slagge.f

来自「famous linear algebra library (LAPACK) p」· F 代码 · 共 290 行

      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