 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ztrtri()

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

ZTRTRI

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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.```
Date
December 2016

Definition at line 111 of file ztrtri.f.

111 *
112 * -- LAPACK computational routine (version 3.7.0) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 * December 2016
116 *
117 * .. Scalar Arguments ..
118  CHARACTER diag, uplo
119  INTEGER info, lda, n
120 * ..
121 * .. Array Arguments ..
122  COMPLEX*16 a( lda, * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  COMPLEX*16 one, zero
129  parameter( one = ( 1.0d+0, 0.0d+0 ),
130  \$ zero = ( 0.0d+0, 0.0d+0 ) )
131 * ..
132 * .. Local Scalars ..
133  LOGICAL nounit, upper
134  INTEGER j, jb, nb, nn
135 * ..
136 * .. External Functions ..
137  LOGICAL lsame
138  INTEGER ilaenv
139  EXTERNAL lsame, ilaenv
140 * ..
141 * .. External Subroutines ..
142  EXTERNAL xerbla, ztrmm, ztrsm, ztrti2
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC max, min
146 * ..
147 * .. Executable Statements ..
148 *
149 * Test the input parameters.
150 *
151  info = 0
152  upper = lsame( uplo, 'U' )
153  nounit = lsame( diag, 'N' )
154  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
155  info = -1
156  ELSE IF( .NOT.nounit .AND. .NOT.lsame( diag, 'U' ) ) THEN
157  info = -2
158  ELSE IF( n.LT.0 ) THEN
159  info = -3
160  ELSE IF( lda.LT.max( 1, n ) ) THEN
161  info = -5
162  END IF
163  IF( info.NE.0 ) THEN
164  CALL xerbla( 'ZTRTRI', -info )
165  RETURN
166  END IF
167 *
168 * Quick return if possible
169 *
170  IF( n.EQ.0 )
171  \$ RETURN
172 *
173 * Check for singularity if non-unit.
174 *
175  IF( nounit ) THEN
176  DO 10 info = 1, n
177  IF( a( info, info ).EQ.zero )
178  \$ RETURN
179  10 CONTINUE
180  info = 0
181  END IF
182 *
183 * Determine the block size for this environment.
184 *
185  nb = ilaenv( 1, 'ZTRTRI', uplo // diag, n, -1, -1, -1 )
186  IF( nb.LE.1 .OR. nb.GE.n ) THEN
187 *
188 * Use unblocked code
189 *
190  CALL ztrti2( uplo, diag, n, a, lda, info )
191  ELSE
192 *
193 * Use blocked code
194 *
195  IF( upper ) THEN
196 *
197 * Compute inverse of upper triangular matrix
198 *
199  DO 20 j = 1, n, nb
200  jb = min( nb, n-j+1 )
201 *
202 * Compute rows 1:j-1 of current block column
203 *
204  CALL ztrmm( 'Left', 'Upper', 'No transpose', diag, j-1,
205  \$ jb, one, a, lda, a( 1, j ), lda )
206  CALL ztrsm( 'Right', 'Upper', 'No transpose', diag, j-1,
207  \$ jb, -one, a( j, j ), lda, a( 1, j ), lda )
208 *
209 * Compute inverse of current diagonal block
210 *
211  CALL ztrti2( 'Upper', diag, jb, a( j, j ), lda, info )
212  20 CONTINUE
213  ELSE
214 *
215 * Compute inverse of lower triangular matrix
216 *
217  nn = ( ( n-1 ) / nb )*nb + 1
218  DO 30 j = nn, 1, -nb
219  jb = min( nb, n-j+1 )
220  IF( j+jb.LE.n ) THEN
221 *
222 * Compute rows j+jb:n of current block column
223 *
224  CALL ztrmm( 'Left', 'Lower', 'No transpose', diag,
225  \$ n-j-jb+1, jb, one, a( j+jb, j+jb ), lda,
226  \$ a( j+jb, j ), lda )
227  CALL ztrsm( 'Right', 'Lower', 'No transpose', diag,
228  \$ n-j-jb+1, jb, -one, a( j, j ), lda,
229  \$ a( j+jb, j ), lda )
230  END IF
231 *
232 * Compute inverse of current diagonal block
233 *
234  CALL ztrti2( 'Lower', diag, jb, a( j, j ), lda, info )
235  30 CONTINUE
236  END IF
237  END IF
238 *
239  RETURN
240 *
241 * End of ZTRTRI
242 *
subroutine ztrti2(UPLO, DIAG, N, A, LDA, INFO)
ZTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
Definition: ztrti2.f:112
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine ztrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRSM
Definition: ztrsm.f:182
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: tstiee.f:83
subroutine ztrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRMM
Definition: ztrmm.f:179
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