LAPACK 3.3.1 Linear Algebra PACKage

# dtrti2.f

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```00001       SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          DIAG, UPLO
00010       INTEGER            INFO, LDA, N
00011 *     ..
00012 *     .. Array Arguments ..
00013       DOUBLE PRECISION   A( LDA, * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  DTRTI2 computes the inverse of a real upper or lower triangular
00020 *  matrix.
00021 *
00022 *  This is the Level 2 BLAS version of the algorithm.
00023 *
00024 *  Arguments
00025 *  =========
00026 *
00027 *  UPLO    (input) CHARACTER*1
00028 *          Specifies whether the matrix A is upper or lower triangular.
00029 *          = 'U':  Upper triangular
00030 *          = 'L':  Lower triangular
00031 *
00032 *  DIAG    (input) CHARACTER*1
00033 *          Specifies whether or not the matrix A is unit triangular.
00034 *          = 'N':  Non-unit triangular
00035 *          = 'U':  Unit triangular
00036 *
00037 *  N       (input) INTEGER
00038 *          The order of the matrix A.  N >= 0.
00039 *
00040 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
00041 *          On entry, the triangular matrix A.  If UPLO = 'U', the
00042 *          leading n by n upper triangular part of the array A contains
00043 *          the upper triangular matrix, and the strictly lower
00044 *          triangular part of A is not referenced.  If UPLO = 'L', the
00045 *          leading n by n lower triangular part of the array A contains
00046 *          the lower triangular matrix, and the strictly upper
00047 *          triangular part of A is not referenced.  If DIAG = 'U', the
00048 *          diagonal elements of A are also not referenced and are
00049 *          assumed to be 1.
00050 *
00051 *          On exit, the (triangular) inverse of the original matrix, in
00052 *          the same storage format.
00053 *
00054 *  LDA     (input) INTEGER
00055 *          The leading dimension of the array A.  LDA >= max(1,N).
00056 *
00057 *  INFO    (output) INTEGER
00058 *          = 0: successful exit
00059 *          < 0: if INFO = -k, the k-th argument had an illegal value
00060 *
00061 *  =====================================================================
00062 *
00063 *     .. Parameters ..
00064       DOUBLE PRECISION   ONE
00065       PARAMETER          ( ONE = 1.0D+0 )
00066 *     ..
00067 *     .. Local Scalars ..
00068       LOGICAL            NOUNIT, UPPER
00069       INTEGER            J
00070       DOUBLE PRECISION   AJJ
00071 *     ..
00072 *     .. External Functions ..
00073       LOGICAL            LSAME
00074       EXTERNAL           LSAME
00075 *     ..
00076 *     .. External Subroutines ..
00077       EXTERNAL           DSCAL, DTRMV, XERBLA
00078 *     ..
00079 *     .. Intrinsic Functions ..
00080       INTRINSIC          MAX
00081 *     ..
00082 *     .. Executable Statements ..
00083 *
00084 *     Test the input parameters.
00085 *
00086       INFO = 0
00087       UPPER = LSAME( UPLO, 'U' )
00088       NOUNIT = LSAME( DIAG, 'N' )
00089       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00090          INFO = -1
00091       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
00092          INFO = -2
00093       ELSE IF( N.LT.0 ) THEN
00094          INFO = -3
00095       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00096          INFO = -5
00097       END IF
00098       IF( INFO.NE.0 ) THEN
00099          CALL XERBLA( 'DTRTI2', -INFO )
00100          RETURN
00101       END IF
00102 *
00103       IF( UPPER ) THEN
00104 *
00105 *        Compute inverse of upper triangular matrix.
00106 *
00107          DO 10 J = 1, N
00108             IF( NOUNIT ) THEN
00109                A( J, J ) = ONE / A( J, J )
00110                AJJ = -A( J, J )
00111             ELSE
00112                AJJ = -ONE
00113             END IF
00114 *
00115 *           Compute elements 1:j-1 of j-th column.
00116 *
00117             CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA,
00118      \$                  A( 1, J ), 1 )
00119             CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
00120    10    CONTINUE
00121       ELSE
00122 *
00123 *        Compute inverse of lower triangular matrix.
00124 *
00125          DO 20 J = N, 1, -1
00126             IF( NOUNIT ) THEN
00127                A( J, J ) = ONE / A( J, J )
00128                AJJ = -A( J, J )
00129             ELSE
00130                AJJ = -ONE
00131             END IF
00132             IF( J.LT.N ) THEN
00133 *
00134 *              Compute elements j+1:n of j-th column.
00135 *
00136                CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J,
00137      \$                     A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
00138                CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
00139             END IF
00140    20    CONTINUE
00141       END IF
00142 *
00143       RETURN
00144 *
00145 *     End of DTRTI2
00146 *
00147       END
```