LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dtrtri()

 subroutine dtrtri ( character uplo, character diag, integer n, double precision, dimension( lda, * ) a, integer lda, integer info )

DTRTRI

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

This is the Level 3 BLAS version of the algorithm.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular.``` [in] DIAG ``` DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is 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 = -i, the i-th argument had an illegal value > 0: if INFO = i, A(i,i) is exactly zero. The triangular matrix is singular and its inverse can not be computed.```

Definition at line 108 of file dtrtri.f.

109*
110* -- LAPACK computational routine --
111* -- LAPACK is a software package provided by Univ. of Tennessee, --
112* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
113*
114* .. Scalar Arguments ..
115 CHARACTER DIAG, UPLO
116 INTEGER INFO, LDA, N
117* ..
118* .. Array Arguments ..
119 DOUBLE PRECISION A( LDA, * )
120* ..
121*
122* =====================================================================
123*
124* .. Parameters ..
125 DOUBLE PRECISION ONE, ZERO
126 parameter( one = 1.0d+0, zero = 0.0d+0 )
127* ..
128* .. Local Scalars ..
129 LOGICAL NOUNIT, UPPER
130 INTEGER J, JB, NB, NN
131* ..
132* .. External Functions ..
133 LOGICAL LSAME
134 INTEGER ILAENV
135 EXTERNAL lsame, ilaenv
136* ..
137* .. External Subroutines ..
138 EXTERNAL dtrmm, dtrsm, dtrti2, xerbla
139* ..
140* .. Intrinsic Functions ..
141 INTRINSIC max, min
142* ..
143* .. Executable Statements ..
144*
145* Test the input parameters.
146*
147 info = 0
148 upper = lsame( uplo, 'U' )
149 nounit = lsame( diag, 'N' )
150 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
151 info = -1
152 ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
153 info = -2
154 ELSE IF( n.LT.0 ) THEN
155 info = -3
156 ELSE IF( lda.LT.max( 1, n ) ) THEN
157 info = -5
158 END IF
159 IF( info.NE.0 ) THEN
160 CALL xerbla( 'DTRTRI', -info )
161 RETURN
162 END IF
163*
164* Quick return if possible
165*
166 IF( n.EQ.0 )
167 \$ RETURN
168*
169* Check for singularity if non-unit.
170*
171 IF( nounit ) THEN
172 DO 10 info = 1, n
173 IF( a( info, info ).EQ.zero )
174 \$ RETURN
175 10 CONTINUE
176 info = 0
177 END IF
178*
179* Determine the block size for this environment.
180*
181 nb = ilaenv( 1, 'DTRTRI', uplo // diag, n, -1, -1, -1 )
182 IF( nb.LE.1 .OR. nb.GE.n ) THEN
183*
184* Use unblocked code
185*
186 CALL dtrti2( uplo, diag, n, a, lda, info )
187 ELSE
188*
189* Use blocked code
190*
191 IF( upper ) THEN
192*
193* Compute inverse of upper triangular matrix
194*
195 DO 20 j = 1, n, nb
196 jb = min( nb, n-j+1 )
197*
198* Compute rows 1:j-1 of current block column
199*
200 CALL dtrmm( 'Left', 'Upper', 'No transpose', diag, j-1,
201 \$ jb, one, a, lda, a( 1, j ), lda )
202 CALL dtrsm( 'Right', 'Upper', 'No transpose', diag, j-1,
203 \$ jb, -one, a( j, j ), lda, a( 1, j ), lda )
204*
205* Compute inverse of current diagonal block
206*
207 CALL dtrti2( 'Upper', diag, jb, a( j, j ), lda, info )
208 20 CONTINUE
209 ELSE
210*
211* Compute inverse of lower triangular matrix
212*
213 nn = ( ( n-1 ) / nb )*nb + 1
214 DO 30 j = nn, 1, -nb
215 jb = min( nb, n-j+1 )
216 IF( j+jb.LE.n ) THEN
217*
218* Compute rows j+jb:n of current block column
219*
220 CALL dtrmm( 'Left', 'Lower', 'No transpose', diag,
221 \$ n-j-jb+1, jb, one, a( j+jb, j+jb ), lda,
222 \$ a( j+jb, j ), lda )
223 CALL dtrsm( 'Right', 'Lower', 'No transpose', diag,
224 \$ n-j-jb+1, jb, -one, a( j, j ), lda,
225 \$ a( j+jb, j ), lda )
226 END IF
227*
228* Compute inverse of current diagonal block
229*
230 CALL dtrti2( 'Lower', diag, jb, a( j, j ), lda, info )
231 30 CONTINUE
232 END IF
233 END IF
234*
235 RETURN
236*
237* End of DTRTRI
238*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine dtrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRMM
Definition dtrmm.f:177
subroutine dtrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
DTRSM
Definition dtrsm.f:181
subroutine dtrti2(uplo, diag, n, a, lda, info)
DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
Definition dtrti2.f:110
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