LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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.```
Date
November 2011

Definition at line 111 of file dtrtri.f.

111 *
112 * -- LAPACK computational routine (version 3.4.0) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 * November 2011
116 *
117 * .. Scalar Arguments ..
118  CHARACTER diag, uplo
119  INTEGER info, lda, n
120 * ..
121 * .. Array Arguments ..
122  DOUBLE PRECISION a( lda, * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  DOUBLE PRECISION one, zero
129  parameter ( one = 1.0d+0, zero = 0.0d+0 )
130 * ..
131 * .. Local Scalars ..
132  LOGICAL nounit, upper
133  INTEGER j, jb, nb, nn
134 * ..
135 * .. External Functions ..
136  LOGICAL lsame
137  INTEGER ilaenv
138  EXTERNAL lsame, ilaenv
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL dtrmm, dtrsm, dtrti2, xerbla
142 * ..
143 * .. Intrinsic Functions ..
144  INTRINSIC max, min
145 * ..
146 * .. Executable Statements ..
147 *
148 * Test the input parameters.
149 *
150  info = 0
151  upper = lsame( uplo, 'U' )
152  nounit = lsame( diag, 'N' )
153  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
154  info = -1
155  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
156  info = -2
157  ELSE IF( n.LT.0 ) THEN
158  info = -3
159  ELSE IF( lda.LT.max( 1, n ) ) THEN
160  info = -5
161  END IF
162  IF( info.NE.0 ) THEN
163  CALL xerbla( 'DTRTRI', -info )
164  RETURN
165  END IF
166 *
167 * Quick return if possible
168 *
169  IF( n.EQ.0 )
170  \$ RETURN
171 *
172 * Check for singularity if non-unit.
173 *
174  IF( nounit ) THEN
175  DO 10 info = 1, n
176  IF( a( info, info ).EQ.zero )
177  \$ RETURN
178  10 CONTINUE
179  info = 0
180  END IF
181 *
182 * Determine the block size for this environment.
183 *
184  nb = ilaenv( 1, 'DTRTRI', uplo // diag, n, -1, -1, -1 )
185  IF( nb.LE.1 .OR. nb.GE.n ) THEN
186 *
187 * Use unblocked code
188 *
189  CALL dtrti2( uplo, diag, n, a, lda, info )
190  ELSE
191 *
192 * Use blocked code
193 *
194  IF( upper ) THEN
195 *
196 * Compute inverse of upper triangular matrix
197 *
198  DO 20 j = 1, n, nb
199  jb = min( nb, n-j+1 )
200 *
201 * Compute rows 1:j-1 of current block column
202 *
203  CALL dtrmm( 'Left', 'Upper', 'No transpose', diag, j-1,
204  \$ jb, one, a, lda, a( 1, j ), lda )
205  CALL dtrsm( 'Right', 'Upper', 'No transpose', diag, j-1,
206  \$ jb, -one, a( j, j ), lda, a( 1, j ), lda )
207 *
208 * Compute inverse of current diagonal block
209 *
210  CALL dtrti2( 'Upper', diag, jb, a( j, j ), lda, info )
211  20 CONTINUE
212  ELSE
213 *
214 * Compute inverse of lower triangular matrix
215 *
216  nn = ( ( n-1 ) / nb )*nb + 1
217  DO 30 j = nn, 1, -nb
218  jb = min( nb, n-j+1 )
219  IF( j+jb.LE.n ) THEN
220 *
221 * Compute rows j+jb:n of current block column
222 *
223  CALL dtrmm( 'Left', 'Lower', 'No transpose', diag,
224  \$ n-j-jb+1, jb, one, a( j+jb, j+jb ), lda,
225  \$ a( j+jb, j ), lda )
226  CALL dtrsm( 'Right', 'Lower', 'No transpose', diag,
227  \$ n-j-jb+1, jb, -one, a( j, j ), lda,
228  \$ a( j+jb, j ), lda )
229  END IF
230 *
231 * Compute inverse of current diagonal block
232 *
233  CALL dtrti2( 'Lower', diag, jb, a( j, j ), lda, info )
234  30 CONTINUE
235  END IF
236  END IF
237 *
238  RETURN
239 *
240 * End of DTRTRI
241 *
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:183
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:179
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dtrti2(UPLO, DIAG, N, A, LDA, INFO)
DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
Definition: dtrti2.f:112
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
Definition: tstiee.f:83
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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