1: *> \brief \b DTFTTR copies a triangular matrix from the rectangular full packed format (TF) to the standard full format (TR).
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DTFTTR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtfttr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtfttr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtfttr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER TRANSR, UPLO
25: * INTEGER INFO, N, LDA
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION A( 0: LDA-1, 0: * ), ARF( 0: * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DTFTTR copies a triangular matrix A from rectangular full packed
38: *> format (TF) to standard full format (TR).
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] TRANSR
45: *> \verbatim
46: *> TRANSR is CHARACTER*1
47: *> = 'N': ARF is in Normal format;
48: *> = 'T': ARF is in Transpose format.
49: *> \endverbatim
50: *>
51: *> \param[in] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> = 'U': A is upper triangular;
55: *> = 'L': A is lower triangular.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the matrices ARF and A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in] ARF
65: *> \verbatim
66: *> ARF is DOUBLE PRECISION array, dimension (N*(N+1)/2).
67: *> On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
68: *> matrix A in RFP format. See the "Notes" below for more
69: *> details.
70: *> \endverbatim
71: *>
72: *> \param[out] A
73: *> \verbatim
74: *> A is DOUBLE PRECISION array, dimension (LDA,N)
75: *> On exit, the triangular matrix A. If UPLO = 'U', the
76: *> leading N-by-N upper triangular part of the array A contains
77: *> the upper triangular matrix, and the strictly lower
78: *> triangular part of A is not referenced. If UPLO = 'L', the
79: *> leading N-by-N lower triangular part of the array A contains
80: *> the lower triangular matrix, and the strictly upper
81: *> triangular part of A is not referenced.
82: *> \endverbatim
83: *>
84: *> \param[in] LDA
85: *> \verbatim
86: *> LDA is INTEGER
87: *> The leading dimension of the array A. LDA >= max(1,N).
88: *> \endverbatim
89: *>
90: *> \param[out] INFO
91: *> \verbatim
92: *> INFO is INTEGER
93: *> = 0: successful exit
94: *> < 0: if INFO = -i, the i-th argument had an illegal value
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: *> \date September 2012
106: *
107: *> \ingroup doubleOTHERcomputational
108: *
109: *> \par Further Details:
110: * =====================
111: *>
112: *> \verbatim
113: *>
114: *> We first consider Rectangular Full Packed (RFP) Format when N is
115: *> even. We give an example where N = 6.
116: *>
117: *> AP is Upper AP is Lower
118: *>
119: *> 00 01 02 03 04 05 00
120: *> 11 12 13 14 15 10 11
121: *> 22 23 24 25 20 21 22
122: *> 33 34 35 30 31 32 33
123: *> 44 45 40 41 42 43 44
124: *> 55 50 51 52 53 54 55
125: *>
126: *>
127: *> Let TRANSR = 'N'. RFP holds AP as follows:
128: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
129: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
130: *> the transpose of the first three columns of AP upper.
131: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
132: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
133: *> the transpose of the last three columns of AP lower.
134: *> This covers the case N even and TRANSR = 'N'.
135: *>
136: *> RFP A RFP A
137: *>
138: *> 03 04 05 33 43 53
139: *> 13 14 15 00 44 54
140: *> 23 24 25 10 11 55
141: *> 33 34 35 20 21 22
142: *> 00 44 45 30 31 32
143: *> 01 11 55 40 41 42
144: *> 02 12 22 50 51 52
145: *>
146: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
147: *> transpose of RFP A above. One therefore gets:
148: *>
149: *>
150: *> RFP A RFP A
151: *>
152: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
153: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
154: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
155: *>
156: *>
157: *> We then consider Rectangular Full Packed (RFP) Format when N is
158: *> odd. We give an example where N = 5.
159: *>
160: *> AP is Upper AP is Lower
161: *>
162: *> 00 01 02 03 04 00
163: *> 11 12 13 14 10 11
164: *> 22 23 24 20 21 22
165: *> 33 34 30 31 32 33
166: *> 44 40 41 42 43 44
167: *>
168: *>
169: *> Let TRANSR = 'N'. RFP holds AP as follows:
170: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
171: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
172: *> the transpose of the first two columns of AP upper.
173: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
174: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
175: *> the transpose of the last two columns of AP lower.
176: *> This covers the case N odd and TRANSR = 'N'.
