1 SUBROUTINE DTFTRI( TRANSR, UPLO, DIAG, N, A, INFO )
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 *
5 * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
6 * -- April 2011 ----
7 *
8 * -- LAPACK is a software package provided by Univ. of Tennessee, --
9 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
10 *
11 * .. Scalar Arguments ..
12 CHARACTER TRANSR, UPLO, DIAG
13 INTEGER INFO, N
14 * ..
15 * .. Array Arguments ..
16 DOUBLE PRECISION A( 0: * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * DTFTRI computes the inverse of a triangular matrix A stored in RFP
23 * format.
24 *
25 * This is a Level 3 BLAS version of the algorithm.
26 *
27 * Arguments
28 * =========
29 *
30 * TRANSR (input) CHARACTER*1
31 * = 'N': The Normal TRANSR of RFP A is stored;
32 * = 'T': The Transpose TRANSR of RFP A is stored.
33 *
34 * UPLO (input) CHARACTER*1
35 * = 'U': A is upper triangular;
36 * = 'L': A is lower triangular.
37 *
38 * DIAG (input) CHARACTER*1
39 * = 'N': A is non-unit triangular;
40 * = 'U': A is unit triangular.
41 *
42 * N (input) INTEGER
43 * The order of the matrix A. N >= 0.
44 *
45 * A (input/output) DOUBLE PRECISION array, dimension (0:nt-1);
46 * nt=N*(N+1)/2. On entry, the triangular factor of a Hermitian
47 * Positive Definite matrix A in RFP format. RFP format is
48 * described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
49 * then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
50 * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
51 * the transpose of RFP A as defined when
52 * TRANSR = 'N'. The contents of RFP A are defined by UPLO as
53 * follows: If UPLO = 'U' the RFP A contains the nt elements of
54 * upper packed A; If UPLO = 'L' the RFP A contains the nt
55 * elements of lower packed A. The LDA of RFP A is (N+1)/2 when
56 * TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is
57 * even and N is odd. See the Note below for more details.
58 *
59 * On exit, the (triangular) inverse of the original matrix, in
60 * the same storage format.
61 *
62 * INFO (output) INTEGER
63 * = 0: successful exit
64 * < 0: if INFO = -i, the i-th argument had an illegal value
65 * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
66 * matrix is singular and its inverse can not be computed.
67 *
68 * Further Details
69 * ===============
70 *
71 * We first consider Rectangular Full Packed (RFP) Format when N is
72 * even. We give an example where N = 6.
73 *
74 * AP is Upper AP is Lower
75 *
76 * 00 01 02 03 04 05 00
77 * 11 12 13 14 15 10 11
78 * 22 23 24 25 20 21 22
79 * 33 34 35 30 31 32 33
80 * 44 45 40 41 42 43 44
81 * 55 50 51 52 53 54 55
82 *
83 *
84 * Let TRANSR = 'N'. RFP holds AP as follows:
85 * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
86 * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
87 * the transpose of the first three columns of AP upper.
88 * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
89 * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
90 * the transpose of the last three columns of AP lower.
91 * This covers the case N even and TRANSR = 'N'.
92 *
93 * RFP A RFP A
94 *
95 * 03 04 05 33 43 53
96 * 13 14 15 00 44 54
97 * 23 24 25 10 11 55
98 * 33 34 35 20 21 22
99 * 00 44 45 30 31 32
100 * 01 11 55 40 41 42
101 * 02 12 22 50 51 52
102 *
103 * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
104 * transpose of RFP A above. One therefore gets:
105 *
106 *
107 * RFP A RFP A
108 *
109 * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
110 * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
111 * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
112 *
113 *
114 * We then consider Rectangular Full Packed (RFP) Format when N is
115 * odd. We give an example where N = 5.
116 *
117 * AP is Upper AP is Lower
118 *
119 * 00 01 02 03 04 00
120 * 11 12 13 14 10 11
121 * 22 23 24 20 21 22
122 * 33 34 30 31 32 33
123 * 44 40 41 42 43 44
124 *
125 *
126 * Let TRANSR = 'N'. RFP holds AP as follows:
127 * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
128 * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
129 * the transpose of the first two columns of AP upper.
130 * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
131 * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
132 * the transpose of the last two columns of AP lower.
133 * This covers the case N odd and TRANSR = 'N'.
