Developer Reference for Intel® oneAPI Math Kernel Library for C
mkl_?geqrf_compact
Syntax
voidmkl_sgeqrf_compact ( MKL_LAYOUTlayout , MKL_INTm , MKL_INTn , float*ap , MKL_INTldap , float*taup , float*work , MKL_INTlwork , MKL_INT*info , MKL_COMPACT_PACKformat , MKL_INTnm );
voidmkl_cgeqrf_compact ( MKL_LAYOUTlayout , MKL_INTm , MKL_INTn , float*ap , MKL_INTldap , float*taup , float*work , MKL_INTlwork , MKL_INT*info , MKL_COMPACT_PACKformat , MKL_INTnm );
voidmkl_dgeqrf_compact ( MKL_LAYOUTlayout , MKL_INTm , MKL_INTn , double*ap , MKL_INTldap , double*taup , double*work , MKL_INTlwork , MKL_INT*info , MKL_COMPACT_PACKformat , MKL_INTnm );
voidmkl_zgeqrf_compact ( MKL_LAYOUTlayout , MKL_INTm , MKL_INTn , double*ap , MKL_INTldap , double*taup , double*work , MKL_INTlwork , MKL_INT*info , MKL_COMPACT_PACKformat , MKL_INTnm );
Description
The routine forms the QR factorization of a set of general, m x n matrices A, stored in Compact format. The routine does not form the Q factors explicitly. Instead, Q is represented as a product of min(m,n) elementary reflectors. The factorization (output) data will also be stored in Compact format. Compact routines have some limitations; see Numerical Limitations .
Input Parameters
- layout
-
Specifies whether two-dimensional array storage is row-major ( MKL_ROW_MAJOR ) or column-major ( MKL_COL_MAJOR ).
- m
-
The number of rows of A c ; m≥ 0.
- n
-
The number of columns of A c ; n≥ 0.
- ap
-
Points to the beginning of the nm A c matrices. On entry, ap contains either the upper or the lower triangular part of A c (see uplo).
- ldap
-
Column stride (column-major layout) or row stride (row-major layout) of A c .
- work
-
Points to the beginning of the workspace array.
- lwork
-
The size of the work array. If lwork = -1, a workspace query is assumed; the routine only calculates the optimal size of the work array and returns this value as the first entry of the work array.
- format
-
Specifies the format of the compact matrices. See Compact Format or mkl_get_format_compact for details.
- nm
-
Total number of matrices stored in Compact format.
Application Notes:
The compact array that will store the elementary reflectors needs to be allocated before the routine is called and unpacked after. First, the routine mkl_?get_size_compact should be called, to determine the size of taup , and memory for taup should be allocated. After calling mkl_?geqrf_compact , taup stores the elementary reflectors in compact form, so should be unpacked using mkl_?geunpack_compact . See Compact Format for more details, or reference the example below. (Note: the following example is meant to demonstrate the calling sequence to allocate memory and unpack taup . All other parameters are assumed to be already set up before the sequence below is executed.)
MKL_R_TYPE *tau_array[nm];
// ...
tau_buffer_size = mkl_?get_size_compact(min(m, n), 1, format, nm);
MKL_R_TYPE *tau_compact = (MKL_R_TYPE *)mkl_malloc(tau_buffer_size, 128);
mkl_?geqrf_compact(layout, m, n, a_compact, ldap, tau_compact, work, lwork, &info, format, nm);
// Note that here MKL_COL_MAJOR is used because tau is a 1-d array
mkl_?geunpack_compact(MKL_COL_MAJOR, min(m, n), 1, tau_array, min(m, n), tau_compact, min(m, n), format, nm);Output Parameters
- ap
-
On exit, A c is overwritten by its factorization data. ap points to the beginning of nm factorizations of A c , stored in Compact format. The factorization data is stored as follows: The elements on and above the diagonal contain the min( m , n )-by- n upper trapezoidal matrix R c ( R c is upper triangular if m ≥ n ); the elements below the diagonal, with tau , present the orthogonal matrix Q c as a product of min( m , n ) elementary reflectors (see Orthogonal Factorizations: LAPACK Computational Routines ). See Compact Format for more details.
- taup
-
Points to the beginning of a set of the tau c arrays, each of which has size min(m,n), stored in Compact format. tau c contains scalars that define elementary reflectors for Q c in its decomposition in a product of elementary reflectors. taup needs to be allocated by the user before calling this routine. See the application notes (below the description) for more details.
- work[0]
-
On exit contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.
- info
-
The parameter is not currently used in this routine. It is reserved for the future use.