SUBROUTINE SLAGGE( M, N, KL, KU, 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, KL, KU, LDA, M, N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) REAL A( LDA, * ), D( * ), WORK( * ) * .. * * Purpose * ======= * * SLAGGE generates a real general m by n matrix A, by pre- and post- * multiplying a real diagonal matrix D with random orthogonal matrices: * A = U*D*V. The lower and upper bandwidths may then be reduced to * kl and ku by additional orthogonal transformations. * * Arguments * ========= * * M (input) INTEGER * The number of rows of the matrix A. M >= 0. * * N (input) INTEGER * The number of columns of the matrix A. N >= 0. * * KL (input) INTEGER * The number of nonzero subdiagonals within the band of A. * 0 <= KL <= M-1. * * KU (input) INTEGER * The number of nonzero superdiagonals within the band of A. * 0 <= KU <= N-1. * * D (input) REAL array, dimension (min(M,N)) * The diagonal elements of the diagonal matrix D. * * A (output) REAL array, dimension (LDA,N) * The generated m by n matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= M. * * 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 (M+N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, J REAL TAU, WA, WB, WN * .. * .. External Subroutines .. EXTERNAL SGEMV, SGER, SLARNV, SSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, SIGN * .. * .. External Functions .. REAL SNRM2 EXTERNAL SNRM2 * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN INFO = -3 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -7 END IF IF( INFO.LT.0 ) THEN CALL XERBLA( 'SLAGGE', -INFO ) RETURN END IF * * initialize A to diagonal matrix * DO 20 J = 1, N DO 10 I = 1, M A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE DO 30 I = 1, MIN( M, N ) A( I, I ) = D( I ) 30 CONTINUE * * pre- and post-multiply A by random orthogonal matrices * DO 40 I = MIN( M, N ), 1, -1 IF( I.LT.M ) THEN * * generate random reflection * CALL SLARNV( 3, ISEED, M-I+1, WORK ) WN = SNRM2( M-I+1, WORK, 1 ) WA = SIGN( WN, WORK( 1 ) ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = WORK( 1 ) + WA CALL SSCAL( M-I, ONE / WB, WORK( 2 ), 1 ) WORK( 1 ) = ONE TAU = WB / WA END IF * * multiply A(i:m,i:n) by random reflection from the left * CALL SGEMV( 'Transpose', M-I+1, N-I+1, ONE, A( I, I ), LDA, \$ WORK, 1, ZERO, WORK( M+1 ), 1 ) CALL SGER( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1, \$ A( I, I ), LDA ) END IF IF( I.LT.N ) THEN * * 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 * * multiply A(i:m,i:n) by random reflection from the right * CALL SGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ), \$ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 ) CALL SGER( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, \$ A( I, I ), LDA ) END IF 40 CONTINUE * * Reduce number of subdiagonals to KL and number of superdiagonals * to KU * DO 70 I = 1, MAX( M-1-KL, N-1-KU ) IF( KL.LE.KU ) THEN * * annihilate subdiagonal elements first (necessary if KL = 0) * IF( I.LE.MIN( M-1-KL, N ) ) THEN * * generate reflection to annihilate A(kl+i+1:m,i) * WN = SNRM2( M-KL-I+1, A( KL+I, I ), 1 ) WA = SIGN( WN, A( KL+I, I ) ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( KL+I, I ) + WA CALL SSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 ) A( KL+I, I ) = ONE TAU = WB / WA END IF * * apply reflection to A(kl+i:m,i+1:n) from the left * CALL SGEMV( 'Transpose', M-KL-I+1, N-I, ONE, \$ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO, \$ WORK, 1 ) CALL SGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1, \$ A( KL+I, I+1 ), LDA ) A( KL+I, I ) = -WA END IF * IF( I.LE.MIN( N-1-KU, M ) ) THEN * * generate reflection to annihilate A(i,ku+i+1:n) * WN = SNRM2( N-KU-I+1, A( I, KU+I ), LDA ) WA = SIGN( WN, A( I, KU+I ) ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( I, KU+I ) + WA CALL SSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA ) A( I, KU+I ) = ONE TAU = WB / WA END IF * * apply reflection to A(i+1:m,ku+i:n) from the right * CALL SGEMV( 'No transpose', M-I, N-KU-I+1, ONE, \$ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO, \$ WORK, 1 ) CALL SGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ), \$ LDA, A( I+1, KU+I ), LDA ) A( I, KU+I ) = -WA END IF ELSE * * annihilate superdiagonal elements first (necessary if * KU = 0) * IF( I.LE.MIN( N-1-KU, M ) ) THEN * * generate reflection to annihilate A(i,ku+i+1:n) * WN = SNRM2( N-KU-I+1, A( I, KU+I ), LDA ) WA = SIGN( WN, A( I, KU+I ) ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( I, KU+I ) + WA CALL SSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA ) A( I, KU+I ) = ONE TAU = WB / WA END IF * * apply reflection to A(i+1:m,ku+i:n) from the right * CALL SGEMV( 'No transpose', M-I, N-KU-I+1, ONE, \$ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO, \$ WORK, 1 ) CALL SGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ), \$ LDA, A( I+1, KU+I ), LDA ) A( I, KU+I ) = -WA END IF * IF( I.LE.MIN( M-1-KL, N ) ) THEN * * generate reflection to annihilate A(kl+i+1:m,i) * WN = SNRM2( M-KL-I+1, A( KL+I, I ), 1 ) WA = SIGN( WN, A( KL+I, I ) ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( KL+I, I ) + WA CALL SSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 ) A( KL+I, I ) = ONE TAU = WB / WA END IF * * apply reflection to A(kl+i:m,i+1:n) from the left * CALL SGEMV( 'Transpose', M-KL-I+1, N-I, ONE, \$ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO, \$ WORK, 1 ) CALL SGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1, \$ A( KL+I, I+1 ), LDA ) A( KL+I, I ) = -WA END IF END IF * DO 50 J = KL + I + 1, M A( J, I ) = ZERO 50 CONTINUE * DO 60 J = KU + I + 1, N A( I, J ) = ZERO 60 CONTINUE 70 CONTINUE RETURN * * End of SLAGGE * END