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