Functions
magma_int_t	magma_clabrd_gpu (magma_int_t m, magma_int_t n, magma_int_t nb, magmaFloatComplex A, magma_int_t lda, magmaFloatComplex_ptr dA, magma_int_t ldda, float d, float e, magmaFloatComplex tauq, magmaFloatComplex taup, magmaFloatComplex X, magma_int_t ldx, magmaFloatComplex_ptr dX, magma_int_t lddx, magmaFloatComplex Y, magma_int_t ldy, magmaFloatComplex_ptr dY, magma_int_t lddy, magmaFloatComplex work, magma_int_t lwork, magma_queue_t queue)
	CLABRD reduces the first NB rows and columns of a complex general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A.

magma_int_t	magma_dlabrd_gpu (magma_int_t m, magma_int_t n, magma_int_t nb, double A, magma_int_t lda, magmaDouble_ptr dA, magma_int_t ldda, double d, double e, double tauq, double taup, double X, magma_int_t ldx, magmaDouble_ptr dX, magma_int_t lddx, double Y, magma_int_t ldy, magmaDouble_ptr dY, magma_int_t lddy, double work, magma_int_t lwork, magma_queue_t queue)
	DLABRD reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A.

magma_int_t	magma_slabrd_gpu (magma_int_t m, magma_int_t n, magma_int_t nb, float A, magma_int_t lda, magmaFloat_ptr dA, magma_int_t ldda, float d, float e, float tauq, float taup, float X, magma_int_t ldx, magmaFloat_ptr dX, magma_int_t lddx, float Y, magma_int_t ldy, magmaFloat_ptr dY, magma_int_t lddy, float work, magma_int_t lwork, magma_queue_t queue)
	SLABRD reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A.

magma_int_t	magma_zlabrd_gpu (magma_int_t m, magma_int_t n, magma_int_t nb, magmaDoubleComplex A, magma_int_t lda, magmaDoubleComplex_ptr dA, magma_int_t ldda, double d, double e, magmaDoubleComplex tauq, magmaDoubleComplex taup, magmaDoubleComplex X, magma_int_t ldx, magmaDoubleComplex_ptr dX, magma_int_t lddx, magmaDoubleComplex Y, magma_int_t ldy, magmaDoubleComplex_ptr dY, magma_int_t lddy, magmaDoubleComplex work, magma_int_t lwork, magma_queue_t queue)
	ZLABRD reduces the first NB rows and columns of a complex general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A.

Detailed Description

Function Documentation

◆ magma_clabrd_gpu()

magma_int_t magma_clabrd_gpu	(	magma_int_t	m,
		magma_int_t	n,
		magma_int_t	nb,
		magmaFloatComplex *	A,
		magma_int_t	lda,
		magmaFloatComplex_ptr	dA,
		magma_int_t	ldda,
		float *	d,
		float *	e,
		magmaFloatComplex *	tauq,
		magmaFloatComplex *	taup,
		magmaFloatComplex *	X,
		magma_int_t	ldx,
		magmaFloatComplex_ptr	dX,
		magma_int_t	lddx,
		magmaFloatComplex *	Y,
		magma_int_t	ldy,
		magmaFloatComplex_ptr	dY,
		magma_int_t	lddy,
		magmaFloatComplex *	work,
		magma_int_t	lwork,
		magma_queue_t	queue )

CLABRD reduces the first NB rows and columns of a complex general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A.

If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form.

This is an auxiliary routine called by CGEBRD.

Parameters

[in]	m	INTEGER The number of rows in the matrix A.
[in]	n	INTEGER The number of columns in the matrix A.
[in]	nb	INTEGER The number of leading rows and columns of A to be reduced.
[in,out]	A	COMPLEX array, dimension (LDA,N) On entry, the m by n general matrix to be reduced. On exit, the first NB rows and columns of the matrix are overwritten; the rest of the array is unchanged. If m >= n, elements on and below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and elements above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. If m < n, elements below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and elements on and above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. See Further Details.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,M).
[in,out]	dA	COMPLEX array, dimension (LDDA,N) Copy of A on GPU.
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]	d	COMPLEX array, dimension (NB) The diagonal elements of the first NB rows and columns of the reduced matrix. D(i) = A(i,i).
[out]	e	COMPLEX array, dimension (NB) The off-diagonal elements of the first NB rows and columns of the reduced matrix.
[out]	tauq	COMPLEX array dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details.
[out]	taup	COMPLEX array, dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details.
[out]	X	COMPLEX array, dimension (LDX,NB) The m-by-nb matrix X required to update the unreduced part of A.
[in]	ldx	INTEGER The leading dimension of the array X. LDX >= M.
[out]	dX	COMPLEX array, dimension (LDDX,NB) Copy of X on GPU.
[in]	lddx	INTEGER The leading dimension of the array dX. LDDX >= M.
[out]	Y	COMPLEX array, dimension (LDY,NB) The n-by-nb matrix Y required to update the unreduced part of A.
[in]	ldy	INTEGER The leading dimension of the array Y. LDY >= N.
[out]	dY	COMPLEX array, dimension (LDDY,NB) Copy of Y on GPU.
[in]	lddy	INTEGER The leading dimension of the array dY. LDDY >= N.
	work	COMPLEX array, dimension (LWORK) Workspace.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max( M, N ).
[in]	queue	magma_queue_t Queue to execute in.

