## [4ede1e]: itpp / base / algebra / ls_solve.h  Maximize  Restore  History

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See the GNU General Public License for more * details. * * You should have received a copy of the GNU General Public License along * with IT++. If not, see . * * ------------------------------------------------------------------------- */ #ifndef LS_SOLVE_H #define LS_SOLVE_H #include namespace itpp { /*! \addtogroup linearequations */ //!@{ /*! \brief Solve linear equation system by LU factorisation. Solves the linear system \f$Ax=b\f$, where \f$A\f$ is a \f$n \times n\f$ matrix. Uses the LAPACK routine DGESV. */ bool ls_solve(const mat &A, const vec &b, vec &x); /*! \brief Solve linear equation system by LU factorisation. Solves the linear system \f$Ax=b\f$, where \f$A\f$ is a \f$n \times n\f$ matrix. Uses the LAPACK routine DGESV. */ vec ls_solve(const mat &A, const vec &b); /*! \brief Solve multiple linear equations by LU factorisation. Solves the linear system \f$AX=B\f$. Here \f$A\f$ is a nonsingular \f$n \times n\f$ matrix. Uses the LAPACK routine DGESV. */ bool ls_solve(const mat &A, const mat &B, mat &X); /*! \brief Solve multiple linear equations by LU factorisation. Solves the linear system \f$AX=B\f$. Here \f$A\f$ is a nonsingular \f$n \times n\f$ matrix. Uses the LAPACK routine DGESV. */ mat ls_solve(const mat &A, const mat &B); /*! \brief Solve linear equation system by LU factorisation. Solves the linear system \f$Ax=b\f$, where \f$A\f$ is a \f$n \times n\f$ matrix. Uses the LAPACK routine ZGESV. */ bool ls_solve(const cmat &A, const cvec &b, cvec &x); /*! \brief Solve linear equation system by LU factorisation. Solves the linear system \f$Ax=b\f$, where \f$A\f$ is a \f$n \times n\f$ matrix. Uses the LAPACK routine ZGESV. */ cvec ls_solve(const cmat &A, const cvec &b); /*! \brief Solve multiple linear equations by LU factorisation. Solves the linear system \f$AX=B\f$. Here \f$A\f$ is a nonsingular \f$n \times n\f$ matrix. Uses the LAPACK routine ZGESV. */ bool ls_solve(const cmat &A, const cmat &B, cmat &X); /*! \brief Solve multiple linear equations by LU factorisation. Solves the linear system \f$AX=B\f$. Here \f$A\f$ is a nonsingular \f$n \times n\f$ matrix. Uses the LAPACK routine ZGESV. */ cmat ls_solve(const cmat &A, const cmat &B); /*! \brief Solve linear equation system by Cholesky factorisation. Solves the linear system \f$Ax=b\f$, where \f$A\f$ is a symmetric positive definite \f$n \times n\f$ matrix. Uses the LAPACK routine DPOSV. */ bool ls_solve_chol(const mat &A, const vec &b, vec &x); /*! \brief Solve linear equation system by Cholesky factorisation. Solves the linear system \f$Ax=b\f$, where \f$A\f$ is a symmetric positive definite \f$n \times n\f$ matrix. Uses the LAPACK routine DPOSV. */ vec ls_solve_chol(const mat &A, const vec &b); /*! \brief Solve linear equation system by Cholesky factorisation. Solves the linear system \f$AX=B\f$, where \f$A\f$ is a symmetric positive definite \f$n \times n\f$ matrix. Uses the LAPACK routine DPOSV. */ bool ls_solve_chol(const mat &A, const mat &B, mat &X); /*! \brief Solve linear equation system by Cholesky factorisation. Solves the linear system \f$AX=B\f$, where \f$A\f$ is a symmetric positive definite \f$n \times n\f$ matrix. Uses the LAPACK routine DPOSV. */ mat ls_solve_chol(const mat &A, const mat &B); /*! \brief Solve linear equation system by Cholesky factorisation. Solves the linear system \f$Ax=b\f$, where \f$A\f$ is a Hermitian positive definite \f$n \times n\f$ matrix. Uses the LAPACK routine ZPOSV. */ bool ls_solve_chol(const cmat &A, const cvec &b, cvec &x); /*! \brief Solve linear equation system by Cholesky factorisation. Solves the linear system \f$Ax=b\f$, where \f$A\f$ is a Hermitian positive definite \f$n \times n\f$ matrix. Uses the LAPACK routine ZPOSV. */ cvec ls_solve_chol(const cmat &A, const cvec &b); /*! \brief Solve linear equation system by Cholesky factorisation. Solves the linear system \f$AX=B\f$, where \f$A\f$ is a Hermitian positive definite \f$n \times n\f$ matrix. Uses the LAPACK routine ZPOSV. */ bool ls_solve_chol(const cmat &A, const cmat &B, cmat &X); /*! \brief Solve linear equation system by Cholesky factorisation. Solves the linear system \f$AX=B\f$, where \f$A\f$ is a Hermitian positive definite \f$n \times n\f$ matrix. Uses the LAPACK routine ZPOSV. */ cmat ls_solve_chol(const cmat &A, const cmat &B); /*! \brief Solves overdetermined linear equation systems. Solves the overdetermined linear system \f$Ax=b\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \geq n\f$. Uses QR-factorization and is built upon the LAPACK routine DGELS. */ bool ls_solve_od(const mat &A, const vec &b, vec &x); /*! \brief Solves overdetermined linear equation systems. Solves the overdetermined linear system \f$Ax=b\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \geq n\f$. Uses QR-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine DGELS. */ vec ls_solve_od(const mat &A, const vec &b); /*! \brief Solves overdetermined linear equation systems. Solves the overdetermined linear system \f$AX=B\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \geq n\f$. Uses QR-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine DGELS. */ bool ls_solve_od(const mat &A, const mat &B, mat &X); /*! \brief Solves overdetermined linear equation systems. Solves the overdetermined linear system \f$AX=B\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \geq n\f$. Uses QR-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine DGELS. */ mat ls_solve_od(const mat &A, const mat &B); /*! \brief Solves overdetermined linear equation systems. Solves the overdetermined linear system \f$Ax=b\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \geq n\f$. Uses QR-factorization and is built upon the LAPACK routine ZGELS. */ bool ls_solve_od(const cmat &A, const cvec &b, cvec &x); /*! \brief Solves overdetermined linear equation systems. Solves the overdetermined linear system \f$Ax=b\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \geq n\f$. Uses QR-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine ZGELS. */ cvec ls_solve_od(const cmat &A, const cvec &b); /*! \brief Solves overdetermined linear equation systems. Solves the overdetermined linear system \f$AX=B\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \geq n\f$. Uses QR-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine ZGELS. */ bool ls_solve_od(const cmat &A, const cmat &B, cmat &X); /*! \brief Solves overdetermined linear equation systems. Solves the overdetermined linear system \f$AX=B\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \geq n\f$. Uses QR-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine ZGELS. */ cmat ls_solve_od(const cmat &A, const cmat &B); /*! \brief Solves underdetermined linear equation systems. Solves the underdetermined linear system \f$Ax=b\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \leq n\f$. Uses LQ-factorization and is built upon the LAPACK routine DGELS. */ bool ls_solve_ud(const mat &A, const vec &b, vec &x); /*! \brief Solves overdetermined linear equation systems. Solves the underdetermined linear system \f$Ax=b\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \leq n\f$. Uses LQ-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine DGELS. */ vec ls_solve_ud(const mat &A, const vec &b); /*! \brief Solves underdetermined linear equation systems. Solves the underdetermined linear system \f$AX=B\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \leq n\f$. Uses LQ-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine DGELS. */ bool ls_solve_ud(const mat &A, const mat &B, mat &X); /*! \brief Solves underdetermined linear equation systems. Solves the underdetermined linear system \f$AX=B\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \leq n\f$. Uses LQ-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine DGELS. */ mat ls_solve_ud(const mat &A, const mat &B); /*! \brief Solves underdetermined linear equation systems. Solves the underdetermined linear system \f$Ax=b\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \leq n\f$. Uses LQ-factorization and is built upon the LAPACK routine ZGELS. */ bool ls_solve_ud(const cmat &A, const cvec &b, cvec &x); /*! \brief Solves overdetermined linear equation systems. Solves the underdetermined linear system \f$Ax=b\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \leq n\f$. Uses LQ-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine ZGELS. */ cvec ls_solve_ud(const cmat &A, const cvec &b); /*! \brief Solves underdetermined linear equation systems. Solves the underdetermined linear system \f$AX=B\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \leq n\f$. Uses LQ-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine ZGELS. */ bool ls_solve_ud(const cmat &A, const cmat &B, cmat &X); /*! \brief Solves underdetermined linear equation systems. Solves the underdetermined linear system \f$AX=B\f$, where \f$A\f$ is a \f$m \times n\f$ matrix and \f$m \leq n\f$. Uses LQ-factorization and assumes