1 SUBROUTINE ZTFTRI( 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 COMPLEX*16 A( 0: * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * ZTFTRI 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 * = 'C': The Conjugate-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) COMPLEX*16 array, dimension ( N*(N+1)/2 );
46 * On entry, the triangular matrix A in RFP format. RFP format
47 * is described by TRANSR, UPLO, and N as follows: If TRANSR =
48 * 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
49 * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
50 * the Conjugate-transpose of RFP A as defined when
51 * TRANSR = 'N'. The contents of RFP A are defined by UPLO as
52 * follows: If UPLO = 'U' the RFP A contains the nt elements of
53 * upper packed A; If UPLO = 'L' the RFP A contains the nt
54 * elements of lower packed A. The LDA of RFP A is (N+1)/2 when
55 * TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
56 * even and N is odd. See the Note below for more details.
57 *
58 * On exit, the (triangular) inverse of the original matrix, in
59 * the same storage format.
60 *
61 * INFO (output) INTEGER
62 * = 0: successful exit
63 * < 0: if INFO = -i, the i-th argument had an illegal value
64 * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
65 * matrix is singular and its inverse can not be computed.
66 *
67 * Further Details
68 * ===============
69 *
70 * We first consider Standard Packed Format when N is even.
71 * We give an example where N = 6.
72 *
73 * AP is Upper AP is Lower
74 *
75 * 00 01 02 03 04 05 00
76 * 11 12 13 14 15 10 11
77 * 22 23 24 25 20 21 22
78 * 33 34 35 30 31 32 33
79 * 44 45 40 41 42 43 44
80 * 55 50 51 52 53 54 55
81 *
82 *
83 * Let TRANSR = 'N'. RFP holds AP as follows:
84 * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
85 * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
86 * conjugate-transpose of the first three columns of AP upper.
87 * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
88 * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
89 * conjugate-transpose of the last three columns of AP lower.
90 * To denote conjugate we place -- above the element. This covers the
91 * case N even and TRANSR = 'N'.
92 *
93 * RFP A RFP A
94 *
95 * -- -- --
96 * 03 04 05 33 43 53
97 * -- --
98 * 13 14 15 00 44 54
99 * --
100 * 23 24 25 10 11 55
101 *
102 * 33 34 35 20 21 22
103 * --
104 * 00 44 45 30 31 32
105 * -- --
106 * 01 11 55 40 41 42
107 * -- -- --
108 * 02 12 22 50 51 52
109 *
110 * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
111 * transpose of RFP A above. One therefore gets:
112 *
113 *
114 * RFP A RFP A
115 *
116 * -- -- -- -- -- -- -- -- -- --
117 * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
118 * -- -- -- -- -- -- -- -- -- --
119 * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
120 * -- -- -- -- -- -- -- -- -- --
121 * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
122 *
123 *
124 * We next consider Standard Packed Format when N is odd.
125 * We give an example where N = 5.
126 *
127 * AP is Upper AP is Lower
128 *
129 * 00 01 02 03 04 00
130 * 11 12 13 14 10 11
131 * 22 23 24 20 21 22
132 * 33 34 30 31 32 33
133 * 44 40 41 42 43 44
134 *
135 *
136 * Let TRANSR = 'N'. RFP holds AP as follows:
137 * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
138 * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
139 * conjugate-transpose of the first two columns of AP upper.
140 * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
141 * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
142 * conjugate-transpose of the last two columns of AP lower.
143 * To denote conjugate we place -- above the element. This covers the
144 * case N odd and TRANSR = 'N'.
