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 $Q R = [Q_1, Q_2] [R1 0]^T$.

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 $Q R = [Q_1, Q_2] [R1 0]^T$.

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.

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.