177: *>
178: *> RFP A RFP A
179: *>
180: *> 02 03 04 00 33 43
181: *> 12 13 14 10 11 44
182: *> 22 23 24 20 21 22
183: *> 00 33 34 30 31 32
184: *> 01 11 44 40 41 42
185: *>
186: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
187: *> transpose of RFP A above. One therefore gets:
188: *>
189: *> RFP A RFP A
190: *>
191: *> 02 12 22 00 01 00 10 20 30 40 50
192: *> 03 13 23 33 11 33 11 21 31 41 51
193: *> 04 14 24 34 44 43 44 22 32 42 52
194: *> \endverbatim
195: *
196: * =====================================================================
197: SUBROUTINE DTFTTR( TRANSR, UPLO, N, ARF, A, LDA, INFO )
198: *
199: * -- LAPACK computational routine (version 3.4.2) --
200: * -- LAPACK is a software package provided by Univ. of Tennessee, --
201: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
202: * September 2012
203: *
204: * .. Scalar Arguments ..
205: CHARACTER TRANSR, UPLO
206: INTEGER INFO, N, LDA
207: * ..
208: * .. Array Arguments ..
209: DOUBLE PRECISION A( 0: LDA-1, 0: * ), ARF( 0: * )
210: * ..
211: *
212: * =====================================================================
213: *
214: * ..
215: * .. Local Scalars ..
216: LOGICAL LOWER, NISODD, NORMALTRANSR
217: INTEGER N1, N2, K, NT, NX2, NP1X2
218: INTEGER I, J, L, IJ
219: * ..
220: * .. External Functions ..
221: LOGICAL LSAME
222: EXTERNAL LSAME
223: * ..
224: * .. External Subroutines ..
225: EXTERNAL XERBLA
226: * ..
227: * .. Intrinsic Functions ..
228: INTRINSIC MAX, MOD
229: * ..
230: * .. Executable Statements ..
231: *
232: * Test the input parameters.
233: *
234: INFO = 0
235: NORMALTRANSR = LSAME( TRANSR, 'N' )
236: LOWER = LSAME( UPLO, 'L' )
237: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
238: INFO = -1
239: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
240: INFO = -2
241: ELSE IF( N.LT.0 ) THEN
242: INFO = -3
243: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
244: INFO = -6
245: END IF
246: IF( INFO.NE.0 ) THEN
247: CALL XERBLA( 'DTFTTR', -INFO )
248: RETURN
249: END IF
250: *
251: * Quick return if possible
252: *
253: IF( N.LE.1 ) THEN
254: IF( N.EQ.1 ) THEN
255: A( 0, 0 ) = ARF( 0 )
256: END IF
257: RETURN
258: END IF
259: *
260: * Size of array ARF(0:nt-1)
261: *
262: NT = N*( N+1 ) / 2
263: *
264: * set N1 and N2 depending on LOWER: for N even N1=N2=K
265: *
266: IF( LOWER ) THEN
267: N2 = N / 2
268: N1 = N - N2
269: ELSE
270: N1 = N / 2
271: N2 = N - N1
272: END IF
273: *
274: * If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2.
275: * If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is
276: * N--by--(N+1)/2.
277: *
278: IF( MOD( N, 2 ).EQ.0 ) THEN
279: K = N / 2
280: NISODD = .FALSE.
281: IF( .NOT.LOWER )
282: $ NP1X2 = N + N + 2
283: ELSE
284: NISODD = .TRUE.
