MAGMA  2.0.0
Matrix Algebra for GPU and Multicore Architectures
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magma_int_t magma_sgeqr2x2_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dT, magmaFloat_ptr ddA, magmaFloat_ptr dwork, magma_int_t *info)
 SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 
magma_int_t magma_sgeqr2x3_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dT, magmaFloat_ptr ddA, magmaFloat_ptr dwork, magma_int_t *info)
 SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 
magma_int_t magma_sgeqr2x_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dT, magmaFloat_ptr ddA, magmaFloat_ptr dwork, magma_int_t *info)
 SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 
magma_int_t magma_sgeqr2_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dwork, magma_int_t *info)
 SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R using the non-blocking Householder QR. More...
 
magma_int_t magma_sgeqr2_batched (magma_int_t m, magma_int_t n, float **dA_array, magma_int_t ldda, float **dtau_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
 SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 
void sgeqrf_copy_upper_batched (magma_int_t n, magma_int_t nb, float **dV_array, magma_int_t lddv, float **dR_array, magma_int_t lddr, magma_int_t batchCount, magma_queue_t queue)
 These are internal routines that might have many assumption. More...
 
magma_int_t magma_sgeqr2x4_gpu (magma_int_t m, magma_int_t n, magmaFloat_ptr dA, magma_int_t ldda, magmaFloat_ptr dtau, magmaFloat_ptr dT, magmaFloat_ptr ddA, magmaFloat_ptr dwork, magma_queue_t queue, magma_int_t *info)
 SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 

Detailed Description

Function Documentation

magma_int_t magma_sgeqr2_batched ( magma_int_t  m,
magma_int_t  n,
float **  dA_array,
magma_int_t  ldda,
float **  dtau_array,
magma_int_t *  info_array,
magma_int_t  batchCount,
magma_queue_t  queue 
)

SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.

This version implements the right-looking QR with non-blocking.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]dA_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,M). To benefit from coalescent memory accesses LDDA must be divisible by 16.
[out]dtau_arrayArray of pointers, dimension (batchCount). Each is a REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]info_arrayArray of INTEGERs, dimension (batchCount), for corresponding matrices.
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value or another error occured, such as memory allocation failed.
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.

Further Details

The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), 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:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

magma_int_t magma_sgeqr2_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dtau,
magmaFloat_ptr  dwork,
magma_int_t *  info 
)

SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R using the non-blocking Householder QR.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]dAREAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]dtauREAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
dwork(workspace) DOUBLE_PRECISION array, dimension (N)
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

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

magma_int_t magma_sgeqr2x2_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dtau,
magmaFloat_ptr  dT,
magmaFloat_ptr  ddA,
magmaFloat_ptr  dwork,
magma_int_t *  info 
)

SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.

This expert routine requires two more arguments than the standard sgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's sgeqr2 routine (see below).

The first is used to output the triangular n x n factor T of the block reflector used in the factorization. The second holds the diagonal nxn blocks of A, i.e., the diagonal submatrices of R. This routine implements the left looking QR.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]dAREAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the unitary matrix Q as a product of elementary reflectors (see Further Details).
the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]dtauREAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]dTREAL array, dimension N x N. Stores the triangular N x N factor T of the block reflector used in the factorization. The lower triangular part is 0.
[out]ddAREAL array, dimension N x N. Stores the elements of the upper N x N diagonal block of A. LAPACK stores this array in A. There are 0s below the diagonal.
dwork(workspace) DOUBLE_PRECISION array, dimension (3 N)
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

Further Details

The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), 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:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

magma_int_t magma_sgeqr2x3_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dtau,
magmaFloat_ptr  dT,
magmaFloat_ptr  ddA,
magmaFloat_ptr  dwork,
magma_int_t *  info 
)

SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.

This expert routine requires two more arguments than the standard sgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's sgeqr2 routine (see below).

The first is used to output the triangular n x n factor T of the block reflector used in the factorization. The second holds the diagonal nxn blocks of A, i.e., the diagonal submatrices of R. This routine implements the left looking QR.

