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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DPPT03 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE DPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, 00012 * RESID ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER UPLO 00016 * INTEGER LDWORK, N 00017 * DOUBLE PRECISION RCOND, RESID 00018 * .. 00019 * .. Array Arguments .. 00020 * DOUBLE PRECISION A( * ), AINV( * ), RWORK( * ), 00021 * $ WORK( LDWORK, * ) 00022 * .. 00023 * 00024 * 00025 *> \par Purpose: 00026 * ============= 00027 *> 00028 *> \verbatim 00029 *> 00030 *> DPPT03 computes the residual for a symmetric packed matrix times its 00031 *> inverse: 00032 *> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ), 00033 *> where EPS is the machine epsilon. 00034 *> \endverbatim 00035 * 00036 * Arguments: 00037 * ========== 00038 * 00039 *> \param[in] UPLO 00040 *> \verbatim 00041 *> UPLO is CHARACTER*1 00042 *> Specifies whether the upper or lower triangular part of the 00043 *> symmetric matrix A is stored: 00044 *> = 'U': Upper triangular 00045 *> = 'L': Lower triangular 00046 *> \endverbatim 00047 *> 00048 *> \param[in] N 00049 *> \verbatim 00050 *> N is INTEGER 00051 *> The number of rows and columns of the matrix A. N >= 0. 00052 *> \endverbatim 00053 *> 00054 *> \param[in] A 00055 *> \verbatim 00056 *> A is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00057 *> The original symmetric matrix A, stored as a packed 00058 *> triangular matrix. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] AINV 00062 *> \verbatim 00063 *> AINV is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00064 *> The (symmetric) inverse of the matrix A, stored as a packed 00065 *> triangular matrix. 00066 *> \endverbatim 00067 *> 00068 *> \param[out] WORK 00069 *> \verbatim 00070 *> WORK is DOUBLE PRECISION array, dimension (LDWORK,N) 00071 *> \endverbatim 00072 *> 00073 *> \param[in] LDWORK 00074 *> \verbatim 00075 *> LDWORK is INTEGER 00076 *> The leading dimension of the array WORK. LDWORK >= max(1,N). 00077 *> \endverbatim 00078 *> 00079 *> \param[out] RWORK 00080 *> \verbatim 00081 *> RWORK is DOUBLE PRECISION array, dimension (N) 00082 *> \endverbatim 00083 *> 00084 *> \param[out] RCOND 00085 *> \verbatim 00086 *> RCOND is DOUBLE PRECISION 00087 *> The reciprocal of the condition number of A, computed as 00088 *> ( 1/norm(A) ) / norm(AINV). 00089 *> \endverbatim 00090 *> 00091 *> \param[out] RESID 00092 *> \verbatim 00093 *> RESID is DOUBLE PRECISION 00094 *> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS ) 00095 *> \endverbatim 00096 * 00097 * Authors: 00098 * ======== 00099 * 00100 *> \author Univ. of Tennessee 00101 *> \author Univ. of California Berkeley 00102 *> \author Univ. of Colorado Denver 00103 *> \author NAG Ltd. 00104 * 00105 *> \date November 2011 00106 * 00107 *> \ingroup double_lin 00108 * 00109 * ===================================================================== 00110 SUBROUTINE DPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND, 00111 $ RESID ) 00112 * 00113 * -- LAPACK test routine (version 3.4.0) -- 00114 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00115 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00116 * November 2011 00117 * 00118 * .. Scalar Arguments .. 