*> \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