1: SUBROUTINE DTFTTP( TRANSR, UPLO, N, ARF, AP, INFO )
2: *
3: * -- LAPACK routine (version 3.2.2) --
4: *
5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
6: * -- June 2010 --
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: * ..
12: * .. Scalar Arguments ..
13: CHARACTER TRANSR, UPLO
14: INTEGER INFO, N
15: * ..
16: * .. Array Arguments ..
17: DOUBLE PRECISION AP( 0: * ), ARF( 0: * )
18: * ..
19: *
20: * Purpose
21: * =======
22: *
23: * DTFTTP copies a triangular matrix A from rectangular full packed
24: * format (TF) to standard packed format (TP).
25: *
26: * Arguments
27: * =========
28: *
29: * TRANSR (input) CHARACTER
30: * = 'N': ARF is in Normal format;
31: * = 'T': ARF is in Transpose format;
32: *
33: * UPLO (input) CHARACTER
34: * = 'U': A is upper triangular;
35: * = 'L': A is lower triangular.
36: *
37: * N (input) INTEGER
38: * The order of the matrix A. N >= 0.
39: *
40: * ARF (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
41: * On entry, the upper or lower triangular matrix A stored in
42: * RFP format. For a further discussion see Notes below.
43: *
44: * AP (output) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ),
45: * On exit, the upper or lower triangular matrix A, packed
46: * columnwise in a linear array. The j-th column of A is stored
47: * in the array AP as follows:
48: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
49: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
50: *
51: * INFO (output) INTEGER
52: * = 0: successful exit
53: * < 0: if INFO = -i, the i-th argument had an illegal value
54: *
55: * Further Details
56: * ===============
57: *
58: * We first consider Rectangular Full Packed (RFP) Format when N is
59: * even. We give an example where N = 6.
60: *
61: * AP is Upper AP is Lower
62: *
63: * 00 01 02 03 04 05 00
64: * 11 12 13 14 15 10 11
65: * 22 23 24 25 20 21 22
66: * 33 34 35 30 31 32 33
67: * 44 45 40 41 42 43 44
68: * 55 50 51 52 53 54 55
69: *
70: *
71: * Let TRANSR = 'N'. RFP holds AP as follows:
72: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
73: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
74: * the transpose of the first three columns of AP upper.
75: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
76: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
77: * the transpose of the last three columns of AP lower.
78: * This covers the case N even and TRANSR = 'N'.
79: *
80: * RFP A RFP A
81: *
82: * 03 04 05 33 43 53
83: * 13 14 15 00 44 54
84: * 23 24 25 10 11 55
85: * 33 34 35 20 21 22
86: * 00 44 45 30 31 32
87: * 01 11 55 40 41 42
88: * 02 12 22 50 51 52
89: *
90: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
91: * transpose of RFP A above. One therefore gets:
92: *
93: *
94: * RFP A RFP A
95: *
96: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
97: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
98: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
99: *
100: *
101: * We then consider Rectangular Full Packed (RFP) Format when N is
102: * odd. We give an example where N = 5.
103: *
104: * AP is Upper AP is Lower
105: *
106: * 00 01 02 03 04 00
107: * 11 12 13 14 10 11
108: * 22 23 24 20 21 22
109: * 33 34 30 31 32 33
110: * 44 40 41 42 43 44
111: *
112: *
113: * Let TRANSR = 'N'. RFP holds AP as follows:
114: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
115: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
116: * the transpose of the first two columns of AP upper.
117: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
118: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
119: * the transpose of the last two columns of AP lower.
120: * This covers the case N odd and TRANSR = 'N'.
121: *
122: * RFP A RFP A
123: *
124: * 02 03 04 00 33 43
125: * 12 13 14 10 11 44
126: * 22 23 24 20 21 22
127: * 00 33 34 30 31 32
128: * 01 11 44 40 41 42
129: *
130: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
131: * transpose of RFP A above. One therefore gets:
132: *
133: * RFP A RFP A
134: *
135: * 02 12 22 00 01 00 10 20 30 40 50
136: * 03 13 23 33 11 33 11 21 31 41 51
137: * 04 14 24 34 44 43 44 22 32 42 52
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: * ..
143: * .. Local Scalars ..
