MAGMA  1.7.0
Matrix Algebra for GPU and Multicore Architectures
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Functions

magma_int_t magma_dgeqr2x2_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dtau, magmaDouble_ptr dT, magmaDouble_ptr ddA, magmaDouble_ptr dwork, magma_int_t *info)
 DGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 
magma_int_t magma_dgeqr2x3_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dtau, magmaDouble_ptr dT, magmaDouble_ptr ddA, magmaDouble_ptr dwork, magma_int_t *info)
 DGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 
magma_int_t magma_dgeqr2x_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dtau, magmaDouble_ptr dT, magmaDouble_ptr ddA, magmaDouble_ptr dwork, magma_int_t *info)
 DGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 
magma_int_t magma_dgeqr2_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dtau, magmaDouble_ptr dwork, magma_int_t *info)
 DGEQR2 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_dgeqr2_batched (magma_int_t m, magma_int_t n, double **dA_array, magma_int_t ldda, double **dtau_array, magma_int_t *info_array, magma_int_t batchCount, magma_queue_t queue)
 DGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 
void dgeqrf_copy_upper_batched (magma_int_t n, magma_int_t nb, double **dV_array, magma_int_t lddv, double **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_dgeqr2x4_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, magmaDouble_ptr dtau, magmaDouble_ptr dT, magmaDouble_ptr ddA, magmaDouble_ptr dwork, magma_queue_t queue, magma_int_t *info)
 DGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. More...
 

Detailed Description

Function Documentation

void dgeqrf_copy_upper_batched ( magma_int_t  n,
magma_int_t  nb,
double **  dV_array,
magma_int_t  lddv,
double **  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 dgeqrf_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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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.
magma_int_t magma_dgeqr2_batched ( magma_int_t  m,
magma_int_t  n,
double **  dA_array,
magma_int_t  ldda,
double **  dtau_array,
magma_int_t *  info_array,
magma_int_t  batchCount,
magma_queue_t  queue 
)

DGEQR2 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 DOUBLE_PRECISION 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 DOUBLE_PRECISION 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_dgeqr2_gpu ( magma_int_t  m,
magma_int_t  n,
magmaDouble_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dtau,
magmaDouble_ptr  dwork,
magma_int_t *  info 
)

DGEQR2 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]dADOUBLE PRECISION 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]dtauDOUBLE PRECISION 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_dgeqr2x2_gpu ( magma_int_t  m,
magma_int_t  n,
magmaDouble_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dtau,
magmaDouble_ptr  dT,
magmaDouble_ptr  ddA,
magmaDouble_ptr  dwork,
magma_int_t *  info 
)

DGEQR2 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 dgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's dgeqr2 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]dADOUBLE_PRECISION 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]dtauDOUBLE_PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]dTDOUBLE_PRECISION 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]ddADOUBLE_PRECISION 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_dgeqr2x3_gpu ( magma_int_t  m,
magma_int_t  n,
magmaDouble_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dtau,
magmaDouble_ptr  dT,
magmaDouble_ptr  ddA,
magmaDouble_ptr  dwork,
magma_int_t *  info 
)

DGEQR2 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 dgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's dgeqr2 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]dADOUBLE_PRECISION 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]dtauDOUBLE_PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]dTDOUBLE_PRECISION 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]ddADOUBLE_PRECISION 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_dgeqr2x4_gpu ( magma_int_t  m,
magma_int_t  n,
magmaDouble_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dtau,
magmaDouble_ptr  dT,
magmaDouble_ptr  ddA,
magmaDouble_ptr  dwork,
magma_queue_t  queue,
magma_int_t *  info 
)

DGEQR2 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 dgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's dgeqr2 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]dADOUBLE_PRECISION 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]dtauDOUBLE_PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]dTDOUBLE_PRECISION 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]ddADOUBLE_PRECISION 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_dgeqr2x_gpu ( magma_int_t  m,
magma_int_t  n,
magmaDouble_ptr  dA,
magma_int_t  ldda,
magmaDouble_ptr  dtau,
magmaDouble_ptr  dT,
magmaDouble_ptr  ddA,
magmaDouble_ptr  dwork,
magma_int_t *  info 
)

DGEQR2 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 dgeqr2, namely, dT and ddA, explained below. The storage for A is also not as in the LAPACK's dgeqr2 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]dADOUBLE_PRECISION 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]dtauDOUBLE_PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out]dTDOUBLE_PRECISION 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]ddADOUBLE_PRECISION 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 (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).