145 *
146 * RFP A RFP A
147 *
148 * -- --
149 * 02 03 04 00 33 43
150 * --
151 * 12 13 14 10 11 44
152 *
153 * 22 23 24 20 21 22
154 * --
155 * 00 33 34 30 31 32
156 * -- --
157 * 01 11 44 40 41 42
158 *
159 * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
160 * transpose of RFP A above. One therefore gets:
161 *
162 *
163 * RFP A RFP A
164 *
165 * -- -- -- -- -- -- -- -- --
166 * 02 12 22 00 01 00 10 20 30 40 50
167 * -- -- -- -- -- -- -- -- --
168 * 03 13 23 33 11 33 11 21 31 41 51
169 * -- -- -- -- -- -- -- -- --
170 * 04 14 24 34 44 43 44 22 32 42 52
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175 COMPLEX*16 CONE
176 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
177 * ..
178 * .. Local Scalars ..
179 LOGICAL LOWER, NISODD, NORMALTRANSR
180 INTEGER N1, N2, K
181 * ..
182 * .. External Functions ..
183 LOGICAL LSAME
184 EXTERNAL LSAME
185 * ..
186 * .. External Subroutines ..
187 EXTERNAL XERBLA, ZTRMM, ZTRTRI
188 * ..
189 * .. Intrinsic Functions ..
190 INTRINSIC MOD
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196 INFO = 0
197 NORMALTRANSR = LSAME( TRANSR, 'N' )
198 LOWER = LSAME( UPLO, 'L' )
199 IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
200 INFO = -1
201 ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
202 INFO = -2
203 ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
204 $ THEN
205 INFO = -3
206 ELSE IF( N.LT.0 ) THEN
207 INFO = -4
208 END IF
209 IF( INFO.NE.0 ) THEN
210 CALL XERBLA( 'ZTFTRI', -INFO )
211 RETURN
212 END IF
213 *
214 * Quick return if possible
215 *
216 IF( N.EQ.0 )
217 $ RETURN
218 *
219 * If N is odd, set NISODD = .TRUE.
220 * If N is even, set K = N/2 and NISODD = .FALSE.
221 *
222 IF( MOD( N, 2 ).EQ.0 ) THEN
223 K = N / 2
224 NISODD = .FALSE.
225 ELSE
226 NISODD = .TRUE.
227 END IF
228 *
229 * Set N1 and N2 depending on LOWER
230 *
231 IF( LOWER ) THEN
232 N2 = N / 2
233 N1 = N - N2
234 ELSE
235 N1 = N / 2
236 N2 = N - N1
237 END IF
238 *
239 *
240 * start execution: there are eight cases
241 *
242 IF( NISODD ) THEN
243 *
244 * N is odd
245 *
246 IF( NORMALTRANSR ) THEN
247 *
248 * N is odd and TRANSR = 'N'
249 *
250 IF( LOWER ) THEN
251 *
252 * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
253 * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
254 * T1 -> a(0), T2 -> a(n), S -> a(n1)
255 *
256 CALL ZTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
257 IF( INFO.GT.0 )
258 $ RETURN
259 CALL ZTRMM( 'R', 'L', 'N', DIAG, N2, N1, -CONE, A( 0 ),
260 $ N, A( N1 ), N )
261 CALL ZTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
262 IF( INFO.GT.0 )
263 $ INFO = INFO + N1
264 IF( INFO.GT.0 )
265 $ RETURN
266 CALL ZTRMM( 'L', 'U', 'C', DIAG, N2, N1, CONE, A( N ), N,
267 $ A( N1 ), N )
268 *
269 ELSE
270 *
271 * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
272 * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
273 * T1 -> a(n2), T2 -> a(n1), S -> a(0)
274 *
275 CALL ZTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
276 IF( INFO.GT.0 )
277 $ RETURN
278 CALL ZTRMM( 'L', 'L', 'C', DIAG, N1, N2, -CONE, A( N2 ),
279 $ N, A( 0 ), N )
280 CALL ZTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
281 IF( INFO.GT.0 )
282 $ INFO = INFO + N1
283 IF( INFO.GT.0 )
284 $ RETURN
285 CALL ZTRMM( 'R', 'U', 'N', DIAG, N1, N2, CONE, A( N1 ),
286 $ N, A( 0 ), N )
287 *
288 END IF
289 *
290 ELSE
291 *
292 * N is odd and TRANSR = 'C'
293 *