that \f$A\f$ is full rank. Based on the LAPACK routine ZGELS. */ cmat ls_solve_ud(const cmat &A, const cmat &B); /*! \brief A general linear equation system solver. Tries to emulate the backslash operator in Matlab by calling ls_solve(A,b,x), ls_solve_od(A,b,x) or ls_solve_ud(A,b,x) */ bool backslash(const mat &A, const vec &b, vec &x); /*! \brief A general linear equation system solver. Tries to emulate the backslash operator in Matlab by calling ls_solve(A,b), ls_solve_od(A,b) or ls_solve_ud(A,b) */ vec backslash(const mat &A, const vec &b); /*! \brief A general linear equation system solver. Tries to emulate the backslash operator in Matlab by calling ls_solve(A,B,X), ls_solve_od(A,B,X), or ls_solve_ud(A,B,X). */ bool backslash(const mat &A, const mat &B, mat &X); /*! \brief A general linear equation system solver. Tries to emulate the backslash operator in Matlab by calling ls_solve(A,B), ls_solve_od(A,B), or ls_solve_ud(A,B). */ mat backslash(const mat &A, const mat &B); /*! \brief A general linear equation system solver. Tries to emulate the backslash operator in Matlab by calling ls_solve(A,b,x), ls_solve_od(A,b,x) or ls_solve_ud(A,b,x) */ bool backslash(const cmat &A, const cvec &b, cvec &x); /*! \brief A general linear equation system solver. Tries to emulate the backslash operator in Matlab by calling ls_solve(A,b), ls_solve_od(A,b) or ls_solve_ud(A,b) */ cvec backslash(const cmat &A, const cvec &b); /*! \brief A general linear equation system solver. Tries to emulate the backslash operator in Matlab by calling ls_solve(A,B,X), ls_solve_od(A,B,X), or ls_solve_ud(A,B,X). */ bool backslash(const cmat &A, const cmat &B, cmat &X); /*! \brief A general linear equation system solver. Tries to emulate the backslash operator in Matlab by calling ls_solve(A,B), ls_solve_od(A,B), or ls_solve_ud(A,B). */ cmat backslash(const cmat &A, const cmat &B); /*! \brief Forward substitution of square matrix. Solves Lx=b, where L is a lower triangular n by n matrix. Assumes that L is nonsingular. Requires n^2 flops. Uses Alg. 3.1.1 in Golub & van Loan "Matrix computations", 3rd ed., p. 89. */ vec forward_substitution(const mat &L, const vec &b); /*! \brief Forward substitution of square matrix. Solves Lx=b, where L is a lower triangular n by n matrix. Assumes that L is nonsingular. Requires n^2 flops. Uses Alg. 3.1.1 in Golub & van Loan "Matrix computations", 3rd ed., p. 89. */ void forward_substitution(const mat &L, const vec &b, vec &x); /*! \brief Forward substitution of band matrices. Solves Lx=b, where L is a lower triangular n by n band-matrix with lower bandwidth p. Assumes that L is nonsingular. Requires about 2np flops (if n >> p). Uses Alg. 4.3.2 in Golub & van Loan "Matrix computations", 3rd ed., p. 153. */ vec forward_substitution(const mat &L, int p, const vec &b); /*! \brief Forward substitution of band matrices. Solves Lx=b, where L is a lower triangular n by n band-matrix with lower bandwidth p. Assumes that L is nonsingular. Requires about 2np flops (if n >> p). Uses Alg. 4.3.2 in Golub & van Loan "Matrix computations", 3rd ed., p. 153. */ void forward_substitution(const mat &L, int p, const vec &b, vec &x); /*! \brief Backward substitution of square matrix. Solves Ux=b, where U is a upper triangular n by n matrix. Assumes that U is nonsingular. Requires n^2 flops. Uses Alg. 3.1.2 in Golub & van Loan "Matrix computations", 3rd ed., p. 89. */ vec backward_substitution(const mat &U, const vec &b); /*! \brief Backward substitution of square matrix. Solves Ux=b, where U is a upper triangular n by n matrix. Assumes that U is nonsingular. Requires n^2 flops. Uses Alg. 3.1.2 in Golub & van Loan "Matrix computations", 3rd ed., p. 89. */ void backward_substitution(const mat &U, const vec &b, vec &x); /*! \brief Backward substitution of band matrix. Solves Ux=b, where U is a upper triangular n by n matrix band-matrix with upper bandwidth q. Assumes that U is nonsingular. Requires about 2nq flops (if n >> q). Uses Alg. 4.3.3 in Golub & van Loan "Matrix computations", 3rd ed., p. 153. */ vec backward_substitution(const mat &U, int q, const vec &b); /*! \brief Backward substitution of band matrix. Solves Ux=b, where U is a upper triangular n by n matrix band-matrix with upper bandwidth q. Assumes that U is nonsingular. Requires about 2nq flops (if n >> q). Uses Alg. 4.3.3 in Golub & van Loan "Matrix computations", 3rd ed., p. 153. */ void backward_substitution(const mat &U, int q, const vec &b, vec &x); //!@} } //namespace itpp #endif // #ifndef LS_SOLVE_H