 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ dtrti2()

 subroutine dtrti2 ( character UPLO, character DIAG, integer N, double precision, dimension( lda, * ) A, integer LDA, integer INFO )

DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).

Purpose:
``` DTRTI2 computes the inverse of a real upper or lower triangular
matrix.

This is the Level 2 BLAS version of the algorithm.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] DIAG ``` DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. On exit, the (triangular) inverse of the original matrix, in the same storage format.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -k, the k-th argument had an illegal value```

Definition at line 109 of file dtrti2.f.

110 *
111 * -- LAPACK computational routine --
112 * -- LAPACK is a software package provided by Univ. of Tennessee, --
113 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
114 *
115 * .. Scalar Arguments ..
116  CHARACTER DIAG, UPLO
117  INTEGER INFO, LDA, N
118 * ..
119 * .. Array Arguments ..
120  DOUBLE PRECISION A( LDA, * )
121 * ..
122 *
123 * =====================================================================
124 *
125 * .. Parameters ..
126  DOUBLE PRECISION ONE
127  parameter( one = 1.0d+0 )
128 * ..
129 * .. Local Scalars ..
130  LOGICAL NOUNIT, UPPER
131  INTEGER J
132  DOUBLE PRECISION AJJ
133 * ..
134 * .. External Functions ..
135  LOGICAL LSAME
136  EXTERNAL lsame
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL dscal, dtrmv, xerbla
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC max
143 * ..
144 * .. Executable Statements ..
145 *
146 * Test the input parameters.
147 *
148  info = 0
149  upper = lsame( uplo, 'U' )
150  nounit = lsame( diag, 'N' )
151  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
152  info = -1
153  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
154  info = -2
155  ELSE IF( n.LT.0 ) THEN
156  info = -3
157  ELSE IF( lda.LT.max( 1, n ) ) THEN
158  info = -5
159  END IF
160  IF( info.NE.0 ) THEN
161  CALL xerbla( 'DTRTI2', -info )
162  RETURN
163  END IF
164 *
165  IF( upper ) THEN
166 *
167 * Compute inverse of upper triangular matrix.
168 *
169  DO 10 j = 1, n
170  IF( nounit ) THEN
171  a( j, j ) = one / a( j, j )
172  ajj = -a( j, j )
173  ELSE
174  ajj = -one
175  END IF
176 *
177 * Compute elements 1:j-1 of j-th column.
178 *
179  CALL dtrmv( 'Upper', 'No transpose', diag, j-1, a, lda,
180  \$ a( 1, j ), 1 )
181  CALL dscal( j-1, ajj, a( 1, j ), 1 )
182  10 CONTINUE
183  ELSE
184 *
185 * Compute inverse of lower triangular matrix.
186 *
187  DO 20 j = n, 1, -1
188  IF( nounit ) THEN
189  a( j, j ) = one / a( j, j )
190  ajj = -a( j, j )
191  ELSE
192  ajj = -one
193  END IF
194  IF( j.LT.n ) THEN
195 *
196 * Compute elements j+1:n of j-th column.
197 *
198  CALL dtrmv( 'Lower', 'No transpose', diag, n-j,
199  \$ a( j+1, j+1 ), lda, a( j+1, j ), 1 )
200  CALL dscal( n-j, ajj, a( j+1, j ), 1 )
201  END IF
202  20 CONTINUE
203  END IF
204 *
205  RETURN
206 *
207 * End of DTRTI2
208 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dtrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRMV
Definition: dtrmv.f:147
Here is the call graph for this function:
Here is the caller graph for this function: