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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DTPT01 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 DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID ) 00012 * 00013 * .. Scalar Arguments .. 00014 * CHARACTER DIAG, UPLO 00015 * INTEGER N 00016 * DOUBLE PRECISION RCOND, RESID 00017 * .. 00018 * .. Array Arguments .. 00019 * DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * ) 00020 * .. 00021 * 00022 * 00023 *> \par Purpose: 00024 * ============= 00025 *> 00026 *> \verbatim 00027 *> 00028 *> DTPT01 computes the residual for a triangular matrix A times its 00029 *> inverse when A is stored in packed format: 00030 *> RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ), 00031 *> where EPS is the machine epsilon. 00032 *> \endverbatim 00033 * 00034 * Arguments: 00035 * ========== 00036 * 00037 *> \param[in] UPLO 00038 *> \verbatim 00039 *> UPLO is CHARACTER*1 00040 *> Specifies whether the matrix A is upper or lower triangular. 00041 *> = 'U': Upper triangular 00042 *> = 'L': Lower triangular 00043 *> \endverbatim 00044 *> 00045 *> \param[in] DIAG 00046 *> \verbatim 00047 *> DIAG is CHARACTER*1 00048 *> Specifies whether or not the matrix A is unit triangular. 00049 *> = 'N': Non-unit triangular 00050 *> = 'U': Unit triangular 00051 *> \endverbatim 00052 *> 00053 *> \param[in] N 00054 *> \verbatim 00055 *> N is INTEGER 00056 *> The order of the matrix A. N >= 0. 00057 *> \endverbatim 00058 *> 00059 *> \param[in] AP 00060 *> \verbatim 00061 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00062 *> The original upper or lower triangular matrix A, packed 00063 *> columnwise in a linear array. The j-th column of A is stored 00064 *> in the array AP as follows: 00065 *> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; 00066 *> if UPLO = 'L', 00067 *> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. 00068 *> \endverbatim 00069 *> 00070 *> \param[in,out] AINVP 00071 *> \verbatim 00072 *> AINVP is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00073 *> On entry, the (triangular) inverse of the matrix A, packed 00074 *> columnwise in a linear array as in AP. 00075 *> On exit, the contents of AINVP are destroyed. 00076 *> \endverbatim 00077 *> 00078 *> \param[out] RCOND 00079 *> \verbatim 00080 *> RCOND is DOUBLE PRECISION 00081 *> The reciprocal condition number of A, computed as 00082 *> 1/(norm(A) * norm(AINV)). 00083 *> \endverbatim 00084 *> 00085 *> \param[out] WORK 00086 *> \verbatim 00087 *> WORK is DOUBLE PRECISION array, dimension (N) 00088 *> \endverbatim 00089 *> 00090 *> \param[out] RESID 00091 *> \verbatim 00092 *> RESID is DOUBLE PRECISION 00093 *> norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ) 00094 *> \endverbatim 00095 * 00096 * Authors: 00097 * ======== 00098 * 00099 *> \author Univ. of Tennessee 00100 *> \author Univ. of California Berkeley 00101 *> \author Univ. of Colorado Denver 00102 *> \author NAG Ltd. 00103 * 00104 *> \date November 2011 00105 * 00106 *> \ingroup double_lin 00107 * 00108 * ===================================================================== 00109 SUBROUTINE DTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID ) 00110 * 00111 * -- LAPACK test routine (version 3.4.0) -- 00112 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00114 * November 2011 00115 * 00116 * .. Scalar Arguments .. 00117 CHARACTER DIAG, UPLO 00118 INTEGER N 00119 DOUBLE PRECISION RCOND, RESID 00120 * .. 00121 * .. Array Arguments .. 00122 DOUBLE PRECISION AINVP( * ), AP( * ), WORK( * ) 00123 * .. 00124 * 00125 * ===================================================================== 00126 * 00127 * .. Parameters .. 00128 DOUBLE PRECISION ZERO, ONE 00129 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00130 * .. 00131 * .. Local Scalars .. 00132 LOGICAL UNITD 00133 INTEGER J, JC 00134 DOUBLE PRECISION AINVNM, ANORM, EPS 00135 * .. 00136 * .. External Functions .. 00137 LOGICAL LSAME 00138 DOUBLE PRECISION DLAMCH, DLANTP 00139 EXTERNAL LSAME, DLAMCH, DLANTP 00140 * .. 00141 * .. External Subroutines .. 00142 EXTERNAL DTPMV 00143 * .. 00144 * .. Intrinsic Functions .. 00145 INTRINSIC DBLE 00146 * .. 00147 * .. Executable Statements .. 00148 * 00149 * Quick exit if N = 0. 00150 * 00151 IF( N.LE.0 ) THEN 00152 RCOND = ONE 00153 RESID = ZERO 00154 RETURN 00155 END IF 00156 * 00157 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0. 00158 * 00159 EPS = DLAMCH( 'Epsilon' ) 00160 ANORM = DLANTP( '1', UPLO, DIAG, N, AP, WORK ) 00161 AINVNM = DLANTP( '1', UPLO, DIAG, N, AINVP, WORK ) 00162 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN 00163 RCOND = ZERO 00164 RESID = ONE / EPS 00165 RETURN 00166 END IF 00167 RCOND = ( ONE / ANORM ) / AINVNM 00168 * 00169 * Compute A * AINV, overwriting AINV. 00170 * 00171 UNITD = LSAME( DIAG, 'U' ) 00172 IF( LSAME( UPLO, 'U' ) ) THEN 00173 JC = 1 00174 DO 10 J = 1, N 00175 IF( UNITD ) 00176 $ AINVP( JC+J-1 ) = ONE 00177 * 00178 * Form the j-th column of A*AINV 00179 * 00180 CALL DTPMV( 'Upper', 'No transpose', DIAG, J, AP, 00181 $ AINVP( JC ), 1 ) 00182 * 00183 * Subtract 1 from the diagonal 00184 * 00185 AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE 00186 JC = JC + J 00187 10 CONTINUE 00188 ELSE 00189 JC = 1 00190 DO 20 J = 1, N 00191 IF( UNITD ) 00192 $ AINVP( JC ) = ONE 00193 * 00194 * Form the j-th column of A*AINV 00195 * 00196 CALL DTPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ), 00197 $ AINVP( JC ), 1 ) 00198 * 00199 * Subtract 1 from the diagonal 00200 * 00201 AINVP( JC ) = AINVP( JC ) - ONE 00202 JC = JC + N - J + 1 00203 20 CONTINUE 00204 END IF 00205 * 00206 * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS) 00207 * 00208 RESID = DLANTP( '1', UPLO, 'Non-unit', N, AINVP, WORK ) 00209 * 00210 RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS 00211 * 00212 RETURN 00213 * 00214 * End of DTPT01 00215 * 00216 END