SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO ) * * -- LAPACK auxiliary test routine (version 3.1) * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION A( LDA, * ), WORK( * ) * .. * * Purpose * ======= * * DLARGE pre- and post-multiplies a real general n by n matrix A * with a random orthogonal matrix: A = U*D*U'. * * Arguments * ========= * * N (input) INTEGER * The order of the matrix A. N >= 0. * * A (input/output) DOUBLE PRECISION array, dimension (LDA,N) * On entry, the original n by n matrix A. * On exit, A is overwritten by U*A*U' for some random * orthogonal matrix U. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= N. * * ISEED (input/output) INTEGER array, dimension (4) * On entry, the seed of the random number generator; the array * elements must be between 0 and 4095, and ISEED(4) must be * odd. * On exit, the seed is updated. * * WORK (workspace) DOUBLE PRECISION array, dimension (2*N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I DOUBLE PRECISION TAU, WA, WB, WN * .. * .. External Subroutines .. EXTERNAL DGEMV, DGER, DLARNV, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, SIGN * .. * .. External Functions .. DOUBLE PRECISION DNRM2 EXTERNAL DNRM2 * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -3 END IF IF( INFO.LT.0 ) THEN CALL XERBLA( 'DLARGE', -INFO ) RETURN END IF * * pre- and post-multiply A by random orthogonal matrix * DO 10 I = N, 1, -1 * * generate random reflection * CALL DLARNV( 3, ISEED, N-I+1, WORK ) WN = DNRM2( N-I+1, WORK, 1 ) WA = SIGN( WN, WORK( 1 ) ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = WORK( 1 ) + WA CALL DSCAL( N-I, ONE / WB, WORK( 2 ), 1 ) WORK( 1 ) = ONE TAU = WB / WA END IF * * multiply A(i:n,1:n) by random reflection from the left * CALL DGEMV( 'Transpose', N-I+1, N, ONE, A( I, 1 ), LDA, WORK, \$ 1, ZERO, WORK( N+1 ), 1 ) CALL DGER( N-I+1, N, -TAU, WORK, 1, WORK( N+1 ), 1, A( I, 1 ), \$ LDA ) * * multiply A(1:n,i:n) by random reflection from the right * CALL DGEMV( 'No transpose', N, N-I+1, ONE, A( 1, I ), LDA, \$ WORK, 1, ZERO, WORK( N+1 ), 1 ) CALL DGER( N, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, A( 1, I ), \$ LDA ) 10 CONTINUE RETURN * * End of DLARGE * END