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, cmat &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, cmat &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 matrices.

void	itpp::forward_substitution (const mat &L, int p, const vec &b, vec &x)
	Forward substitution of band matrices.

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.

Detailed Description

Function Documentation

ITPP_EXPORT bool itpp::ls_solve	(	const mat &	A,
		const vec &	b,
		vec &	x
	)

Solve linear equation system by LU factorisation.

Solves the linear system $Ax=b$ , where $A$ is a $n \times n$ matrix. Uses the LAPACK routine DGESV.

Definition at line 268 of file ls_solve.cpp.

References it_error.

Referenced by itpp::backslash(), and itpp::ls_solve().

ITPP_EXPORT vec itpp::ls_solve	(	const mat &	A,
		const vec &	b
	)

Solve linear equation system by LU factorisation.

Solves the linear system $Ax=b$ , where $A$ is a $n \times n$ matrix. Uses the LAPACK routine DGESV.

Definition at line 294 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve().

bool itpp::ls_solve	(	const mat &	A,
		const mat &	B,
		mat &	X
	)

Solve multiple linear equations by LU factorisation.

Solves the linear system $AX=B$ . Here $A$ is a nonsingular $n \times n$ matrix. Uses the LAPACK routine DGESV.

Definition at line 274 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT mat itpp::ls_solve	(	const mat &	A,
		const mat &	B
	)

Solve multiple linear equations by LU factorisation.

Solves the linear system $AX=B$ . Here $A$ is a nonsingular $n \times n$ matrix. Uses the LAPACK routine DGESV.

Definition at line 303 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve().

ITPP_EXPORT bool itpp::ls_solve	(	const cmat &	A,
		const cvec &	b,
		cvec &	x
	)

Solve linear equation system by LU factorisation.

Solves the linear system $Ax=b$ , where $A$ is a $n \times n$ matrix. Uses the LAPACK routine ZGESV.

Definition at line 280 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT cvec itpp::ls_solve	(	const cmat &	A,
		const cvec &	b
	)

Solve linear equation system by LU factorisation.

Solves the linear system $Ax=b$ , where $A$ is a $n \times n$ matrix. Uses the LAPACK routine ZGESV.

Definition at line 312 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve().

ITPP_EXPORT bool itpp::ls_solve	(	const cmat &	A,
		const cmat &	B,
		cmat &	X
	)

Solve multiple linear equations by LU factorisation.

Solves the linear system $AX=B$ . Here $A$ is a nonsingular $n \times n$ matrix. Uses the LAPACK routine ZGESV.

Definition at line 286 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT cmat itpp::ls_solve	(	const cmat &	A,
		const cmat &	B
	)

Solve multiple linear equations by LU factorisation.

Solves the linear system $AX=B$ . Here $A$ is a nonsingular $n \times n$ matrix. Uses the LAPACK routine ZGESV.

Definition at line 321 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve().

ITPP_EXPORT bool itpp::ls_solve_chol	(	const mat &	A,
		const vec &	b,
		vec &	x
	)

Solve linear equation system by Cholesky factorisation.

Solves the linear system $Ax=b$ , where $A$ is a symmetric positive definite $n \times n$ matrix. Uses the LAPACK routine DPOSV.

Definition at line 128 of file ls_solve.cpp.

References it_error.

Referenced by itpp::ls_solve_chol().

ITPP_EXPORT vec itpp::ls_solve_chol	(	const mat &	A,
		const vec &	b
	)

Solve linear equation system by Cholesky factorisation.

Solves the linear system $Ax=b$ , where $A$ is a symmetric positive definite $n \times n$ matrix. Uses the LAPACK routine DPOSV.

Definition at line 154 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_chol().

ITPP_EXPORT bool itpp::ls_solve_chol	(	const mat &	A,
		const mat &	B,
		mat &	X
	)

Solve linear equation system by Cholesky factorisation.

Solves the linear system $AX=B$ , where $A$ is a symmetric positive definite $n \times n$ matrix. Uses the LAPACK routine DPOSV.

