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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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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 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrti2.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrti2.f"> 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