Collaboration diagram for QR decomposition of a Matrix:

Functions
tpt_status	tpt_mat_qr_f32 (const tpt_matrix_instance_f32 aInMat, const f32_t threshold, tpt_matrix_instance_f32 aOutR, tpt_matrix_instance_f32 aOutQ, f32_t aOutTau, f32_t aTmpA, f32_t aTmpB)
	QR decomposition of a m x n floating point matrix with m >= n.
tpt_status	tpt_mat_qr_f64 (const tpt_matrix_instance_f64 aInMat, const f64_t threshold, tpt_matrix_instance_f64 aOutR, tpt_matrix_instance_f64 aOutQ, f64_t aOutTau, f64_t aTmpA, f64_t aTmpB)
	QR decomposition of a m x n double floating point matrix with m>= n.

Detailed Description

Computes the QR decomposition of a matrix M using Householder algorithm.

$\‍[ M = Q R \‍]$

where Q is an orthogonal matrix and R is upper triangular. No pivoting strategy is used.、 The returned value for R is using a format a bit similar to LAPACK : it is not just containing the matrix R but also the Householder reflectors. The function is also returning a vector $\tau$ that is containing the scaling factor for the reflectors. Returned value R has the structure:

$\‍[ \begin{pmatrix} r_{11} & r_{12} & \dots & r_{1n} \\ v_{12} & r_{22} & \dots & r_{2n} \\ v_{13} & v_{22} & \dots & r_{3n} \\ \vdots & \vdots & \ddots & \vdots \\ v_{1m} & v_{2(m-1)} & \dots & r_{mn} \\ \end{pmatrix} \‍]$

/// where///

$\‍[ v_1 = \begin{pmatrix} 1 \\ v_{12} \\ \vdots \\ v_{1m} \\ \end{pmatrix} \‍]$

is the first householder reflector. The Householder Matrix is given by $H_1$

$\‍[ H_1 = I - \tau_1 v_1 v_1^T \‍]$

The Matrix Q is the product of the Householder matrices:

$\‍[ Q = H_1 H_2 \dots H_n \‍]$

The computation of the matrix Q by this function is optional.

And the matrix R, would be the returned value R without the householder reflectors:

$\‍[ \begin{pmatrix} r_{11} & r_{12} & \dots & r_{1n} \\ 0 & r_{22} & \dots & r_{2n} \\ 0 & 0 & \dots & r_{3n} \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \dots & r_{mn} \\ \end{pmatrix} \‍]$

Function Documentation

◆ tpt_mat_qr_f32()

tpt_status tpt_mat_qr_f32	(	const tpt_matrix_instance_f32 *	aInMat,
		const f32_t	threshold,
		tpt_matrix_instance_f32 *	aOutR,
		tpt_matrix_instance_f32 *	aOutQ,
		f32_t *	aOutTau,
		f32_t *	aTmpA,
		f32_t *	aTmpB )

QR decomposition of a m x n floating point matrix with m >= n.

QR decomposition of a matrix.

Parameters

[in]	aInMat	points to input matrix structure. The source matrix is modified by the function.
[in]	threshold	norm2 threshold.
[out]	aOutR	points to output R matrix structure of dimension m x n
[out]	aOutQ	points to output Q matrix structure of dimension m x m (can be NULL)
[out]	aOutTau	points to Householder scaling factors of dimension n
[in,out]	aTmpA	points to a temporary vector of dimension m.
[in,out]	aTmpB	points to a temporary vector of dimension m.

Returns

execution status

TPT_MATH_SUCCESS : Operation successful
TPT_MATH_SIZE_MISMATCH : Matrix size check failed

aOutQ is optional:: aOutQ can be a NULL pointer. In this case, the argument will be ignored and the output Q matrix won't be computed.

Norm2 threshold: For the meaning of this argument please refer to the MatrixHouseholder documentation

◆ tpt_mat_qr_f64()

tpt_status tpt_mat_qr_f64	(	const tpt_matrix_instance_f64 *	aInMat,
		const f64_t	threshold,
		tpt_matrix_instance_f64 *	aOutR,
		tpt_matrix_instance_f64 *	aOutQ,
		f64_t *	aOutTau,
		f64_t *	aTmpA,
		f64_t *	aTmpB )

QR decomposition of a m x n double floating point matrix with m>= n.