MAGMA  1.5.0
Matrix Algebra for GPU and Multicore Architectures
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single precision

Functions

magma_int_t magma_sgeqlf (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)
 SGEQLF computes a QL factorization of a REAL M-by-N matrix A: A = Q * L. More...
 
magma_int_t magma_sormql (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, float *A, magma_int_t lda, float *tau, float *C, magma_int_t ldc, float *work, magma_int_t lwork, magma_int_t *info)
 SORMQL overwrites the general real M-by-N matrix C with. More...
 
magma_int_t magma_sormql2_gpu (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, float *dA, magma_int_t ldda, float *tau, float *dC, magma_int_t lddc, float *wA, magma_int_t ldwa, magma_int_t *info)
 SORMQL overwrites the general real M-by-N matrix C with. More...
 

Detailed Description

Function Documentation

magma_int_t magma_sgeqlf ( 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 
)

SGEQLF computes a QL factorization of a REAL M-by-N matrix A: A = Q * L.

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]AREAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L; the remaining elements, 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]tauREAL 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(1) returns the optimal LWORK.
Higher performance is achieved if WORK is in pinned memory, e.g. allocated using magma_malloc_pinned.
[in]lworkINTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB can be obtained through magma_get_sgeqlf_nb(M).
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 by XERBLA.
[out]infoINTEGER
  • = 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).

magma_int_t magma_sormql ( magma_side_t  side,
magma_trans_t  trans,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float *  A,
magma_int_t  lda,
float *  tau,
float *  C,
magma_int_t  ldc,
float *  work,
magma_int_t  lwork,
magma_int_t *  info 
)

SORMQL overwrites the general real M-by-N matrix C with.

                          SIDE = MagmaLeft   SIDE = MagmaRight
TRANS = MagmaNoTrans:     Q * C              C * Q
TRANS = MagmaTrans:   Q**T * C           C * Q**T

where Q is a real unitary matrix defined as the product of k elementary reflectors

  Q = H(k) . . . H(2) H(1)

as returned by SGEQLF. Q is of order M if SIDE = MagmaLeft and of order N if SIDE = MagmaRight.

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**T from the Left;
  • = MagmaRight: apply Q or Q**T from the Right.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Transpose, apply Q**T.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]kINTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = MagmaLeft, M >= K >= 0; if SIDE = MagmaRight, N >= K >= 0.
[in]AREAL array, dimension (LDA,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQLF in the last k columns of its array argument A. A is modified by the routine but restored on exit.
[in]ldaINTEGER The leading dimension of the array A. If SIDE = MagmaLeft, LDA >= max(1,M); if SIDE = MagmaRight, LDA >= max(1,N).
[in]tauREAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQLF.
[in,out]CREAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
[in]ldcINTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]work(workspace) REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]lworkINTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and LWORK >= M*NB if SIDE = MagmaRight, 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 by XERBLA.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
magma_int_t magma_sormql2_gpu ( magma_side_t  side,
magma_trans_t  trans,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
float *  dA,
magma_int_t  ldda,
float *  tau,
float *  dC,
magma_int_t  lddc,
float *  wA,
magma_int_t  ldwa,
magma_int_t *  info 
)

SORMQL overwrites the general real M-by-N matrix C with.

                           SIDE = MagmaLeft   SIDE = MagmaRight
TRANS = MagmaNoTrans:      Q * C              C * Q
TRANS = MagmaTrans:    Q**T * C           C * Q**T

where Q is a real unitary matrix defined as the product of k elementary reflectors

  Q = H(k) . . . H(2) H(1)

as returned by SGEQLF. Q is of order M if SIDE = MagmaLeft and of order N if SIDE = MagmaRight.

Parameters
[in]sidemagma_side_t
  • = MagmaLeft: apply Q or Q**T from the Left;
  • = MagmaRight: apply Q or Q**T from the Right.
[in]transmagma_trans_t
  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Transpose, apply Q**T.
[in]mINTEGER The number of rows of the matrix C. M >= 0.
[in]nINTEGER The number of columns of the matrix C. N >= 0.
[in]kINTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = MagmaLeft, M >= K >= 0; if SIDE = MagmaRight, N >= K >= 0.
[in]dAREAL array, dimension (LDA,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQLF in the last k columns of its array argument A. The diagonal and the lower part are destroyed, the reflectors are not modified.
[in]lddaINTEGER The leading dimension of the array DA. LDDA >= max(1,M) if SIDE = MagmaLeft; LDDA >= max(1,N) if SIDE = MagmaRight.
[in]tauREAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQLF.
[in,out]dCREAL array, dimension (LDDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
[in]lddcINTEGER The leading dimension of the array C. LDDC >= max(1,M).
[in]wA(workspace) REAL array, dimension (LDWA,M) if SIDE = MagmaLeft (LDWA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by SSYTRD_GPU.
[in]ldwaINTEGER The leading dimension of the array wA. LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight.
[out]infoINTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value