LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dtrti2.f
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00001 *> \brief \b DTRTI2
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DTRTI2 + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrti2.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          DIAG, UPLO
00025 *       INTEGER            INFO, LDA, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       DOUBLE PRECISION   A( LDA, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> DTRTI2 computes the inverse of a real upper or lower triangular
00038 *> matrix.
00039 *>
00040 *> This is the Level 2 BLAS version of the algorithm.
00041 *> \endverbatim
00042 *
00043 *  Arguments:
00044 *  ==========
00045 *
00046 *> \param[in] UPLO
00047 *> \verbatim
00048 *>          UPLO is CHARACTER*1
00049 *>          Specifies whether the matrix A is upper or lower triangular.
00050 *>          = 'U':  Upper triangular
00051 *>          = 'L':  Lower triangular
00052 *> \endverbatim
00053 *>
00054 *> \param[in] DIAG
00055 *> \verbatim
00056 *>          DIAG is CHARACTER*1
00057 *>          Specifies whether or not the matrix A is unit triangular.
00058 *>          = 'N':  Non-unit triangular
00059 *>          = 'U':  Unit triangular
00060 *> \endverbatim
00061 *>
00062 *> \param[in] N
00063 *> \verbatim
00064 *>          N is INTEGER
00065 *>          The order of the matrix A.  N >= 0.
00066 *> \endverbatim
00067 *>
00068 *> \param[in,out] A
00069 *> \verbatim
00070 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
00071 *>          On entry, the triangular matrix A.  If UPLO = 'U', the
00072 *>          leading n by n upper triangular part of the array A contains
00073 *>          the upper triangular matrix, and the strictly lower
00074 *>          triangular part of A is not referenced.  If UPLO = 'L', the
00075 *>          leading n by n lower triangular part of the array A contains
00076 *>          the lower triangular matrix, and the strictly upper
00077 *>          triangular part of A is not referenced.  If DIAG = 'U', the
00078 *>          diagonal elements of A are also not referenced and are
00079 *>          assumed to be 1.
00080 *>
00081 *>          On exit, the (triangular) inverse of the original matrix, in
00082 *>          the same storage format.
00083 *> \endverbatim
00084 *>
00085 *> \param[in] LDA
00086 *> \verbatim
00087 *>          LDA is INTEGER
00088 *>          The leading dimension of the array A.  LDA >= max(1,N).
00089 *> \endverbatim
00090 *>
00091 *> \param[out] INFO
00092 *> \verbatim
00093 *>          INFO is INTEGER
00094 *>          = 0: successful exit
00095 *>          < 0: if INFO = -k, the k-th argument had an illegal value
00096 *> \endverbatim
00097 *
00098 *  Authors:
00099 *  ========
00100 *
00101 *> \author Univ. of Tennessee 
00102 *> \author Univ. of California Berkeley 
00103 *> \author Univ. of Colorado Denver 
00104 *> \author NAG Ltd. 
00105 *
00106 *> \date November 2011
00107 *
00108 *> \ingroup doubleOTHERcomputational
00109 *
00110 *  =====================================================================
00111       SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
00112 *
00113 *  -- LAPACK computational 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          DIAG, UPLO
00120       INTEGER            INFO, LDA, N
00121 *     ..
00122 *     .. Array Arguments ..
00123       DOUBLE PRECISION   A( LDA, * )
00124 *     ..
00125 *
00126 *  =====================================================================
00127 *
00128 *     .. Parameters ..
00129       DOUBLE PRECISION   ONE
00130       PARAMETER          ( ONE = 1.0D+0 )
00131 *     ..
00132 *     .. Local Scalars ..
00133       LOGICAL            NOUNIT, UPPER
00134       INTEGER            J
00135       DOUBLE PRECISION   AJJ
00136 *     ..
00137 *     .. External Functions ..
00138       LOGICAL            LSAME
00139       EXTERNAL           LSAME
00140 *     ..
00141 *     .. External Subroutines ..
00142       EXTERNAL           DSCAL, DTRMV, XERBLA
00143 *     ..
00144 *     .. Intrinsic Functions ..
00145       INTRINSIC          MAX
00146 *     ..
00147 *     .. Executable Statements ..
00148 *
00149 *     Test the input parameters.
00150 *
00151       INFO = 0
00152       UPPER = LSAME( UPLO, 'U' )
00153       NOUNIT = LSAME( DIAG, 'N' )
00154       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00155          INFO = -1
00156       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
00157          INFO = -2
00158       ELSE IF( N.LT.0 ) THEN
00159          INFO = -3
00160       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00161          INFO = -5
00162       END IF
00163       IF( INFO.NE.0 ) THEN
00164          CALL XERBLA( 'DTRTI2', -INFO )
00165          RETURN
00166       END IF
00167 *
00168       IF( UPPER ) THEN
00169 *
00170 *        Compute inverse of upper triangular matrix.
00171 *
00172          DO 10 J = 1, N
00173             IF( NOUNIT ) THEN
00174                A( J, J ) = ONE / A( J, J )
00175                AJJ = -A( J, J )
00176             ELSE
00177                AJJ = -ONE
00178             END IF
00179 *
00180 *           Compute elements 1:j-1 of j-th column.
00181 *
00182             CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA,
00183      $                  A( 1, J ), 1 )
00184             CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
00185    10    CONTINUE
00186       ELSE
00187 *
00188 *        Compute inverse of lower triangular matrix.
00189 *
00190          DO 20 J = N, 1, -1
00191             IF( NOUNIT ) THEN
00192                A( J, J ) = ONE / A( J, J )
00193                AJJ = -A( J, J )
00194             ELSE
00195                AJJ = -ONE
00196             END IF
00197             IF( J.LT.N ) THEN
00198 *
00199 *              Compute elements j+1:n of j-th column.
00200 *
00201                CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J,
00202      $                     A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
00203                CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
00204             END IF
00205    20    CONTINUE
00206       END IF
00207 *
00208       RETURN
00209 *
00210 *     End of DTRTI2
00211 *
00212       END
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