Nakata Maho
fa23a2dc2d
The four TESTING/LIN routines currently document ISEED as an INTEGER array of dimension (4), but their dummy argument declarations use ISEED(*). All four routines pass ISEED to CLARND or ZLARND, whose interfaces require ISEED(4) and document that the fourth element must be odd. Replace the assumed-size declaration with an explicit size of 4 in both the commented argument declarations and the actual dummy argument declarations, so that the source matches the documented contract and the callee interfaces. No functional change is intended.
260 lines
7.0 KiB
FortranFixed
260 lines
7.0 KiB
FortranFixed
*> \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( 4 )
|
|
* 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 )
|
|
IMPLICIT NONE
|
|
*
|
|
* -- 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( 4 )
|
|
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
|