LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
stpt01.f
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00001 *> \brief \b STPT01
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 STPT01( UPLO, DIAG, N, AP, AINVP, RCOND, WORK, RESID )
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       CHARACTER          DIAG, UPLO
00015 *       INTEGER            N
00016 *       REAL               RCOND, RESID
00017 *       ..
00018 *       .. Array Arguments ..
00019 *       REAL               AINVP( * ), AP( * ), WORK( * )
00020 *       ..
00021 *  
00022 *
00023 *> \par Purpose:
00024 *  =============
00025 *>
00026 *> \verbatim
00027 *>
00028 *> STPT01 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 REAL 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 REAL 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 REAL
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 REAL array, dimension (N)
00088 *> \endverbatim
00089 *>
00090 *> \param[out] RESID
00091 *> \verbatim
00092 *>          RESID is REAL
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 single_lin
00107 *
00108 *  =====================================================================
00109       SUBROUTINE STPT01( 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       REAL               RCOND, RESID
00120 *     ..
00121 *     .. Array Arguments ..
00122       REAL               AINVP( * ), AP( * ), WORK( * )
00123 *     ..
00124 *
00125 *  =====================================================================
00126 *
00127 *     .. Parameters ..
00128       REAL               ZERO, ONE
00129       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00130 *     ..
00131 *     .. Local Scalars ..
00132       LOGICAL            UNITD
00133       INTEGER            J, JC
00134       REAL               AINVNM, ANORM, EPS
00135 *     ..
00136 *     .. External Functions ..
00137       LOGICAL            LSAME
00138       REAL               SLAMCH, SLANTP
00139       EXTERNAL           LSAME, SLAMCH, SLANTP
00140 *     ..
00141 *     .. External Subroutines ..
00142       EXTERNAL           STPMV
00143 *     ..
00144 *     .. Intrinsic Functions ..
00145       INTRINSIC          REAL
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 = SLAMCH( 'Epsilon' )
00160       ANORM = SLANTP( '1', UPLO, DIAG, N, AP, WORK )
00161       AINVNM = SLANTP( '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 STPMV( '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 STPMV( '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 = SLANTP( '1', UPLO, 'Non-unit', N, AINVP, WORK )
00209 *
00210       RESID = ( ( RESID*RCOND ) / REAL( N ) ) / EPS
00211 *
00212       RETURN
00213 *
00214 *     End of STPT01
00215 *
00216       END
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