1: *> \brief \b ZTRTRI
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZTRTRI + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrtri.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrtri.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrtri.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTRTRI( UPLO, DIAG, N, A, LDA, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER DIAG, UPLO
25: * INTEGER INFO, LDA, N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 A( LDA, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZTRTRI computes the inverse of a complex upper or lower triangular
38: *> matrix A.
39: *>
40: *> This is the Level 3 BLAS version of the algorithm.
41: *> \endverbatim
42: *
43: * Arguments:
44: * ==========
45: *
46: *> \param[in] UPLO
47: *> \verbatim
48: *> UPLO is CHARACTER*1
49: *> = 'U': A is upper triangular;
50: *> = 'L': A is lower triangular.
51: *> \endverbatim
52: *>
53: *> \param[in] DIAG
54: *> \verbatim
55: *> DIAG is CHARACTER*1
56: *> = 'N': A is non-unit triangular;
57: *> = 'U': A is unit triangular.
58: *> \endverbatim
59: *>
60: *> \param[in] N
61: *> \verbatim
62: *> N is INTEGER
63: *> The order of the matrix A. N >= 0.
64: *> \endverbatim
65: *>
66: *> \param[in,out] A
67: *> \verbatim
68: *> A is COMPLEX*16 array, dimension (LDA,N)
69: *> On entry, the triangular matrix A. If UPLO = 'U', the
70: *> leading N-by-N upper triangular part of the array A contains
71: *> the upper triangular matrix, and the strictly lower
72: *> triangular part of A is not referenced. If UPLO = 'L', the
73: *> leading N-by-N lower triangular part of the array A contains
74: *> the lower triangular matrix, and the strictly upper
75: *> triangular part of A is not referenced. If DIAG = 'U', the
76: *> diagonal elements of A are also not referenced and are
77: *> assumed to be 1.
78: *> On exit, the (triangular) inverse of the original matrix, in
79: *> the same storage format.
80: *> \endverbatim
81: *>
82: *> \param[in] LDA
83: *> \verbatim
84: *> LDA is INTEGER
85: *> The leading dimension of the array A. LDA >= max(1,N).
86: *> \endverbatim
87: *>
88: *> \param[out] INFO
89: *> \verbatim
90: *> INFO is INTEGER
91: *> = 0: successful exit
92: *> < 0: if INFO = -i, the i-th argument had an illegal value
93: *> > 0: if INFO = i, A(i,i) is exactly zero. The triangular
94: *> matrix is singular and its inverse can not be computed.
95: *> \endverbatim
96: *
97: * Authors:
98: * ========
99: *
100: *> \author Univ. of Tennessee
101: *> \author Univ. of California Berkeley
102: *> \author Univ. of Colorado Denver
103: *> \author NAG Ltd.
104: *
105: *> \ingroup complex16OTHERcomputational
106: *
107: * =====================================================================
108: SUBROUTINE ZTRTRI( UPLO, DIAG, N, A, LDA, INFO )
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: *
240: END
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