144: LOGICAL LOWER, NISODD, NORMALTRANSR
145: INTEGER N1, N2, K, NT
146: INTEGER I, J, IJ
147: INTEGER IJP, JP, LDA, JS
148: * ..
149: * .. External Functions ..
150: LOGICAL LSAME
151: EXTERNAL LSAME
152: * ..
153: * .. External Subroutines ..
154: EXTERNAL XERBLA
155: * ..
156: * .. Executable Statements ..
157: *
158: * Test the input parameters.
159: *
160: INFO = 0
161: NORMALTRANSR = LSAME( TRANSR, 'N' )
162: LOWER = LSAME( UPLO, 'L' )
163: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
164: INFO = -1
165: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
166: INFO = -2
167: ELSE IF( N.LT.0 ) THEN
168: INFO = -3
169: END IF
170: IF( INFO.NE.0 ) THEN
171: CALL XERBLA( 'DTFTTP', -INFO )
172: RETURN
173: END IF
174: *
175: * Quick return if possible
176: *
177: IF( N.EQ.0 )
178: + RETURN
179: *
180: IF( N.EQ.1 ) THEN
181: IF( NORMALTRANSR ) THEN
182: AP( 0 ) = ARF( 0 )
183: ELSE
184: AP( 0 ) = ARF( 0 )
185: END IF
186: RETURN
187: END IF
188: *
189: * Size of array ARF(0:NT-1)
190: *
191: NT = N*( N+1 ) / 2
192: *
193: * Set N1 and N2 depending on LOWER
194: *
195: IF( LOWER ) THEN
196: N2 = N / 2
197: N1 = N - N2
198: ELSE
199: N1 = N / 2
200: N2 = N - N1
201: END IF
202: *
203: * If N is odd, set NISODD = .TRUE.
204: * If N is even, set K = N/2 and NISODD = .FALSE.
205: *
206: * set lda of ARF^C; ARF^C is (0:(N+1)/2-1,0:N-noe)
207: * where noe = 0 if n is even, noe = 1 if n is odd
208: *
209: IF( MOD( N, 2 ).EQ.0 ) THEN
210: K = N / 2
211: NISODD = .FALSE.
212: LDA = N + 1
213: ELSE
214: NISODD = .TRUE.
215: LDA = N
216: END IF
217: *
218: * ARF^C has lda rows and n+1-noe cols
219: *
220: IF( .NOT.NORMALTRANSR )
221: + LDA = ( N+1 ) / 2
222: *
223: * start execution: there are eight cases
224: *
225: IF( NISODD ) THEN
226: *
227: * N is odd
228: *
229: IF( NORMALTRANSR ) THEN
230: *
231: * N is odd and TRANSR = 'N'
232: *
233: IF( LOWER ) THEN
234: *
235: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) )
236: * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0)
237: * T1 -> a(0), T2 -> a(n), S -> a(n1); lda = n
238: *
239: IJP = 0
240: JP = 0
241: DO J = 0, N2
242: DO I = J, N - 1
243: IJ = I + JP
244: AP( IJP ) = ARF( IJ )
245: IJP = IJP + 1
246: END DO
247: JP = JP + LDA
248: END DO
249: DO I = 0, N2 - 1
250: DO J = 1 + I, N2
251: IJ = I + J*LDA
252: AP( IJP ) = ARF( IJ )
253: IJP = IJP + 1
254: END DO
255: END DO
256: *
257: ELSE
258: *
259: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1)
260: * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0)
261: * T1 -> a(n2), T2 -> a(n1), S -> a(0)
262: *
263: IJP = 0
264: DO J = 0, N1 - 1
265: IJ = N2 + J
266: DO I = 0, J
267: AP( IJP ) = ARF( IJ )
268: IJP = IJP + 1
269: IJ = IJ + LDA
270: END DO
271: END DO
272: JS = 0
273: DO J = N1, N - 1
274: IJ = JS
275: DO IJ = JS, JS + J
276: AP( IJP ) = ARF( IJ )
277: IJP = IJP + 1
278: END DO
279: JS = JS + LDA
280: END DO
281: *
282: END IF
283: *
284: ELSE
285: *
286: * N is odd and TRANSR = 'T'
287: *
288: IF( LOWER ) THEN
289: *
290: * SRPA for LOWER, TRANSPOSE and N is odd
291: * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1)
292: * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1
293: *
294: IJP = 0
295: DO I = 0, N2
