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1.1 bertrand 1: SUBROUTINE ZTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
2: *
3: * -- LAPACK routine (version 3.2.1) --
4: *
5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
6: * -- April 2009 --
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
13: INTEGER INFO, N
14: * ..
15: * .. Array Arguments ..
16: COMPLEX*16 AP( 0: * ), ARF( 0: * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * ZTFTTP copies a triangular matrix A from rectangular full packed
23: * format (TF) to standard packed format (TP).
24: *
25: * Arguments
26: * =========
27: *
28: * TRANSR (input) CHARACTER
29: * = 'N': ARF is in Normal format;
30: * = 'C': ARF is in Conjugate-transpose format;
31: *
32: * UPLO (input) CHARACTER
33: * = 'U': A is upper triangular;
34: * = 'L': A is lower triangular.
35: *
36: * N (input) INTEGER
37: * The order of the matrix A. N >= 0.
38: *
39: * ARF (input) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
40: * On entry, the upper or lower triangular matrix A stored in
41: * RFP format. For a further discussion see Notes below.
42: *
43: * AP (output) COMPLEX*16 array, dimension ( N*(N+1)/2 ),
44: * On exit, the upper or lower triangular matrix A, packed
45: * columnwise in a linear array. The j-th column of A is stored
46: * in the array AP as follows:
47: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
48: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
49: *
50: * INFO (output) INTEGER
51: * = 0: successful exit
52: * < 0: if INFO = -i, the i-th argument had an illegal value
53: *
54: * Further Details
55: * ===============
56: *
57: * We first consider Standard Packed Format when N is even.
58: * We give an example where N = 6.
59: *
60: * AP is Upper AP is Lower
61: *
62: * 00 01 02 03 04 05 00
63: * 11 12 13 14 15 10 11
64: * 22 23 24 25 20 21 22
65: * 33 34 35 30 31 32 33
66: * 44 45 40 41 42 43 44
67: * 55 50 51 52 53 54 55
68: *
69: *
70: * Let TRANSR = 'N'. RFP holds AP as follows:
71: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
72: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
73: * conjugate-transpose of the first three columns of AP upper.
74: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
75: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
76: * conjugate-transpose of the last three columns of AP lower.
77: * To denote conjugate we place -- above the element. This covers the
78: * case N even and TRANSR = 'N'.
79: *
80: * RFP A RFP A
81: *
82: * -- -- --
83: * 03 04 05 33 43 53
84: * -- --
85: * 13 14 15 00 44 54
86: * --
87: * 23 24 25 10 11 55
88: *
89: * 33 34 35 20 21 22
90: * --
91: * 00 44 45 30 31 32
92: * -- --
93: * 01 11 55 40 41 42
94: * -- -- --
95: * 02 12 22 50 51 52
96: *
97: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
98: * transpose of RFP A above. One therefore gets:
99: *
100: *
101: * RFP A RFP A
102: *
103: * -- -- -- -- -- -- -- -- -- --
104: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
105: * -- -- -- -- -- -- -- -- -- --
106: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
107: * -- -- -- -- -- -- -- -- -- --
108: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
109: *
110: *
111: * We next consider Standard Packed Format when N is odd.
112: * We give an example where N = 5.
113: *
114: * AP is Upper AP is Lower
115: *
116: * 00 01 02 03 04 00
117: * 11 12 13 14 10 11
118: * 22 23 24 20 21 22
119: * 33 34 30 31 32 33
120: * 44 40 41 42 43 44
121: *
122: *
123: * Let TRANSR = 'N'. RFP holds AP as follows:
124: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
125: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
126: * conjugate-transpose of the first two columns of AP upper.
127: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
128: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
129: * conjugate-transpose of the last two columns of AP lower.
130: * To denote conjugate we place -- above the element. This covers the
131: * case N odd and TRANSR = 'N'.
132: *
133: * RFP A RFP A
134: *
135: * -- --
136: * 02 03 04 00 33 43
137: * --
138: * 12 13 14 10 11 44
139: *
140: * 22 23 24 20 21 22
141: * --
142: * 00 33 34 30 31 32
143: * -- --
144: * 01 11 44 40 41 42
145: *
146: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
147: * transpose of RFP A above. One therefore gets:
148: *
149: *
150: * RFP A RFP A
151: *
152: * -- -- -- -- -- -- -- -- --
153: * 02 12 22 00 01 00 10 20 30 40 50
154: * -- -- -- -- -- -- -- -- --
155: * 03 13 23 33 11 33 11 21 31 41 51
156: * -- -- -- -- -- -- -- -- --
157: * 04 14 24 34 44 43 44 22 32 42 52
158: *
159: * =====================================================================
160: *
161: * .. Parameters ..
