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1.10 bertrand 1: *> \brief \b ZTPTTF copies a triangular matrix from the standard packed format (TP) to the rectangular full packed format (TF).
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 ZTPTTF + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztpttf.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztpttf.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztpttf.f">
1.7 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.7 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
1.14 bertrand 22: *
1.7 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER TRANSR, UPLO
25: * INTEGER INFO, N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 AP( 0: * ), ARF( 0: * )
1.14 bertrand 29: *
1.7 bertrand 30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> ZTPTTF copies a triangular matrix A from standard packed format (TP)
37: *> to rectangular full packed format (TF).
38: *> \endverbatim
39: *
40: * Arguments:
41: * ==========
42: *
43: *> \param[in] TRANSR
44: *> \verbatim
45: *> TRANSR is CHARACTER*1
46: *> = 'N': ARF in Normal format is wanted;
47: *> = 'C': ARF in Conjugate-transpose format is wanted.
48: *> \endverbatim
49: *>
50: *> \param[in] UPLO
51: *> \verbatim
52: *> UPLO is CHARACTER*1
53: *> = 'U': A is upper triangular;
54: *> = 'L': A is lower triangular.
55: *> \endverbatim
56: *>
57: *> \param[in] N
58: *> \verbatim
59: *> N is INTEGER
60: *> The order of the matrix A. N >= 0.
61: *> \endverbatim
62: *>
63: *> \param[in] AP
64: *> \verbatim
65: *> AP is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
66: *> On entry, the upper or lower triangular matrix A, packed
67: *> columnwise in a linear array. The j-th column of A is stored
68: *> in the array AP as follows:
69: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
70: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
71: *> \endverbatim
72: *>
73: *> \param[out] ARF
74: *> \verbatim
75: *> ARF is COMPLEX*16 array, dimension ( N*(N+1)/2 ),
76: *> On exit, the upper or lower triangular matrix A stored in
77: *> RFP format. For a further discussion see Notes below.
78: *> \endverbatim
79: *>
80: *> \param[out] INFO
81: *> \verbatim
82: *> INFO is INTEGER
83: *> = 0: successful exit
84: *> < 0: if INFO = -i, the i-th argument had an illegal value
85: *> \endverbatim
86: *
87: * Authors:
88: * ========
89: *
1.14 bertrand 90: *> \author Univ. of Tennessee
91: *> \author Univ. of California Berkeley
92: *> \author Univ. of Colorado Denver
93: *> \author NAG Ltd.
1.7 bertrand 94: *
95: *> \ingroup complex16OTHERcomputational
96: *
97: *> \par Further Details:
98: * =====================
99: *>
100: *> \verbatim
101: *>
102: *> We first consider Standard Packed Format when N is even.
103: *> We give an example where N = 6.
104: *>
105: *> AP is Upper AP is Lower
106: *>
107: *> 00 01 02 03 04 05 00
108: *> 11 12 13 14 15 10 11
109: *> 22 23 24 25 20 21 22
110: *> 33 34 35 30 31 32 33
111: *> 44 45 40 41 42 43 44
112: *> 55 50 51 52 53 54 55
113: *>
114: *>
115: *> Let TRANSR = 'N'. RFP holds AP as follows:
116: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
117: *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
118: *> conjugate-transpose of the first three columns of AP upper.
119: *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
120: *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
121: *> conjugate-transpose of the last three columns of AP lower.
122: *> To denote conjugate we place -- above the element. This covers the
123: *> case N even and TRANSR = 'N'.
124: *>
125: *> RFP A RFP A
126: *>
127: *> -- -- --
128: *> 03 04 05 33 43 53
129: *> -- --
130: *> 13 14 15 00 44 54
131: *> --
132: *> 23 24 25 10 11 55
133: *>
134: *> 33 34 35 20 21 22
135: *> --
136: *> 00 44 45 30 31 32
137: *> -- --
138: *> 01 11 55 40 41 42
139: *> -- -- --
140: *> 02 12 22 50 51 52
141: *>
142: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
143: *> transpose of RFP A above. One therefore gets:
144: *>
145: *>
146: *> RFP A RFP A
147: *>
148: *> -- -- -- -- -- -- -- -- -- --
149: *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
150: *> -- -- -- -- -- -- -- -- -- --
151: *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
152: *> -- -- -- -- -- -- -- -- -- --
153: *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
154: *>
155: *>
156: *> We next consider Standard Packed Format when N is odd.
157: *> We give an example where N = 5.
158: *>
159: *> AP is Upper AP is Lower
160: *>
161: *> 00 01 02 03 04 00
162: *> 11 12 13 14 10 11
163: *> 22 23 24 20 21 22
164: *> 33 34 30 31 32 33
165: *> 44 40 41 42 43 44
166: *>
167: *>
168: *> Let TRANSR = 'N'. RFP holds AP as follows:
169: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
170: *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
171: *> conjugate-transpose of the first two columns of AP upper.
172: *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
173: *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
174: *> conjugate-transpose of the last two columns of AP lower.
