DOUBLE PRECISION FUNCTION DQRT11( M, K, A, LDA, TAU, WORK, LWORK ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER K, LDA, LWORK, M * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * Purpose * ======= * * DQRT11 computes the test ratio * * || Q'*Q - I || / (eps * m) * * where the orthogonal matrix Q is represented as a product of * elementary transformations. Each transformation has the form * * H(k) = I - tau(k) v(k) v(k)' * * where tau(k) is stored in TAU(k) and v(k) is an m-vector of the form * [ 0 ... 0 1 x(k) ]', where x(k) is a vector of length m-k stored * in A(k+1:m,k). * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix A. * * K (input) INTEGER * The number of columns of A whose subdiagonal entries * contain information about orthogonal transformations. * * A (input) DOUBLE PRECISION array, dimension (LDA,K) * The (possibly partial) output of a QR reduction routine. * * LDA (input) INTEGER * The leading dimension of the array A. * * TAU (input) DOUBLE PRECISION array, dimension (K) * The scaling factors tau for the elementary transformations as * computed by the QR factorization routine. * * WORK (workspace) DOUBLE PRECISION array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= M*M + M. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER INFO, J * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DLASET, DORM2R, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Local Arrays .. DOUBLE PRECISION RDUMMY( 1 ) * .. * .. Executable Statements .. * DQRT11 = ZERO * * Test for sufficient workspace * IF( LWORK.LT.M*M+M ) THEN CALL XERBLA( 'DQRT11', 7 ) RETURN END IF * * Quick return if possible * IF( M.LE.0 ) \$ RETURN * CALL DLASET( 'Full', M, M, ZERO, ONE, WORK, M ) * * Form Q * CALL DORM2R( 'Left', 'No transpose', M, M, K, A, LDA, TAU, WORK, \$ M, WORK( M*M+1 ), INFO ) * * Form Q'*Q * CALL DORM2R( 'Left', 'Transpose', M, M, K, A, LDA, TAU, WORK, M, \$ WORK( M*M+1 ), INFO ) * DO 10 J = 1, M WORK( ( J-1 )*M+J ) = WORK( ( J-1 )*M+J ) - ONE 10 CONTINUE * DQRT11 = DLANGE( 'One-norm', M, M, WORK, M, RDUMMY ) / \$ ( DBLE( M )*DLAMCH( 'Epsilon' ) ) * RETURN * * End of DQRT11 * END