Functions | |
bool | itpp::ls_solve (const mat &A, const vec &b, vec &x) |
Solve linear equation system by LU factorisation. | |
vec | itpp::ls_solve (const mat &A, const vec &b) |
Solve linear equation system by LU factorisation. | |
bool | itpp::ls_solve (const mat &A, const mat &B, mat &X) |
Solve multiple linear equations by LU factorisation. | |
mat | itpp::ls_solve (const mat &A, const mat &B) |
Solve multiple linear equations by LU factorisation. | |
bool | itpp::ls_solve (const cmat &A, const cvec &b, cvec &x) |
Solve linear equation system by LU factorisation. | |
cvec | itpp::ls_solve (const cmat &A, const cvec &b) |
Solve linear equation system by LU factorisation. | |
bool | itpp::ls_solve (const cmat &A, const cmat &B, cmat &X) |
Solve multiple linear equations by LU factorisation. | |
cmat | itpp::ls_solve (const cmat &A, const cmat &B) |
Solve multiple linear equations by LU factorisation. | |
bool | itpp::ls_solve_chol (const mat &A, const vec &b, vec &x) |
Solve linear equation system by Cholesky factorisation. | |
vec | itpp::ls_solve_chol (const mat &A, const vec &b) |
Solve linear equation system by Cholesky factorisation. | |
bool | itpp::ls_solve_chol (const mat &A, const mat &B, mat &X) |
Solve linear equation system by Cholesky factorisation. | |
mat | itpp::ls_solve_chol (const mat &A, const mat &B) |
Solve linear equation system by Cholesky factorisation. | |
bool | itpp::ls_solve_chol (const cmat &A, const cvec &b, cvec &x) |
Solve linear equation system by Cholesky factorisation. | |
cvec | itpp::ls_solve_chol (const cmat &A, const cvec &b) |
Solve linear equation system by Cholesky factorisation. | |
bool | itpp::ls_solve_chol (const cmat &A, const cmat &B, cmat &X) |
Solve linear equation system by Cholesky factorisation. | |
cmat | itpp::ls_solve_chol (const cmat &A, const cmat &B) |
Solve linear equation system by Cholesky factorisation. | |
bool | itpp::ls_solve_od (const mat &A, const vec &b, vec &x) |
Solves overdetermined linear equation systems. | |
vec | itpp::ls_solve_od (const mat &A, const vec &b) |
Solves overdetermined linear equation systems. | |
bool | itpp::ls_solve_od (const mat &A, const mat &B, mat &X) |
Solves overdetermined linear equation systems. | |
mat | itpp::ls_solve_od (const mat &A, const mat &B) |
Solves overdetermined linear equation systems. | |
bool | itpp::ls_solve_od (const cmat &A, const cvec &b, cvec &x) |
Solves overdetermined linear equation systems. | |
cvec | itpp::ls_solve_od (const cmat &A, const cvec &b) |
Solves overdetermined linear equation systems. | |
bool | itpp::ls_solve_od (const cmat &A, const cmat &B, mat &X) |
Solves overdetermined linear equation systems. | |
cmat | itpp::ls_solve_od (const cmat &A, const cmat &B) |
Solves overdetermined linear equation systems. | |
bool | itpp::ls_solve_ud (const mat &A, const vec &b, vec &x) |
Solves underdetermined linear equation systems. | |
vec | itpp::ls_solve_ud (const mat &A, const vec &b) |
Solves overdetermined linear equation systems. | |
bool | itpp::ls_solve_ud (const mat &A, const mat &B, mat &X) |
Solves underdetermined linear equation systems. | |
mat | itpp::ls_solve_ud (const mat &A, const mat &B) |
Solves underdetermined linear equation systems. | |
bool | itpp::ls_solve_ud (const cmat &A, const cvec &b, cvec &x) |
Solves underdetermined linear equation systems. | |
cvec | itpp::ls_solve_ud (const cmat &A, const cvec &b) |
Solves overdetermined linear equation systems. | |
bool | itpp::ls_solve_ud (const cmat &A, const cmat &B, mat &X) |
Solves underdetermined linear equation systems. | |
cmat | itpp::ls_solve_ud (const cmat &A, const cmat &B) |
Solves underdetermined linear equation systems. | |
bool | itpp::backslash (const mat &A, const vec &b, vec &x) |
A general linear equation system solver. | |
vec | itpp::backslash (const mat &A, const vec &b) |
A general linear equation system solver. | |
bool | itpp::backslash (const mat &A, const mat &B, mat &X) |
A general linear equation system solver. | |
mat | itpp::backslash (const mat &A, const mat &B) |
A general linear equation system solver. | |
bool | itpp::backslash (const cmat &A, const cvec &b, cvec &x) |
A general linear equation system solver. | |
cvec | itpp::backslash (const cmat &A, const cvec &b) |
A general linear equation system solver. | |
bool | itpp::backslash (const cmat &A, const cmat &B, cmat &X) |
A general linear equation system solver. | |
cmat | itpp::backslash (const cmat &A, const cmat &B) |
A general linear equation system solver. | |
vec | itpp::forward_substitution (const mat &L, const vec &b) |
Forward substitution of square matrix. | |
void | itpp::forward_substitution (const mat &L, const vec &b, vec &x) |
Forward substitution of square matrix. | |
vec | itpp::forward_substitution (const mat &L, int p, const vec &b) |
Forward substitution of band matricies. | |
void | itpp::forward_substitution (const mat &L, int p, const vec &b, vec &x) |
Forward substitution of band matricies. | |
vec | itpp::backward_substitution (const mat &U, const vec &b) |
Backward substitution of square matrix. | |
void | itpp::backward_substitution (const mat &U, const vec &b, vec &x) |
Backward substitution of square matrix. | |
vec | itpp::backward_substitution (const mat &U, int q, const vec &b) |
Backward substitution of band matrix. | |
void | itpp::backward_substitution (const mat &U, int q, const vec &b, vec &x) |
Backward substitution of band matrix. |
Solve linear equation system by LU factorisation.