Further Details

The matrices Q and P are represented as products of elementary reflectors:

Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'

where tauq and taup are complex scalars, and v and u are complex vectors.

If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

The elements of the vectors v and u together form the m-by-nb matrix V and the nb-by-n matrix U' which are needed, with X and Y, to apply the transformation to the unreduced part of the matrix, using a block update of the form: A := A - V*Y' - X*U'.

The contents of A on exit are illustrated by the following examples with nb = 2:

m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):

  (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 )
  (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 )
  (  v1  v2  a   a   a  )           (  v1  1   a   a   a   a  )
  (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
  (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
  (  v1  v2  a   a   a  )

where a denotes an element of the original matrix which is unchanged, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).

◆ magma_dlabrd_gpu()

magma_int_t magma_dlabrd_gpu	(	magma_int_t	m,
		magma_int_t	n,
		magma_int_t	nb,
		double *	A,
		magma_int_t	lda,
		magmaDouble_ptr	dA,
		magma_int_t	ldda,
		double *	d,
		double *	e,
		double *	tauq,
		double *	taup,
		double *	X,
		magma_int_t	ldx,
		magmaDouble_ptr	dX,
		magma_int_t	lddx,
		double *	Y,
		magma_int_t	ldy,
		magmaDouble_ptr	dY,
		magma_int_t	lddy,
		double *	work,
		magma_int_t	lwork,
		magma_queue_t	queue )

DLABRD reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A.

If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form.

This is an auxiliary routine called by DGEBRD.

Parameters

[in]	m	INTEGER The number of rows in the matrix A.
[in]	n	INTEGER The number of columns in the matrix A.
[in]	nb	INTEGER The number of leading rows and columns of A to be reduced.
[in,out]	A	DOUBLE PRECISION array, dimension (LDA,N) On entry, the m by n general matrix to be reduced. On exit, the first NB rows and columns of the matrix are overwritten; the rest of the array is unchanged. If m >= n, elements on and below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and elements above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. If m < n, elements below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and elements on and above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. See Further Details.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,M).
[in,out]	dA	DOUBLE PRECISION array, dimension (LDDA,N) Copy of A on GPU.
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]	d	DOUBLE PRECISION array, dimension (NB) The diagonal elements of the first NB rows and columns of the reduced matrix. D(i) = A(i,i).
[out]	e	DOUBLE PRECISION array, dimension (NB) The off-diagonal elements of the first NB rows and columns of the reduced matrix.
[out]	tauq	DOUBLE PRECISION array dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details.
[out]	taup	DOUBLE PRECISION array, dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details.
[out]	X	DOUBLE PRECISION array, dimension (LDX,NB) The m-by-nb matrix X required to update the unreduced part of A.
[in]	ldx	INTEGER The leading dimension of the array X. LDX >= M.
[out]	dX	DOUBLE PRECISION array, dimension (LDDX,NB) Copy of X on GPU.
[in]	lddx	INTEGER The leading dimension of the array dX. LDDX >= M.
[out]	Y	DOUBLE PRECISION array, dimension (LDY,NB) The n-by-nb matrix Y required to update the unreduced part of A.
[in]	ldy	INTEGER The leading dimension of the array Y. LDY >= N.
[out]	dY	DOUBLE PRECISION array, dimension (LDDY,NB) Copy of Y on GPU.
[in]	lddy	INTEGER The leading dimension of the array dY. LDDY >= N.
	work	DOUBLE PRECISION array, dimension (LWORK) Workspace.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max( M, N ).
[in]	queue	magma_queue_t Queue to execute in.

Further Details

The matrices Q and P are represented as products of elementary reflectors:

Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'

where tauq and taup are real scalars, and v and u are real vectors.