294 IF( LOWER ) THEN
295 *
296 * SRPA for LOWER, TRANSPOSE and N is odd
297 * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
298 *
299 CALL ZTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
300 IF( INFO.GT.0 )
301 $ RETURN
302 CALL ZTRMM( 'L', 'U', 'N', DIAG, N1, N2, -CONE, A( 0 ),
303 $ N1, A( N1*N1 ), N1 )
304 CALL ZTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
305 IF( INFO.GT.0 )
306 $ INFO = INFO + N1
307 IF( INFO.GT.0 )
308 $ RETURN
309 CALL ZTRMM( 'R', 'L', 'C', DIAG, N1, N2, CONE, A( 1 ),
310 $ N1, A( N1*N1 ), N1 )
311 *
312 ELSE
313 *
314 * SRPA for UPPER, TRANSPOSE and N is odd
315 * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
316 *
317 CALL ZTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
318 IF( INFO.GT.0 )
319 $ RETURN
320 CALL ZTRMM( 'R', 'U', 'C', DIAG, N2, N1, -CONE,
321 $ A( N2*N2 ), N2, A( 0 ), N2 )
322 CALL ZTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
323 IF( INFO.GT.0 )
324 $ INFO = INFO + N1
325 IF( INFO.GT.0 )
326 $ RETURN
327 CALL ZTRMM( 'L', 'L', 'N', DIAG, N2, N1, CONE,
328 $ A( N1*N2 ), N2, A( 0 ), N2 )
329 END IF
330 *
331 END IF
332 *
333 ELSE
334 *
335 * N is even
336 *
337 IF( NORMALTRANSR ) THEN
338 *
339 * N is even and TRANSR = 'N'
340 *
341 IF( LOWER ) THEN
342 *
343 * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
344 * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
345 * T1 -> a(1), T2 -> a(0), S -> a(k+1)
346 *
347 CALL ZTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
348 IF( INFO.GT.0 )
349 $ RETURN
350 CALL ZTRMM( 'R', 'L', 'N', DIAG, K, K, -CONE, A( 1 ),
351 $ N+1, A( K+1 ), N+1 )
352 CALL ZTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
353 IF( INFO.GT.0 )
354 $ INFO = INFO + K
355 IF( INFO.GT.0 )
356 $ RETURN
357 CALL ZTRMM( 'L', 'U', 'C', DIAG, K, K, CONE, A( 0 ), N+1,
358 $ A( K+1 ), N+1 )
359 *
360 ELSE
361 *
362 * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
363 * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
364 * T1 -> a(k+1), T2 -> a(k), S -> a(0)
365 *
366 CALL ZTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
367 IF( INFO.GT.0 )
368 $ RETURN
369 CALL ZTRMM( 'L', 'L', 'C', DIAG, K, K, -CONE, A( K+1 ),
370 $ N+1, A( 0 ), N+1 )
371 CALL ZTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
372 IF( INFO.GT.0 )
373 $ INFO = INFO + K
374 IF( INFO.GT.0 )
375 $ RETURN
376 CALL ZTRMM( 'R', 'U', 'N', DIAG, K, K, CONE, A( K ), N+1,
377 $ A( 0 ), N+1 )
378 END IF
379 ELSE
380 *
381 * N is even and TRANSR = 'C'
382 *
383 IF( LOWER ) THEN
384 *
385 * SRPA for LOWER, TRANSPOSE and N is even (see paper)
386 * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
387 * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
388 *
389 CALL ZTRTRI( 'U', DIAG, K, A( K ), K, INFO )
390 IF( INFO.GT.0 )
391 $ RETURN
392 CALL ZTRMM( 'L', 'U', 'N', DIAG, K, K, -CONE, A( K ), K,
393 $ A( K*( K+1 ) ), K )
394 CALL ZTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
395 IF( INFO.GT.0 )
396 $ INFO = INFO + K
397 IF( INFO.GT.0 )
398 $ RETURN
399 CALL ZTRMM( 'R', 'L', 'C', DIAG, K, K, CONE, A( 0 ), K,
400 $ A( K*( K+1 ) ), K )
401 ELSE
402 *
403 * SRPA for UPPER, TRANSPOSE and N is even (see paper)
404 * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
405 * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
406 *
407 CALL ZTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
408 IF( INFO.GT.0 )
409 $ RETURN