Definition at line 134 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT mat itpp::ls_solve_chol	(	const mat &	A,
		const mat &	B
	)

Solve linear equation system by Cholesky factorisation.

Solves the linear system $AX=B$ , where $A$ is a symmetric positive definite $n \times n$ matrix. Uses the LAPACK routine DPOSV.

Definition at line 163 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_chol().

ITPP_EXPORT bool itpp::ls_solve_chol	(	const cmat &	A,
		const cvec &	b,
		cvec &	x
	)

Solve linear equation system by Cholesky factorisation.

Solves the linear system $Ax=b$ , where $A$ is a Hermitian positive definite $n \times n$ matrix. Uses the LAPACK routine ZPOSV.

Definition at line 140 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT cvec itpp::ls_solve_chol	(	const cmat &	A,
		const cvec &	b
	)

Solve linear equation system by Cholesky factorisation.

Solves the linear system $Ax=b$ , where $A$ is a Hermitian positive definite $n \times n$ matrix. Uses the LAPACK routine ZPOSV.

Definition at line 172 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_chol().

ITPP_EXPORT bool itpp::ls_solve_chol	(	const cmat &	A,
		const cmat &	B,
		cmat &	X
	)

Solve linear equation system by Cholesky factorisation.

Solves the linear system $AX=B$ , where $A$ is a Hermitian positive definite $n \times n$ matrix. Uses the LAPACK routine ZPOSV.

Definition at line 146 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT cmat itpp::ls_solve_chol	(	const cmat &	A,
		const cmat &	B
	)

Solve linear equation system by Cholesky factorisation.

Solves the linear system $AX=B$ , where $A$ is a Hermitian positive definite $n \times n$ matrix. Uses the LAPACK routine ZPOSV.

Definition at line 181 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_chol().

ITPP_EXPORT bool itpp::ls_solve_od	(	const mat &	A,
		const vec &	b,
		vec &	x
	)

Solves overdetermined linear equation systems.

Solves the overdetermined linear system $Ax=b$ , where $A$ is a $m \times n$ matrix and $m \geq n$ . Uses QR-factorization and is built upon the LAPACK routine DGELS.

Definition at line 424 of file ls_solve.cpp.

References it_error.

Referenced by itpp::backslash(), and itpp::ls_solve_od().

ITPP_EXPORT vec itpp::ls_solve_od	(	const mat &	A,
		const vec &	b
	)

Solves overdetermined linear equation systems.

Solves the overdetermined linear system $Ax=b$ , where $A$ is a $m \times n$ matrix and $m \geq n$ . Uses QR-factorization and assumes that $A$ is full rank. Based on the LAPACK routine DGELS.

Definition at line 450 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_od().

ITPP_EXPORT bool itpp::ls_solve_od	(	const mat &	A,
		const mat &	B,
		mat &	X
	)

Solves overdetermined linear equation systems.

Solves the overdetermined linear system $AX=B$ , where $A$ is a $m \times n$ matrix and $m \geq n$ . Uses QR-factorization and assumes that $A$ is full rank. Based on the LAPACK routine DGELS.

Definition at line 430 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT mat itpp::ls_solve_od	(	const mat &	A,
		const mat &	B
	)

Solves overdetermined linear equation systems.

Solves the overdetermined linear system $AX=B$ , where $A$ is a $m \times n$ matrix and $m \geq n$ . Uses QR-factorization and assumes that $A$ is full rank. Based on the LAPACK routine DGELS.

Definition at line 459 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_od().

ITPP_EXPORT bool itpp::ls_solve_od	(	const cmat &	A,
		const cvec &	b,
		cvec &	x
	)

Solves overdetermined linear equation systems.

Solves the overdetermined linear system $Ax=b$ , where $A$ is a $m \times n$ matrix and $m \geq n$ . Uses QR-factorization and is built upon the LAPACK routine ZGELS.

Definition at line 436 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT cvec itpp::ls_solve_od	(	const cmat &	A,
		const cvec &	b
	)

Solves overdetermined linear equation systems.

Solves the overdetermined linear system $Ax=b$ , where $A$ is a $m \times n$ matrix and $m \geq n$ . Uses QR-factorization and assumes that $A$ is full rank. Based on the LAPACK routine ZGELS.

Definition at line 468 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_od().

ITPP_EXPORT bool itpp::ls_solve_od	(	const cmat &	A,
		const cmat &	B,
		cmat &	X
	)

Solves overdetermined linear equation systems.

Solves the overdetermined linear system $AX=B$ , where $A$ is a $m \times n$ matrix and $m \geq n$ . Uses QR-factorization and assumes that $A$ is full rank. Based on the LAPACK routine ZGELS.

Definition at line 442 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT cmat itpp::ls_solve_od	(	const cmat &	A,
		const cmat &	B
	)

Solves overdetermined linear equation systems.

Solves the overdetermined linear system $AX=B$ , where $A$ is a $m \times n$ matrix and $m \geq n$ . Uses QR-factorization and assumes that $A$ is full rank. Based on the LAPACK routine ZGELS.

Definition at line 477 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_od().

ITPP_EXPORT bool itpp::ls_solve_ud	(	const mat &	A,
		const vec &	b,
		vec &	x
	)

Solves underdetermined linear equation systems.

Solves the underdetermined linear system $Ax=b$ , where $A$ is a $m \times n$ matrix and $m \leq n$ . Uses LQ-factorization and is built upon the LAPACK routine DGELS.

Definition at line 585 of file ls_solve.cpp.

References it_error.

Referenced by itpp::backslash(), and itpp::ls_solve_ud().

ITPP_EXPORT vec itpp::ls_solve_ud	(	const mat &	A,
		const vec &	b
	)

Solves overdetermined linear equation systems.

Solves the underdetermined linear system $Ax=b$ , where $A$ is a $m \times n$ matrix and $m \leq n$ . Uses LQ-factorization and assumes that $A$ is full rank. Based on the LAPACK routine DGELS.

Definition at line 612 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_ud().

ITPP_EXPORT bool itpp::ls_solve_ud	(	const mat &	A,
		const mat &	B,
		mat &	X
	)

Solves underdetermined linear equation systems.

Solves the underdetermined linear system $AX=B$ , where $A$ is a $m \times n$ matrix and $m \leq n$ . Uses LQ-factorization and assumes that $A$ is full rank. Based on the LAPACK routine DGELS.

Definition at line 591 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT mat itpp::ls_solve_ud	(	const mat &	A,
		const mat &	B
	)

Solves underdetermined linear equation systems.

Solves the underdetermined linear system $AX=B$ , where $A$ is a $m \times n$ matrix and $m \leq n$ . Uses LQ-factorization and assumes that $A$ is full rank. Based on the LAPACK routine DGELS.

Definition at line 621 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_ud().

ITPP_EXPORT bool itpp::ls_solve_ud	(	const cmat &	A,
		const cvec &	b,
		cvec &	x
	)

Solves underdetermined linear equation systems.

Solves the underdetermined linear system $Ax=b$ , where $A$ is a $m \times n$ matrix and $m \leq n$ . Uses LQ-factorization and is built upon the LAPACK routine ZGELS.

Definition at line 597 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT cvec itpp::ls_solve_ud	(	const cmat &	A,
		const cvec &	b
	)

Solves overdetermined linear equation systems.

Solves the underdetermined linear system $Ax=b$ , where $A$ is a $m \times n$ matrix and $m \leq n$ . Uses LQ-factorization and assumes that $A$ is full rank. Based on the LAPACK routine ZGELS.

Definition at line 630 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_ud().

ITPP_EXPORT bool itpp::ls_solve_ud	(	const cmat &	A,
		const cmat &	B,
		cmat &	X
	)

Solves underdetermined linear equation systems.

Solves the underdetermined linear system $AX=B$ , where $A$ is a $m \times n$ matrix and $m \leq n$ . Uses LQ-factorization and assumes that $A$ is full rank. Based on the LAPACK routine ZGELS.