134 *
135 * RFP A RFP A
136 *
137 * 02 03 04 00 33 43
138 * 12 13 14 10 11 44
139 * 22 23 24 20 21 22
140 * 00 33 34 30 31 32
141 * 01 11 44 40 41 42
142 *
143 * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
144 * transpose of RFP A above. One therefore gets:
145 *
146 * RFP A RFP A
147 *
148 * 02 12 22 00 01 00 10 20 30 40 50
149 * 03 13 23 33 11 33 11 21 31 41 51
150 * 04 14 24 34 44 43 44 22 32 42 52
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155 DOUBLE PRECISION ONE
156 PARAMETER ( ONE = 1.0D+0 )
157 * ..
158 * .. Local Scalars ..
159 LOGICAL LOWER, NISODD, NORMALTRANSR
160 INTEGER N1, N2, K
161 * ..
162 * .. External Functions ..
163 LOGICAL LSAME
164 EXTERNAL LSAME
165 * ..
166 * .. External Subroutines ..
167 EXTERNAL XERBLA, DTRMM, DTRTRI
168 * ..
169 * .. Intrinsic Functions ..
170 INTRINSIC MOD
171 * ..
172 * .. Executable Statements ..
173 *
174 * Test the input parameters.
175 *
176 INFO = 0
177 NORMALTRANSR = LSAME( TRANSR, 'N' )
178 LOWER = LSAME( UPLO, 'L' )
179 IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
180 INFO = -1
181 ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
182 INFO = -2
183 ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
184 $ THEN
185 INFO = -3
186 ELSE IF( N.LT.0 ) THEN
187 INFO = -4
188 END IF
189 IF( INFO.NE.0 ) THEN
190 CALL XERBLA( 'DTFTRI', -INFO )
191 RETURN
192 END IF
193 *
194 * Quick return if possible
195 *
196 IF( N.EQ.0 )
197 $ RETURN
198 *
199 * If N is odd, set NISODD = .TRUE.
200 * If N is even, set K = N/2 and NISODD = .FALSE.
201 *
202 IF( MOD( N, 2 ).EQ.0 ) THEN
203 K = N / 2
204 NISODD = .FALSE.
205 ELSE
206 NISODD = .TRUE.
207 END IF
208 *
209 * Set N1 and N2 depending on LOWER
210 *
211 IF( LOWER ) THEN
212 N2 = N / 2
213 N1 = N - N2
214 ELSE
215 N1 = N / 2
216 N2 = N - N1
217 END IF
218 *
219 *
220 * start execution: there are eight cases
221 *
222 IF( NISODD ) THEN
223 *
224 * N is odd
225 *
226 IF( NORMALTRANSR ) THEN
227 *
228 * N is odd and TRANSR = 'N'
229 *
230 IF( LOWER ) THEN
231 *
232 * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
233 * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
234 * T1 -> a(0), T2 -> a(n), S -> a(n1)
235 *
236 CALL DTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
237 IF( INFO.GT.0 )
238 $ RETURN
239 CALL DTRMM( 'R', 'L', 'N', DIAG, N2, N1, -ONE, A( 0 ),
240 $ N, A( N1 ), N )
241 CALL DTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
242 IF( INFO.GT.0 )
243 $ INFO = INFO + N1
244 IF( INFO.GT.0 )
245 $ RETURN
246 CALL DTRMM( 'L', 'U', 'T', DIAG, N2, N1, ONE, A( N ), N,
247 $ A( N1 ), N )
248 *
249 ELSE
250 *
251 * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
252 * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
253 * T1 -> a(n2), T2 -> a(n1), S -> a(0)
254 *
255 CALL DTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
256 IF( INFO.GT.0 )
257 $ RETURN
258 CALL DTRMM( 'L', 'L', 'T', DIAG, N1, N2, -ONE, A( N2 ),
259 $ N, A( 0 ), N )
260 CALL DTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
261 IF( INFO.GT.0 )
262 $ INFO = INFO + N1
263 IF( INFO.GT.0 )
264 $ RETURN
265 CALL DTRMM( 'R', 'U', 'N', DIAG, N1, N2, ONE, A( N1 ),
266 $ N, A( 0 ), N )
267 *
268 END IF
269 *
270 ELSE
271 *
272 * N is odd and TRANSR = 'T'
273 *
274 IF( LOWER ) THEN
275 *
276 * SRPA for LOWER, TRANSPOSE and N is odd
277 * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
278 *
279 CALL DTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
280 IF( INFO.GT.0 )
281 $ RETURN
282 CALL DTRMM( 'L', 'U', 'N', DIAG, N1, N2, -ONE, A( 0 ),
283 $ N1, A( N1*N1 ), N1 )
284 CALL DTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
285 IF( INFO.GT.0 )