This version adds internal blocking.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]dAREAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the unitary matrix Q as a product of elementary reflectors (see Further Details).
the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]dtauREAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]dTREAL array, dimension N x N. Stores the triangular N x N factor T of the block reflector used in the factorization. The lower triangular part is 0.
[out]ddAREAL array, dimension N x N. Stores the elements of the upper N x N diagonal block of A. LAPACK stores this array in A. There are 0s below the diagonal.
dwork(workspace) DOUBLE_PRECISION array, dimension (3 N)
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

Further Details

The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), 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:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

magma_int_t magma_sgeqr2x4_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dtau,
magmaFloat_ptr  dT,
magmaFloat_ptr  ddA,
magmaFloat_ptr  dwork,
magma_queue_t  queue,
magma_int_t *  info 
)

SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.

This expert routine requires two more arguments than the standard sgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's sgeqr2 routine (see below).

The first is used to output the triangular n x n factor T of the block reflector used in the factorization. The second holds the diagonal nxn blocks of A, i.e., the diagonal submatrices of R. This routine implements the left looking QR.

This version adds internal blocking.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. N >= 0.
[in,out]dAREAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the unitary matrix Q as a product of elementary reflectors (see Further Details).
the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]dtauREAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]dTREAL array, dimension N x N. Stores the triangular N x N factor T of the block reflector used in the factorization. The lower triangular part is 0.
[out]ddAREAL array, dimension N x N. Stores the elements of the upper N x N diagonal block of A. LAPACK stores this array in A. There are 0s below the diagonal.
dwork(workspace) DOUBLE_PRECISION array, dimension (3 N)
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
[in]queuemagma_queue_t Queue to execute in.

Further Details

The matrix Q is represented as a product of elementary reflectors

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

Each H(i) has the form

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

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

magma_int_t magma_sgeqr2x_gpu ( magma_int_t  m,
magma_int_t  n,
magmaFloat_ptr  dA,
magma_int_t  ldda,
magmaFloat_ptr  dtau,
magmaFloat_ptr  dT,
magmaFloat_ptr  ddA,
magmaFloat_ptr  dwork,
magma_int_t *  info 
)

SGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R.

This expert routine requires two more arguments than the standard sgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's sgeqr2 routine (see below).

The first is used to output the triangular n x n factor T of the block reflector used in the factorization. The second holds the diagonal nxn blocks of A, i.e., the diagonal submatrices of R.

This version implements the right-looking QR. A hard-coded requirement for N is to be <= min(M, 128). For larger N one should use a blocking QR version.

Parameters
[in]mINTEGER The number of rows of the matrix A. M >= 0.
[in]nINTEGER The number of columns of the matrix A. 0 <= N <= min(M, 128).
[in,out]dAREAL array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the unitary matrix Q as a product of elementary reflectors (see Further Details).
the elements on and above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]dtauREAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]dTREAL array, dimension N x N. Stores the triangular N x N factor T of the block reflector used in the factorization. The lower triangular part is 0.
[out]ddAREAL array, dimension N x N. Stores the elements of the upper N x N diagonal block of A. LAPACK stores this array in A. There are 0s below the diagonal.
dwork(workspace) REAL array, dimension (N)
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

Further Details

The matrix Q is represented as a product of elementary reflectors

Q = H(1) H(2) . . . H(k), 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:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).

void sgeqrf_copy_upper_batched ( magma_int_t  n,
magma_int_t  nb,
float **  dV_array,
magma_int_t  lddv,
float **  dR_array,
magma_int_t  lddr,
magma_int_t  batchCount,
magma_queue_t  queue 
)

These are internal routines that might have many assumption.

They are used in sgeqrf_batched.cpp

Copy part of the data in dV to dR

Parameters
[in]nINTEGER The order of the matrix . N >= 0.
[in]nbINTEGER Tile size in matrix. nb <= N.
[in]dV_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDA,N).
[in]lddvINTEGER The leading dimension of each array V. LDDV >= max(1,N).
[in,out]dR_arrayArray of pointers, dimension (batchCount). Each is a REAL array on the GPU, dimension (LDDR,N).
[in]lddrINTEGER The leading dimension of each array R. LDDR >= max(1,N).
[in]batchCountINTEGER The number of matrices to operate on.
[in]queuemagma_queue_t Queue to execute in.