00119 CHARACTER UPLO 00120 INTEGER LDWORK, N 00121 DOUBLE PRECISION RCOND, RESID 00122 * .. 00123 * .. Array Arguments .. 00124 DOUBLE PRECISION A( * ), AINV( * ), RWORK( * ), 00125 $ WORK( LDWORK, * ) 00126 * .. 00127 * 00128 * ===================================================================== 00129 * 00130 * .. Parameters .. 00131 DOUBLE PRECISION ZERO, ONE 00132 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00133 * .. 00134 * .. Local Scalars .. 00135 INTEGER I, J, JJ 00136 DOUBLE PRECISION AINVNM, ANORM, EPS 00137 * .. 00138 * .. External Functions .. 00139 LOGICAL LSAME 00140 DOUBLE PRECISION DLAMCH, DLANGE, DLANSP 00141 EXTERNAL LSAME, DLAMCH, DLANGE, DLANSP 00142 * .. 00143 * .. Intrinsic Functions .. 00144 INTRINSIC DBLE 00145 * .. 00146 * .. External Subroutines .. 00147 EXTERNAL DCOPY, DSPMV 00148 * .. 00149 * .. Executable Statements .. 00150 * 00151 * Quick exit if N = 0. 00152 * 00153 IF( N.LE.0 ) THEN 00154 RCOND = ONE 00155 RESID = ZERO 00156 RETURN 00157 END IF 00158 * 00159 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. 00160 * 00161 EPS = DLAMCH( 'Epsilon' ) 00162 ANORM = DLANSP( '1', UPLO, N, A, RWORK ) 00163 AINVNM = DLANSP( '1', UPLO, N, AINV, RWORK ) 00164 IF( ANORM.LE.ZERO .OR. AINVNM.EQ.ZERO ) THEN 00165 RCOND = ZERO 00166 RESID = ONE / EPS 00167 RETURN 00168 END IF 00169 RCOND = ( ONE / ANORM ) / AINVNM 00170 * 00171 * UPLO = 'U': 00172 * Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and 00173 * expand it to a full matrix, then multiply by A one column at a 00174 * time, moving the result one column to the left. 00175 * 00176 IF( LSAME( UPLO, 'U' ) ) THEN 00177 * 00178 * Copy AINV 00179 * 00180 JJ = 1 00181 DO 10 J = 1, N - 1 00182 CALL DCOPY( J, AINV( JJ ), 1, WORK( 1, J+1 ), 1 ) 00183 CALL DCOPY( J-1, AINV( JJ ), 1, WORK( J, 2 ), LDWORK ) 00184 JJ = JJ + J 00185 10 CONTINUE 00186 JJ = ( ( N-1 )*N ) / 2 + 1 00187 CALL DCOPY( N-1, AINV( JJ ), 1, WORK( N, 2 ), LDWORK ) 00188 * 00189 * Multiply by A 00190 * 00191 DO 20 J = 1, N - 1 00192 CALL DSPMV( 'Upper', N, -ONE, A, WORK( 1, J+1 ), 1, ZERO, 00193 $ WORK( 1, J ), 1 ) 00194 20 CONTINUE 00195 CALL DSPMV( 'Upper', N, -ONE, A, AINV( JJ ), 1, ZERO, 00196 $ WORK( 1, N ), 1 ) 00197 * 00198 * UPLO = 'L': 00199 * Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1) 00200 * and multiply by A, moving each column to the right. 00201 * 00202 ELSE 00203 * 00204 * Copy AINV 00205 * 00206 CALL DCOPY( N-1, AINV( 2 ), 1, WORK( 1, 1 ), LDWORK ) 00207 JJ = N + 1 00208 DO 30 J = 2, N 00209 CALL DCOPY( N-J+1, AINV( JJ ), 1, WORK( J, J-1 ), 1 ) 00210 CALL DCOPY( N-J, AINV( JJ+1 ), 1, WORK( J, J ), LDWORK ) 00211 JJ = JJ + N - J + 1 00212 30 CONTINUE 00213 * 00214 * Multiply by A 00215 * 00216 DO 40 J = N, 2, -1 00217 CALL DSPMV( 'Lower', N, -ONE, A, WORK( 1, J-1 ), 1, ZERO, 00218 $ WORK( 1, J ), 1 ) 00219 40 CONTINUE 00220 CALL DSPMV( 'Lower', N, -ONE, A, AINV( 1 ), 1, ZERO, 00221 $ WORK( 1, 1 ), 1 ) 00222 * 00223 END IF 00224 * 00225 * Add the identity matrix to WORK . 00226 * 00227 DO 50 I = 1, N 00228 WORK( I, I ) = WORK( I, I ) + ONE 00229 50 CONTINUE 00230 * 00231 * Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS) 00232 * 00233 RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK ) 00234 * 00235 RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N ) 00236 * 00237 RETURN 00238 * 00239 * End of DPPT03 00240 * 00241 END