1: *> \brief \b DTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DTFTTP + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtfttp.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtfttp.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtfttp.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER TRANSR, UPLO
25: * INTEGER INFO, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DTFTTP copies a triangular matrix A from rectangular full packed
38: *> format (TF) to standard packed format (TP).
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 matrix 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 or lower triangular matrix A stored in
68: *> RFP format. For a further discussion see Notes below.
69: *> \endverbatim
70: *>
71: *> \param[out] AP
72: *> \verbatim
73: *> AP is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
74: *> On exit, the upper or lower triangular matrix A, packed
75: *> columnwise in a linear array. The j-th column of A is stored
76: *> in the array AP as follows:
77: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
78: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
79: *> \endverbatim
80: *>
81: *> \param[out] INFO
82: *> \verbatim
83: *> INFO is INTEGER
84: *> = 0: successful exit
85: *> < 0: if INFO = -i, the i-th argument had an illegal value
86: *> \endverbatim
87: *
88: * Authors:
89: * ========
90: *
91: *> \author Univ. of Tennessee
92: *> \author Univ. of California Berkeley
93: *> \author Univ. of Colorado Denver
94: *> \author NAG Ltd.
95: *
96: *> \ingroup doubleOTHERcomputational
97: *
98: *> \par Further Details:
99: * =====================
100: *>
101: *> \verbatim
102: *>
103: *> We first consider Rectangular Full Packed (RFP) Format when N is
104: *> even. We give an example where N = 6.
105: *>
106: *> AP is Upper AP is Lower
107: *>
108: *> 00 01 02 03 04 05 00
109: *> 11 12 13 14 15 10 11
110: *> 22 23 24 25 20 21 22
111: *> 33 34 35 30 31 32 33
112: *> 44 45 40 41 42 43 44
113: *> 55 50 51 52 53 54 55
114: *>
115: *>
116: *> Let TRANSR = 'N'. RFP holds AP as follows:
117: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
118: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
119: *> the transpose of the first three columns of AP upper.
120: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
121: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
122: *> the transpose of the last three columns of AP lower.
123: *> This covers the case N even and TRANSR = 'N'.
124: *>
125: *> RFP A RFP A
126: *>
127: *> 03 04 05 33 43 53
128: *> 13 14 15 00 44 54
129: *> 23 24 25 10 11 55
130: *> 33 34 35 20 21 22
131: *> 00 44 45 30 31 32
132: *> 01 11 55 40 41 42
133: *> 02 12 22 50 51 52
134: *>
135: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
136: *> transpose of RFP A above. One therefore gets:
137: *>
138: *>
139: *> RFP A RFP A
140: *>
141: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
142: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
143: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
144: *>
145: *>
146: *> We then consider Rectangular Full Packed (RFP) Format when N is
147: *> odd. We give an example where N = 5.
148: *>
149: *> AP is Upper AP is Lower
150: *>
151: *> 00 01 02 03 04 00
152: *> 11 12 13 14 10 11
153: *> 22 23 24 20 21 22
154: *> 33 34 30 31 32 33
155: *> 44 40 41 42 43 44
156: *>
157: *>
158: *> Let TRANSR = 'N'. RFP holds AP as follows:
159: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
160: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
161: *> the transpose of the first two columns of AP upper.
162: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
163: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
164: *> the transpose of the last two columns of AP lower.
165: *> This covers the case N odd and TRANSR = 'N'.
166: *>
167: *> RFP A RFP A
168: *>
169: *> 02 03 04 00 33 43
170: *> 12 13 14 10 11 44
171: *> 22 23 24 20 21 22
172: *> 00 33 34 30 31 32
173: *> 01 11 44 40 41 42
174: *>
175: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
176: *> transpose of RFP A above. One therefore gets:
177: *>
178: *> RFP A RFP A
179: *>
180: *> 02 12 22 00 01 00 10 20 30 40 50
181: *> 03 13 23 33 11 33 11 21 31 41 51
182: *> 04 14 24 34 44 43 44 22 32 42 52
183: *> \endverbatim
184: *>
185: * =====================================================================
186: SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
187: *
188: * -- LAPACK computational routine --
189: * -- LAPACK is a software package provided by Univ. of Tennessee, --
190: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
191: *
192: * .. Scalar Arguments ..
