1*> \brief \b CPTT01 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE CPTT01( N, D, E, DF, EF, WORK, RESID ) 12* 13* .. Scalar Arguments .. 14* INTEGER N 15* REAL RESID 16* .. 17* .. Array Arguments .. 18* REAL D( * ), DF( * ) 19* COMPLEX E( * ), EF( * ), WORK( * ) 20* .. 21* 22* 23*> \par Purpose: 24* ============= 25*> 26*> \verbatim 27*> 28*> CPTT01 reconstructs a tridiagonal matrix A from its L*D*L' 29*> factorization and computes the residual 30*> norm(L*D*L' - A) / ( n * norm(A) * EPS ), 31*> where EPS is the machine epsilon. 32*> \endverbatim 33* 34* Arguments: 35* ========== 36* 37*> \param[in] N 38*> \verbatim 39*> N is INTEGTER 40*> The order of the matrix A. 41*> \endverbatim 42*> 43*> \param[in] D 44*> \verbatim 45*> D is REAL array, dimension (N) 46*> The n diagonal elements of the tridiagonal matrix A. 47*> \endverbatim 48*> 49*> \param[in] E 50*> \verbatim 51*> E is COMPLEX array, dimension (N-1) 52*> The (n-1) subdiagonal elements of the tridiagonal matrix A. 53*> \endverbatim 54*> 55*> \param[in] DF 56*> \verbatim 57*> DF is REAL array, dimension (N) 58*> The n diagonal elements of the factor L from the L*D*L' 59*> factorization of A. 60*> \endverbatim 61*> 62*> \param[in] EF 63*> \verbatim 64*> EF is COMPLEX array, dimension (N-1) 65*> The (n-1) subdiagonal elements of the factor L from the 66*> L*D*L' factorization of A. 67*> \endverbatim 68*> 69*> \param[out] WORK 70*> \verbatim 71*> WORK is COMPLEX array, dimension (2*N) 72*> \endverbatim 73*> 74*> \param[out] RESID 75*> \verbatim 76*> RESID is REAL 77*> norm(L*D*L' - A) / (n * norm(A) * EPS) 78*> \endverbatim 79* 80* Authors: 81* ======== 82* 83*> \author Univ. of Tennessee 84*> \author Univ. of California Berkeley 85*> \author Univ. of Colorado Denver 86*> \author NAG Ltd. 87* 88*> \ingroup complex_lin 89* 90* ===================================================================== 91 SUBROUTINE CPTT01( N, D, E, DF, EF, WORK, RESID ) 92* 93* -- LAPACK test routine -- 94* -- LAPACK is a software package provided by Univ. of Tennessee, -- 95* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 96* 97* .. Scalar Arguments .. 98 INTEGER N 99 REAL RESID 100* .. 101* .. Array Arguments .. 102 REAL D( * ), DF( * ) 103 COMPLEX E( * ), EF( * ), WORK( * ) 104* .. 105* 106* ===================================================================== 107* 108* .. Parameters .. 109 REAL ONE, ZERO 110 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 111* .. 112* .. Local Scalars .. 113 INTEGER I 114 REAL ANORM, EPS 115 COMPLEX DE 116* .. 117* .. External Functions .. 118 REAL SLAMCH 119 EXTERNAL SLAMCH 120* .. 121* .. Intrinsic Functions .. 122 INTRINSIC ABS, CONJG, MAX, REAL 123* .. 124* .. Executable Statements .. 125* 126* Quick return if possible 127* 128 IF( N.LE.0 ) THEN 129 RESID = ZERO 130 RETURN 131 END IF 132* 133 EPS = SLAMCH( 'Epsilon' ) 134* 135* Construct the difference L*D*L' - A. 136* 137 WORK( 1 ) = DF( 1 ) - D( 1 ) 138 DO 10 I = 1, N - 1 139 DE = DF( I )*EF( I ) 140 WORK( N+I ) = DE - E( I ) 141 WORK( 1+I ) = DE*CONJG( EF( I ) ) + DF( I+1 ) - D( I+1 ) 142 10 CONTINUE 143* 144* Compute the 1-norms of the tridiagonal matrices A and WORK. 145* 146 IF( N.EQ.1 ) THEN 147 ANORM = D( 1 ) 148 RESID = ABS( WORK( 1 ) ) 149 ELSE 150 ANORM = MAX( D( 1 )+ABS( E( 1 ) ), D( N )+ABS( E( N-1 ) ) ) 151 RESID = MAX( ABS( WORK( 1 ) )+ABS( WORK( N+1 ) ), 152 $ ABS( WORK( N ) )+ABS( WORK( 2*N-1 ) ) ) 153 DO 20 I = 2, N - 1 154 ANORM = MAX( ANORM, D( I )+ABS( E( I ) )+ABS( E( I-1 ) ) ) 155 RESID = MAX( RESID, ABS( WORK( I ) )+ABS( WORK( N+I-1 ) )+ 156 $ ABS( WORK( N+I ) ) ) 157 20 CONTINUE 158 END IF 159* 160* Compute norm(L*D*L' - A) / (n * norm(A) * EPS) 161* 162 IF( ANORM.LE.ZERO ) THEN 163 IF( RESID.NE.ZERO ) 164 $ RESID = ONE / EPS 165 ELSE 166 RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS 167 END IF 168* 169 RETURN 170* 171* End of CPTT01 172* 173 END 174