If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

The elements of the vectors v and u together form the m-by-nb matrix V and the nb-by-n matrix U' which are needed, with X and Y, to apply the transformation to the unreduced part of the matrix, using a block update of the form: A := A - V*Y' - X*U'.

The contents of A on exit are illustrated by the following examples with nb = 2:

m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):

  (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 )
  (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 )
  (  v1  v2  a   a   a  )           (  v1  1   a   a   a   a  )
  (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
  (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
  (  v1  v2  a   a   a  )

where a denotes an element of the original matrix which is unchanged, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).

◆ magma_slabrd_gpu()

magma_int_t magma_slabrd_gpu	(	magma_int_t	m,
		magma_int_t	n,
		magma_int_t	nb,
		float *	A,
		magma_int_t	lda,
		magmaFloat_ptr	dA,
		magma_int_t	ldda,
		float *	d,
		float *	e,
		float *	tauq,
		float *	taup,
		float *	X,
		magma_int_t	ldx,
		magmaFloat_ptr	dX,
		magma_int_t	lddx,
		float *	Y,
		magma_int_t	ldy,
		magmaFloat_ptr	dY,
		magma_int_t	lddy,
		float *	work,
		magma_int_t	lwork,
		magma_queue_t	queue )

SLABRD reduces the first NB rows and columns of a real general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A.

If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form.

This is an auxiliary routine called by SGEBRD.

Parameters

[in]	m	INTEGER The number of rows in the matrix A.
[in]	n	INTEGER The number of columns in the matrix A.
[in]	nb	INTEGER The number of leading rows and columns of A to be reduced.
[in,out]	A	REAL array, dimension (LDA,N) On entry, the m by n general matrix to be reduced. On exit, the first NB rows and columns of the matrix are overwritten; the rest of the array is unchanged. If m >= n, elements on and below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and elements above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. If m < n, elements below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and elements on and above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. See Further Details.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,M).
[in,out]	dA	REAL array, dimension (LDDA,N) Copy of A on GPU.
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]	d	REAL array, dimension (NB) The diagonal elements of the first NB rows and columns of the reduced matrix. D(i) = A(i,i).
[out]	e	REAL array, dimension (NB) The off-diagonal elements of the first NB rows and columns of the reduced matrix.
[out]	tauq	REAL array dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details.
[out]	taup	REAL array, dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details.
[out]	X	REAL array, dimension (LDX,NB) The m-by-nb matrix X required to update the unreduced part of A.
[in]	ldx	INTEGER The leading dimension of the array X. LDX >= M.
[out]	dX	REAL array, dimension (LDDX,NB) Copy of X on GPU.
[in]	lddx	INTEGER The leading dimension of the array dX. LDDX >= M.
[out]	Y	REAL array, dimension (LDY,NB) The n-by-nb matrix Y required to update the unreduced part of A.
[in]	ldy	INTEGER The leading dimension of the array Y. LDY >= N.
[out]	dY	REAL array, dimension (LDDY,NB) Copy of Y on GPU.
[in]	lddy	INTEGER The leading dimension of the array dY. LDDY >= N.
	work	REAL array, dimension (LWORK) Workspace.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max( M, N ).
[in]	queue	magma_queue_t Queue to execute in.

Further Details

The matrices Q and P are represented as products of elementary reflectors:

Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'

where tauq and taup are real scalars, and v and u are real vectors.

If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

The elements of the vectors v and u together form the m-by-nb matrix V and the nb-by-n matrix U' which are needed, with X and Y, to apply the transformation to the unreduced part of the matrix, using a block update of the form: A := A - V*Y' - X*U'.

The contents of A on exit are illustrated by the following examples with nb = 2:

m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):

  (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 )
  (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 )
  (  v1  v2  a   a   a  )           (  v1  1   a   a   a   a  )
  (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
  (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
  (  v1  v2  a   a   a  )

where a denotes an element of the original matrix which is unchanged, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).

◆ magma_zlabrd_gpu()

magma_int_t magma_zlabrd_gpu	(	magma_int_t	m,
		magma_int_t	n,
		magma_int_t	nb,
		magmaDoubleComplex *	A,
		magma_int_t	lda,
		magmaDoubleComplex_ptr	dA,
		magma_int_t	ldda,
		double *	d,
		double *	e,
		magmaDoubleComplex *	tauq,
		magmaDoubleComplex *	taup,
		magmaDoubleComplex *	X,
		magma_int_t	ldx,
		magmaDoubleComplex_ptr	dX,
		magma_int_t	lddx,
		magmaDoubleComplex *	Y,
		magma_int_t	ldy,
		magmaDoubleComplex_ptr	dY,
		magma_int_t	lddy,
		magmaDoubleComplex *	work,
		magma_int_t	lwork,
		magma_queue_t	queue )

ZLABRD reduces the first NB rows and columns of a complex general m by n matrix A to upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of A.