286 $ INFO = INFO + N1
287 IF( INFO.GT.0 )
288 $ RETURN
289 CALL DTRMM( 'R', 'L', 'T', DIAG, N1, N2, ONE, A( 1 ),
290 $ N1, A( N1*N1 ), N1 )
291 *
292 ELSE
293 *
294 * SRPA for UPPER, TRANSPOSE and N is odd
295 * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
296 *
297 CALL DTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
298 IF( INFO.GT.0 )
299 $ RETURN
300 CALL DTRMM( 'R', 'U', 'T', DIAG, N2, N1, -ONE,
301 $ A( N2*N2 ), N2, A( 0 ), N2 )
302 CALL DTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
303 IF( INFO.GT.0 )
304 $ INFO = INFO + N1
305 IF( INFO.GT.0 )
306 $ RETURN
307 CALL DTRMM( 'L', 'L', 'N', DIAG, N2, N1, ONE,
308 $ A( N1*N2 ), N2, A( 0 ), N2 )
309 END IF
310 *
311 END IF
312 *
313 ELSE
314 *
315 * N is even
316 *
317 IF( NORMALTRANSR ) THEN
318 *
319 * N is even and TRANSR = 'N'
320 *
321 IF( LOWER ) THEN
322 *
323 * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
324 * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
325 * T1 -> a(1), T2 -> a(0), S -> a(k+1)
326 *
327 CALL DTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
328 IF( INFO.GT.0 )
329 $ RETURN
330 CALL DTRMM( 'R', 'L', 'N', DIAG, K, K, -ONE, A( 1 ),
331 $ N+1, A( K+1 ), N+1 )
332 CALL DTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
333 IF( INFO.GT.0 )
334 $ INFO = INFO + K
335 IF( INFO.GT.0 )
336 $ RETURN
337 CALL DTRMM( 'L', 'U', 'T', DIAG, K, K, ONE, A( 0 ), N+1,
338 $ A( K+1 ), N+1 )
339 *
340 ELSE
341 *
342 * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
343 * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
344 * T1 -> a(k+1), T2 -> a(k), S -> a(0)
345 *
346 CALL DTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
347 IF( INFO.GT.0 )
348 $ RETURN
349 CALL DTRMM( 'L', 'L', 'T', DIAG, K, K, -ONE, A( K+1 ),
350 $ N+1, A( 0 ), N+1 )
351 CALL DTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
352 IF( INFO.GT.0 )
353 $ INFO = INFO + K
354 IF( INFO.GT.0 )
355 $ RETURN
356 CALL DTRMM( 'R', 'U', 'N', DIAG, K, K, ONE, A( K ), N+1,
357 $ A( 0 ), N+1 )
358 END IF
359 ELSE
360 *
361 * N is even and TRANSR = 'T'
362 *
363 IF( LOWER ) THEN
364 *
365 * SRPA for LOWER, TRANSPOSE and N is even (see paper)
366 * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
367 * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
368 *
369 CALL DTRTRI( 'U', DIAG, K, A( K ), K, INFO )
370 IF( INFO.GT.0 )
371 $ RETURN
372 CALL DTRMM( 'L', 'U', 'N', DIAG, K, K, -ONE, A( K ), K,
373 $ A( K*( K+1 ) ), K )
374 CALL DTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
375 IF( INFO.GT.0 )
376 $ INFO = INFO + K
377 IF( INFO.GT.0 )
378 $ RETURN
379 CALL DTRMM( 'R', 'L', 'T', DIAG, K, K, ONE, A( 0 ), K,
380 $ A( K*( K+1 ) ), K )
381 ELSE
382 *
383 * SRPA for UPPER, TRANSPOSE and N is even (see paper)
384 * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
385 * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
386 *
387 CALL DTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
388 IF( INFO.GT.0 )
389 $ RETURN
390 CALL DTRMM( 'R', 'U', 'T', DIAG, K, K, -ONE,
391 $ A( K*( K+1 ) ), K, A( 0 ), K )
392 CALL DTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
393 IF( INFO.GT.0 )
394 $ INFO = INFO + K
395 IF( INFO.GT.0 )
396 $ RETURN
397 CALL DTRMM( 'L', 'L', 'N', DIAG, K, K, ONE, A( K*K ), K,
398 $ A( 0 ), K )
399 END IF
400 END IF
401 END IF
402 *
403 RETURN
404 *
405 * End of DTFTRI
406 *
407 END
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 *
5 * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
6 * -- April 2011 ----
7 *
8 * -- LAPACK is a software package provided by Univ. of Tennessee, --
9 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
10 *
11 * .. Scalar Arguments ..
