SUBROUTINE CGEQL2( M, N, A, LDA, TAU, WORK, INFO ) * * -- LAPACK routine (version 3.2.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2010 * * .. Scalar Arguments .. INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. COMPLEX A( LDA, * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * CGEQL2 computes a QL factorization of a complex m by n matrix A: * A = Q * L. * * Arguments * ========= * * M (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) COMPLEX array, dimension (LDA,N) * On entry, the m by n matrix A. * On exit, if m >= n, the lower triangle of the subarray * A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; * if m <= n, the elements on and below the (n-m)-th * superdiagonal contain the m by n lower trapezoidal matrix L; * the remaining elements, with the array TAU, represent the * unitary 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) COMPLEX array, dimension (min(M,N)) * The scalar factors of the elementary reflectors (see Further * Details). * * WORK (workspace) COMPLEX array, dimension (N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * Further Details * =============== * * 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' * * where tau is a complex scalar, and v is a complex vector with * v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in * A(1:m-k+i-1,n-k+i), and tau in TAU(i). * * ===================================================================== * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, K COMPLEX ALPHA * .. * .. External Subroutines .. EXTERNAL CLARF, CLARFG, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG, MAX, MIN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -4 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CGEQL2', -INFO ) RETURN END IF * K = MIN( M, N ) * DO 10 I = K, 1, -1 * * Generate elementary reflector H(i) to annihilate * A(1:m-k+i-1,n-k+i) * ALPHA = A( M-K+I, N-K+I ) CALL CLARFG( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) ) * * Apply H(i)' to A(1:m-k+i,1:n-k+i-1) from the left * A( M-K+I, N-K+I ) = ONE CALL CLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1, \$ CONJG( TAU( I ) ), A, LDA, WORK ) A( M-K+I, N-K+I ) = ALPHA 10 CONTINUE RETURN * * End of CGEQL2 * END