MAGMA  2.3.0
Matrix Algebra for GPU and Multicore Architectures
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gelqf: LQ factorization

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 M-by-N 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 M-by-N 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 M-by-N 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 M-by-N 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 M-by-N 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 M-by-N 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 M-by-N 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 M-by-N matrix dA: dA = L * Q. More...
 

Detailed Description

Function Documentation

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 M-by-N matrix A: A = L * Q.

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]ACOMPLEX 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]tauCOMPLEX 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]lworkINTEGER 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]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 complex scalar, and v is a complex 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_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 M-by-N matrix dA: dA = L * Q.

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]dACOMPLEX 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]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]tauCOMPLEX 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]lworkINTEGER 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]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 complex scalar, and v is a complex 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_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 M-by-N matrix A: A = L * Q.

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]ADOUBLE PRECISION 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]tauDOUBLE 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]lworkINTEGER 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]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(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_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 M-by-N matrix dA: dA = L * Q.

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]dADOUBLE PRECISION 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]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]tauDOUBLE 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]lworkINTEGER 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]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(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 ( 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]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, 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]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[0] returns the optimal LWORK.
[in]lworkINTEGER 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]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(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]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]dAREAL 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]lddaINTEGER The leading dimension of the array dA. LDDA >= 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[0] 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,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]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(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_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 M-by-N matrix A: A = L * Q.

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]ACOMPLEX_16 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]ldaINTEGER The leading dimension of the array A. LDA >= max(1,M).
[out]tauCOMPLEX_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]lworkINTEGER 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]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 complex scalar, and v is a complex 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_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 M-by-N matrix dA: dA = L * Q.

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]dACOMPLEX_16 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]lddaINTEGER The leading dimension of the array dA. LDDA >= max(1,M).
[out]tauCOMPLEX_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]lworkINTEGER 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]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 complex scalar, and v is a complex 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).