12 CHARACTER TRANSR, UPLO, DIAG
13 INTEGER INFO, N
14 * ..
15 * .. Array Arguments ..
16 DOUBLE PRECISION A( 0: * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * DTFTRI computes the inverse of a triangular matrix A stored in RFP
23 * format.
24 *
25 * This is a Level 3 BLAS version of the algorithm.
26 *
27 * Arguments
28 * =========
29 *
30 * TRANSR (input) CHARACTER*1
31 * = 'N': The Normal TRANSR of RFP A is stored;
32 * = 'T': The Transpose TRANSR of RFP A is stored.
33 *
34 * UPLO (input) CHARACTER*1
35 * = 'U': A is upper triangular;
36 * = 'L': A is lower triangular.
37 *
38 * DIAG (input) CHARACTER*1
39 * = 'N': A is non-unit triangular;
40 * = 'U': A is unit triangular.
41 *
42 * N (input) INTEGER
43 * The order of the matrix A. N >= 0.
44 *
45 * A (input/output) DOUBLE PRECISION array, dimension (0:nt-1);
46 * nt=N*(N+1)/2. On entry, the triangular factor of a Hermitian
47 * Positive Definite matrix A in RFP format. RFP format is
48 * described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
49 * then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
50 * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is
51 * the transpose of RFP A as defined when
52 * TRANSR = 'N'. The contents of RFP A are defined by UPLO as
53 * follows: If UPLO = 'U' the RFP A contains the nt elements of
54 * upper packed A; If UPLO = 'L' the RFP A contains the nt
55 * elements of lower packed A. The LDA of RFP A is (N+1)/2 when
56 * TRANSR = 'T'. When TRANSR is 'N' the LDA is N+1 when N is
57 * even and N is odd. See the Note below for more details.
58 *
59 * On exit, the (triangular) inverse of the original matrix, in
60 * the same storage format.
61 *
62 * INFO (output) INTEGER
63 * = 0: successful exit
64 * < 0: if INFO = -i, the i-th argument had an illegal value
65 * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
66 * matrix is singular and its inverse can not be computed.
67 *
68 * Further Details
69 * ===============
70 *
71 * We first consider Rectangular Full Packed (RFP) Format when N is
72 * even. We give an example where N = 6.
73 *
74 * AP is Upper AP is Lower
75 *
76 * 00 01 02 03 04 05 00
77 * 11 12 13 14 15 10 11
78 * 22 23 24 25 20 21 22
79 * 33 34 35 30 31 32 33
80 * 44 45 40 41 42 43 44
81 * 55 50 51 52 53 54 55
82 *
83 *
84 * Let TRANSR = 'N'. RFP holds AP as follows:
85 * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
86 * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
87 * the transpose of the first three columns of AP upper.
88 * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
89 * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
90 * the transpose of the last three columns of AP lower.
91 * This covers the case N even and TRANSR = 'N'.
92 *
93 * RFP A RFP A
94 *
95 * 03 04 05 33 43 53
96 * 13 14 15 00 44 54
97 * 23 24 25 10 11 55
98 * 33 34 35 20 21 22
99 * 00 44 45 30 31 32
100 * 01 11 55 40 41 42
101 * 02 12 22 50 51 52
102 *
103 * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
104 * transpose of RFP A above. One therefore gets:
105 *
106 *
107 * RFP A RFP A
108 *
109 * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
110 * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
111 * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
112 *
113 *
114 * We then consider Rectangular Full Packed (RFP) Format when N is
115 * odd. We give an example where N = 5.
116 *
117 * AP is Upper AP is Lower
118 *
119 * 00 01 02 03 04 00
120 * 11 12 13 14 10 11
121 * 22 23 24 20 21 22
122 * 33 34 30 31 32 33
123 * 44 40 41 42 43 44
124 *
125 *
126 * Let TRANSR = 'N'. RFP holds AP as follows:
127 * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
128 * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
129 * the transpose of the first two columns of AP upper.
130 * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
131 * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
132 * the transpose of the last two columns of AP lower.
133 * This covers the case N odd and TRANSR = 'N'.