410 CALL ZTRMM( 'R', 'U', 'C', DIAG, K, K, -CONE,
411 $ A( K*( K+1 ) ), K, A( 0 ), K )
412 CALL ZTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
413 IF( INFO.GT.0 )
414 $ INFO = INFO + K
415 IF( INFO.GT.0 )
416 $ RETURN
417 CALL ZTRMM( 'L', 'L', 'N', DIAG, K, K, CONE, A( K*K ), K,
418 $ A( 0 ), K )
419 END IF
420 END IF
421 END IF
422 *
423 RETURN
424 *
425 * End of ZTFTRI
426 *
427 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 COMPLEX*16 A( 0: * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * ZTFTRI 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 * = 'C': The Conjugate-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) COMPLEX*16 array, dimension ( N*(N+1)/2 );
46 * On entry, the triangular matrix A in RFP format. RFP format
47 * is described by TRANSR, UPLO, and N as follows: If TRANSR =
48 * 'N' then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
49 * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
50 * the Conjugate-transpose of RFP A as defined when
51 * TRANSR = 'N'. The contents of RFP A are defined by UPLO as
52 * follows: If UPLO = 'U' the RFP A contains the nt elements of
53 * upper packed A; If UPLO = 'L' the RFP A contains the nt
54 * elements of lower packed A. The LDA of RFP A is (N+1)/2 when
55 * TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is
56 * even and N is odd. See the Note below for more details.
57 *
58 * On exit, the (triangular) inverse of the original matrix, in
59 * the same storage format.
60 *
61 * INFO (output) INTEGER
62 * = 0: successful exit
63 * < 0: if INFO = -i, the i-th argument had an illegal value
64 * > 0: if INFO = i, A(i,i) is exactly zero. The triangular
65 * matrix is singular and its inverse can not be computed.
66 *
67 * Further Details
68 * ===============
69 *
70 * We first consider Standard Packed Format when N is even.
71 * We give an example where N = 6.
72 *
73 * AP is Upper AP is Lower
74 *
75 * 00 01 02 03 04 05 00
76 * 11 12 13 14 15 10 11
77 * 22 23 24 25 20 21 22
78 * 33 34 35 30 31 32 33
79 * 44 45 40 41 42 43 44
80 * 55 50 51 52 53 54 55
81 *
82 *
83 * Let TRANSR = 'N'. RFP holds AP as follows:
84 * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
85 * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
86 * conjugate-transpose of the first three columns of AP upper.
87 * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
88 * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
89 * conjugate-transpose of the last three columns of AP lower.
90 * To denote conjugate we place -- above the element. This covers the
91 * case N even and TRANSR = 'N'.
92 *
93 * RFP A RFP A
94 *
95 * -- -- --
96 * 03 04 05 33 43 53
97 * -- --
98 * 13 14 15 00 44 54
99 * --
100 * 23 24 25 10 11 55
101 *
102 * 33 34 35 20 21 22
103 * --
104 * 00 44 45 30 31 32
105 * -- --
106 * 01 11 55 40 41 42
107 * -- -- --
108 * 02 12 22 50 51 52
109 *
110 * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
111 * transpose of RFP A above. One therefore gets:
112 *
113 *
114 * RFP A RFP A
115 *
116 * -- -- -- -- -- -- -- -- -- --
117 * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
118 * -- -- -- -- -- -- -- -- -- --
119 * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
120 * -- -- -- -- -- -- -- -- -- --
121 * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
122 *
123 *
124 * We next consider Standard Packed Format when N is odd.