285: IF( .NOT.LOWER )
286: $ NX2 = N + N
287: END IF
288: *
289: IF( NISODD ) THEN
290: *
291: * N is odd
292: *
293: IF( NORMALTRANSR ) THEN
294: *
295: * N is odd and TRANSR = 'N'
296: *
297: IF( LOWER ) THEN
298: *
299: * N is odd, TRANSR = 'N', and UPLO = 'L'
300: *
301: IJ = 0
302: DO J = 0, N2
303: DO I = N1, N2 + J
304: A( N2+J, I ) = ARF( IJ )
305: IJ = IJ + 1
306: END DO
307: DO I = J, N - 1
308: A( I, J ) = ARF( IJ )
309: IJ = IJ + 1
310: END DO
311: END DO
312: *
313: ELSE
314: *
315: * N is odd, TRANSR = 'N', and UPLO = 'U'
316: *
317: IJ = NT - N
318: DO J = N - 1, N1, -1
319: DO I = 0, J
320: A( I, J ) = ARF( IJ )
321: IJ = IJ + 1
322: END DO
323: DO L = J - N1, N1 - 1
324: A( J-N1, L ) = ARF( IJ )
325: IJ = IJ + 1
326: END DO
327: IJ = IJ - NX2
328: END DO
329: *
330: END IF
331: *
332: ELSE
333: *
334: * N is odd and TRANSR = 'T'
335: *
336: IF( LOWER ) THEN
337: *
338: * N is odd, TRANSR = 'T', and UPLO = 'L'
339: *
340: IJ = 0
341: DO J = 0, N2 - 1
342: DO I = 0, J
343: A( J, I ) = ARF( IJ )
344: IJ = IJ + 1
345: END DO
346: DO I = N1 + J, N - 1
347: A( I, N1+J ) = ARF( IJ )
348: IJ = IJ + 1
349: END DO
350: END DO
351: DO J = N2, N - 1
352: DO I = 0, N1 - 1
353: A( J, I ) = ARF( IJ )
354: IJ = IJ + 1
355: END DO
356: END DO
357: *
358: ELSE
359: *
360: * N is odd, TRANSR = 'T', and UPLO = 'U'
361: *
362: IJ = 0
363: DO J = 0, N1
364: DO I = N1, N - 1
365: A( J, I ) = ARF( IJ )
366: IJ = IJ + 1
367: END DO
368: END DO
369: DO J = 0, N1 - 1
370: DO I = 0, J
371: A( I, J ) = ARF( IJ )
372: IJ = IJ + 1
373: END DO
374: DO L = N2 + J, N - 1
375: A( N2+J, L ) = ARF( IJ )
376: IJ = IJ + 1
377: END DO
378: END DO
379: *
380: END IF
381: *
382: END IF
383: *
384: ELSE
385: *
386: * N is even
387: *
388: IF( NORMALTRANSR ) THEN
389: *
390: * N is even and TRANSR = 'N'
391: *
392: IF( LOWER ) THEN
393: *
394: * N is even, TRANSR = 'N', and UPLO = 'L'
395: *
396: IJ = 0
397: DO J = 0, K - 1
398: DO I = K, K + J
399: A( K+J, I ) = ARF( IJ )
400: IJ = IJ + 1
401: END DO
402: DO I = J, N - 1
403: A( I, J ) = ARF( IJ )
404: IJ = IJ + 1
405: END DO
406: END DO
407: *
408: ELSE
409: *
410: * N is even, TRANSR = 'N', and UPLO = 'U'
411: *
412: IJ = NT - N - 1
413: DO J = N - 1, K, -1
414: DO I = 0, J
415: A( I, J ) = ARF( IJ )
416: IJ = IJ + 1
417: END DO
418: DO L = J - K, K - 1
419: A( J-K, L ) = ARF( IJ )
420: IJ = IJ + 1
421: END DO
422: IJ = IJ - NP1X2
423: END DO
424: *
425: END IF
426: *
427: ELSE
428: *
429: * N is even and TRANSR = 'T'
430: *
431: IF( LOWER ) THEN
432: *
433: * N is even, TRANSR = 'T', and UPLO = 'L'
434: *
435: IJ = 0
436: J = K
437: DO I = K, N - 1
438: A( I, J ) = ARF( IJ )
439: IJ = IJ + 1
440: END DO
441: DO J = 0, K - 2
442: DO I = 0, J
443: A( J, I ) = ARF( IJ )
444: IJ = IJ + 1
445: END DO
446: DO I = K + 1 + J, N - 1
447: A( I, K+1+J ) = ARF( IJ )
448: IJ = IJ + 1
449: END DO
450: END DO
451: DO J = K - 1, N - 1
452: DO I = 0, K - 1
453: A( J, I ) = ARF( IJ )
454: IJ = IJ + 1
455: END DO
456: END DO
457: *
458: ELSE
459: *
460: * N is even, TRANSR = 'T', and UPLO = 'U'
461: *
462: IJ = 0
463: DO J = 0, K
464: DO I = K, N - 1
465: A( J, I ) = ARF( IJ )
466: IJ = IJ + 1
467: END DO
468: END DO
469: DO J = 0, K - 2
470: DO I = 0, J
471: A( I, J ) = ARF( IJ )
472: IJ = IJ + 1
473: END DO
474: DO L = K + 1 + J, N - 1
475: A( K+1+J, L ) = ARF( IJ )
476: IJ = IJ + 1
477: END DO
478: END DO
479: * Note that here, on exit of the loop, J = K-1
480: DO I = 0, J
481: A( I, J ) = ARF( IJ )
482: IJ = IJ + 1
483: END DO
484: *
485: END IF
486: *
487: END IF
488: *
489: END IF
490: *
491: RETURN
492: *
493: * End of DTFTTR
494: *
495: END
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