Definition at line 603 of file ls_solve.cpp.

References it_error.

ITPP_EXPORT cmat itpp::ls_solve_ud	(	const cmat &	A,
		const cmat &	B
	)

Solves underdetermined linear equation systems.

Solves the underdetermined linear system $AX=B$ , where $A$ is a $m \times n$ matrix and $m \leq n$ . Uses LQ-factorization and assumes that $A$ is full rank. Based on the LAPACK routine ZGELS.

Definition at line 639 of file ls_solve.cpp.

References it_assert_debug, and itpp::ls_solve_ud().

ITPP_EXPORT bool itpp::backslash	(	const mat &	A,
		const vec &	b,
		vec &	x
	)

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 651 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().

ITPP_EXPORT vec itpp::backslash	(	const mat &	A,
		const vec &	b
	)

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 667 of file ls_solve.cpp.

References itpp::backslash(), and it_assert_debug.

ITPP_EXPORT bool itpp::backslash	(	const mat &	A,
		const mat &	B,
		mat &	X
	)

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 677 of file ls_solve.cpp.

References itpp::ls_solve(), itpp::ls_solve_od(), and itpp::ls_solve_ud().

ITPP_EXPORT mat itpp::backslash	(	const mat &	A,
		const mat &	B
	)

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 693 of file ls_solve.cpp.

References itpp::backslash(), and it_assert_debug.

ITPP_EXPORT bool itpp::backslash	(	const cmat &	A,
		const cvec &	b,
		cvec &	x
	)

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 703 of file ls_solve.cpp.

References itpp::ls_solve(), itpp::ls_solve_od(), and itpp::ls_solve_ud().

ITPP_EXPORT cvec itpp::backslash	(	const cmat &	A,
		const cvec &	b
	)

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 719 of file ls_solve.cpp.

References itpp::backslash(), and it_assert_debug.

ITPP_EXPORT bool itpp::backslash	(	const cmat &	A,
		const cmat &	B,
		cmat &	X
	)

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 729 of file ls_solve.cpp.

References itpp::ls_solve(), itpp::ls_solve_od(), and itpp::ls_solve_ud().

ITPP_EXPORT cmat itpp::backslash	(	const cmat &	A,
		const cmat &	B
	)

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 744 of file ls_solve.cpp.

References itpp::backslash(), and it_assert_debug.

ITPP_EXPORT vec itpp::forward_substitution	(	const mat &	L,
		const vec &	b
	)

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 756 of file ls_solve.cpp.

Referenced by itpp::forward_substitution().

ITPP_EXPORT void itpp::forward_substitution	(	const mat &	L,
		const vec &	b,
		vec &	x
	)

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 766 of file ls_solve.cpp.

References it_assert.

ITPP_EXPORT vec itpp::forward_substitution	(	const mat &	L,
		int	p,
		const vec &	b
	)

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.

Definition at line 787 of file ls_solve.cpp.

References itpp::forward_substitution().

ITPP_EXPORT void itpp::forward_substitution	(	const mat &	L,
		int	p,
		const vec &	b,
		vec &	x
	)

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.

Definition at line 797 of file ls_solve.cpp.

References it_assert, and itpp::min().

ITPP_EXPORT vec itpp::backward_substitution	(	const mat &	U,
		const vec &	b
	)

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 813 of file ls_solve.cpp.

Referenced by itpp::backward_substitution().

ITPP_EXPORT void itpp::backward_substitution	(	const mat &	U,
		const vec &	b,
		vec &	x
	)

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 821 of file ls_solve.cpp.

References it_assert.

ITPP_EXPORT vec itpp::backward_substitution	(	const mat &	U,
		int	q,
		const vec &	b
	)

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 842 of file ls_solve.cpp.

References itpp::backward_substitution().

ITPP_EXPORT void itpp::backward_substitution	(	const mat &	U,
		int	q,
		const vec &	b,
		vec &	x
	)

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 850 of file ls_solve.cpp.

References it_assert, and itpp::max().

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