MAGMA  2.0.0
Matrix Algebra for GPU and Multicore Architectures

Functions

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_queue_t queue, 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...
 

Detailed Description

Function Documentation

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_queue_t  queue,
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 orthogonal 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) REAL array, dimension (N)
[in]queuemagma_queue_t Queue to execute in.
[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 (LDDA,N) On entry, the m by n matrix A. On exit, the orthogonal 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 orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array A. LDDA >= 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 (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 (LDDA,N) On entry, the m by n matrix A. On exit, the orthogonal 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 orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array A. LDDA >= 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 (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_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 (LDDA,N) On entry, the m by n matrix A. On exit, the orthogonal 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 orthogonal matrix Q as a product of elementary reflectors (see Further Details).
[in]lddaINTEGER The leading dimension of the array A. LDDA >= 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).