linalg_lq Module

On input, an M-by-N matrix where the elements above the diagonal contain the elementary reflectors generated from the LQ factorization performed by lq_factor. On and below the diagonal the matrix contains the matrix $L$. On output, the elements above the diagonal are zeroed sucht hat the remaining matrix is the M-by-N lower trapezoidal matrix $L$ where only the M-by-M submatrix is the lower triangular matrix $L$. Notice, M must be less than or equal to N for this routine.

A MIN(M, N)-element array containing the scalar factors of each elementary reflector defined in $L$.

An N-by-N matrix where the orthogonal matrix $Q$ will be written.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

On input, an M-by-N matrix where the elements above the diagonal contain the elementary reflectors generated from the LQ factorization performed by lq_factor. On and below the diagonal the matrix contains the matrix $L$. On output, the elements above the diagonal are zeroed sucht hat the remaining matrix is the M-by-N lower trapezoidal matrix $L$ where only the M-by-M submatrix is the lower triangular matrix $L$. Notice, M must be less than or equal to N for this routine.

A MIN(M, N)-element array containing the scalar factors of each elementary reflector defined in $L$.

An N-by-N matrix where the orthogonal matrix $Q$ will be written.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

On input, the M-by-N matrix to factor. On output, the elements on and below the diagonal contain the MIN(M, N)-by-N lower trapezoidal matrix $L$ ($L$ is lower triangular if M >= N). The elements above the diagonal, along with the array tau, represent the orthogonal matrix $Q$ as a product of elementary reflectors.

A MIN(M, N)-element array used to store the scalar factors of the elementary reflectors.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

On input, the M-by-N matrix to factor. On output, the elements on and below the diagonal contain the MIN(M, N)-by-N lower trapezoidal matrix $L$ ($L$ is lower triangular if M >= N). The elements above the diagonal, along with the array tau, represent the orthogonal matrix $Q$ as a product of elementary reflectors.

A MIN(M, N)-element array used to store the scalar factors of the elementary reflectors.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

Set to true to compute $C = op(Q) C$; else, set to false to compute $C = C op(Q)$.

Set to true to compute $op(Q) = Q^T$; else, set to false to compute $op(Q) = Q$.

On input, an K-by-P matrix containing the elementary reflectors output from the LQ factorization. If lside is set to true, P = M; else, if lside is set to false, P = N.

A K-element array containing the scalar factors of each elementary reflector defined in a.

On input, the M-by-N matrix C. On output, the product of the orthogonal matrix Q and the original matrix C.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

Set to true to compute $C = op(Q) C$; else, set to false to compute $C = C op(Q)$.

Set to true to compute $op(Q) = Q^H$; else, set to false to compute $op(Q) = Q$.

On input, an K-by-P matrix containing the elementary reflectors output from the LQ factorization. If lside is set to true, P = M; else, if lside is set to false, P = N.

A K-element array containing the scalar factors of each elementary reflector defined in a.

On input, the M-by-N matrix C. On output, the product of the orthogonal matrix Q and the original matrix C.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

Set to true to compute $op(Q) = Q^T$; else, set to false to compute $op(Q) = Q$.

On input, an K-by-M matrix containing the elementary reflectors output from the LQ factorization. Notice, the contents of this matrix are restored on exit.

A K-element array containing the scalar factors of each elementary reflector defined in a.

On input, the M-element vector $\vec{c}$. On output, the product of the orthogonal matrix $Q$ and the original vector $\vec{c}$.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

Set to true to compute $op(Q) = Q^H$; else, set to false to compute $op(Q) = Q$.

On input, an K-by-M matrix containing the elementary reflectors output from the LQ factorization. Notice, the contents of this matrix are restored on exit.

A K-element array containing the scalar factors of each elementary reflector defined in a.

On input, the M-element vector $\vec{c}$. On output, the product of the orthogonal matrix $Q$ and the original vector $\vec{c}$.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

On input, the M-by-N LQ factored matrix as returned by lq_factor.
On output, the contents of this matrix are restored. Notice, N must be greater than or equal to M.

A MIN(M, N)-element array containing the scalar factors of the elementary reflectors as returned by lq_factor.

On input, an N-by-NRHS matrix where the first M rows contain the right-hand-side matrix $B$. On output, the N-by-NRHS solution matrix $X$.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

On input, the M-by-N LQ factored matrix as returned by lq_factor.
On output, the contents of this matrix are restored. Notice, N must be greater than or equal to M.

A MIN(M, N)-element array containing the scalar factors of the elementary reflectors as returned by lq_factor.

On input, an N-by-NRHS matrix where the first M rows contain the right-hand-side matrix $B$. On output, the N-by-NRHS solution matrix $X$.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

!! On input, the M-by-N LQ factored matrix as returned by lq_factor.
On output, the contents of this matrix are restored. Notice, N must be greater than or equal to M.

A MIN(M, N)-element array containing the scalar factors of the elementary reflectors as returned by lq_factor.

On input, an N-element vector where the first M rows contain the right-hand-side vector $\vec{b}$. On output, the N-element vector $\vec{x}$.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.

!! On input, the M-by-N LQ factored matrix as returned by lq_factor.
On output, the contents of this matrix are restored. Notice, N must be greater than or equal to M.

A MIN(M, N)-element array containing the scalar factors of the elementary reflectors as returned by lq_factor.

On input, an N-element vector where the first M rows contain the right-hand-side vector $\vec{b}$. On output, the N-element vector $\vec{x}$.

An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.

An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.

The error object to be updated.