134 *
135 * RFP A RFP A
136 *
137 * 02 03 04 00 33 43
138 * 12 13 14 10 11 44
139 * 22 23 24 20 21 22
140 * 00 33 34 30 31 32
141 * 01 11 44 40 41 42
142 *
143 * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
144 * transpose of RFP A above. One therefore gets:
145 *
146 * RFP A RFP A
147 *
148 * 02 12 22 00 01 00 10 20 30 40 50
149 * 03 13 23 33 11 33 11 21 31 41 51
150 * 04 14 24 34 44 43 44 22 32 42 52
151 *
152 * =====================================================================
153 *
154 * .. Parameters ..
155 DOUBLE PRECISION ONE
156 PARAMETER ( ONE = 1.0D+0 )
157 * ..
158 * .. Local Scalars ..
159 LOGICAL LOWER, NISODD, NORMALTRANSR
160 INTEGER N1, N2, K
161 * ..
162 * .. External Functions ..
163 LOGICAL LSAME
164 EXTERNAL LSAME
165 * ..
166 * .. External Subroutines ..
167 EXTERNAL XERBLA, DTRMM, DTRTRI
168 * ..
169 * .. Intrinsic Functions ..
170 INTRINSIC MOD
171 * ..
172 * .. Executable Statements ..
173 *
174 * Test the input parameters.
175 *
176 INFO = 0
177 NORMALTRANSR = LSAME( TRANSR, 'N' )
178 LOWER = LSAME( UPLO, 'L' )
179 IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
180 INFO = -1
181 ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
182 INFO = -2
183 ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
184 $ THEN
185 INFO = -3
186 ELSE IF( N.LT.0 ) THEN
187 INFO = -4
188 END IF
189 IF( INFO.NE.0 ) THEN
190 CALL XERBLA( 'DTFTRI', -INFO )
191 RETURN
192 END IF
193 *
194 * Quick return if possible
195 *
196 IF( N.EQ.0 )
197 $ RETURN
198 *
199 * If N is odd, set NISODD = .TRUE.
200 * If N is even, set K = N/2 and NISODD = .FALSE.
201 *
202 IF( MOD( N, 2 ).EQ.0 ) THEN
203 K = N / 2
204 NISODD = .FALSE.
205 ELSE
206 NISODD = .TRUE.
207 END IF
208 *
209 * Set N1 and N2 depending on LOWER
210 *
211 IF( LOWER ) THEN
212 N2 = N / 2
213 N1 = N - N2
214 ELSE
215 N1 = N / 2
216 N2 = N - N1
217 END IF
218 *
219 *
220 * start execution: there are eight cases
221 *
222 IF( NISODD ) THEN
223 *
224 * N is odd
225 *
226 IF( NORMALTRANSR ) THEN
227 *
228 * N is odd and TRANSR = 'N'
229 *
230 IF( LOWER ) THEN
231 *
232 * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
233 * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
234 * T1 -> a(0), T2 -> a(n), S -> a(n1)
235 *
236 CALL DTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
237 IF( INFO.GT.0 )
238 $ RETURN
239 CALL DTRMM( 'R', 'L', 'N', DIAG, N2, N1, -ONE, A( 0 ),
240 $ N, A( N1 ), N )
241 CALL DTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
242 IF( INFO.GT.0 )
243 $ INFO = INFO + N1
244 IF( INFO.GT.0 )
245 $ RETURN
246 CALL DTRMM( 'L', 'U', 'T', DIAG, N2, N1, ONE, A( N ), N,
247 $ A( N1 ), N )
248 *
249 ELSE
250 *
251 * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
252 * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
253 * T1 -> a(n2), T2 -> a(n1), S -> a(0)
254 *
255 CALL DTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
256 IF( INFO.GT.0 )
257 $ RETURN
258 CALL DTRMM( 'L', 'L', 'T', DIAG, N1, N2, -ONE, A( N2 ),
259 $ N, A( 0 ), N )
260 CALL DTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
261 IF( INFO.GT.0 )
262 $ INFO = INFO + N1
263 IF( INFO.GT.0 )
264 $ RETURN
265 CALL DTRMM( 'R', 'U', 'N', DIAG, N1, N2, ONE, A( N1 ),
266 $ N, A( 0 ), N )
267 *
268 END IF
269 *
270 ELSE
271 *
272 * N is odd and TRANSR = 'T'
273 *
274 IF( LOWER ) THEN
275 *
276 * SRPA for LOWER, TRANSPOSE and N is odd
277 * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
278 *
279 CALL DTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
280 IF( INFO.GT.0 )
281 $ RETURN
