MAGMA
2.3.0
Matrix Algebra for GPU and Multicore Architectures

Functions  
magma_int_t  magma_cgelqf (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) 
CGELQF computes an LQ factorization of a COMPLEX MbyN matrix A: A = L * Q. More...  
magma_int_t  magma_cgelqf_gpu (magma_int_t m, magma_int_t n, magmaFloatComplex_ptr dA, magma_int_t ldda, magmaFloatComplex *tau, magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info) 
CGELQF computes an LQ factorization of a COMPLEX MbyN matrix dA: dA = L * Q. More...  
magma_int_t  magma_dgelqf (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) 
DGELQF computes an LQ factorization of a DOUBLE PRECISION MbyN matrix A: A = L * Q. More...  
magma_int_t  magma_dgelqf_gpu (magma_int_t m, magma_int_t n, magmaDouble_ptr dA, magma_int_t ldda, double *tau, double *work, magma_int_t lwork, magma_int_t *info) 
DGELQF computes an LQ factorization of a DOUBLE PRECISION MbyN matrix dA: dA = L * Q. More...  
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 MbyN matrix A: A = L * Q. More...  
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 MbyN matrix dA: dA = L * Q. More...  
magma_int_t  magma_zgelqf (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) 
ZGELQF computes an LQ factorization of a COMPLEX_16 MbyN matrix A: A = L * Q. More...  
magma_int_t  magma_zgelqf_gpu (magma_int_t m, magma_int_t n, magmaDoubleComplex_ptr dA, magma_int_t ldda, magmaDoubleComplex *tau, magmaDoubleComplex *work, magma_int_t lwork, magma_int_t *info) 
ZGELQF computes an LQ factorization of a COMPLEX_16 MbyN matrix dA: dA = L * Q. More...  
magma_int_t magma_cgelqf  (  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  
) 
CGELQF computes an LQ factorization of a COMPLEX MbyN matrix A: A = L * Q.
[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, the elements on and below the diagonal of the array contain the mbymin(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  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. 
[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. TODO: work is currently unused. cgeqrf2 allocates its own work of (m + n)*nb. 
[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(1:i1) = 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_cgelqf_gpu  (  magma_int_t  m, 
magma_int_t  n,  
magmaFloatComplex_ptr  dA,  
magma_int_t  ldda,  
magmaFloatComplex *  tau,  
magmaFloatComplex *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
CGELQF computes an LQ factorization of a COMPLEX MbyN matrix dA: dA = L * Q.
[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  COMPLEX array on the GPU, dimension (LDDA,N) On entry, the MbyN matrix dA. On exit, the elements on and below the diagonal of the array contain the mbymin(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  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,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

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(1:i1) = 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_dgelqf  (  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  
) 
DGELQF computes an LQ factorization of a DOUBLE PRECISION MbyN matrix A: A = L * Q.
[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, the elements on and below the diagonal of the array contain the mbymin(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  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. 
[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. TODO: work is currently unused. dgeqrf2 allocates its own work of (m + n)*nb. 
[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(1:i1) = 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_dgelqf_gpu  (  magma_int_t  m, 
magma_int_t  n,  
magmaDouble_ptr  dA,  
magma_int_t  ldda,  
double *  tau,  
double *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
DGELQF computes an LQ factorization of a DOUBLE PRECISION MbyN matrix dA: dA = L * Q.
[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  DOUBLE PRECISION array on the GPU, dimension (LDDA,N) On entry, the MbyN matrix dA. On exit, the elements on and below the diagonal of the array contain the mbymin(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  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,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

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:i1) = 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  (  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 MbyN matrix A: A = L * Q.
[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, the elements on and below the diagonal of the array contain the mbymin(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. 
[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. TODO: work is currently unused. sgeqrf2 allocates its own work of (m + n)*nb. 
[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(1:i1) = 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 MbyN matrix dA: dA = L * Q.
[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 MbyN matrix dA. On exit, the elements on and below the diagonal of the array contain the mbymin(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

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:i1) = 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_zgelqf  (  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  
) 
ZGELQF computes an LQ factorization of a COMPLEX_16 MbyN matrix A: A = L * Q.
[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, the elements on and below the diagonal of the array contain the mbymin(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  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. 
[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. TODO: work is currently unused. zgeqrf2 allocates its own work of (m + n)*nb. 
[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(1:i1) = 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_zgelqf_gpu  (  magma_int_t  m, 
magma_int_t  n,  
magmaDoubleComplex_ptr  dA,  
magma_int_t  ldda,  
magmaDoubleComplex *  tau,  
magmaDoubleComplex *  work,  
magma_int_t  lwork,  
magma_int_t *  info  
) 
ZGELQF computes an LQ factorization of a COMPLEX_16 MbyN matrix dA: dA = L * Q.
[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  COMPLEX_16 array on the GPU, dimension (LDDA,N) On entry, the MbyN matrix dA. On exit, the elements on and below the diagonal of the array contain the mbymin(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  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,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

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