SUBROUTINE SLAGSY( N, K, D, 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, K, LDA, N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) REAL A( LDA, * ), D( * ), WORK( * ) * .. * * Purpose * ======= * * SLAGSY generates a real symmetric matrix A, by pre- and post- * multiplying a real diagonal matrix D with a random orthogonal matrix: * A = U*D*U'. The semi-bandwidth may then be reduced to k by additional * orthogonal transformations. * * Arguments * ========= * * N (input) INTEGER * The order of the matrix A. N >= 0. * * K (input) INTEGER * The number of nonzero subdiagonals within the band of A. * 0 <= K <= N-1. * * D (input) REAL array, dimension (N) * The diagonal elements of the diagonal matrix D. * * A (output) REAL array, dimension (LDA,N) * The generated n by n symmetric matrix A (the full matrix is * stored). * * 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) REAL array, dimension (2*N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE, HALF PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, HALF = 0.5E+0 ) * .. * .. Local Scalars .. INTEGER I, J REAL ALPHA, TAU, WA, WB, WN * .. * .. External Subroutines .. EXTERNAL SAXPY, SGEMV, SGER, SLARNV, SSCAL, SSYMV, \$ SSYR2, XERBLA * .. * .. External Functions .. REAL SDOT, SNRM2 EXTERNAL SDOT, SNRM2 * .. * .. Intrinsic Functions .. INTRINSIC MAX, SIGN * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( N.LT.0 ) THEN INFO = -1 ELSE IF( K.LT.0 .OR. K.GT.N-1 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF IF( INFO.LT.0 ) THEN CALL XERBLA( 'SLAGSY', -INFO ) RETURN END IF * * initialize lower triangle of A to diagonal matrix * DO 20 J = 1, N DO 10 I = J + 1, N A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE DO 30 I = 1, N A( I, I ) = D( I ) 30 CONTINUE * * Generate lower triangle of symmetric matrix * DO 40 I = N - 1, 1, -1 * * generate random reflection * CALL SLARNV( 3, ISEED, N-I+1, WORK ) WN = SNRM2( N-I+1, WORK, 1 ) WA = SIGN( WN, WORK( 1 ) ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = WORK( 1 ) + WA CALL SSCAL( N-I, ONE / WB, WORK( 2 ), 1 ) WORK( 1 ) = ONE TAU = WB / WA END IF * * apply random reflection to A(i:n,i:n) from the left * and the right * * compute y := tau * A * u * CALL SSYMV( 'Lower', N-I+1, TAU, A( I, I ), LDA, WORK, 1, ZERO, \$ WORK( N+1 ), 1 ) * * compute v := y - 1/2 * tau * ( y, u ) * u * ALPHA = -HALF*TAU*SDOT( N-I+1, WORK( N+1 ), 1, WORK, 1 ) CALL SAXPY( N-I+1, ALPHA, WORK, 1, WORK( N+1 ), 1 ) * * apply the transformation as a rank-2 update to A(i:n,i:n) * CALL SSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1, \$ A( I, I ), LDA ) 40 CONTINUE * * Reduce number of subdiagonals to K * DO 60 I = 1, N - 1 - K * * generate reflection to annihilate A(k+i+1:n,i) * WN = SNRM2( N-K-I+1, A( K+I, I ), 1 ) WA = SIGN( WN, A( K+I, I ) ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( K+I, I ) + WA CALL SSCAL( N-K-I, ONE / WB, A( K+I+1, I ), 1 ) A( K+I, I ) = ONE TAU = WB / WA END IF * * apply reflection to A(k+i:n,i+1:k+i-1) from the left * CALL SGEMV( 'Transpose', N-K-I+1, K-1, ONE, A( K+I, I+1 ), LDA, \$ A( K+I, I ), 1, ZERO, WORK, 1 ) CALL SGER( N-K-I+1, K-1, -TAU, A( K+I, I ), 1, WORK, 1, \$ A( K+I, I+1 ), LDA ) * * apply reflection to A(k+i:n,k+i:n) from the left and the right * * compute y := tau * A * u * CALL SSYMV( 'Lower', N-K-I+1, TAU, A( K+I, K+I ), LDA, \$ A( K+I, I ), 1, ZERO, WORK, 1 ) * * compute v := y - 1/2 * tau * ( y, u ) * u * ALPHA = -HALF*TAU*SDOT( N-K-I+1, WORK, 1, A( K+I, I ), 1 ) CALL SAXPY( N-K-I+1, ALPHA, A( K+I, I ), 1, WORK, 1 ) * * apply symmetric rank-2 update to A(k+i:n,k+i:n) * CALL SSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1, \$ A( K+I, K+I ), LDA ) * A( K+I, I ) = -WA DO 50 J = K + I + 1, N A( J, I ) = ZERO 50 CONTINUE 60 CONTINUE * * Store full symmetric matrix * DO 80 J = 1, N DO 70 I = J + 1, N A( J, I ) = A( I, J ) 70 CONTINUE 80 CONTINUE RETURN * * End of SLAGSY * END