162: * ..
163: * .. Local Scalars ..
164: LOGICAL LOWER, NISODD, NORMALTRANSR
165: INTEGER N1, N2, K, NT
166: INTEGER I, J, IJ
167: INTEGER IJP, JP, LDA, JS
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: EXTERNAL LSAME
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL XERBLA
175: * ..
176: * .. Intrinsic Functions ..
177: INTRINSIC DCONJG
178: * ..
179: * .. Intrinsic Functions ..
180: * ..
181: * .. Executable Statements ..
182: *
183: * Test the input parameters.
184: *
185: INFO = 0
186: NORMALTRANSR = LSAME( TRANSR, 'N' )
187: LOWER = LSAME( UPLO, 'L' )
188: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
189: INFO = -1
190: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
191: INFO = -2
192: ELSE IF( N.LT.0 ) THEN
193: INFO = -3
194: END IF
195: IF( INFO.NE.0 ) THEN
196: CALL XERBLA( 'ZTFTTP', -INFO )
197: RETURN
198: END IF
199: *
200: * Quick return if possible
201: *
202: IF( N.EQ.0 )
203: + RETURN
204: *
205: IF( N.EQ.1 ) THEN
206: IF( NORMALTRANSR ) THEN
207: AP( 0 ) = ARF( 0 )
208: ELSE
209: AP( 0 ) = DCONJG( ARF( 0 ) )
210: END IF
211: RETURN
212: END IF
213: *
214: * Size of array ARF(0:NT-1)
215: *
216: NT = N*( N+1 ) / 2
217: *
218: * Set N1 and N2 depending on LOWER
219: *
220: IF( LOWER ) THEN
221: N2 = N / 2
222: N1 = N - N2
223: ELSE
224: N1 = N / 2
225: N2 = N - N1
226: END IF
227: *
228: * If N is odd, set NISODD = .TRUE.
229: * If N is even, set K = N/2 and NISODD = .FALSE.
230: *
231: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
232: * where noe = 0 if n is even, noe = 1 if n is odd
233: *
234: IF( MOD( N, 2 ).EQ.0 ) THEN
235: K = N / 2
236: NISODD = .FALSE.
237: LDA = N + 1
238: ELSE
239: NISODD = .TRUE.
240: LDA = N
241: END IF
242: *
243: * ARF^C has lda rows and n+1-noe cols
244: *
245: IF( .NOT.NORMALTRANSR )
246: + LDA = ( N+1 ) / 2
247: *
248: * start execution: there are eight cases
249: *
250: IF( NISODD ) THEN
251: *
252: * N is odd
253: *
254: IF( NORMALTRANSR ) THEN
255: *
256: * N is odd and TRANSR = 'N'
257: *
258: IF( LOWER ) THEN
259: *
260: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
261: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
262: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
263: *
264: IJP = 0
265: JP = 0
266: DO J = 0, N2
267: DO I = J, N - 1
268: IJ = I + JP
269: AP( IJP ) = ARF( IJ )
270: IJP = IJP + 1
271: END DO
272: JP = JP + LDA
273: END DO
274: DO I = 0, N2 - 1
275: DO J = 1 + I, N2
276: IJ = I + J*LDA
277: AP( IJP ) = DCONJG( ARF( IJ ) )
278: IJP = IJP + 1
279: END DO
280: END DO
281: *
282: ELSE
283: *
284: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
285: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
286: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
287: *
288: IJP = 0
289: DO J = 0, N1 - 1
290: IJ = N2 + J
291: DO I = 0, J
292: AP( IJP ) = DCONJG( ARF( IJ ) )
293: IJP = IJP + 1
294: IJ = IJ + LDA
295: END DO
296: END DO
297: JS = 0
298: DO J = N1, N - 1
299: IJ = JS
300: DO IJ = JS, JS + J
301: AP( IJP ) = ARF( IJ )
302: IJP = IJP + 1
303: END DO
304: JS = JS + LDA
305: END DO
306: *
307: END IF
308: *
309: ELSE
310: *
311: * N is odd and TRANSR = 'C'
312: *
313: IF( LOWER ) THEN
314: *
315: * SRPA for LOWER, TRANSPOSE and N is odd
316: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
317: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
