 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ ctrtri()

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

CTRTRI

Purpose:
CTRTRI 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 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 ctrtri.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 A( LDA, * )
120 * ..
121 *
122 * =====================================================================
123 *
124 * .. Parameters ..
125  COMPLEX ONE, ZERO
126  parameter( one = ( 1.0e+0, 0.0e+0 ),
127  \$ zero = ( 0.0e+0, 0.0e+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 ctrmm, ctrsm, ctrti2, xerbla
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( 'CTRTRI', -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, 'CTRTRI', uplo // diag, n, -1, -1, -1 )
183  IF( nb.LE.1 .OR. nb.GE.n ) THEN
184 *
185 * Use unblocked code
186 *
187  CALL ctrti2( 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 ctrmm( 'Left', 'Upper', 'No transpose', diag, j-1,
202  \$ jb, one, a, lda, a( 1, j ), lda )
203  CALL ctrsm( '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 ctrti2( '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 ctrmm( '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 ctrsm( '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 ctrti2( 'Lower', diag, jb, a( j, j ), lda, info )
232  30 CONTINUE
233  END IF
234  END IF
235 *
236  RETURN
237 *
238 * End of CTRTRI
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 ctrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRMM
Definition: ctrmm.f:177
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
subroutine ctrti2(UPLO, DIAG, N, A, LDA, INFO)
CTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
Definition: ctrti2.f:110
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