sgelq2.f (3) - Linux Man Pages
subroutine sgelq2 (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)
SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
SGELQ2 computes an LQ factorization of a real m by n matrix A: A = L * 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.
A is REAL 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).
LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).
TAU is REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).
WORK is REAL array, dimension (M)
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
- September 2012
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**T 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).
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