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SGEQRF(l)) SGEQRF(l)NAMESGEQRF - compute a QR factorization of a real M-by-N matrix ASYNOPSISSUBROUTINE SGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) INTEGER INFO, LDA, LWORK, M, N REAL A( LDA, * ), TAU( * ), WORK( * )PURPOSESGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R.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 above the diagonal of the array contain the min(M,N)-by-N upper trapezoidal matrix R (R is upper trian- gular if m >= n); the elements below the diagonal, with the array TAU, represent the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Fur- ther 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/output) REAL array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. If LWORK =, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO =-1, 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(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i).LAPACK version 3.015 June 2000 SGEQRF(l)

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