LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ztrtri()

 subroutine ztrtri ( character UPLO, character DIAG, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer INFO )

ZTRTRI

Purpose:
``` ZTRTRI computes the inverse of a complex 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 COMPLEX*16 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 ztrtri.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 COMPLEX*16 A( LDA, * )
120* ..
121*
122* =====================================================================
123*
124* .. Parameters ..
125 COMPLEX*16 ONE, ZERO
126 parameter( one = ( 1.0d+0, 0.0d+0 ),
127 \$ zero = ( 0.0d+0, 0.0d+0 ) )
128* ..
129* .. Local Scalars ..
130 LOGICAL NOUNIT, UPPER
131 INTEGER J, JB, NB, NN
132* ..
133* .. External Functions ..
134 LOGICAL LSAME
135 INTEGER ILAENV
136 EXTERNAL lsame, ilaenv
137* ..
138* .. External Subroutines ..
139 EXTERNAL xerbla, ztrmm, ztrsm, ztrti2
140* ..
141* .. Intrinsic Functions ..
142 INTRINSIC max, min
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( 'ZTRTRI', -info )
162 RETURN
163 END IF
164*
165* Quick return if possible
166*
167 IF( n.EQ.0 )
168 \$ RETURN
169*
170* Check for singularity if non-unit.
171*
172 IF( nounit ) THEN
173 DO 10 info = 1, n
174 IF( a( info, info ).EQ.zero )
175 \$ RETURN
176 10 CONTINUE
177 info = 0
178 END IF
179*
180* Determine the block size for this environment.
181*
182 nb = ilaenv( 1, 'ZTRTRI', uplo // diag, n, -1, -1, -1 )
183 IF( nb.LE.1 .OR. nb.GE.n ) THEN
184*
185* Use unblocked code
186*
187 CALL ztrti2( uplo, diag, n, a, lda, info )
188 ELSE
189*
190* Use blocked code
191*
192 IF( upper ) THEN
193*
194* Compute inverse of upper triangular matrix
195*
196 DO 20 j = 1, n, nb
197 jb = min( nb, n-j+1 )
198*
199* Compute rows 1:j-1 of current block column
200*
201 CALL ztrmm( 'Left', 'Upper', 'No transpose', diag, j-1,
202 \$ jb, one, a, lda, a( 1, j ), lda )
203 CALL ztrsm( 'Right', 'Upper', 'No transpose', diag, j-1,
204 \$ jb, -one, a( j, j ), lda, a( 1, j ), lda )
205*
206* Compute inverse of current diagonal block
207*
208 CALL ztrti2( 'Upper', diag, jb, a( j, j ), lda, info )
209 20 CONTINUE
210 ELSE
211*
212* Compute inverse of lower triangular matrix
213*
214 nn = ( ( n-1 ) / nb )*nb + 1
215 DO 30 j = nn, 1, -nb
216 jb = min( nb, n-j+1 )
217 IF( j+jb.LE.n ) THEN
218*
219* Compute rows j+jb:n of current block column
220*
221 CALL ztrmm( 'Left', 'Lower', 'No transpose', diag,
222 \$ n-j-jb+1, jb, one, a( j+jb, j+jb ), lda,
223 \$ a( j+jb, j ), lda )
224 CALL ztrsm( 'Right', 'Lower', 'No transpose', diag,
225 \$ n-j-jb+1, jb, -one, a( j, j ), lda,
226 \$ a( j+jb, j ), lda )
227 END IF
228*
229* Compute inverse of current diagonal block
230*
231 CALL ztrti2( 'Lower', diag, jb, a( j, j ), lda, info )
232 30 CONTINUE
233 END IF
234 END IF
235*
236 RETURN
237*
238* End of ZTRTRI
239*
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:180
subroutine ztrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRMM
Definition: ztrmm.f:177
subroutine ztrti2(UPLO, DIAG, N, A, LDA, INFO)
ZTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
Definition: ztrti2.f:110
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