Functions
magma_int_t	magma_cgelqf (magma_int_t m, magma_int_t n, magmaFloatComplex A, magma_int_t lda, magmaFloatComplex tau, magmaFloatComplex work, magma_int_t lwork, magma_int_t info)
	CGELQF computes an LQ factorization of a COMPLEX M-by-N matrix A: A = L * Q. More...

magma_int_t	magma_cgelqf_gpu (magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex tau, magmaFloatComplex work, magma_int_t lwork, magma_int_t *info)
	CGELQF computes an LQ factorization of a COMPLEX M-by-N matrix dA: dA = L * Q. More...

magma_int_t	magma_dgelqf (magma_int_t m, magma_int_t n, double A, magma_int_t lda, double tau, double work, magma_int_t lwork, magma_int_t info)
	DGELQF computes an LQ factorization of a DOUBLE PRECISION M-by-N matrix A: A = L * Q. More...

magma_int_t	magma_dgelqf_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, double tau, double work, magma_int_t lwork, magma_int_t *info)
	DGELQF computes an LQ factorization of a DOUBLE PRECISION M-by-N matrix dA: dA = L * Q. More...

magma_int_t	magma_sgelqf (magma_int_t m, magma_int_t n, float A, magma_int_t lda, float tau, float work, magma_int_t lwork, magma_int_t info)
	SGELQF computes an LQ factorization of a REAL M-by-N matrix A: A = L * Q. More...

magma_int_t	magma_sgelqf_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, float tau, float work, magma_int_t lwork, magma_int_t *info)
	SGELQF computes an LQ factorization of a REAL M-by-N matrix dA: dA = L * Q. More...

magma_int_t	magma_zgelqf (magma_int_t m, magma_int_t n, magmaDoubleComplex A, magma_int_t lda, magmaDoubleComplex tau, magmaDoubleComplex work, magma_int_t lwork, magma_int_t info)
	ZGELQF computes an LQ factorization of a COMPLEX_16 M-by-N matrix A: A = L * Q. More...

magma_int_t	magma_zgelqf_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex tau, magmaDoubleComplex work, magma_int_t lwork, magma_int_t *info)
	ZGELQF computes an LQ factorization of a COMPLEX_16 M-by-N matrix dA: dA = L * Q. More...

Detailed Description

Function Documentation

magma_int_t magma_cgelqf	(	magma_int_t	m,
		magma_int_t	n,
		magmaFloatComplex *	A,
		magma_int_t	lda,
		magmaFloatComplex *	tau,
		magmaFloatComplex *	work,
		magma_int_t	lwork,
		magma_int_t *	info
	)

CGELQF computes an LQ factorization of a COMPLEX M-by-N matrix A: A = L * Q.

Parameters

[in]	m	INTEGER The number of rows of the matrix A. M >= 0.
[in]	n	INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	A	COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	tau	COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work	(workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= MNB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued. TODO: work is currently unused. cgeqrf2 allocates its own work of (m + n)nb.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

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) is stored on exit in A(i,i+1:n), and tau in TAU(i).

magma_int_t magma_cgelqf_gpu	(	magma_int_t	m,
		magma_int_t	n,
		magmaFloatComplex_ptr	dA,
		magma_int_t	ldda,
		magmaFloatComplex *	tau,
		magmaFloatComplex *	work,
		magma_int_t	lwork,
		magma_int_t *	info
	)

CGELQF computes an LQ factorization of a COMPLEX M-by-N matrix dA: dA = L * Q.

Parameters

[in]	m	INTEGER The number of rows of the matrix A. M >= 0.
[in]	n	INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	dA	COMPLEX array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix dA. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]	tau	COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work	(workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. Higher performance is achieved if WORK is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

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) is stored on exit in A(i,i+1:n), and tau in TAU(i).

magma_int_t magma_dgelqf	(	magma_int_t	m,
		magma_int_t	n,
		double *	A,
		magma_int_t	lda,
		double *	tau,
		double *	work,
		magma_int_t	lwork,
		magma_int_t *	info
	)

DGELQF computes an LQ factorization of a DOUBLE PRECISION M-by-N matrix A: A = L * Q.

