217 lines
6.1 KiB
FortranFixed
217 lines
6.1 KiB
FortranFixed
SUBROUTINE ZLATSP( UPLO, N, X, ISEED )
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*
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* -- LAPACK auxiliary test routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER N
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* ..
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* .. Array Arguments ..
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INTEGER ISEED( * )
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COMPLEX*16 X( * )
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* ..
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*
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* Purpose
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* =======
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*
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* ZLATSP generates a special test matrix for the complex symmetric
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* (indefinite) factorization for packed matrices. The pivot blocks of
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* the generated matrix will be in the following order:
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* 2x2 pivot block, non diagonalizable
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* 1x1 pivot block
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* 2x2 pivot block, diagonalizable
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* (cycle repeats)
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* A row interchange is required for each non-diagonalizable 2x2 block.
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*
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* Arguments
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* =========
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*
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* UPLO (input) CHARACTER
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* Specifies whether the generated matrix is to be upper or
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* lower triangular.
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* = 'U': Upper triangular
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* = 'L': Lower triangular
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*
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* N (input) INTEGER
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* The dimension of the matrix to be generated.
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*
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* X (output) COMPLEX*16 array, dimension (N*(N+1)/2)
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* The generated matrix in packed storage format. The matrix
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* consists of 3x3 and 2x2 diagonal blocks which result in the
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* pivot sequence given above. The matrix outside these
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* diagonal blocks is zero.
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*
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* ISEED (input/output) INTEGER array, dimension (4)
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* On entry, the seed for the random number generator. The last
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* of the four integers must be odd. (modified on exit)
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 EYE
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PARAMETER ( EYE = ( 0.0D0, 1.0D0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER J, JJ, N5
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DOUBLE PRECISION ALPHA, ALPHA3, BETA
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COMPLEX*16 A, B, C, R
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* ..
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* .. External Functions ..
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COMPLEX*16 ZLARND
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EXTERNAL ZLARND
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, SQRT
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* ..
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* .. Executable Statements ..
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*
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* Initialize constants
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*
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ALPHA = ( 1.D0+SQRT( 17.D0 ) ) / 8.D0
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BETA = ALPHA - 1.D0 / 1000.D0
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ALPHA3 = ALPHA*ALPHA*ALPHA
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*
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* Fill the matrix with zeros.
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*
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DO 10 J = 1, N*( N+1 ) / 2
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X( J ) = 0.0D0
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10 CONTINUE
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*
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* UPLO = 'U': Upper triangular storage
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*
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IF( UPLO.EQ.'U' ) THEN
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N5 = N / 5
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N5 = N - 5*N5 + 1
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*
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JJ = N*( N+1 ) / 2
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DO 20 J = N, N5, -5
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A = ALPHA3*ZLARND( 5, ISEED )
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B = ZLARND( 5, ISEED ) / ALPHA
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C = A - 2.D0*B*EYE
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R = C / BETA
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X( JJ ) = A
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X( JJ-2 ) = B
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JJ = JJ - J
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X( JJ ) = ZLARND( 2, ISEED )
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X( JJ-1 ) = R
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JJ = JJ - ( J-1 )
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X( JJ ) = C
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JJ = JJ - ( J-2 )
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X( JJ ) = ZLARND( 2, ISEED )
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JJ = JJ - ( J-3 )
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X( JJ ) = ZLARND( 2, ISEED )
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IF( ABS( X( JJ+( J-3 ) ) ).GT.ABS( X( JJ ) ) ) THEN
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X( JJ+( J-4 ) ) = 2.0D0*X( JJ+( J-3 ) )
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ELSE
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X( JJ+( J-4 ) ) = 2.0D0*X( JJ )
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END IF
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JJ = JJ - ( J-4 )
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20 CONTINUE
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*
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* Clean-up for N not a multiple of 5.
