sgeqrt.f (3) - Linux Man Pages
subroutine sgeqrt (integerM, integerN, integerNB, real, dimension( lda, * )A, integerLDA, real, dimension( ldt, * )T, integerLDT, real, dimension( * )WORK, integerINFO)
SGEQRT computes a blocked QR factorization of a real M-by-N matrix A using the compact WY representation of Q.
M is INTEGER The number of rows of the matrix A. M >= 0.
N is INTEGER The number of columns of the matrix A. N >= 0.
NB is INTEGER The block size to be used in the blocked QR. MIN(M,N) >= NB >= 1.
A is REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper triangular if M >= N); the elements below the diagonal are the columns of V.
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
T is REAL array, dimension (LDT,MIN(M,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See below for further details.
LDT is INTEGER The leading dimension of the array T. LDT >= NB.
WORK is REAL array, dimension (NB*N)
INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- November 2011
The matrix V stores the elementary reflectors H(i) in the i-th column below the diagonal. For example, if M=5 and N=3, the matrix V is V = ( 1 ) ( v1 1 ) ( v1 v2 1 ) ( v1 v2 v3 ) ( v1 v2 v3 ) where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. Let K=MIN(M,N). The number of blocks is B = ceiling(K/NB), where each block is of order NB except for the last block, which is of order IB = K - (B-1)*NB. For each of the B blocks, a upper triangular block reflector factor is computed: T1, T2, ..., TB. The NB-by-NB (and IB-by-IB for the last block) T's are stored in the NB-by-N matrix T as T = (T1 T2 ... TB).
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