LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
stptri.f
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00001 *> \brief \b STPTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download STPTRI + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/stptri.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/stptri.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE STPTRI( UPLO, DIAG, N, AP, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          DIAG, UPLO
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       REAL               AP( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> STPTRI computes the inverse of a real upper or lower triangular
00038 *> matrix A stored in packed format.
00039 *> \endverbatim
00040 *
00041 *  Arguments:
00042 *  ==========
00043 *
00044 *> \param[in] UPLO
00045 *> \verbatim
00046 *>          UPLO is CHARACTER*1
00047 *>          = 'U':  A is upper triangular;
00048 *>          = 'L':  A is lower triangular.
00049 *> \endverbatim
00050 *>
00051 *> \param[in] DIAG
00052 *> \verbatim
00053 *>          DIAG is CHARACTER*1
00054 *>          = 'N':  A is non-unit triangular;
00055 *>          = 'U':  A is unit triangular.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The order of the matrix A.  N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in,out] AP
00065 *> \verbatim
00066 *>          AP is REAL array, dimension (N*(N+1)/2)
00067 *>          On entry, the upper or lower triangular matrix A, stored
00068 *>          columnwise in a linear array.  The j-th column of A is stored
00069 *>          in the array AP as follows:
00070 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00071 *>          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
00072 *>          See below for further details.
00073 *>          On exit, the (triangular) inverse of the original matrix, in
00074 *>          the same packed storage format.
00075 *> \endverbatim
00076 *>
00077 *> \param[out] INFO
00078 *> \verbatim
00079 *>          INFO is INTEGER
00080 *>          = 0:  successful exit
00081 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00082 *>          > 0:  if INFO = i, A(i,i) is exactly zero.  The triangular
00083 *>                matrix is singular and its inverse can not be computed.
00084 *> \endverbatim
00085 *
00086 *  Authors:
00087 *  ========
00088 *
00089 *> \author Univ. of Tennessee 
00090 *> \author Univ. of California Berkeley 
00091 *> \author Univ. of Colorado Denver 
00092 *> \author NAG Ltd. 
00093 *
00094 *> \date November 2011
00095 *
00096 *> \ingroup realOTHERcomputational
00097 *
00098 *> \par Further Details:
00099 *  =====================
00100 *>
00101 *> \verbatim
00102 *>
00103 *>  A triangular matrix A can be transferred to packed storage using one
00104 *>  of the following program segments:
00105 *>
00106 *>  UPLO = 'U':                      UPLO = 'L':
00107 *>
00108 *>        JC = 1                           JC = 1
00109 *>        DO 2 J = 1, N                    DO 2 J = 1, N
00110 *>           DO 1 I = 1, J                    DO 1 I = J, N
00111 *>              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
00112 *>      1    CONTINUE                    1    CONTINUE
00113 *>           JC = JC + J                      JC = JC + N - J + 1
00114 *>      2 CONTINUE                       2 CONTINUE
00115 *> \endverbatim
00116 *>
00117 *  =====================================================================
00118       SUBROUTINE STPTRI( UPLO, DIAG, N, AP, INFO )
00119 *
00120 *  -- LAPACK computational routine (version 3.4.0) --
00121 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00122 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00123 *     November 2011
00124 *
00125 *     .. Scalar Arguments ..
00126       CHARACTER          DIAG, UPLO
00127       INTEGER            INFO, N
00128 *     ..
00129 *     .. Array Arguments ..
00130       REAL               AP( * )
00131 *     ..
00132 *
00133 *  =====================================================================
00134 *
00135 *     .. Parameters ..
00136       REAL               ONE, ZERO
00137       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00138 *     ..
00139 *     .. Local Scalars ..
00140       LOGICAL            NOUNIT, UPPER
00141       INTEGER            J, JC, JCLAST, JJ
00142       REAL               AJJ
00143 *     ..
00144 *     .. External Functions ..
00145       LOGICAL            LSAME
00146       EXTERNAL           LSAME
00147 *     ..
00148 *     .. External Subroutines ..
00149       EXTERNAL           SSCAL, STPMV, XERBLA
00150 *     ..
00151 *     .. Executable Statements ..
00152 *
00153 *     Test the input parameters.
00154 *
00155       INFO = 0
00156       UPPER = LSAME( UPLO, 'U' )
00157       NOUNIT = LSAME( DIAG, 'N' )
00158       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00159          INFO = -1
00160       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
00161          INFO = -2
00162       ELSE IF( N.LT.0 ) THEN
00163          INFO = -3
00164       END IF
00165       IF( INFO.NE.0 ) THEN
00166          CALL XERBLA( 'STPTRI', -INFO )
00167          RETURN
00168       END IF
00169 *
00170 *     Check for singularity if non-unit.
00171 *
00172       IF( NOUNIT ) THEN
00173          IF( UPPER ) THEN
00174             JJ = 0
00175             DO 10 INFO = 1, N
00176                JJ = JJ + INFO
00177                IF( AP( JJ ).EQ.ZERO )
00178      $            RETURN
00179    10       CONTINUE
00180          ELSE
00181             JJ = 1
00182             DO 20 INFO = 1, N
00183                IF( AP( JJ ).EQ.ZERO )
00184      $            RETURN
00185                JJ = JJ + N - INFO + 1
00186    20       CONTINUE
00187          END IF
00188          INFO = 0
00189       END IF
00190 *
00191       IF( UPPER ) THEN
00192 *
00193 *        Compute inverse of upper triangular matrix.
00194 *
00195          JC = 1
00196          DO 30 J = 1, N
00197             IF( NOUNIT ) THEN
00198                AP( JC+J-1 ) = ONE / AP( JC+J-1 )
00199                AJJ = -AP( JC+J-1 )
00200             ELSE
00201                AJJ = -ONE
00202             END IF
00203 *
00204 *           Compute elements 1:j-1 of j-th column.
00205 *
00206             CALL STPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
00207      $                  AP( JC ), 1 )
00208             CALL SSCAL( J-1, AJJ, AP( JC ), 1 )
00209             JC = JC + J
00210    30    CONTINUE
00211 *
00212       ELSE
00213 *
00214 *        Compute inverse of lower triangular matrix.
00215 *
00216          JC = N*( N+1 ) / 2
00217          DO 40 J = N, 1, -1
00218             IF( NOUNIT ) THEN
00219                AP( JC ) = ONE / AP( JC )
00220                AJJ = -AP( JC )
00221             ELSE
00222                AJJ = -ONE
00223             END IF
00224             IF( J.LT.N ) THEN
00225 *
00226 *              Compute elements j+1:n of j-th column.
00227 *
00228                CALL STPMV( 'Lower', 'No transpose', DIAG, N-J,
00229      $                     AP( JCLAST ), AP( JC+1 ), 1 )
00230                CALL SSCAL( N-J, AJJ, AP( JC+1 ), 1 )
00231             END IF
00232             JCLAST = JC
00233             JC = JC - N + J - 2
00234    40    CONTINUE
00235       END IF
00236 *
00237       RETURN
00238 *
00239 *     End of STPTRI
00240 *
00241       END
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