You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
264 lines
7.1 KiB
264 lines
7.1 KiB
*> \brief \b CLATSP
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CLATSP( UPLO, N, X, ISEED )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER ISEED( * )
|
|
* COMPLEX X( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CLATSP generates a special test matrix for the complex symmetric
|
|
*> (indefinite) factorization for packed matrices. 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 array, dimension (N*(N+1)/2)
|
|
*> The generated matrix in packed storage format. The matrix
|
|
*> consists of 3x3 and 2x2 diagonal blocks which result in the
|
|
*> pivot sequence given above. The matrix outside these
|
|
*> diagonal blocks is zero.
|
|
*> \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 complex_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE CLATSP( UPLO, N, X, 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 N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER ISEED( * )
|
|
COMPLEX X( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
COMPLEX EYE
|
|
PARAMETER ( EYE = ( 0.0, 1.0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER J, JJ, N5
|
|
REAL ALPHA, ALPHA3, BETA
|
|
COMPLEX A, B, C, R
|
|
* ..
|
|
* .. External Functions ..
|
|
COMPLEX CLARND
|
|
EXTERNAL CLARND
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, SQRT
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Initialize constants
|
|
*
|
|
ALPHA = ( 1.+SQRT( 17. ) ) / 8.
|
|
BETA = ALPHA - 1. / 1000.
|
|
ALPHA3 = ALPHA*ALPHA*ALPHA
|
|
*
|
|
* Fill the matrix with zeros.
|
|
*
|
|
DO 10 J = 1, N*( N+1 ) / 2
|
|
X( J ) = 0.0
|
|
10 CONTINUE
|
|
*
|
|
* UPLO = 'U': Upper triangular storage
|
|
*
|
|
IF( UPLO.EQ.'U' ) THEN
|
|
N5 = N / 5
|
|
N5 = N - 5*N5 + 1
|
|
*
|
|
JJ = N*( N+1 ) / 2
|
|
DO 20 J = N, N5, -5
|
|
A = ALPHA3*CLARND( 5, ISEED )
|
|
B = CLARND( 5, ISEED ) / ALPHA
|
|
C = A - 2.*B*EYE
|
|
R = C / BETA
|
|
X( JJ ) = A
|
|
X( JJ-2 ) = B
|
|
JJ = JJ - J
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
X( JJ-1 ) = R
|
|
JJ = JJ - ( J-1 )
|
|
X( JJ ) = C
|
|
JJ = JJ - ( J-2 )
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
JJ = JJ - ( J-3 )
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
IF( ABS( X( JJ+( J-3 ) ) ).GT.ABS( X( JJ ) ) ) THEN
|
|
X( JJ+( J-4 ) ) = 2.0*X( JJ+( J-3 ) )
|
|
ELSE
|
|
X( JJ+( J-4 ) ) = 2.0*X( JJ )
|
|
END IF
|
|
JJ = JJ - ( J-4 )
|
|
20 CONTINUE
|
|
*
|
|
* Clean-up for N not a multiple of 5.
|
|
*
|
|
J = N5 - 1
|
|
IF( J.GT.2 ) THEN
|
|
A = ALPHA3*CLARND( 5, ISEED )
|
|
B = CLARND( 5, ISEED ) / ALPHA
|
|
C = A - 2.*B*EYE
|
|
R = C / BETA
|
|
X( JJ ) = A
|
|
X( JJ-2 ) = B
|
|
JJ = JJ - J
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
X( JJ-1 ) = R
|
|
JJ = JJ - ( J-1 )
|
|
X( JJ ) = C
|
|
JJ = JJ - ( J-2 )
|
|
J = J - 3
|
|
END IF
|
|
IF( J.GT.1 ) THEN
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
X( JJ-J ) = CLARND( 2, ISEED )
|
|
IF( ABS( X( JJ ) ).GT.ABS( X( JJ-J ) ) ) THEN
|
|
X( JJ-1 ) = 2.0*X( JJ )
|
|
ELSE
|
|
X( JJ-1 ) = 2.0*X( JJ-J )
|
|
END IF
|
|
JJ = JJ - J - ( J-1 )
|
|
J = J - 2
|
|
ELSE IF( J.EQ.1 ) THEN
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
J = J - 1
|
|
END IF
|
|
*
|
|
* UPLO = 'L': Lower triangular storage
|
|
*
|
|
ELSE
|
|
N5 = N / 5
|
|
N5 = N5*5
|
|
*
|
|
JJ = 1
|
|
DO 30 J = 1, N5, 5
|
|
A = ALPHA3*CLARND( 5, ISEED )
|
|
B = CLARND( 5, ISEED ) / ALPHA
|
|
C = A - 2.*B*EYE
|
|
R = C / BETA
|
|
X( JJ ) = A
|
|
X( JJ+2 ) = B
|
|
JJ = JJ + ( N-J+1 )
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
X( JJ+1 ) = R
|
|
JJ = JJ + ( N-J )
|
|
X( JJ ) = C
|
|
JJ = JJ + ( N-J-1 )
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
JJ = JJ + ( N-J-2 )
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
IF( ABS( X( JJ-( N-J-2 ) ) ).GT.ABS( X( JJ ) ) ) THEN
|
|
X( JJ-( N-J-2 )+1 ) = 2.0*X( JJ-( N-J-2 ) )
|
|
ELSE
|
|
X( JJ-( N-J-2 )+1 ) = 2.0*X( JJ )
|
|
END IF
|
|
JJ = JJ + ( N-J-3 )
|
|
30 CONTINUE
|
|
*
|
|
* Clean-up for N not a multiple of 5.
|
|
*
|
|
J = N5 + 1
|
|
IF( J.LT.N-1 ) THEN
|
|
A = ALPHA3*CLARND( 5, ISEED )
|
|
B = CLARND( 5, ISEED ) / ALPHA
|
|
C = A - 2.*B*EYE
|
|
R = C / BETA
|
|
X( JJ ) = A
|
|
X( JJ+2 ) = B
|
|
JJ = JJ + ( N-J+1 )
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
X( JJ+1 ) = R
|
|
JJ = JJ + ( N-J )
|
|
X( JJ ) = C
|
|
JJ = JJ + ( N-J-1 )
|
|
J = J + 3
|
|
END IF
|
|
IF( J.LT.N ) THEN
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
X( JJ+( N-J+1 ) ) = CLARND( 2, ISEED )
|
|
IF( ABS( X( JJ ) ).GT.ABS( X( JJ+( N-J+1 ) ) ) ) THEN
|
|
X( JJ+1 ) = 2.0*X( JJ )
|
|
ELSE
|
|
X( JJ+1 ) = 2.0*X( JJ+( N-J+1 ) )
|
|
END IF
|
|
JJ = JJ + ( N-J+1 ) + ( N-J )
|
|
J = J + 2
|
|
ELSE IF( J.EQ.N ) THEN
|
|
X( JJ ) = CLARND( 2, ISEED )
|
|
JJ = JJ + ( N-J+1 )
|
|
J = J + 1
|
|
END IF
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CLATSP
|
|
*
|
|
END
|
|
|