193: CHARACTER TRANSR, UPLO
194: INTEGER INFO, N
195: * ..
196: * .. Array Arguments ..
197: DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
198: * ..
199: *
200: * =====================================================================
201: *
202: * .. Parameters ..
203: * ..
204: * .. Local Scalars ..
205: LOGICAL LOWER, NISODD, NORMALTRANSR
206: INTEGER N1, N2, K, NT
207: INTEGER I, J, IJ
208: INTEGER IJP, JP, LDA, JS
209: * ..
210: * .. External Functions ..
211: LOGICAL LSAME
212: EXTERNAL LSAME
213: * ..
214: * .. External Subroutines ..
215: EXTERNAL XERBLA
216: * ..
217: * .. Executable Statements ..
218: *
219: * Test the input parameters.
220: *
221: INFO = 0
222: NORMALTRANSR = LSAME( TRANSR, 'N' )
223: LOWER = LSAME( UPLO, 'L' )
224: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
225: INFO = -1
226: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
227: INFO = -2
228: ELSE IF( N.LT.0 ) THEN
229: INFO = -3
230: END IF
231: IF( INFO.NE.0 ) THEN
232: CALL XERBLA( 'DTFTTP', -INFO )
233: RETURN
234: END IF
235: *
236: * Quick return if possible
237: *
238: IF( N.EQ.0 )
239: $ RETURN
240: *
241: IF( N.EQ.1 ) THEN
242: IF( NORMALTRANSR ) THEN
243: AP( 0 ) = ARF( 0 )
244: ELSE
245: AP( 0 ) = ARF( 0 )
246: END IF
247: RETURN
248: END IF
249: *
250: * Size of array ARF(0:NT-1)
251: *
252: NT = N*( N+1 ) / 2
253: *
254: * Set N1 and N2 depending on LOWER
255: *
256: IF( LOWER ) THEN
257: N2 = N / 2
258: N1 = N - N2
259: ELSE
260: N1 = N / 2
261: N2 = N - N1
262: END IF
263: *
264: * If N is odd, set NISODD = .TRUE.
265: * If N is even, set K = N/2 and NISODD = .FALSE.
266: *
267: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
268: * where noe = 0 if n is even, noe = 1 if n is odd
269: *
270: IF( MOD( N, 2 ).EQ.0 ) THEN
271: K = N / 2
272: NISODD = .FALSE.
273: LDA = N + 1
274: ELSE
275: NISODD = .TRUE.
276: LDA = N
277: END IF
278: *
279: * ARF^C has lda rows and n+1-noe cols
280: *
281: IF( .NOT.NORMALTRANSR )
282: $ LDA = ( N+1 ) / 2
283: *
284: * start execution: there are eight cases
285: *
286: IF( NISODD ) THEN
287: *
288: * N is odd
289: *
290: IF( NORMALTRANSR ) THEN
291: *
292: * N is odd and TRANSR = 'N'
293: *
294: IF( LOWER ) THEN
295: *
296: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
297: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
298: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
299: *
300: IJP = 0
301: JP = 0
302: DO J = 0, N2
303: DO I = J, N - 1
304: IJ = I + JP
305: AP( IJP ) = ARF( IJ )
306: IJP = IJP + 1
307: END DO
308: JP = JP + LDA
309: END DO
310: DO I = 0, N2 - 1
311: DO J = 1 + I, N2
312: IJ = I + J*LDA
313: AP( IJP ) = ARF( IJ )
314: IJP = IJP + 1
315: END DO
316: END DO
317: *
318: ELSE
319: *
320: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
321: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
322: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
323: *
324: IJP = 0
325: DO J = 0, N1 - 1
326: IJ = N2 + J
327: DO I = 0, J
328: AP( IJP ) = ARF( IJ )
329: IJP = IJP + 1
330: IJ = IJ + LDA
331: END DO
332: END DO
333: JS = 0
334: DO J = N1, N - 1
335: IJ = JS
336: DO IJ = JS, JS + J
337: AP( IJP ) = ARF( IJ )
338: IJP = IJP + 1
339: END DO
340: JS = JS + LDA
341: END DO
342: *
343: END IF
344: *
345: ELSE
346: *
347: * N is odd and TRANSR = 'T'
348: *
349: IF( LOWER ) THEN
350: *
351: * SRPA for LOWER, TRANSPOSE and N is odd