Solves the linear system , where
is a
matrix. Uses the LAPACK routine DGESV.
Definition at line 197 of file ls_solve.cpp.
References it_assert1.
Referenced by itpp::backslash(), and itpp::ls_solve().
Solve linear equation system by LU factorisation.
Solves the linear system , where
is a
matrix. Uses the LAPACK routine DGESV.
Definition at line 297 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve().
Solve multiple linear equations by LU factorisation.
Solves the linear system . Here
is a nonsingular
matrix. Uses the LAPACK routine DGESV.
Definition at line 215 of file ls_solve.cpp.
References it_assert1.
Solve multiple linear equations by LU factorisation.
Solves the linear system . Here
is a nonsingular
matrix. Uses the LAPACK routine DGESV.
Definition at line 306 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve().
Solve linear equation system by LU factorisation.
Solves the linear system , where
is a
matrix. Uses the LAPACK routine ZGESV.
Definition at line 233 of file ls_solve.cpp.
References it_assert1.
Solve linear equation system by LU factorisation.
Solves the linear system , where
is a
matrix. Uses the LAPACK routine ZGESV.
Definition at line 315 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve().
Solve multiple linear equations by LU factorisation.
Solves the linear system . Here
is a nonsingular
matrix. Uses the LAPACK routine ZGESV.
Definition at line 251 of file ls_solve.cpp.
References it_assert1.
Solve multiple linear equations by LU factorisation.
Solves the linear system . Here
is a nonsingular
matrix. Uses the LAPACK routine ZGESV.
Definition at line 324 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve().
Solve linear equation system by Cholesky factorisation.
Solves the linear system , where
is a symmetric postive definite
matrix. Uses the LAPACK routine DPOSV.
Definition at line 52 of file ls_solve.cpp.
References it_assert1.
Referenced by itpp::ls_solve_chol().
Solve linear equation system by Cholesky factorisation.
Solves the linear system , where
is a symmetric postive definite
matrix. Uses the LAPACK routine DPOSV.
Definition at line 157 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_chol().
Solve linear equation system by Cholesky factorisation.
Solves the linear system , where
is a symmetric postive definite
matrix. Uses the LAPACK routine DPOSV.
Definition at line 72 of file ls_solve.cpp.
References it_assert1.
Solve linear equation system by Cholesky factorisation.
Solves the linear system , where
is a symmetric postive definite
matrix. Uses the LAPACK routine DPOSV.
Definition at line 166 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_chol().
Solve linear equation system by Cholesky factorisation.
Solves the linear system , where
is a Hermitian postive definite
matrix. Uses the LAPACK routine ZPOSV.
Definition at line 91 of file ls_solve.cpp.
References it_assert1.
Solve linear equation system by Cholesky factorisation.
Solves the linear system , where
is a Hermitian postive definite
matrix. Uses the LAPACK routine ZPOSV.
Definition at line 175 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_chol().
Solve linear equation system by Cholesky factorisation.
Solves the linear system , where
is a Hermitian postive definite
matrix. Uses the LAPACK routine ZPOSV.
Definition at line 110 of file ls_solve.cpp.
References it_assert1.
Solve linear equation system by Cholesky factorisation.
Solves the linear system , where
is a Hermitian postive definite
matrix. Uses the LAPACK routine ZPOSV.
Definition at line 184 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_chol().
Solves overdetermined linear equation systems.
Solves the overdetermined linear system , where
is a
matrix and
. Uses QR-factorization and is built upon the LAPACK routine DGELS.
Definition at line 337 of file ls_solve.cpp.
References it_assert1, and max.
Referenced by itpp::backslash(), and itpp::ls_solve_od().
Solves overdetermined linear equation systems.
Solves the overdetermined linear system , where
is a
matrix and
. Uses QR-factorization and assumes that
is full rank. Based on the LAPACK routine DGELS.
Definition at line 453 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_od().
Solves overdetermined linear equation systems.
Solves the overdetermined linear system , where
is a
matrix and
. Uses QR-factorization and assumes that
is full rank. Based on the LAPACK routine DGELS.
Definition at line 359 of file ls_solve.cpp.
References it_assert1, and max.
