single-complex precision
[QL factorization]

Functions

magma_int_t magma_cgeqlf (magma_int_t m, magma_int_t n, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info)
 CGEQLF computes a QL factorization of a COMPLEX M-by-N matrix A: A = Q * L.
magma_int_t magma_cunmql (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau, magmaFloatComplex *C, magma_int_t ldc, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info)
 CUNMQL overwrites the general complex M-by-N matrix C with.
magma_int_t magma_cunmql2_gpu (magma_side_t side, magma_trans_t trans, magma_int_t m, magma_int_t n, magma_int_t k, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex *tau, magmaFloatComplex_ptr dC, magma_int_t lddc, magmaFloatComplex *wA, magma_int_t ldwa, magma_int_t *info)
 CUNMQL overwrites the general complex M-by-N matrix C with.

Function Documentation

magma_int_t magma_cgeqlf ( magma_int_t  m,
magma_int_t  n,
magmaFloatComplex *  A,
magma_int_t  lda,
magmaFloatComplex *  tau,
magmaFloatComplex *  work,
magma_int_t  lwork,
magma_int_t *  info 
)

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

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 COMPLEX 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] lda INTEGER The leading dimension of the array A. LDA >= max(1,M).
[out] tau COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
[out] work (workspace) COMPLEX 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,N,2*NB^2). For optimum performance LWORK >= max(N*NB, 2*NB^2) where NB can be obtained through magma_get_cgeqlf_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] 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 complex scalar, and v is a complex 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_cunmql ( magma_side_t  side,
magma_trans_t  trans,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
magmaFloatComplex *  A,
magma_int_t  lda,
magmaFloatComplex *  tau,
magmaFloatComplex *  C,
magma_int_t  ldc,
magmaFloatComplex *  work,
magma_int_t  lwork,
magma_int_t *  info 
)

CUNMQL overwrites the general complex M-by-N matrix C with.

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

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

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

as returned by CGEQLF. 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;
  • = Magma_ConjTrans: 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 COMPLEX 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 CGEQLF in the last k columns 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. If SIDE = MagmaLeft, LDA >= max(1,M); if SIDE = MagmaRight, LDA >= max(1,N).
[in] tau COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQLF.
[in,out] C COMPLEX 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) COMPLEX 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
magma_int_t magma_cunmql2_gpu ( magma_side_t  side,
magma_trans_t  trans,
magma_int_t  m,
magma_int_t  n,
magma_int_t  k,
magmaFloatComplex_ptr  dA,
magma_int_t  ldda,
magmaFloatComplex *  tau,
magmaFloatComplex_ptr  dC,
magma_int_t  lddc,
magmaFloatComplex *  wA,
magma_int_t  ldwa,
magma_int_t *  info 
)

CUNMQL overwrites the general complex M-by-N matrix C with.

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

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

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

as returned by CGEQLF. 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;
  • = Magma_ConjTrans: 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] dA COMPLEX 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 CGEQLF in the last k columns of its array argument A. The diagonal and the lower part are destroyed, the reflectors are not modified.
[in] ldda INTEGER The leading dimension of the array DA. LDDA >= max(1,M) if SIDE = MagmaLeft; LDDA >= max(1,N) if SIDE = MagmaRight.
[in] tau COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQLF.
[in,out] dC COMPLEX array, dimension (LDDC,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] lddc INTEGER The leading dimension of the array C. LDDC >= max(1,M).
[in] wA (workspace) COMPLEX array, dimension (LDWA,M) if SIDE = MagmaLeft (LDWA,N) if SIDE = MagmaRight The vectors which define the elementary reflectors, as returned by CHETRD_GPU.
[in] ldwa INTEGER The leading dimension of the array wA. LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight.
[out] info INTEGER

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

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