numeric-linalg

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*> \brief \b ZLATSY
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLATSY( UPLO, N, X, LDX, ISEED )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            LDX, N
*       ..
*       .. Array Arguments ..
*       INTEGER            ISEED( * )
*       COMPLEX*16         X( LDX, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLATSY generates a special test matrix for the complex symmetric
*> (indefinite) factorization.  The pivot blocks of the generated matrix
*> will be in the following order:
*>    2x2 pivot block, non diagonalizable
*>    1x1 pivot block
*>    2x2 pivot block, diagonalizable
*>    (cycle repeats)
*> A row interchange is required for each non-diagonalizable 2x2 block.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER
*>          Specifies whether the generated matrix is to be upper or
*>          lower triangular.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The dimension of the matrix to be generated.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension (LDX,N)
*>          The generated matrix, consisting of 3x3 and 2x2 diagonal
*>          blocks which result in the pivot sequence given above.
*>          The matrix outside of these diagonal blocks is zero.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the array X.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*>          ISEED is INTEGER array, dimension (4)
*>          On entry, the seed for the random number generator.  The last
*>          of the four integers must be odd.  (modified on exit)
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
*  =====================================================================
      SUBROUTINE ZLATSY( UPLO, N, X, LDX, ISEED )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            LDX, N
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( * )
      COMPLEX*16         X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         EYE
      PARAMETER          ( EYE = ( 0.0D0, 1.0D0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J, N5
      DOUBLE PRECISION   ALPHA, ALPHA3, BETA
      COMPLEX*16         A, B, C, R
*     ..
*     .. External Functions ..
      COMPLEX*16         ZLARND
      EXTERNAL           ZLARND
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, SQRT
*     ..
*     .. Executable Statements ..
*
*     Initialize constants
*
      ALPHA = ( 1.D0+SQRT( 17.D0 ) ) / 8.D0
      BETA = ALPHA - 1.D0 / 1000.D0
      ALPHA3 = ALPHA*ALPHA*ALPHA
*
*     UPLO = 'U':  Upper triangular storage
*
      IF( UPLO.EQ.'U' ) THEN
*
*        Fill the upper triangle of the matrix with zeros.
*
         DO 20 J = 1, N
            DO 10 I = 1, J
               X( I, J ) = 0.0D0
   10       CONTINUE
   20    CONTINUE
         N5 = N / 5
         N5 = N - 5*N5 + 1
*
         DO 30 I = N, N5, -5
            A = ALPHA3*ZLARND( 5, ISEED )
            B = ZLARND( 5, ISEED ) / ALPHA
            C = A - 2.D0*B*EYE
            R = C / BETA
            X( I, I ) = A
            X( I-2, I ) = B
            X( I-2, I-1 ) = R
            X( I-2, I-2 ) = C
            X( I-1, I-1 ) = ZLARND( 2, ISEED )
            X( I-3, I-3 ) = ZLARND( 2, ISEED )
            X( I-4, I-4 ) = ZLARND( 2, ISEED )
            IF( ABS( X( I-3, I-3 ) ).GT.ABS( X( I-4, I-4 ) ) ) THEN
               X( I-4, I-3 ) = 2.0D0*X( I-3, I-3 )
            ELSE
               X( I-4, I-3 ) = 2.0D0*X( I-4, I-4 )
            END IF
   30    CONTINUE
*
*        Clean-up for N not a multiple of 5.
*
         I = N5 - 1
         IF( I.GT.2 ) THEN
            A = ALPHA3*ZLARND( 5, ISEED )
            B = ZLARND( 5, ISEED ) / ALPHA
            C = A - 2.D0*B*EYE
            R = C / BETA
            X( I, I ) = A
            X( I-2, I ) = B
            X( I-2, I-1 ) = R
            X( I-2, I-2 ) = C
            X( I-1, I-1 ) = ZLARND( 2, ISEED )
            I = I - 3
         END IF
         IF( I.GT.1 ) THEN
            X( I, I ) = ZLARND( 2, ISEED )
            X( I-1, I-1 ) = ZLARND( 2, ISEED )
            IF( ABS( X( I, I ) ).GT.ABS( X( I-1, I-1 ) ) ) THEN
               X( I-1, I ) = 2.0D0*X( I, I )
            ELSE
               X( I-1, I ) = 2.0D0*X( I-1, I-1 )
            END IF
            I = I - 2
         ELSE IF( I.EQ.1 ) THEN
            X( I, I ) = ZLARND( 2, ISEED )
            I = I - 1
         END IF
*
*     UPLO = 'L':  Lower triangular storage
*
      ELSE
*
*        Fill the lower triangle of the matrix with zeros.
*
         DO 50 J = 1, N
            DO 40 I = J, N
               X( I, J ) = 0.0D0
   40       CONTINUE
   50    CONTINUE
         N5 = N / 5
         N5 = N5*5
*
         DO 60 I = 1, N5, 5
            A = ALPHA3*ZLARND( 5, ISEED )
            B = ZLARND( 5, ISEED ) / ALPHA
            C = A - 2.D0*B*EYE
            R = C / BETA
            X( I, I ) = A
            X( I+2, I ) = B
            X( I+2, I+1 ) = R
            X( I+2, I+2 ) = C
            X( I+1, I+1 ) = ZLARND( 2, ISEED )
            X( I+3, I+3 ) = ZLARND( 2, ISEED )
            X( I+4, I+4 ) = ZLARND( 2, ISEED )
            IF( ABS( X( I+3, I+3 ) ).GT.ABS( X( I+4, I+4 ) ) ) THEN
               X( I+4, I+3 ) = 2.0D0*X( I+3, I+3 )
            ELSE
               X( I+4, I+3 ) = 2.0D0*X( I+4, I+4 )
            END IF
   60    CONTINUE
*
*        Clean-up for N not a multiple of 5.
*
         I = N5 + 1
         IF( I.LT.N-1 ) THEN
            A = ALPHA3*ZLARND( 5, ISEED )
            B = ZLARND( 5, ISEED ) / ALPHA
            C = A - 2.D0*B*EYE
            R = C / BETA
            X( I, I ) = A
            X( I+2, I ) = B
            X( I+2, I+1 ) = R
            X( I+2, I+2 ) = C
            X( I+1, I+1 ) = ZLARND( 2, ISEED )
            I = I + 3
         END IF
         IF( I.LT.N ) THEN
            X( I, I ) = ZLARND( 2, ISEED )
            X( I+1, I+1 ) = ZLARND( 2, ISEED )
            IF( ABS( X( I, I ) ).GT.ABS( X( I+1, I+1 ) ) ) THEN
               X( I+1, I ) = 2.0D0*X( I, I )
            ELSE
               X( I+1, I ) = 2.0D0*X( I+1, I+1 )
            END IF
            I = I + 2
         ELSE IF( I.EQ.N ) THEN
            X( I, I ) = ZLARND( 2, ISEED )
            I = I + 1
         END IF
      END IF
*
      RETURN
*
*     End of ZLATSY
*
      END