282 CALL DTRMM( 'L', 'U', 'N', DIAG, N1, N2, -ONE, A( 0 ),
283 $ N1, A( N1*N1 ), N1 )
284 CALL DTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
285 IF( INFO.GT.0 )
286 $ INFO = INFO + N1
287 IF( INFO.GT.0 )
288 $ RETURN
289 CALL DTRMM( 'R', 'L', 'T', DIAG, N1, N2, ONE, A( 1 ),
290 $ N1, A( N1*N1 ), N1 )
291 *
292 ELSE
293 *
294 * SRPA for UPPER, TRANSPOSE and N is odd
295 * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
296 *
297 CALL DTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
298 IF( INFO.GT.0 )
299 $ RETURN
300 CALL DTRMM( 'R', 'U', 'T', DIAG, N2, N1, -ONE,
301 $ A( N2*N2 ), N2, A( 0 ), N2 )
302 CALL DTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
303 IF( INFO.GT.0 )
304 $ INFO = INFO + N1
305 IF( INFO.GT.0 )
306 $ RETURN
307 CALL DTRMM( 'L', 'L', 'N', DIAG, N2, N1, ONE,
308 $ A( N1*N2 ), N2, A( 0 ), N2 )
309 END IF
310 *
311 END IF
312 *
313 ELSE
314 *
315 * N is even
316 *
317 IF( NORMALTRANSR ) THEN
318 *
319 * N is even and TRANSR = 'N'
320 *
321 IF( LOWER ) THEN
322 *
323 * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
324 * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
325 * T1 -> a(1), T2 -> a(0), S -> a(k+1)
326 *
327 CALL DTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
328 IF( INFO.GT.0 )
329 $ RETURN
330 CALL DTRMM( 'R', 'L', 'N', DIAG, K, K, -ONE, A( 1 ),
331 $ N+1, A( K+1 ), N+1 )
332 CALL DTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
333 IF( INFO.GT.0 )
334 $ INFO = INFO + K
335 IF( INFO.GT.0 )
336 $ RETURN
337 CALL DTRMM( 'L', 'U', 'T', DIAG, K, K, ONE, A( 0 ), N+1,
338 $ A( K+1 ), N+1 )
339 *
340 ELSE
341 *
342 * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
343 * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
344 * T1 -> a(k+1), T2 -> a(k), S -> a(0)
345 *
346 CALL DTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
347 IF( INFO.GT.0 )
348 $ RETURN
349 CALL DTRMM( 'L', 'L', 'T', DIAG, K, K, -ONE, A( K+1 ),
350 $ N+1, A( 0 ), N+1 )
351 CALL DTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
352 IF( INFO.GT.0 )
353 $ INFO = INFO + K
354 IF( INFO.GT.0 )
355 $ RETURN
356 CALL DTRMM( 'R', 'U', 'N', DIAG, K, K, ONE, A( K ), N+1,
357 $ A( 0 ), N+1 )
358 END IF
359 ELSE
360 *
361 * N is even and TRANSR = 'T'
362 *
363 IF( LOWER ) THEN
364 *
365 * SRPA for LOWER, TRANSPOSE and N is even (see paper)
366 * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
367 * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
368 *
369 CALL DTRTRI( 'U', DIAG, K, A( K ), K, INFO )
370 IF( INFO.GT.0 )
371 $ RETURN
372 CALL DTRMM( 'L', 'U', 'N', DIAG, K, K, -ONE, A( K ), K,
373 $ A( K*( K+1 ) ), K )
374 CALL DTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
375 IF( INFO.GT.0 )
376 $ INFO = INFO + K
377 IF( INFO.GT.0 )
378 $ RETURN
379 CALL DTRMM( 'R', 'L', 'T', DIAG, K, K, ONE, A( 0 ), K,
380 $ A( K*( K+1 ) ), K )
381 ELSE
382 *
383 * SRPA for UPPER, TRANSPOSE and N is even (see paper)
384 * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
385 * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
386 *
387 CALL DTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
388 IF( INFO.GT.0 )
389 $ RETURN
390 CALL DTRMM( 'R', 'U', 'T', DIAG, K, K, -ONE,
391 $ A( K*( K+1 ) ), K, A( 0 ), K )
392 CALL DTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
393 IF( INFO.GT.0 )
394 $ INFO = INFO + K
395 IF( INFO.GT.0 )
396 $ RETURN
397 CALL DTRMM( 'L', 'L', 'N', DIAG, K, K, ONE, A( K*K ), K,
398 $ A( 0 ), K )
399 END IF
400 END IF
401 END IF
402 *
403 RETURN
404 *
405 * End of DTFTRI
406 *
407 END