linalg_rz Module

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

Set to true if $op(Z) = Z^{T}$; else, set to false if $op(Z) = Z$.

The number of columns in matrix $A$ containing the meaningful part of the Householder vectors. If lside is true, $M \ge L \ge 0$; else, if lside is false, $N \ge L \ge 0$.

On input the $K$-by-$LTA$ matrix $Z$, where $LTA = M$ if lside is true; else, $LTA = N$ if lside is false. The I-th row must contain the Householder vector in the last $k$ rows. Notice, the contents of this matrix are restored on exit.

A $K$-element array containing the scalar factors of the elementary reflectors, where $M \ge K \ge 0$ if lside is true; else, $N \ge K \ge 0$ if lside is false.

On input, the $M$-by-$N$ matrix $C$. On output, the product of the orthogonal matrix $Z$ 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 @p work, and returns without performing any actual calculations.

The error object to be updated.

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

Set to true if $op(Z) = Z^{T}$; else, set to false if $op(Z) = Z$.

The number of columns in matrix $A$ containing the meaningful part of the Householder vectors. If lside is true, $M \ge L \ge 0$; else, if lside is false, $N \ge L \ge 0$.

On input the $K$-by-$LTA$ matrix $Z$, where $LTA = M$ if lside is true; else, $LTA = N$ if lside is false. The I-th row must contain the Householder vector in the last $k$ rows. Notice, the contents of this matrix are restored on exit.

A $K$-element array containing the scalar factors of the elementary reflectors, where $M \ge K \ge 0$ if lside is true; else, $N \ge K \ge 0$ if lside is false.

On input, the $M$-by-$N$ matrix $C$. On output, the product of the orthogonal matrix $Z$ 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 @p work, and returns without performing any actual calculations.

The error object to be updated.

Set to true if $op(Z) = Z^{T}$; else, set to false if $op(Z) = Z$.

The number of columns in matrix $A$ containing the meaningful part of the Householder vectors.

On input the $M$-by-$M$ matrix $Z$. The I-th row must contain the Householder vector in the last $k$ rows. Notice, the contents of this matrix are restored on exit.

An $M$-element array containing the scalar factors of the elementary reflectors.

On input, the $M$-element array $C$. On output, the product of $Z$ and $C$.

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 @p work, and returns without performing any actual calculations.

The error object to be updated.

Set to true if $op(Z) = Z^{T}$; else, set to false if $op(Z) = Z$.

The number of columns in matrix $A$ containing the meaningful part of the Householder vectors.

On input the $M$-by-$M$ matrix $Z$. The I-th row must contain the Householder vector in the last $k$ rows. Notice, the contents of this matrix are restored on exit.

An $M$-element array containing the scalar factors of the elementary reflectors.

On input, the $M$-element array $C$. On output, the product of $Z$ and $C$.

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 @p work, and returns without performing any actual calculations.

The error object to be updated.

On input, the M-by-N upper trapezoidal matrix to factor. On output, the leading M-by-M upper triangular part of the matrix contains the upper triangular matrix $R$, and elements N-L+1 to N of the first M rows of $A$, with the array tau, represent the orthogonal matrix $Z$ as a product of M elementary reflectors.

An M-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 @p work, and returns without performing any actual calculations.

The error object to be updated.

On input, the M-by-N upper trapezoidal matrix to factor. On output, the leading M-by-M upper triangular part of the matrix contains the upper triangular matrix $R$, and elements N-L+1 to N of the first M rows of $A$, with the array tau, represent the orthogonal matrix $Z$ as a product of M elementary reflectors.

An M-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 @p work, and returns without performing any actual calculations.

The error object to be updated.