Parameters

[in]	m	INTEGER The number of rows of the matrix A. M >= 0.
[in]	n	INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	A	DOUBLE PRECISION array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	tau	DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work	(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= MNB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued. TODO: work is currently unused. dgeqrf2 allocates its own work of (m + n)nb.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).

magma_int_t magma_dgelqf_gpu	(	magma_int_t	m,
		magma_int_t	n,
		magmaDouble_ptr	dA,
		magma_int_t	ldda,
		double *	tau,
		double *	work,
		magma_int_t	lwork,
		magma_int_t *	info
	)

DGELQF computes an LQ factorization of a DOUBLE PRECISION M-by-N matrix dA: dA = L * Q.

Parameters

[in]	m	INTEGER The number of rows of the matrix A. M >= 0.
[in]	n	INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	dA	DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix dA. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]	tau	DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work	(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. Higher performance is achieved if WORK is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).

magma_int_t magma_sgelqf	(	magma_int_t	m,
		magma_int_t	n,
		float *	A,
		magma_int_t	lda,
		float *	tau,
		float *	work,
		magma_int_t	lwork,
		magma_int_t *	info
	)

SGELQF computes an LQ factorization of a REAL M-by-N matrix A: A = L * Q.

Parameters

[in]	m	INTEGER The number of rows of the matrix A. M >= 0.
[in]	n	INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	A	REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	tau	REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work	(workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= MNB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued. TODO: work is currently unused. sgeqrf2 allocates its own work of (m + n)nb.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).

magma_int_t magma_sgelqf_gpu	(	magma_int_t	m,
		magma_int_t	n,
		magmaFloat_ptr	dA,
		magma_int_t	ldda,
		float *	tau,
		float *	work,
		magma_int_t	lwork,
		magma_int_t *	info
	)

SGELQF computes an LQ factorization of a REAL M-by-N matrix dA: dA = L * Q.

Parameters

[in]	m	INTEGER The number of rows of the matrix A. M >= 0.
[in]	n	INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	dA	REAL array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix dA. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]	tau	REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work	(workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. Higher performance is achieved if WORK is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

where tau is a real scalar, and v is a real vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n), and tau in TAU(i).

magma_int_t magma_zgelqf	(	magma_int_t	m,
		magma_int_t	n,
		magmaDoubleComplex *	A,
		magma_int_t	lda,
		magmaDoubleComplex *	tau,
		magmaDoubleComplex *	work,
		magma_int_t	lwork,
		magma_int_t *	info
	)

ZGELQF computes an LQ factorization of a COMPLEX_16 M-by-N matrix A: A = L * Q.

Parameters

[in]	m	INTEGER The number of rows of the matrix A. M >= 0.
[in]	n	INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	A	COMPLEX_16 array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details). Higher performance is achieved if A is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]	lda	INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]	tau	COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work	(workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= MNB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued. TODO: work is currently unused. zgeqrf2 allocates its own work of (m + n)nb.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

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) is stored on exit in A(i,i+1:n), and tau in TAU(i).

magma_int_t magma_zgelqf_gpu	(	magma_int_t	m,
		magma_int_t	n,
		magmaDoubleComplex_ptr	dA,
		magma_int_t	ldda,
		magmaDoubleComplex *	tau,
		magmaDoubleComplex *	work,
		magma_int_t	lwork,
		magma_int_t *	info
	)

ZGELQF computes an LQ factorization of a COMPLEX_16 M-by-N matrix dA: dA = L * Q.

Parameters

[in]	m	INTEGER The number of rows of the matrix A. M >= 0.
[in]	n	INTEGER The number of columns of the matrix A. N >= 0.
[in,out]	dA	COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix dA. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]	ldda	INTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]	tau	COMPLEX_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]	work	(workspace) COMPLEX_16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK[0] returns the optimal LWORK. Higher performance is achieved if WORK is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]	lwork	INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, where NB is the optimal blocksize. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.
[out]	info	INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

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) is stored on exit in A(i,i+1:n), and tau in TAU(i).

Functions

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Further Details