SUBROUTINE ZGEQR2P( 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*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * ZGEQR2P computes a QR factorization of a complex m by n matrix A: * A = Q * R. * * 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*16 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 triangular if m >= n); the elements below the diagonal, * 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*16 array, dimension (min(M,N)) * The scalar factors of the elementary reflectors (see Further * Details). * * WORK (workspace) COMPLEX*16 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(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 complex scalar, and v is a complex 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). * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, K COMPLEX*16 ALPHA * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF, ZLARFGP * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, 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( 'ZGEQR2P', -INFO ) RETURN END IF * K = MIN( M, N ) * DO 10 I = 1, K * * Generate elementary reflector H(i) to annihilate A(i+1:m,i) * CALL ZLARFGP( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1, \$ TAU( I ) ) IF( I.LT.N ) THEN * * Apply H(i)' to A(i:m,i+1:n) from the left * ALPHA = A( I, I ) A( I, I ) = ONE CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1, \$ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK ) A( I, I ) = ALPHA END IF 10 CONTINUE RETURN * * End of ZGEQR2P * END