1*> \brief \b ZPTT01 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 ZPTT01( N, D, E, DF, EF, WORK, RESID ) 12* 13* .. Scalar Arguments .. 14* INTEGER N 15* DOUBLE PRECISION RESID 16* .. 17* .. Array Arguments .. 18* DOUBLE PRECISION D( * ), DF( * ) 19* COMPLEX*16 E( * ), EF( * ), WORK( * ) 20* .. 21* 22* 23*> \par Purpose: 24* ============= 25*> 26*> \verbatim 27*> 28*> ZPTT01 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 DOUBLE PRECISION 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*16 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 DOUBLE PRECISION 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*16 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*16 array, dimension (2*N) 72*> \endverbatim 73*> 74*> \param[out] RESID 75*> \verbatim 76*> RESID is DOUBLE PRECISION 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*> \date December 2016 89* 90*> \ingroup complex16_lin 91* 92* ===================================================================== 93 SUBROUTINE ZPTT01( N, D, E, DF, EF, WORK, RESID ) 94* 95* -- LAPACK test routine (version 3.7.0) -- 96* -- LAPACK is a software package provided by Univ. of Tennessee, -- 97* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 98* December 2016 99* 100* .. Scalar Arguments .. 101 INTEGER N 102 DOUBLE PRECISION RESID 103* .. 104* .. Array Arguments .. 105 DOUBLE PRECISION D( * ), DF( * ) 106 COMPLEX*16 E( * ), EF( * ), WORK( * ) 107* .. 108* 109* ===================================================================== 110* 111* .. Parameters .. 112 DOUBLE PRECISION ONE, ZERO 113 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 114* .. 115* .. Local Scalars .. 116 INTEGER I 117 DOUBLE PRECISION ANORM, EPS 118 COMPLEX*16 DE 119* .. 120* .. External Functions .. 121 DOUBLE PRECISION DLAMCH 122 EXTERNAL DLAMCH 123* .. 124* .. Intrinsic Functions .. 125 INTRINSIC ABS, DBLE, DCONJG, MAX 126* .. 127* .. Executable Statements .. 128* 129* Quick return if possible 130* 131 IF( N.LE.0 ) THEN 132 RESID = ZERO 133 RETURN 134 END IF 135* 136 EPS = DLAMCH( 'Epsilon' ) 137* 138* Construct the difference L*D*L' - A. 139* 140 WORK( 1 ) = DF( 1 ) - D( 1 ) 141 DO 10 I = 1, N - 1 142 DE = DF( I )*EF( I ) 143 WORK( N+I ) = DE - E( I ) 144 WORK( 1+I ) = DE*DCONJG( EF( I ) ) + DF( I+1 ) - D( I+1 ) 145 10 CONTINUE 146* 147* Compute the 1-norms of the tridiagonal matrices A and WORK. 148* 149 IF( N.EQ.1 ) THEN 150 ANORM = D( 1 ) 151 RESID = ABS( WORK( 1 ) ) 152 ELSE 153 ANORM = MAX( D( 1 )+ABS( E( 1 ) ), D( N )+ABS( E( N-1 ) ) ) 154 RESID = MAX( ABS( WORK( 1 ) )+ABS( WORK( N+1 ) ), 155 $ ABS( WORK( N ) )+ABS( WORK( 2*N-1 ) ) ) 156 DO 20 I = 2, N - 1 157 ANORM = MAX( ANORM, D( I )+ABS( E( I ) )+ABS( E( I-1 ) ) ) 158 RESID = MAX( RESID, ABS( WORK( I ) )+ABS( WORK( N+I-1 ) )+ 159 $ ABS( WORK( N+I ) ) ) 160 20 CONTINUE 161 END IF 162* 163* Compute norm(L*D*L' - A) / (n * norm(A) * EPS) 164* 165 IF( ANORM.LE.ZERO ) THEN 166 IF( RESID.NE.ZERO ) 167 $ RESID = ONE / EPS 168 ELSE 169 RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS 170 END IF 171* 172 RETURN 173* 174* End of ZPTT01 175* 176 END 177