352: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
353: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
354: *
355: IJP = 0
356: DO I = 0, N2
357: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
358: AP( IJP ) = ARF( IJ )
359: IJP = IJP + 1
360: END DO
361: END DO
362: JS = 1
363: DO J = 0, N2 - 1
364: DO IJ = JS, JS + N2 - J - 1
365: AP( IJP ) = ARF( IJ )
366: IJP = IJP + 1
367: END DO
368: JS = JS + LDA + 1
369: END DO
370: *
371: ELSE
372: *
373: * SRPA for UPPER, TRANSPOSE and N is odd
374: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
375: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
376: *
377: IJP = 0
378: JS = N2*LDA
379: DO J = 0, N1 - 1
380: DO IJ = JS, JS + J
381: AP( IJP ) = ARF( IJ )
382: IJP = IJP + 1
383: END DO
384: JS = JS + LDA
385: END DO
386: DO I = 0, N1
387: DO IJ = I, I + ( N1+I )*LDA, LDA
388: AP( IJP ) = ARF( IJ )
389: IJP = IJP + 1
390: END DO
391: END DO
392: *
393: END IF
394: *
395: END IF
396: *
397: ELSE
398: *
399: * N is even
400: *
401: IF( NORMALTRANSR ) THEN
402: *
403: * N is even and TRANSR = 'N'
404: *
405: IF( LOWER ) THEN
406: *
407: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
408: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
409: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
410: *
411: IJP = 0
412: JP = 0
413: DO J = 0, K - 1
414: DO I = J, N - 1
415: IJ = 1 + I + JP
416: AP( IJP ) = ARF( IJ )
417: IJP = IJP + 1
418: END DO
419: JP = JP + LDA
420: END DO
421: DO I = 0, K - 1
422: DO J = I, K - 1
423: IJ = I + J*LDA
424: AP( IJP ) = ARF( IJ )
425: IJP = IJP + 1
426: END DO
427: END DO
428: *
429: ELSE
430: *
431: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
432: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
433: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
434: *
435: IJP = 0
436: DO J = 0, K - 1
437: IJ = K + 1 + J
438: DO I = 0, J
439: AP( IJP ) = ARF( IJ )
440: IJP = IJP + 1
441: IJ = IJ + LDA
442: END DO
443: END DO
444: JS = 0
445: DO J = K, N - 1
446: IJ = JS
447: DO IJ = JS, JS + J
448: AP( IJP ) = ARF( IJ )
449: IJP = IJP + 1
450: END DO
451: JS = JS + LDA
452: END DO
453: *
454: END IF
455: *
456: ELSE
457: *
458: * N is even and TRANSR = 'T'
459: *
460: IF( LOWER ) THEN
461: *
462: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
463: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
464: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
465: *
466: IJP = 0
467: DO I = 0, K - 1
468: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
469: AP( IJP ) = ARF( IJ )
470: IJP = IJP + 1
471: END DO
472: END DO
473: JS = 0
474: DO J = 0, K - 1
475: DO IJ = JS, JS + K - J - 1
476: AP( IJP ) = ARF( IJ )
477: IJP = IJP + 1
478: END DO
479: JS = JS + LDA + 1
480: END DO
481: *
482: ELSE
483: *
484: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
485: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
486: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
487: *
488: IJP = 0
489: JS = ( K+1 )*LDA
490: DO J = 0, K - 1
491: DO IJ = JS, JS + J
492: AP( IJP ) = ARF( IJ )
493: IJP = IJP + 1
494: END DO
495: JS = JS + LDA
496: END DO
497: DO I = 0, K - 1
498: DO IJ = I, I + ( K+I )*LDA, LDA
499: AP( IJP ) = ARF( IJ )
500: IJP = IJP + 1
501: END DO
502: END DO
503: *
504: END IF
505: *
506: END IF
507: *
508: END IF
509: *
510: RETURN
511: *
512: * End of DTFTTP
513: *
514: END
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