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SGERQ2(l)) SGERQ2(l)NAMESGERQ2 - compute an RQ factorization of a real m by n matrix ASYNOPSISSUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO ) INTEGER INFO, LDA, M, N REAL A( LDA, * ), TAU( * ), WORK( * )PURPOSESGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * 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, if m <= n, the upper triangle of the sub- array A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trape- zoidal matrix R; the remaining elements, with the array TAU, represent the orthog- onal 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).LAPACK version 3.015 June 2000 SGERQ2(l)

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