318: *
319: IJP = 0
320: DO I = 0, N2
321: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
322: AP( IJP ) = DCONJG( ARF( IJ ) )
323: IJP = IJP + 1
324: END DO
325: END DO
326: JS = 1
327: DO J = 0, N2 - 1
328: DO IJ = JS, JS + N2 - J - 1
329: AP( IJP ) = ARF( IJ )
330: IJP = IJP + 1
331: END DO
332: JS = JS + LDA + 1
333: END DO
334: *
335: ELSE
336: *
337: * SRPA for UPPER, TRANSPOSE and N is odd
338: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
339: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
340: *
341: IJP = 0
342: JS = N2*LDA
343: DO J = 0, N1 - 1
344: DO IJ = JS, JS + J
345: AP( IJP ) = ARF( IJ )
346: IJP = IJP + 1
347: END DO
348: JS = JS + LDA
349: END DO
350: DO I = 0, N1
351: DO IJ = I, I + ( N1+I )*LDA, LDA
352: AP( IJP ) = DCONJG( ARF( IJ ) )
353: IJP = IJP + 1
354: END DO
355: END DO
356: *
357: END IF
358: *
359: END IF
360: *
361: ELSE
362: *
363: * N is even
364: *
365: IF( NORMALTRANSR ) THEN
366: *
367: * N is even and TRANSR = 'N'
368: *
369: IF( LOWER ) THEN
370: *
371: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
372: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
373: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
374: *
375: IJP = 0
376: JP = 0
377: DO J = 0, K - 1
378: DO I = J, N - 1
379: IJ = 1 + I + JP
380: AP( IJP ) = ARF( IJ )
381: IJP = IJP + 1
382: END DO
383: JP = JP + LDA
384: END DO
385: DO I = 0, K - 1
386: DO J = I, K - 1
387: IJ = I + J*LDA
388: AP( IJP ) = DCONJG( ARF( IJ ) )
389: IJP = IJP + 1
390: END DO
391: END DO
392: *
393: ELSE
394: *
395: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
396: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
397: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
398: *
399: IJP = 0
400: DO J = 0, K - 1
401: IJ = K + 1 + J
402: DO I = 0, J
403: AP( IJP ) = DCONJG( ARF( IJ ) )
404: IJP = IJP + 1
405: IJ = IJ + LDA
406: END DO
407: END DO
408: JS = 0
409: DO J = K, N - 1
410: IJ = JS
411: DO IJ = JS, JS + J
412: AP( IJP ) = ARF( IJ )
413: IJP = IJP + 1
414: END DO
415: JS = JS + LDA
416: END DO
417: *
418: END IF
419: *
420: ELSE
421: *
422: * N is even and TRANSR = 'C'
423: *
424: IF( LOWER ) THEN
425: *
426: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
427: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
428: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
429: *
430: IJP = 0
431: DO I = 0, K - 1
432: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
433: AP( IJP ) = DCONJG( ARF( IJ ) )
434: IJP = IJP + 1
435: END DO
436: END DO
437: JS = 0
438: DO J = 0, K - 1
439: DO IJ = JS, JS + K - J - 1
440: AP( IJP ) = ARF( IJ )
441: IJP = IJP + 1
442: END DO
443: JS = JS + LDA + 1
444: END DO
445: *
446: ELSE
447: *
448: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
449: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
450: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
451: *
452: IJP = 0
453: JS = ( K+1 )*LDA
454: DO J = 0, K - 1
455: DO IJ = JS, JS + J
456: AP( IJP ) = ARF( IJ )
457: IJP = IJP + 1
458: END DO
459: JS = JS + LDA
460: END DO
461: DO I = 0, K - 1
462: DO IJ = I, I + ( K+I )*LDA, LDA
463: AP( IJP ) = DCONJG( ARF( IJ ) )
464: IJP = IJP + 1
465: END DO
466: END DO
467: *
468: END IF
469: *
470: END IF
471: *
472: END IF
473: *
474: RETURN
475: *
476: * End of ZTFTTP
477: *
478: END