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SGELQ2(l)) SGELQ2(l)NAMESGELQ2 - compute an LQ factorization of a real m by n matrix ASYNOPSISSUBROUTINE SGELQ2( M, N, A, LDA, TAU, WORK, INFO ) INTEGER INFO, LDA, M, N REAL A( LDA, * ), TAU( * ), WORK( * )PURPOSESGELQ2 computes an LQ factorization of a real m by n matrix A: A = L * Q.ARGUMENTSM (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) 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 trian- gular 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 (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (workspace) REAL array, dimension (M) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iFURTHER DETAILSThe 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).LAPACK version 3.015 June 2000 SGELQ2(l)

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