseMatrix< double > &result, double scalar)
 Scales a DenseMatrix<double> by a scalar in place. Uses BLAS if possible.
template<>
complex dot (const DenseMatrix< complex > &m1, const DenseMatrix< complex > &m2)
 Computes the dot product of two DenseMatrix<complex> objects. Uses BLAS if possible.
template<>
double dot (const DenseMatrix< double > &m1, const DenseMatrix< double > &m2)
 Computes the Hilbert-Schmidt dot product of two DenseMatrix<double> objects. Uses BLAS if possible.
template<>
complex c_dot (const DenseMatrix< complex > &m1, const DenseMatrix< complex > &m2)
 Computes the conjugate dot product of two DenseMatrix<complex> objects. Uses BLAS if possible.
template<>
double c_dot (const DenseMatrix< double > &m1, const DenseMatrix< double > &m2)
 Computes the Hilbert-Schmidt conjugate dot product of two DenseMatrix<double> objects. Uses BLAS if possible.
template<>
void Multiply (DenseVector< complex > &result, const DenseMatrix< complex > &m, const DenseVector< complex > &v)
 Multiplies a DenseVector<complex> by a DenseMatrix<complex> from the left and stores the result in another DenseVector<complex>. Uses BLAS if possible.
template<>
void Multiply (DenseVector< double > &result, const DenseMatrix< double > &m, const DenseVector< double > &v)
 Multiplies a DenseVector<double> by a DenseMatrix<double> from the left and stores the result in another DenseVector<double>. Uses BLAS if possible.
template<>
void Multiply (DenseVector< complex > &result, const DenseVector< complex > &v, const DenseMatrix< complex > &m)
 Multiplies a DenseVector<complex> by a DenseMatrix<complex> from the right and stores the result in another DenseVector<complex>. Uses BLAS if possible.
template<>
void Multiply (DenseVector< double > &result, const DenseVector< double > &v, const DenseMatrix< double > &m)
 Multiplies a DenseVector<double> by a DenseMatrix<double> from the right and stores the result in another DenseVector<double>. Uses BLAS if possible.

Variables

const double Pi = M_PI
 Defined in linalg.cpp as M_PI.
std::ofstream * ProfileStream = NULL
 Output stream, used by Profile(), which opens it to "profile.log".

Detailed Description

Source code for most of the DenseVector<T> and DenseMatrix<T> methods, where T = double or T = std::complex<double>. Also some miscellaneous stuff.

Function Documentation

bool CholeskyFactor (  DenseMatrix< double > &  M,
bool  UpperTriangle = true
) 
 

Computes the Cholesky factorization of a symmetric positive definite matrix in place.

The input matrix $ M $ will be replaced by an upper triangular matrix $ U $ such that $ U^T U = M $ , unless the optional second parameter is set to false, in which case the result will be a lower triangular matrix $ L $ such that $ L L^T = M $ . In either case, the values on the diagonal will be non-negative.

The input matrix is assumed to be symmetric positive definite. Either the upper or lower triangle (depending on the value of UpperTriangle) will be ignored, and if the matrix turns out not to be positive, the routine will fail. The return value is "TRUE" unless the routine failed.

IMPORTANT NOTE: The input matrix will be overwritten. ingroup LAPACK

bool CholeskyFactor (  DenseMatrix< complex > &  M,
bool  UpperTriangle = true
) 
 

Computes the Cholesky factorization of a Hermitian positive definite matrix in place.

The input matrix $ M $ will be replaced by an upper triangular matrix $ U $ such that $ U^\dagger U = M $ , unless the optional second parameter is set to false, in which case the result will be a lower triangular matrix $ L $ such that $ L L^\dagger = M $ . In either case, the values on the diagonal will be real and non-negative.

The input matrix is assumed to be Hermitian positive definite. Either the upper or lower triangle (depending on the value of UpperTriangle) will be ignored, and if the matrix turns out not to be positive, the routine will fail. The return value is "TRUE" unless the routine failed.

IMPORTANT NOTE: The input matrix will be overwritten. ingroup LAPACK

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