SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * DORGL2 generates an m by n real matrix Q with orthonormal rows, * which is defined as the first m rows of a product of k elementary * reflectors of order n * * Q = H(k) . . . H(2) H(1) * * as returned by DGELQF. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix Q. M >= 0. * * N (input) INTEGER * The number of columns of the matrix Q. N >= M. * * K (input) INTEGER * The number of elementary reflectors whose product defines the * matrix Q. M >= K >= 0. * * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) * On entry, the i-th row must contain the vector which defines * the elementary reflector H(i), for i = 1,2,...,k, as returned * by DGELQF in the first k rows of its array argument A. * On exit, the m-by-n matrix Q. * * LDA (input) INTEGER * The first dimension of the array A. LDA >= max(1,M). * * TAU (input) DOUBLE PRECISION array, dimension (K) * TAU(i) must contain the scalar factor of the elementary * reflector H(i), as returned by DGELQF. * * WORK (workspace) DOUBLE PRECISION array, dimension (M) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument has an illegal value * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J, L * .. * .. External Subroutines .. EXTERNAL DLARF, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORGL2', -INFO ) RETURN END IF * * Quick return if possible * IF( M.LE.0 ) $ RETURN * IF( K.LT.M ) THEN * * Initialise rows k+1:m to rows of the unit matrix * DO 20 J = 1, N DO 10 L = K + 1, M A( L, J ) = ZERO 10 CONTINUE IF( J.GT.K .AND. J.LE.M ) $ A( J, J ) = ONE 20 CONTINUE END IF * DO 40 I = K, 1, -1 * * Apply H(i) to A(i:m,i:n) from the right * IF( I.LT.N ) THEN IF( I.LT.M ) THEN A( I, I ) = ONE CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, $ TAU( I ), A( I+1, I ), LDA, WORK ) END IF CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA ) END IF A( I, I ) = ONE - TAU( I ) * * Set A(i,1:i-1) to zero * DO 30 L = 1, I - 1 A( I, L ) = ZERO 30 CONTINUE 40 CONTINUE RETURN * * End of DORGL2 * END