form_qr Interface

On input, an M-by-N matrix where the elements below the diagonal contain the elementary reflectors generated from the QR factorization. On and above the diagonal, the matrix contains the matrix $R$. On output, the elements below the diagonal are zeroed such that the remaining matrix is simply the M-by-N matrix $R$.

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

An M-by-M matrix where the full orthogonal matrix $Q$ will be written. In the event that M > N, $Q$ may be supplied as M-by-N, and therefore only return the useful submatrix $Q_1$ $Q = [Q_1 Q_2]$ as the factorization can be written as $Q R = [Q_1, Q_2] [R1 0]^T$.

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 below the diagonal contain the elementary reflectors generated from the QR factorization. On and above the diagonal, the matrix contains the matrix $R$. On output, the elements below the diagonal are zeroed such that the remaining matrix is simply the M-by-N matrix $R$.

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

An M-by-M matrix where the full orthogonal matrix $Q$ will be written. In the event that M > N, $Q$ may be supplied as M-by-N, and therefore only return the useful submatrix $Q_1$ $Q = [Q_1 Q_2]$ as the factorization can be written as $Q R = [Q_1, Q_2] [R1 0]^T$.

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 below the diagonal contain the elementary reflectors generated from the QR factorization. On and above the diagonal, the matrix contains the matrix $R$. On output, the elements below the diagonal are zeroed such that the remaining matrix is simply the M-by-N matrix $R$.

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

An N-element column pivot array as returned by the QR factorization.

An M-by-M matrix where the full orthogonal matrix $Q$ will be written. In the event that M > N, $Q$ may be supplied as M-by-N, and therefore only return the useful submatrix $Q_1$ $Q = [Q_1 Q_2]$ as the factorization can be written as $Q R = [Q_1, Q_2] [R1 0]^T$.

An N-by-N matrix where the pivot matrix 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 below the diagonal contain the elementary reflectors generated from the QR factorization. On and above the diagonal, the matrix contains the matrix $R$. On output, the elements below the diagonal are zeroed such that the remaining matrix is simply the M-by-N matrix $R$.

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

An N-element column pivot array as returned by the QR factorization.

An M-by-M matrix where the full orthogonal matrix $Q$ will be written. In the event that M > N, $Q$ may be supplied as M-by-N, and therefore only return the useful submatrix $Q_1$ $Q = [Q_1 Q_2]$ as the factorization can be written as $Q R = [Q_1, Q_2] [R1 0]^T$.

An N-by-N matrix where the pivot matrix 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.