single precision
[LQ factorization]

Functions

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.
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.
magma_int_t magma_sormlq (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)
 SORMLQ overwrites the general real M-by-N matrix C with.

Function Documentation

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.
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_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_sormlq ( 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 
)

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

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

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

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

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

Parameters:
[in] side magma_side_t

  • = MagmaLeft: apply Q or Q**H from the Left;
  • = MagmaRight: apply Q or Q**H from the Right.
[in] trans magma_trans_t

  • = MagmaNoTrans: No transpose, apply Q;
  • = MagmaTrans: Conjugate transpose, apply Q**H.
[in] m INTEGER The number of rows of the matrix C. M >= 0.
[in] n INTEGER The number of columns of the matrix C. N >= 0.
[in] k INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = MagmaLeft, M >= K >= 0; if SIDE = MagmaRight, N >= K >= 0.
[in] A REAL array, dimension (LDA,M) if SIDE = MagmaLeft, (LDA,N) if SIDE = MagmaRight. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQF in the first k rows of its array argument A. A is modified by the routine but restored on exit.
[in] lda INTEGER The leading dimension of the array A. LDA >= max(1,K).
[in] tau REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGELQF.
[in,out] C REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
[in] ldc INTEGER 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[0] returns the optimal LWORK.
[in] lwork INTEGER The dimension of the array WORK. If SIDE = MagmaLeft, LWORK >= max(1,N); if SIDE = MagmaRight, LWORK >= max(1,M). For optimum performance if SIDE = MagmaLeft, LWORK >= N*NB; if SIDE = MagmaRight, 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 by XERBLA.
[out] info INTEGER

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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