125 * We give an example where N = 5.
126 *
127 * AP is Upper AP is Lower
128 *
129 * 00 01 02 03 04 00
130 * 11 12 13 14 10 11
131 * 22 23 24 20 21 22
132 * 33 34 30 31 32 33
133 * 44 40 41 42 43 44
134 *
135 *
136 * Let TRANSR = 'N'. RFP holds AP as follows:
137 * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
138 * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
139 * conjugate-transpose of the first two columns of AP upper.
140 * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
141 * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
142 * conjugate-transpose of the last two columns of AP lower.
143 * To denote conjugate we place -- above the element. This covers the
144 * case N odd and TRANSR = 'N'.
145 *
146 * RFP A RFP A
147 *
148 * -- --
149 * 02 03 04 00 33 43
150 * --
151 * 12 13 14 10 11 44
152 *
153 * 22 23 24 20 21 22
154 * --
155 * 00 33 34 30 31 32
156 * -- --
157 * 01 11 44 40 41 42
158 *
159 * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
160 * transpose of RFP A above. One therefore gets:
161 *
162 *
163 * RFP A RFP A
164 *
165 * -- -- -- -- -- -- -- -- --
166 * 02 12 22 00 01 00 10 20 30 40 50
167 * -- -- -- -- -- -- -- -- --
168 * 03 13 23 33 11 33 11 21 31 41 51
169 * -- -- -- -- -- -- -- -- --
170 * 04 14 24 34 44 43 44 22 32 42 52
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175 COMPLEX*16 CONE
176 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
177 * ..
178 * .. Local Scalars ..
179 LOGICAL LOWER, NISODD, NORMALTRANSR
180 INTEGER N1, N2, K
181 * ..
182 * .. External Functions ..
183 LOGICAL LSAME
184 EXTERNAL LSAME
185 * ..
186 * .. External Subroutines ..
187 EXTERNAL XERBLA, ZTRMM, ZTRTRI
188 * ..
189 * .. Intrinsic Functions ..
190 INTRINSIC MOD
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196 INFO = 0
197 NORMALTRANSR = LSAME( TRANSR, 'N' )
198 LOWER = LSAME( UPLO, 'L' )
199 IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
200 INFO = -1
201 ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
202 INFO = -2
203 ELSE IF( .NOT.LSAME( DIAG, 'N' ) .AND. .NOT.LSAME( DIAG, 'U' ) )
204 $ THEN
205 INFO = -3
206 ELSE IF( N.LT.0 ) THEN
207 INFO = -4
208 END IF
209 IF( INFO.NE.0 ) THEN
210 CALL XERBLA( 'ZTFTRI', -INFO )
211 RETURN
212 END IF
213 *
214 * Quick return if possible
215 *
216 IF( N.EQ.0 )
217 $ RETURN
218 *
219 * If N is odd, set NISODD = .TRUE.
220 * If N is even, set K = N/2 and NISODD = .FALSE.