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*
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J = N5 - 1
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IF( J.GT.2 ) THEN
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A = ALPHA3*ZLARND( 5, ISEED )
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B = ZLARND( 5, ISEED ) / ALPHA
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C = A - 2.D0*B*EYE
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R = C / BETA
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X( JJ ) = A
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X( JJ-2 ) = B
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JJ = JJ - J
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X( JJ ) = ZLARND( 2, ISEED )
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X( JJ-1 ) = R
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JJ = JJ - ( J-1 )
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X( JJ ) = C
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JJ = JJ - ( J-2 )
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J = J - 3
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END IF
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IF( J.GT.1 ) THEN
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X( JJ ) = ZLARND( 2, ISEED )
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X( JJ-J ) = ZLARND( 2, ISEED )
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IF( ABS( X( JJ ) ).GT.ABS( X( JJ-J ) ) ) THEN
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X( JJ-1 ) = 2.0D0*X( JJ )
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ELSE
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X( JJ-1 ) = 2.0D0*X( JJ-J )
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END IF
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JJ = JJ - J - ( J-1 )
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J = J - 2
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ELSE IF( J.EQ.1 ) THEN
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X( JJ ) = ZLARND( 2, ISEED )
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J = J - 1
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END IF
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*
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* UPLO = 'L': Lower triangular storage
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*
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ELSE
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N5 = N / 5
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N5 = N5*5
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*
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JJ = 1
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DO 30 J = 1, N5, 5
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A = ALPHA3*ZLARND( 5, ISEED )
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B = ZLARND( 5, ISEED ) / ALPHA
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C = A - 2.D0*B*EYE
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R = C / BETA
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X( JJ ) = A
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X( JJ+2 ) = B
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JJ = JJ + ( N-J+1 )
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X( JJ ) = ZLARND( 2, ISEED )
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X( JJ+1 ) = R
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JJ = JJ + ( N-J )
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X( JJ ) = C
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JJ = JJ + ( N-J-1 )
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X( JJ ) = ZLARND( 2, ISEED )
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JJ = JJ + ( N-J-2 )
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X( JJ ) = ZLARND( 2, ISEED )
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IF( ABS( X( JJ-( N-J-2 ) ) ).GT.ABS( X( JJ ) ) ) THEN
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X( JJ-( N-J-2 )+1 ) = 2.0D0*X( JJ-( N-J-2 ) )
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ELSE
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X( JJ-( N-J-2 )+1 ) = 2.0D0*X( JJ )
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END IF
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JJ = JJ + ( N-J-3 )
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30 CONTINUE
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*
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* Clean-up for N not a multiple of 5.
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*
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J = N5 + 1
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IF( J.LT.N-1 ) THEN
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A = ALPHA3*ZLARND( 5, ISEED )
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B = ZLARND( 5, ISEED ) / ALPHA
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C = A - 2.D0*B*EYE
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R = C / BETA
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X( JJ ) = A
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X( JJ+2 ) = B
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JJ = JJ + ( N-J+1 )
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X( JJ ) = ZLARND( 2, ISEED )
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X( JJ+1 ) = R
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JJ = JJ + ( N-J )
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X( JJ ) = C
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JJ = JJ + ( N-J-1 )
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J = J + 3
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END IF
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IF( J.LT.N ) THEN
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X( JJ ) = ZLARND( 2, ISEED )
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X( JJ+( N-J+1 ) ) = ZLARND( 2, ISEED )
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IF( ABS( X( JJ ) ).GT.ABS( X( JJ+( N-J+1 ) ) ) ) THEN
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X( JJ+1 ) = 2.0D0*X( JJ )
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ELSE
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X( JJ+1 ) = 2.0D0*X( JJ+( N-J+1 ) )
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END IF
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JJ = JJ + ( N-J+1 ) + ( N-J )
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J = J + 2
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ELSE IF( J.EQ.N ) THEN
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X( JJ ) = ZLARND( 2, ISEED )
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JJ = JJ + ( N-J+1 )
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J = J + 1
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END IF
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END IF
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*
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RETURN
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*
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* End of ZLATSP
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*
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END
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