Annotation of rpl/lapack/lapack/dtfttp.f, revision 1.14
1.10 bertrand 1: *> \brief \b DTFTTP copies a triangular matrix from the rectangular full packed format (TF) to the standard packed format (TP).
1.1 bertrand 2: *
1.7 bertrand 3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.14 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
1.7 bertrand 8: *> \htmlonly
1.14 ! bertrand 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">
1.7 bertrand 15: *> [TXT]</a>
1.14 ! bertrand 16: *> \endhtmlonly
1.7 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
1.14 ! bertrand 22: *
1.7 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER TRANSR, UPLO
25: * INTEGER INFO, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
29: * ..
1.14 ! bertrand 30: *
1.7 bertrand 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: *
1.14 ! bertrand 91: *> \author Univ. of Tennessee
! 92: *> \author Univ. of California Berkeley
! 93: *> \author Univ. of Colorado Denver
! 94: *> \author NAG Ltd.
1.7 bertrand 95: *
1.14 ! bertrand 96: *> \date December 2016
1.7 bertrand 97: *
98: *> \ingroup doubleOTHERcomputational
99: *
100: *> \par Further Details:
101: * =====================
102: *>
103: *> \verbatim
104: *>
105: *> We first consider Rectangular Full Packed (RFP) Format when N is
106: *> even. We give an example where N = 6.
107: *>
108: *> AP is Upper AP is Lower
109: *>
110: *> 00 01 02 03 04 05 00
111: *> 11 12 13 14 15 10 11
112: *> 22 23 24 25 20 21 22
113: *> 33 34 35 30 31 32 33
114: *> 44 45 40 41 42 43 44
115: *> 55 50 51 52 53 54 55
116: *>
117: *>
118: *> Let TRANSR = 'N'. RFP holds AP as follows:
119: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
120: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
121: *> the transpose of the first three columns of AP upper.
122: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
123: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
124: *> the transpose of the last three columns of AP lower.
125: *> This covers the case N even and TRANSR = 'N'.
126: *>
127: *> RFP A RFP A
128: *>
129: *> 03 04 05 33 43 53
130: *> 13 14 15 00 44 54
131: *> 23 24 25 10 11 55
132: *> 33 34 35 20 21 22
133: *> 00 44 45 30 31 32
134: *> 01 11 55 40 41 42
135: *> 02 12 22 50 51 52
136: *>
137: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
138: *> transpose of RFP A above. One therefore gets:
139: *>
140: *>
141: *> RFP A RFP A
142: *>
143: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
144: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
145: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
146: *>
147: *>
148: *> We then consider Rectangular Full Packed (RFP) Format when N is
149: *> odd. We give an example where N = 5.
150: *>
151: *> AP is Upper AP is Lower
152: *>
153: *> 00 01 02 03 04 00
154: *> 11 12 13 14 10 11
155: *> 22 23 24 20 21 22
156: *> 33 34 30 31 32 33
157: *> 44 40 41 42 43 44
158: *>
159: *>
160: *> Let TRANSR = 'N'. RFP holds AP as follows:
161: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
162: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
163: *> the transpose of the first two columns of AP upper.
164: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
165: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
166: *> the transpose of the last two columns of AP lower.
167: *> This covers the case N odd and TRANSR = 'N'.
168: *>
169: *> RFP A RFP A
170: *>
171: *> 02 03 04 00 33 43
172: *> 12 13 14 10 11 44
173: *> 22 23 24 20 21 22
174: *> 00 33 34 30 31 32
175: *> 01 11 44 40 41 42
176: *>
177: *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
178: *> transpose of RFP A above. One therefore gets:
179: *>
180: *> RFP A RFP A
181: *>
182: *> 02 12 22 00 01 00 10 20 30 40 50
183: *> 03 13 23 33 11 33 11 21 31 41 51
184: *> 04 14 24 34 44 43 44 22 32 42 52
185: *> \endverbatim
186: *>
187: * =====================================================================
188: SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
189: *
1.14 ! bertrand 190: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 191: * -- LAPACK is a software package provided by Univ. of Tennessee, --
192: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 ! bertrand 193: * December 2016
1.1 bertrand 194: *
195: * .. Scalar Arguments ..