175: *> To denote conjugate we place -- above the element. This covers the
176: *> case N odd and TRANSR = 'N'.
177: *>
178: *> RFP A RFP A
179: *>
180: *> -- --
181: *> 02 03 04 00 33 43
182: *> --
183: *> 12 13 14 10 11 44
184: *>
185: *> 22 23 24 20 21 22
186: *> --
187: *> 00 33 34 30 31 32
188: *> -- --
189: *> 01 11 44 40 41 42
190: *>
191: *> Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
192: *> transpose of RFP A above. One therefore gets:
193: *>
194: *>
195: *> RFP A RFP A
196: *>
197: *> -- -- -- -- -- -- -- -- --
198: *> 02 12 22 00 01 00 10 20 30 40 50
199: *> -- -- -- -- -- -- -- -- --
200: *> 03 13 23 33 11 33 11 21 31 41 51
201: *> -- -- -- -- -- -- -- -- --
202: *> 04 14 24 34 44 43 44 22 32 42 52
203: *> \endverbatim
204: *>
205: * =====================================================================
206: SUBROUTINE ZTPTTF( TRANSR, UPLO, N, AP, ARF, INFO )
207: *
1.17 ! bertrand 208: * -- LAPACK computational routine --
1.1 bertrand 209: * -- LAPACK is a software package provided by Univ. of Tennessee, --
210: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
211: *
212: * .. Scalar Arguments ..
213: CHARACTER TRANSR, UPLO
214: INTEGER INFO, N
215: * ..
216: * .. Array Arguments ..
217: COMPLEX*16 AP( 0: * ), ARF( 0: * )
218: *
219: * =====================================================================
220: *
221: * .. Parameters ..
222: * ..
223: * .. Local Scalars ..
224: LOGICAL LOWER, NISODD, NORMALTRANSR
225: INTEGER N1, N2, K, NT
226: INTEGER I, J, IJ
227: INTEGER IJP, JP, LDA, JS
228: * ..
229: * .. External Functions ..
230: LOGICAL LSAME
231: EXTERNAL LSAME
232: * ..
233: * .. External Subroutines ..
234: EXTERNAL XERBLA
235: * ..
236: * .. Intrinsic Functions ..
237: INTRINSIC DCONJG, MOD
238: * ..
239: * .. Executable Statements ..
240: *
241: * Test the input parameters.
242: *
243: INFO = 0
244: NORMALTRANSR = LSAME( TRANSR, 'N' )
245: LOWER = LSAME( UPLO, 'L' )
246: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
247: INFO = -1
248: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
249: INFO = -2
250: ELSE IF( N.LT.0 ) THEN
251: INFO = -3
252: END IF
253: IF( INFO.NE.0 ) THEN
254: CALL XERBLA( 'ZTPTTF', -INFO )
255: RETURN
256: END IF
257: *
258: * Quick return if possible
259: *
260: IF( N.EQ.0 )
1.6 bertrand 261: $ RETURN
1.1 bertrand 262: *
263: IF( N.EQ.1 ) THEN
264: IF( NORMALTRANSR ) THEN
265: ARF( 0 ) = AP( 0 )
266: ELSE
267: ARF( 0 ) = DCONJG( AP( 0 ) )
268: END IF
269: RETURN
270: END IF
271: *
272: * Size of array ARF(0:NT-1)
273: *
274: NT = N*( N+1 ) / 2
275: *
276: * Set N1 and N2 depending on LOWER
277: *
278: IF( LOWER ) THEN
279: N2 = N / 2
280: N1 = N - N2
281: ELSE
282: N1 = N / 2
283: N2 = N - N1
284: END IF
285: *
286: * If N is odd, set NISODD = .TRUE.
287: * If N is even, set K = N/2 and NISODD = .FALSE.
288: *
289: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
290: * where noe = 0 if n is even, noe = 1 if n is odd
291: *
292: IF( MOD( N, 2 ).EQ.0 ) THEN
293: K = N / 2
294: NISODD = .FALSE.
295: LDA = N + 1
296: ELSE
297: NISODD = .TRUE.
