tslqt: LQ factorization of a rectangular matrix of two tiles

Functions
	__attribute__ ((weak))

Detailed Description

Function Documentation

__attribute__

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(weak)

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Computes an LQ factorization of a rectangular matrix formed by coupling side-by-side a complex m-by-m lower triangular tile A1 and a complex m-by-n tile A2:

| A1 A2 | = L * Q

The tile Q is represented as a product of elementary reflectors

Q = H(k)^H . . . H(2)^H H(1)^H, where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v^H

where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n)^H is stored on exit in A2(i,1:n), and tau in tau(i).

Parameters

[in]	m	The number of rows of the tile A1 and A2. m >= 0. The number of columns of the tile A1.
[in]	n	The number of columns of the tile A2. n >= 0.
[in]	ib	The inner-blocking size. ib >= 0.
[in,out]	A1	On entry, the m-by-m tile A1. On exit, the elements on and below the diagonal of the array contain the m-by-m lower trapezoidal tile L; the elements above the diagonal are not referenced.
[in]	lda1	The leading dimension of the array A1. lda1 >= max(1,m).
[in,out]	A2	On entry, the m-by-n tile A2. On exit, all the elements with the array tau, represent the unitary tile Q as a product of elementary reflectors (see Further Details).
[in]	lda2	The leading dimension of the tile A2. lda2 >= max(1,m).
[out]	T	The ib-by-m triangular factor T of the block reflector. T is upper triangular by block (economic storage); The rest of the array is not referenced.
[in]	ldt	The leading dimension of the array T. ldt >= ib.
	tau	Auxiliarry workspace array of length m.
	work	Auxiliary workspace array of length ib*m.

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value

Computes an LQ factorization of a rectangular matrix formed by coupling side-by-side a complex m-by-m lower triangular tile A1 and a complex m-by-n tile A2:

| A1 A2 | = L * Q

The tile Q is represented as a product of elementary reflectors

Q = H(k)^T . . . H(2)^T H(1)^T, where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v^T

where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n)^T is stored on exit in A2(i,1:n), and tau in tau(i).

Parameters

[in]	m	The number of rows of the tile A1 and A2. m >= 0. The number of columns of the tile A1.
[in]	n	The number of columns of the tile A2. n >= 0.
[in]	ib	The inner-blocking size. ib >= 0.
[in,out]	A1	On entry, the m-by-m tile A1. On exit, the elements on and below the diagonal of the array contain the m-by-m lower trapezoidal tile L; the elements above the diagonal are not referenced.
[in]	lda1	The leading dimension of the array A1. lda1 >= max(1,m).
[in,out]	A2	On entry, the m-by-n tile A2. On exit, all the elements with the array tau, represent the orthogonal tile Q as a product of elementary reflectors (see Further Details).
[in]	lda2	The leading dimension of the tile A2. lda2 >= max(1,m).
[out]	T	The ib-by-m triangular factor T of the block reflector. T is upper triangular by block (economic storage); The rest of the array is not referenced.
[in]	ldt	The leading dimension of the array T. ldt >= ib.
	tau	Auxiliarry workspace array of length m.
	work	Auxiliary workspace array of length ib*m.

Return values

PlasmaSuccess	successful exit
<	0 if -i, the i-th argument had an illegal value