221 *
222 IF( MOD( N, 2 ).EQ.0 ) THEN
223 K = N / 2
224 NISODD = .FALSE.
225 ELSE
226 NISODD = .TRUE.
227 END IF
228 *
229 * Set N1 and N2 depending on LOWER
230 *
231 IF( LOWER ) THEN
232 N2 = N / 2
233 N1 = N - N2
234 ELSE
235 N1 = N / 2
236 N2 = N - N1
237 END IF
238 *
239 *
240 * start execution: there are eight cases
241 *
242 IF( NISODD ) THEN
243 *
244 * N is odd
245 *
246 IF( NORMALTRANSR ) THEN
247 *
248 * N is odd and TRANSR = 'N'
249 *
250 IF( LOWER ) THEN
251 *
252 * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
253 * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
254 * T1 -> a(0), T2 -> a(n), S -> a(n1)
255 *
256 CALL ZTRTRI( 'L', DIAG, N1, A( 0 ), N, INFO )
257 IF( INFO.GT.0 )
258 $ RETURN
259 CALL ZTRMM( 'R', 'L', 'N', DIAG, N2, N1, -CONE, A( 0 ),
260 $ N, A( N1 ), N )
261 CALL ZTRTRI( 'U', DIAG, N2, A( N ), N, INFO )
262 IF( INFO.GT.0 )
263 $ INFO = INFO + N1
264 IF( INFO.GT.0 )
265 $ RETURN
266 CALL ZTRMM( 'L', 'U', 'C', DIAG, N2, N1, CONE, A( N ), N,
267 $ A( N1 ), N )
268 *
269 ELSE
270 *
271 * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
272 * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
273 * T1 -> a(n2), T2 -> a(n1), S -> a(0)
274 *
275 CALL ZTRTRI( 'L', DIAG, N1, A( N2 ), N, INFO )
276 IF( INFO.GT.0 )
277 $ RETURN
278 CALL ZTRMM( 'L', 'L', 'C', DIAG, N1, N2, -CONE, A( N2 ),
279 $ N, A( 0 ), N )
280 CALL ZTRTRI( 'U', DIAG, N2, A( N1 ), N, INFO )
281 IF( INFO.GT.0 )
282 $ INFO = INFO + N1
283 IF( INFO.GT.0 )
284 $ RETURN
285 CALL ZTRMM( 'R', 'U', 'N', DIAG, N1, N2, CONE, A( N1 ),
286 $ N, A( 0 ), N )
287 *
288 END IF
289 *
290 ELSE
291 *
292 * N is odd and TRANSR = 'C'
293 *
294 IF( LOWER ) THEN
295 *
296 * SRPA for LOWER, TRANSPOSE and N is odd
297 * T1 -> a(0), T2 -> a(1), S -> a(0+n1*n1)
298 *
299 CALL ZTRTRI( 'U', DIAG, N1, A( 0 ), N1, INFO )
300 IF( INFO.GT.0 )
301 $ RETURN
302 CALL ZTRMM( 'L', 'U', 'N', DIAG, N1, N2, -CONE, A( 0 ),
303 $ N1, A( N1*N1 ), N1 )
304 CALL ZTRTRI( 'L', DIAG, N2, A( 1 ), N1, INFO )
305 IF( INFO.GT.0 )
306 $ INFO = INFO + N1
307 IF( INFO.GT.0 )
308 $ RETURN
309 CALL ZTRMM( 'R', 'L', 'C', DIAG, N1, N2, CONE, A( 1 ),
310 $ N1, A( N1*N1 ), N1 )
311 *
312 ELSE
313 *
314 * SRPA for UPPER, TRANSPOSE and N is odd
315 * T1 -> a(0+n2*n2), T2 -> a(0+n1*n2), S -> a(0)
316 *
317 CALL ZTRTRI( 'U', DIAG, N1, A( N2*N2 ), N2, INFO )
318 IF( INFO.GT.0 )
319 $ RETURN
320 CALL ZTRMM( 'R', 'U', 'C', DIAG, N2, N1, -CONE,
321 $ A( N2*N2 ), N2, A( 0 ), N2 )
322 CALL ZTRTRI( 'L', DIAG, N2, A( N1*N2 ), N2, INFO )
323 IF( INFO.GT.0 )
324 $ INFO = INFO + N1
325 IF( INFO.GT.0 )
326 $ RETURN
327 CALL ZTRMM( 'L', 'L', 'N', DIAG, N2, N1, CONE,