298: LDA = N
299: END IF
300: *
301: * ARF^C has lda rows and n+1-noe cols
302: *
303: IF( .NOT.NORMALTRANSR )
1.6 bertrand 304: $ LDA = ( N+1 ) / 2
1.1 bertrand 305: *
306: * start execution: there are eight cases
307: *
308: IF( NISODD ) THEN
309: *
310: * N is odd
311: *
312: IF( NORMALTRANSR ) THEN
313: *
314: * N is odd and TRANSR = 'N'
315: *
316: IF( LOWER ) THEN
317: *
318: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
319: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
320: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
321: *
322: IJP = 0
323: JP = 0
324: DO J = 0, N2
325: DO I = J, N - 1
326: IJ = I + JP
327: ARF( IJ ) = AP( IJP )
328: IJP = IJP + 1
329: END DO
330: JP = JP + LDA
331: END DO
332: DO I = 0, N2 - 1
333: DO J = 1 + I, N2
334: IJ = I + J*LDA
335: ARF( IJ ) = DCONJG( AP( IJP ) )
336: IJP = IJP + 1
337: END DO
338: END DO
339: *
340: ELSE
341: *
342: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
343: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
344: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
345: *
346: IJP = 0
347: DO J = 0, N1 - 1
348: IJ = N2 + J
349: DO I = 0, J
350: ARF( IJ ) = DCONJG( AP( IJP ) )
351: IJP = IJP + 1
352: IJ = IJ + LDA
353: END DO
354: END DO
355: JS = 0
356: DO J = N1, N - 1
357: IJ = JS
358: DO IJ = JS, JS + J
359: ARF( IJ ) = AP( IJP )
360: IJP = IJP + 1
361: END DO
362: JS = JS + LDA
363: END DO
364: *
365: END IF
366: *
367: ELSE
368: *
369: * N is odd and TRANSR = 'C'
370: *
371: IF( LOWER ) THEN
372: *
373: * SRPA for LOWER, TRANSPOSE and N is odd
374: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
375: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
376: *
377: IJP = 0
378: DO I = 0, N2
379: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
380: ARF( IJ ) = DCONJG( AP( IJP ) )
381: IJP = IJP + 1
382: END DO
383: END DO
384: JS = 1
385: DO J = 0, N2 - 1
386: DO IJ = JS, JS + N2 - J - 1
387: ARF( IJ ) = AP( IJP )
388: IJP = IJP + 1
389: END DO
390: JS = JS + LDA + 1
391: END DO
392: *
393: ELSE
394: *
395: * SRPA for UPPER, TRANSPOSE and N is odd
396: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
397: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
398: *
399: IJP = 0
400: JS = N2*LDA
401: DO J = 0, N1 - 1
402: DO IJ = JS, JS + J
403: ARF( IJ ) = AP( IJP )
404: IJP = IJP + 1
405: END DO
406: JS = JS + LDA
407: END DO
408: DO I = 0, N1
409: DO IJ = I, I + ( N1+I )*LDA, LDA
410: ARF( IJ ) = DCONJG( AP( IJP ) )
411: IJP = IJP + 1
412: END DO
413: END DO
414: *
415: END IF
416: *
417: END IF
418: *
419: ELSE
420: *
421: * N is even
422: *
423: IF( NORMALTRANSR ) THEN
424: *
425: * N is even and TRANSR = 'N'
426: *
427: IF( LOWER ) THEN
428: *
429: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
430: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
431: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
432: *
433: IJP = 0
434: JP = 0
435: DO J = 0, K - 1
436: DO I = J, N - 1
437: IJ = 1 + I + JP
438: ARF( IJ ) = AP( IJP )
439: IJP = IJP + 1
440: END DO
441: JP = JP + LDA
442: END DO
443: DO I = 0, K - 1
444: DO J = I, K - 1
445: IJ = I + J*LDA
446: ARF( IJ ) = DCONJG( AP( IJP ) )
447: IJP = IJP + 1
448: END DO
449: END DO
450: *
451: ELSE
452: *
453: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
454: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
455: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
456: *
457: IJP = 0
458: DO J = 0, K - 1
459: IJ = K + 1 + J
460: DO I = 0, J
461: ARF( IJ ) = DCONJG( AP( IJP ) )
462: IJP = IJP + 1
463: IJ = IJ + LDA
464: END DO
465: END DO
466: JS = 0
467: DO J = K, N - 1
468: IJ = JS
469: DO IJ = JS, JS + J
470: ARF( IJ ) = AP( IJP )
471: IJP = IJP + 1
472: END DO
473: JS = JS + LDA
474: END DO
475: *
476: END IF
477: *
478: ELSE
479: *
480: * N is even and TRANSR = 'C'
481: *
482: IF( LOWER ) THEN
483: *
484: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
485: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
486: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
487: *
488: IJP = 0
489: DO I = 0, K - 1
490: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
491: ARF( IJ ) = DCONJG( AP( IJP ) )
492: IJP = IJP + 1
493: END DO
494: END DO
495: JS = 0
496: DO J = 0, K - 1
497: DO IJ = JS, JS + K - J - 1
498: ARF( IJ ) = AP( IJP )
499: IJP = IJP + 1
500: END DO
501: JS = JS + LDA + 1
502: END DO
503: *
504: ELSE
505: *
506: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
507: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
508: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
509: *
510: IJP = 0
511: JS = ( K+1 )*LDA
512: DO J = 0, K - 1
513: DO IJ = JS, JS + J
514: ARF( IJ ) = AP( IJP )
515: IJP = IJP + 1
516: END DO
517: JS = JS + LDA
518: END DO
519: DO I = 0, K - 1
520: DO IJ = I, I + ( K+I )*LDA, LDA
521: ARF( IJ ) = DCONJG( AP( IJP ) )
522: IJP = IJP + 1
523: END DO
524: END DO
525: *
526: END IF
527: *
528: END IF
529: *
530: END IF
531: *
532: RETURN
533: *
534: * End of ZTPTTF
535: *
536: END