196: CHARACTER TRANSR, UPLO
197: INTEGER INFO, N
198: * ..
199: * .. Array Arguments ..
200: DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
201: * ..
202: *
203: * =====================================================================
204: *
205: * .. Parameters ..
206: * ..
207: * .. Local Scalars ..
208: LOGICAL LOWER, NISODD, NORMALTRANSR
209: INTEGER N1, N2, K, NT
210: INTEGER I, J, IJ
211: INTEGER IJP, JP, LDA, JS
212: * ..
213: * .. External Functions ..
214: LOGICAL LSAME
215: EXTERNAL LSAME
216: * ..
217: * .. External Subroutines ..
218: EXTERNAL XERBLA
219: * ..
220: * .. Executable Statements ..
221: *
222: * Test the input parameters.
223: *
224: INFO = 0
225: NORMALTRANSR = LSAME( TRANSR, 'N' )
226: LOWER = LSAME( UPLO, 'L' )
227: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
228: INFO = -1
229: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
230: INFO = -2
231: ELSE IF( N.LT.0 ) THEN
232: INFO = -3
233: END IF
234: IF( INFO.NE.0 ) THEN
235: CALL XERBLA( 'DTFTTP', -INFO )
236: RETURN
237: END IF
238: *
239: * Quick return if possible
240: *
241: IF( N.EQ.0 )
1.6 bertrand 242: $ RETURN
1.1 bertrand 243: *
244: IF( N.EQ.1 ) THEN
245: IF( NORMALTRANSR ) THEN
246: AP( 0 ) = ARF( 0 )
247: ELSE
248: AP( 0 ) = ARF( 0 )
249: END IF
250: RETURN
251: END IF
252: *
253: * Size of array ARF(0:NT-1)
254: *
255: NT = N*( N+1 ) / 2
256: *
257: * Set N1 and N2 depending on LOWER
258: *
259: IF( LOWER ) THEN
260: N2 = N / 2
261: N1 = N - N2
262: ELSE
263: N1 = N / 2
264: N2 = N - N1
265: END IF
266: *
267: * If N is odd, set NISODD = .TRUE.
268: * If N is even, set K = N/2 and NISODD = .FALSE.
269: *
270: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
271: * where noe = 0 if n is even, noe = 1 if n is odd
272: *
273: IF( MOD( N, 2 ).EQ.0 ) THEN
274: K = N / 2
275: NISODD = .FALSE.
276: LDA = N + 1
277: ELSE
278: NISODD = .TRUE.
279: LDA = N
280: END IF
281: *
282: * ARF^C has lda rows and n+1-noe cols
283: *
284: IF( .NOT.NORMALTRANSR )
1.6 bertrand 285: $ LDA = ( N+1 ) / 2
1.1 bertrand 286: *
287: * start execution: there are eight cases
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: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
300: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
301: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
302: *
303: IJP = 0
304: JP = 0
305: DO J = 0, N2
306: DO I = J, N - 1
307: IJ = I + JP
308: AP( IJP ) = ARF( IJ )
309: IJP = IJP + 1
310: END DO
311: JP = JP + LDA
312: END DO
313: DO I = 0, N2 - 1
314: DO J = 1 + I, N2
315: IJ = I + J*LDA
316: AP( IJP ) = ARF( IJ )
317: IJP = IJP + 1
318: END DO
319: END DO
320: *
321: ELSE
322: *
323: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
324: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
325: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
326: *
327: IJP = 0
328: DO J = 0, N1 - 1
329: IJ = N2 + J
330: DO I = 0, J
331: AP( IJP ) = ARF( IJ )
332: IJP = IJP + 1
333: IJ = IJ + LDA
334: END DO
335: END DO
336: JS = 0
337: DO J = N1, N - 1
338: IJ = JS
339: DO IJ = JS, JS + J
340: AP( IJP ) = ARF( IJ )
341: IJP = IJP + 1
342: END DO
343: JS = JS + LDA
344: END DO
345: *
346: END IF
347: *
348: ELSE
349: *
350: * N is odd and TRANSR = 'T'
351: *
352: IF( LOWER ) THEN
353: *
354: * SRPA for LOWER, TRANSPOSE and N is odd
355: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