328 $ A( N1*N2 ), N2, A( 0 ), N2 )
329 END IF
330 *
331 END IF
332 *
333 ELSE
334 *
335 * N is even
336 *
337 IF( NORMALTRANSR ) THEN
338 *
339 * N is even and TRANSR = 'N'
340 *
341 IF( LOWER ) THEN
342 *
343 * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
344 * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
345 * T1 -> a(1), T2 -> a(0), S -> a(k+1)
346 *
347 CALL ZTRTRI( 'L', DIAG, K, A( 1 ), N+1, INFO )
348 IF( INFO.GT.0 )
349 $ RETURN
350 CALL ZTRMM( 'R', 'L', 'N', DIAG, K, K, -CONE, A( 1 ),
351 $ N+1, A( K+1 ), N+1 )
352 CALL ZTRTRI( 'U', DIAG, K, A( 0 ), N+1, INFO )
353 IF( INFO.GT.0 )
354 $ INFO = INFO + K
355 IF( INFO.GT.0 )
356 $ RETURN
357 CALL ZTRMM( 'L', 'U', 'C', DIAG, K, K, CONE, A( 0 ), N+1,
358 $ A( K+1 ), N+1 )
359 *
360 ELSE
361 *
362 * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
363 * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
364 * T1 -> a(k+1), T2 -> a(k), S -> a(0)
365 *
366 CALL ZTRTRI( 'L', DIAG, K, A( K+1 ), N+1, INFO )
367 IF( INFO.GT.0 )
368 $ RETURN
369 CALL ZTRMM( 'L', 'L', 'C', DIAG, K, K, -CONE, A( K+1 ),
370 $ N+1, A( 0 ), N+1 )
371 CALL ZTRTRI( 'U', DIAG, K, A( K ), N+1, INFO )
372 IF( INFO.GT.0 )
373 $ INFO = INFO + K
374 IF( INFO.GT.0 )
375 $ RETURN
376 CALL ZTRMM( 'R', 'U', 'N', DIAG, K, K, CONE, A( K ), N+1,
377 $ A( 0 ), N+1 )
378 END IF
379 ELSE
380 *
381 * N is even and TRANSR = 'C'
382 *
383 IF( LOWER ) THEN
384 *
385 * SRPA for LOWER, TRANSPOSE and N is even (see paper)
386 * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
387 * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
388 *
389 CALL ZTRTRI( 'U', DIAG, K, A( K ), K, INFO )
390 IF( INFO.GT.0 )
391 $ RETURN
392 CALL ZTRMM( 'L', 'U', 'N', DIAG, K, K, -CONE, A( K ), K,
393 $ A( K*( K+1 ) ), K )
394 CALL ZTRTRI( 'L', DIAG, K, A( 0 ), K, INFO )
395 IF( INFO.GT.0 )
396 $ INFO = INFO + K
397 IF( INFO.GT.0 )
398 $ RETURN
399 CALL ZTRMM( 'R', 'L', 'C', DIAG, K, K, CONE, A( 0 ), K,
400 $ A( K*( K+1 ) ), K )
401 ELSE
402 *
403 * SRPA for UPPER, TRANSPOSE and N is even (see paper)
404 * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
405 * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
406 *
407 CALL ZTRTRI( 'U', DIAG, K, A( K*( K+1 ) ), K, INFO )
408 IF( INFO.GT.0 )
409 $ RETURN
410 CALL ZTRMM( 'R', 'U', 'C', DIAG, K, K, -CONE,
411 $ A( K*( K+1 ) ), K, A( 0 ), K )
412 CALL ZTRTRI( 'L', DIAG, K, A( K*K ), K, INFO )
413 IF( INFO.GT.0 )
414 $ INFO = INFO + K
415 IF( INFO.GT.0 )
416 $ RETURN
417 CALL ZTRMM( 'L', 'L', 'N', DIAG, K, K, CONE, A( K*K ), K,
418 $ A( 0 ), K )
419 END IF
420 END IF
421 END IF
422 *
423 RETURN
424 *
425 * End of ZTFTRI
426 *
427 END