296: DO IJ = I*( LDA+1 ), N*LDA - 1, LDA
297: AP( IJP ) = ARF( IJ )
298: IJP = IJP + 1
299: END DO
300: END DO
301: JS = 1
302: DO J = 0, N2 - 1
303: DO IJ = JS, JS + N2 - J - 1
304: AP( IJP ) = ARF( IJ )
305: IJP = IJP + 1
306: END DO
307: JS = JS + LDA + 1
308: END DO
309: *
310: ELSE
311: *
312: * SRPA for UPPER, TRANSPOSE and N is odd
313: * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0)
314: * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2
315: *
316: IJP = 0
317: JS = N2*LDA
318: DO J = 0, N1 - 1
319: DO IJ = JS, JS + J
320: AP( IJP ) = ARF( IJ )
321: IJP = IJP + 1
322: END DO
323: JS = JS + LDA
324: END DO
325: DO I = 0, N1
326: DO IJ = I, I + ( N1+I )*LDA, LDA
327: AP( IJP ) = ARF( IJ )
328: IJP = IJP + 1
329: END DO
330: END DO
331: *
332: END IF
333: *
334: END IF
335: *
336: ELSE
337: *
338: * N is even
339: *
340: IF( NORMALTRANSR ) THEN
341: *
342: * N is even and TRANSR = 'N'
343: *
344: IF( LOWER ) THEN
345: *
346: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
347: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
348: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
349: *
350: IJP = 0
351: JP = 0
352: DO J = 0, K - 1
353: DO I = J, N - 1
354: IJ = 1 + I + JP
355: AP( IJP ) = ARF( IJ )
356: IJP = IJP + 1
357: END DO
358: JP = JP + LDA
359: END DO
360: DO I = 0, K - 1
361: DO J = I, K - 1
362: IJ = I + J*LDA
363: AP( IJP ) = ARF( IJ )
364: IJP = IJP + 1
365: END DO
366: END DO
367: *
368: ELSE
369: *
370: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
371: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
372: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
373: *
374: IJP = 0
375: DO J = 0, K - 1
376: IJ = K + 1 + J
377: DO I = 0, J
378: AP( IJP ) = ARF( IJ )
379: IJP = IJP + 1
380: IJ = IJ + LDA
381: END DO
382: END DO
383: JS = 0
384: DO J = K, N - 1
385: IJ = JS
386: DO IJ = JS, JS + J
387: AP( IJP ) = ARF( IJ )
388: IJP = IJP + 1
389: END DO
390: JS = JS + LDA
391: END DO
392: *
393: END IF
394: *
395: ELSE
396: *
397: * N is even and TRANSR = 'T'
398: *
399: IF( LOWER ) THEN
400: *
401: * SRPA for LOWER, TRANSPOSE and N is even (see paper)
402: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1)
403: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
404: *
405: IJP = 0
406: DO I = 0, K - 1
407: DO IJ = I + ( I+1 )*LDA, ( N+1 )*LDA - 1, LDA
408: AP( IJP ) = ARF( IJ )
409: IJP = IJP + 1
410: END DO
411: END DO
412: JS = 0
413: DO J = 0, K - 1
414: DO IJ = JS, JS + K - J - 1
415: AP( IJP ) = ARF( IJ )
416: IJP = IJP + 1
417: END DO
418: JS = JS + LDA + 1
419: END DO
420: *
421: ELSE
422: *
423: * SRPA for UPPER, TRANSPOSE and N is even (see paper)
424: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0)
425: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
426: *
427: IJP = 0
428: JS = ( K+1 )*LDA
429: DO J = 0, K - 1
430: DO IJ = JS, JS + J
431: AP( IJP ) = ARF( IJ )
432: IJP = IJP + 1
433: END DO
434: JS = JS + LDA
435: END DO
436: DO I = 0, K - 1
437: DO IJ = I, I + ( K+I )*LDA, LDA
438: AP( IJP ) = ARF( IJ )
439: IJP = IJP + 1
440: END DO
441: END DO
442: *
443: END IF
444: *
445: END IF
446: *
447: END IF
448: *
449: RETURN
450: *
451: * End of DTFTTP
452: *
453: END
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