If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower bidiagonal form.

This is an auxiliary routine called by ZGEBRD.

Parameters

[in]	m	INTEGER The number of rows in the matrix A.
[in]	n	INTEGER The number of columns in the matrix A.
[in]	nb	INTEGER The number of leading rows and columns of A to be reduced.
[in,out]	A	COMPLEX_16 array, dimension (LDA,N) On entry, the m by n general matrix to be reduced. On exit, the first NB rows and columns of the matrix are overwritten; the rest of the array is unchanged. If m >= n, elements on and below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors; and elements above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. If m < n, elements below the diagonal in the first NB columns, with the array TAUQ, represent the orthogonal matrix Q as a product of elementary reflectors, and elements on and above the diagonal in the first NB rows, with the array TAUP, represent the orthogonal matrix P as a product of elementary reflectors. See Further Details.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,M).
[in,out]	dA	COMPLEX_16 array, dimension (LDDA,N) Copy of A on GPU.
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]	d	COMPLEX_16 array, dimension (NB) The diagonal elements of the first NB rows and columns of the reduced matrix. D(i) = A(i,i).
[out]	e	COMPLEX_16 array, dimension (NB) The off-diagonal elements of the first NB rows and columns of the reduced matrix.
[out]	tauq	COMPLEX_16 array dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix Q. See Further Details.
[out]	taup	COMPLEX_16 array, dimension (NB) The scalar factors of the elementary reflectors which represent the orthogonal matrix P. See Further Details.
[out]	X	COMPLEX_16 array, dimension (LDX,NB) The m-by-nb matrix X required to update the unreduced part of A.
[in]	ldx	INTEGER The leading dimension of the array X. LDX >= M.
[out]	dX	COMPLEX_16 array, dimension (LDDX,NB) Copy of X on GPU.
[in]	lddx	INTEGER The leading dimension of the array dX. LDDX >= M.
[out]	Y	COMPLEX_16 array, dimension (LDY,NB) The n-by-nb matrix Y required to update the unreduced part of A.
[in]	ldy	INTEGER The leading dimension of the array Y. LDY >= N.
[out]	dY	COMPLEX_16 array, dimension (LDDY,NB) Copy of Y on GPU.
[in]	lddy	INTEGER The leading dimension of the array dY. LDDY >= N.
	work	COMPLEX_16 array, dimension (LWORK) Workspace.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max( M, N ).
[in]	queue	magma_queue_t Queue to execute in.

Further Details

The matrices Q and P are represented as products of elementary reflectors:

Q = H(1) H(2) . . . H(nb) and P = G(1) G(2) . . . G(nb)

Each H(i) and G(i) has the form:

H(i) = I - tauq * v * v' and G(i) = I - taup * u * u'

where tauq and taup are complex scalars, and v and u are complex vectors.

If m >= n, v(1:i-1) = 0, v(i) = 1, and v(i:m) is stored on exit in A(i:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

If m < n, v(1:i) = 0, v(i+1) = 1, and v(i+1:m) is stored on exit in A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i:n) is stored on exit in A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

The elements of the vectors v and u together form the m-by-nb matrix V and the nb-by-n matrix U' which are needed, with X and Y, to apply the transformation to the unreduced part of the matrix, using a block update of the form: A := A - V*Y' - X*U'.

The contents of A on exit are illustrated by the following examples with nb = 2:

m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):

  (  1   1   u1  u1  u1 )           (  1   u1  u1  u1  u1  u1 )
  (  v1  1   1   u2  u2 )           (  1   1   u2  u2  u2  u2 )
  (  v1  v2  a   a   a  )           (  v1  1   a   a   a   a  )
  (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
  (  v1  v2  a   a   a  )           (  v1  v2  a   a   a   a  )
  (  v1  v2  a   a   a  )

where a denotes an element of the original matrix which is unchanged, vi denotes an element of the vector defining H(i), and ui an element of the vector defining G(i).

Functions

Detailed Description

Function Documentation

◆ magma_clabrd_gpu()

Further Details

◆ magma_dlabrd_gpu()

Further Details

◆ magma_slabrd_gpu()

Further Details

◆ magma_zlabrd_gpu()

Further Details