REAL FUNCTION SQPT01( M, N, K, A, AF, LDA, TAU, JPVT, \$ WORK, LWORK ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER K, LDA, LWORK, M, N * .. * .. Array Arguments .. INTEGER JPVT( * ) REAL A( LDA, * ), AF( LDA, * ), TAU( * ), \$ WORK( LWORK ) * .. * * Purpose * ======= * * SQPT01 tests the QR-factorization with pivoting of a matrix A. The * array AF contains the (possibly partial) QR-factorization of A, where * the upper triangle of AF(1:k,1:k) is a partial triangular factor, * the entries below the diagonal in the first k columns are the * Householder vectors, and the rest of AF contains a partially updated * matrix. * * This function returns ||A*P - Q*R||/(||norm(A)||*eps*M) * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrices A and AF. * * N (input) INTEGER * The number of columns of the matrices A and AF. * * K (input) INTEGER * The number of columns of AF that have been reduced * to upper triangular form. * * A (input) REAL array, dimension (LDA, N) * The original matrix A. * * AF (input) REAL array, dimension (LDA,N) * The (possibly partial) output of SGEQPF. The upper triangle * of AF(1:k,1:k) is a partial triangular factor, the entries * below the diagonal in the first k columns are the Householder * vectors, and the rest of AF contains a partially updated * matrix. * * LDA (input) INTEGER * The leading dimension of the arrays A and AF. * * TAU (input) REAL array, dimension (K) * Details of the Householder transformations as returned by * SGEQPF. * * JPVT (input) INTEGER array, dimension (N) * Pivot information as returned by SGEQPF. * * WORK (workspace) REAL array, dimension (LWORK) * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= M*N+N. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 ) * .. * .. Local Scalars .. INTEGER I, INFO, J REAL NORMA * .. * .. Local Arrays .. REAL RWORK( 1 ) * .. * .. External Functions .. REAL SLAMCH, SLANGE EXTERNAL SLAMCH, SLANGE * .. * .. External Subroutines .. EXTERNAL SAXPY, SCOPY, SORMQR, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, REAL * .. * .. Executable Statements .. * SQPT01 = ZERO * * Test if there is enough workspace * IF( LWORK.LT.M*N+N ) THEN CALL XERBLA( 'SQPT01', 10 ) RETURN END IF * * Quick return if possible * IF( M.LE.0 .OR. N.LE.0 ) \$ RETURN * NORMA = SLANGE( 'One-norm', M, N, A, LDA, RWORK ) * DO 30 J = 1, K DO 10 I = 1, MIN( J, M ) WORK( ( J-1 )*M+I ) = AF( I, J ) 10 CONTINUE DO 20 I = J + 1, M WORK( ( J-1 )*M+I ) = ZERO 20 CONTINUE 30 CONTINUE DO 40 J = K + 1, N CALL SCOPY( M, AF( 1, J ), 1, WORK( ( J-1 )*M+1 ), 1 ) 40 CONTINUE * CALL SORMQR( 'Left', 'No transpose', M, N, K, AF, LDA, TAU, WORK, \$ M, WORK( M*N+1 ), LWORK-M*N, INFO ) * DO 50 J = 1, N * * Compare i-th column of QR and jpvt(i)-th column of A * CALL SAXPY( M, -ONE, A( 1, JPVT( J ) ), 1, WORK( ( J-1 )*M+1 ), \$ 1 ) 50 CONTINUE * SQPT01 = SLANGE( 'One-norm', M, N, WORK, M, RWORK ) / \$ ( REAL( MAX( M, N ) )*SLAMCH( 'Epsilon' ) ) IF( NORMA.NE.ZERO ) \$ SQPT01 = SQPT01 / NORMA * RETURN * * End of SQPT01 * END