356: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
357: *
358: IJP = 0
359: DO I = 0, N2
360: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
361: AP( IJP ) = ARF( IJ )
362: IJP = IJP + 1
363: END DO
364: END DO
365: JS = 1
366: DO J = 0, N2 - 1
367: DO IJ = JS, JS + N2 - J - 1
368: AP( IJP ) = ARF( IJ )
369: IJP = IJP + 1
370: END DO
371: JS = JS + LDA + 1
372: END DO
373: *
374: ELSE
375: *
376: * SRPA for UPPER, TRANSPOSE and N is odd
377: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
378: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
379: *
380: IJP = 0
381: JS = N2*LDA
382: DO J = 0, N1 - 1
383: DO IJ = JS, JS + J
384: AP( IJP ) = ARF( IJ )
385: IJP = IJP + 1
386: END DO
387: JS = JS + LDA
388: END DO
389: DO I = 0, N1
390: DO IJ = I, I + ( N1+I )*LDA, LDA
391: AP( IJP ) = ARF( IJ )
392: IJP = IJP + 1
393: END DO
394: END DO
395: *
396: END IF
397: *
398: END IF
399: *
400: ELSE
401: *
402: * N is even
403: *
404: IF( NORMALTRANSR ) THEN
405: *
406: * N is even and TRANSR = 'N'
407: *
408: IF( LOWER ) THEN
409: *
410: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
411: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
412: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
413: *
414: IJP = 0
415: JP = 0
416: DO J = 0, K - 1
417: DO I = J, N - 1
418: IJ = 1 + I + JP
419: AP( IJP ) = ARF( IJ )
420: IJP = IJP + 1
421: END DO
422: JP = JP + LDA
423: END DO
424: DO I = 0, K - 1
425: DO J = I, K - 1
426: IJ = I + J*LDA
427: AP( IJP ) = ARF( IJ )
428: IJP = IJP + 1
429: END DO
430: END DO
431: *
432: ELSE
433: *
434: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
435: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
436: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
437: *
438: IJP = 0
439: DO J = 0, K - 1
440: IJ = K + 1 + J
441: DO I = 0, J
442: AP( IJP ) = ARF( IJ )
443: IJP = IJP + 1
444: IJ = IJ + LDA
445: END DO
446: END DO
447: JS = 0
448: DO J = K, N - 1
449: IJ = JS
450: DO IJ = JS, JS + J
451: AP( IJP ) = ARF( IJ )
452: IJP = IJP + 1
453: END DO
454: JS = JS + LDA
455: END DO
456: *
457: END IF
458: *
459: ELSE
460: *
461: * N is even and TRANSR = 'T'
462: *
463: IF( LOWER ) THEN
464: *
465: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
466: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
467: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
468: *
469: IJP = 0
470: DO I = 0, K - 1
471: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
472: AP( IJP ) = ARF( IJ )
473: IJP = IJP + 1
474: END DO
475: END DO
476: JS = 0
477: DO J = 0, K - 1
478: DO IJ = JS, JS + K - J - 1
479: AP( IJP ) = ARF( IJ )
480: IJP = IJP + 1
481: END DO
482: JS = JS + LDA + 1
483: END DO
484: *
485: ELSE
486: *
487: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
488: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
489: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
490: *
491: IJP = 0
492: JS = ( K+1 )*LDA
493: DO J = 0, K - 1
494: DO IJ = JS, JS + J
495: AP( IJP ) = ARF( IJ )
496: IJP = IJP + 1
497: END DO
498: JS = JS + LDA
499: END DO
500: DO I = 0, K - 1
501: DO IJ = I, I + ( K+I )*LDA, LDA
502: AP( IJP ) = ARF( IJ )
503: IJP = IJP + 1
504: END DO
505: END DO
506: *
507: END IF
508: *
509: END IF
510: *
511: END IF
512: *
513: RETURN
514: *
515: * End of DTFTTP
516: *
517: END
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