MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

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 MbyN matrix A: A = Q * L. More...  
magma_int_t  magma_dgeqlf (magma_int_t m, magma_int_t n, double *A, magma_int_t lda, double *tau, double *work, magma_int_t lwork, magma_int_t *info) 
DGEQLF computes a QL factorization of a DOUBLE PRECISION MbyN matrix A: A = Q * L. More...  
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 MbyN matrix A: A = Q * L. More...  
magma_int_t  magma_zgeqlf (magma_int_t m, magma_int_t n, magmaDoubleComplex *A, magma_int_t lda, magmaDoubleComplex *tau, magmaDoubleComplex *work, magma_int_t lwork, magma_int_t *info) 
ZGEQLF computes a QL factorization of a COMPLEX_16 MbyN matrix A: A = Q * L. More...  
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 MbyN matrix A: A = Q * L.
[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 MbyN matrix A. On exit, if m >= n, the lower triangle of the subarray A(mn+1:m,1:n) contains the NbyN lower triangular matrix L; if m <= n, the elements on and below the (nm)th superdiagonal contain the MbyN 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, N ). 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

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(mk+i+1:m) = 0 and v(mk+i) = 1; v(1:mk+i1) is stored on exit in A(1:mk+i1,nk+i), and tau in TAU(i).
magma_int_t magma_dgeqlf  (  magma_int_t  m, 
magma_int_t  n,  
double *  A,  
magma_int_t  lda,  
double *  tau,  
double *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
DGEQLF computes a QL factorization of a DOUBLE PRECISION MbyN matrix A: A = Q * L.
[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  DOUBLE PRECISION array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, if m >= n, the lower triangle of the subarray A(mn+1:m,1:n) contains the NbyN lower triangular matrix L; if m <= n, the elements on and below the (nm)th superdiagonal contain the MbyN 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  DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). 
[out]  work  (workspace) DOUBLE PRECISION 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_dgeqlf_nb( M, N ). 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

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(mk+i+1:m) = 0 and v(mk+i) = 1; v(1:mk+i1) is stored on exit in A(1:mk+i1,nk+i), and tau in TAU(i).
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 MbyN matrix A: A = Q * L.
[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 MbyN matrix A. On exit, if m >= n, the lower triangle of the subarray A(mn+1:m,1:n) contains the NbyN lower triangular matrix L; if m <= n, the elements on and below the (nm)th superdiagonal contain the MbyN 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  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,N,2*NB^2). For optimum performance LWORK >= max(N*NB, 2*NB^2) where NB can be obtained through magma_get_sgeqlf_nb( M, N ). 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

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(mk+i+1:m) = 0 and v(mk+i) = 1; v(1:mk+i1) is stored on exit in A(1:mk+i1,nk+i), and tau in TAU(i).
magma_int_t magma_zgeqlf  (  magma_int_t  m, 
magma_int_t  n,  
magmaDoubleComplex *  A,  
magma_int_t  lda,  
magmaDoubleComplex *  tau,  
magmaDoubleComplex *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
ZGEQLF computes a QL factorization of a COMPLEX_16 MbyN matrix A: A = Q * L.
[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_16 array, dimension (LDA,N) On entry, the MbyN matrix A. On exit, if m >= n, the lower triangle of the subarray A(mn+1:m,1:n) contains the NbyN lower triangular matrix L; if m <= n, the elements on and below the (nm)th superdiagonal contain the MbyN 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_16 array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). 
[out]  work  (workspace) COMPLEX_16 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_zgeqlf_nb( M, N ). 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

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(mk+i+1:m) = 0 and v(mk+i) = 1; v(1:mk+i1) is stored on exit in A(1:mk+i1,nk+i), and tau in TAU(i).