Solves overdetermined linear equation systems.
Solves the overdetermined linear system , where
is a
matrix and
. Uses QR-factorization and assumes that
is full rank. Based on the LAPACK routine DGELS.
Definition at line 462 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_od().
Solves overdetermined linear equation systems.
Solves the overdetermined linear system , where
is a
matrix and
. Uses QR-factorization and is built upon the LAPACK routine ZGELS.
Definition at line 381 of file ls_solve.cpp.
References it_assert1, and max.
Solves overdetermined linear equation systems.
Solves the overdetermined linear system , where
is a
matrix and
. Uses QR-factorization and assumes that
is full rank. Based on the LAPACK routine ZGELS.
Definition at line 471 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_od().
Solves overdetermined linear equation systems.
Solves the overdetermined linear system , where
is a
matrix and
. Uses QR-factorization and assumes that
is full rank. Based on the LAPACK routine ZGELS.
Solves overdetermined linear equation systems.
Solves the overdetermined linear system , where
is a
matrix and
. Uses QR-factorization and assumes that
is full rank. Based on the LAPACK routine ZGELS.
Definition at line 480 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_od().
Solves underdetermined linear equation systems.
Solves the underdetermined linear system , where
is a
matrix and
. Uses LQ-factorization and is built upon the LAPACK routine DGELS.
Definition at line 492 of file ls_solve.cpp.
References it_assert1, and max.
Referenced by itpp::backslash(), and itpp::ls_solve_ud().
Solves overdetermined linear equation systems.
Solves the underdetermined linear system , where
is a
matrix and
. Uses LQ-factorization and assumes that
is full rank. Based on the LAPACK routine DGELS.
Definition at line 615 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_ud().
Solves underdetermined linear equation systems.
Solves the underdetermined linear system , where
is a
matrix and
. Uses LQ-factorization and assumes that
is full rank. Based on the LAPACK routine DGELS.
Definition at line 515 of file ls_solve.cpp.
References it_assert1, and max.
Solves underdetermined linear equation systems.
Solves the underdetermined linear system , where
is a
matrix and
. Uses LQ-factorization and assumes that
is full rank. Based on the LAPACK routine DGELS.
Definition at line 624 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_ud().
Solves underdetermined linear equation systems.
Solves the underdetermined linear system , where
is a
matrix and
. Uses LQ-factorization and is built upon the LAPACK routine ZGELS.
Definition at line 539 of file ls_solve.cpp.
References it_assert1, and max.
Solves overdetermined linear equation systems.
Solves the underdetermined linear system , where
is a
matrix and
. Uses LQ-factorization and assumes that
is full rank. Based on the LAPACK routine ZGELS.
Definition at line 633 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_ud().
Solves underdetermined linear equation systems.
Solves the underdetermined linear system , where
is a
matrix and
. Uses LQ-factorization and assumes that
is full rank. Based on the LAPACK routine ZGELS.
Solves underdetermined linear equation systems.
Solves the underdetermined linear system , where
is a
matrix and
. Uses LQ-factorization and assumes that
is full rank. Based on the LAPACK routine ZGELS.
Definition at line 642 of file ls_solve.cpp.
References it_assert1, and itpp::ls_solve_ud().
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)
Definition at line 654 of file ls_solve.cpp.
References itpp::ls_solve(), itpp::ls_solve_od(), and itpp::ls_solve_ud().
Referenced by itpp::arma_estimator(), itpp::backslash(), and itpp::modified_yule_walker().
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)
Definition at line 670 of file ls_solve.cpp.
References itpp::backslash(), and it_assert1.
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).
Definition at line 680 of file ls_solve.cpp.
References itpp::ls_solve(), itpp::ls_solve_od(), and itpp::ls_solve_ud().
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).
Definition at line 696 of file ls_solve.cpp.
References itpp::backslash(), and it_assert1.
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)
Definition at line 706 of file ls_solve.cpp.
References itpp::ls_solve(), itpp::ls_solve_od(), and itpp::ls_solve_ud().
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)
Definition at line 722 of file ls_solve.cpp.
References itpp::backslash(), and it_assert1.
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).
Definition at line 732 of file ls_solve.cpp.
References itpp::ls_solve(), itpp::ls_solve_od(), and itpp::ls_solve_ud().
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).
Definition at line 747 of file ls_solve.cpp.
References itpp::backslash(), and it_assert1.
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.
Definition at line 759 of file ls_solve.cpp.
Referenced by itpp::forward_substitution().
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.
Definition at line 769 of file ls_solve.cpp.
References it_assert.
Forward substitution of band matricies.
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.
Definition at line 790 of file ls_solve.cpp.
References itpp::forward_substitution().
Forward substitution of band matricies.
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.
Definition at line 800 of file ls_solve.cpp.
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.
Definition at line 816 of file ls_solve.cpp.
Referenced by itpp::backward_substitution().
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.
Definition at line 824 of file ls_solve.cpp.
References it_assert.
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.
Definition at line 845 of file ls_solve.cpp.
References itpp::backward_substitution().
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.
Definition at line 853 of file ls_solve.cpp.
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