1: SUBROUTINE ZPFTRI( TRANSR, UPLO, N, A, INFO )
2: *
3: * -- LAPACK routine (version 3.3.0) --
4: *
5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
6: * November 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: * .. Scalar Arguments ..
12: CHARACTER TRANSR, UPLO
13: INTEGER INFO, N
14: * .. Array Arguments ..
15: COMPLEX*16 A( 0: * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZPFTRI computes the inverse of a complex Hermitian positive definite
22: * matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
23: * computed by ZPFTRF.
24: *
25: * Arguments
26: * =========
27: *
28: * TRANSR (input) CHARACTER*1
29: * = 'N': The Normal TRANSR of RFP A is stored;
30: * = 'C': The Conjugate-transpose TRANSR of RFP A is stored.
31: *
32: * UPLO (input) CHARACTER*1
33: * = 'U': Upper triangle of A is stored;
34: * = 'L': Lower triangle of A is stored.
35: *
36: * N (input) INTEGER
37: * The order of the matrix A. N >= 0.
38: *
39: * A (input/output) COMPLEX*16 array, dimension ( N*(N+1)/2 );
40: * On entry, the Hermitian matrix A in RFP format. RFP format is
41: * described by TRANSR, UPLO, and N as follows: If TRANSR = 'N'
42: * then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is
43: * (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'C' then RFP is
44: * the Conjugate-transpose of RFP A as defined when
45: * TRANSR = 'N'. The contents of RFP A are defined by UPLO as
46: * follows: If UPLO = 'U' the RFP A contains the nt elements of
47: * upper packed A. If UPLO = 'L' the RFP A contains the elements
48: * of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR =
49: * 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and N
50: * is odd. See the Note below for more details.
51: *
52: * On exit, the Hermitian inverse of the original matrix, in the
53: * same storage format.
54: *
55: * INFO (output) INTEGER
56: * = 0: successful exit
57: * < 0: if INFO = -i, the i-th argument had an illegal value
58: * > 0: if INFO = i, the (i,i) element of the factor U or L is
59: * zero, and the inverse could not be computed.
60: *
61: * Further Details
62: * ===============
63: *
64: * We first consider Standard Packed Format when N is even.
65: * We give an example where N = 6.
66: *
67: * AP is Upper AP is Lower
68: *
69: * 00 01 02 03 04 05 00
70: * 11 12 13 14 15 10 11
71: * 22 23 24 25 20 21 22
72: * 33 34 35 30 31 32 33
73: * 44 45 40 41 42 43 44
74: * 55 50 51 52 53 54 55
75: *
76: *
77: * Let TRANSR = 'N'. RFP holds AP as follows:
78: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
79: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
80: * conjugate-transpose of the first three columns of AP upper.
81: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
82: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
83: * conjugate-transpose of the last three columns of AP lower.
84: * To denote conjugate we place -- above the element. This covers the
85: * case N even and TRANSR = 'N'.
86: *
87: * RFP A RFP A
88: *
89: * -- -- --
90: * 03 04 05 33 43 53
91: * -- --
92: * 13 14 15 00 44 54
93: * --
94: * 23 24 25 10 11 55
95: *
96: * 33 34 35 20 21 22
97: * --
98: * 00 44 45 30 31 32
99: * -- --
100: * 01 11 55 40 41 42
101: * -- -- --
102: * 02 12 22 50 51 52
103: *
104: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
105: * transpose of RFP A above. One therefore gets:
106: *
107: *
108: * RFP A RFP A
109: *
110: * -- -- -- -- -- -- -- -- -- --
111: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
112: * -- -- -- -- -- -- -- -- -- --
113: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
114: * -- -- -- -- -- -- -- -- -- --
115: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
116: *
117: *
118: * We next consider Standard Packed Format when N is odd.
119: * We give an example where N = 5.
120: *
121: * AP is Upper AP is Lower
122: *
123: * 00 01 02 03 04 00
124: * 11 12 13 14 10 11
125: * 22 23 24 20 21 22
126: * 33 34 30 31 32 33
127: * 44 40 41 42 43 44
128: *
129: *
130: * Let TRANSR = 'N'. RFP holds AP as follows:
131: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
132: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
133: * conjugate-transpose of the first two columns of AP upper.
134: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
135: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
136: * conjugate-transpose of the last two columns of AP lower.
137: * To denote conjugate we place -- above the element. This covers the
138: * case N odd and TRANSR = 'N'.
139: *
140: * RFP A RFP A
141: *
142: * -- --
143: * 02 03 04 00 33 43
144: * --
145: * 12 13 14 10 11 44
146: *
147: * 22 23 24 20 21 22
148: * --
149: * 00 33 34 30 31 32
150: * -- --
151: * 01 11 44 40 41 42
152: *
153: * Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
154: * transpose of RFP A above. One therefore gets:
155: *
156: *
157: * RFP A RFP A
158: *
159: * -- -- -- -- -- -- -- -- --
160: * 02 12 22 00 01 00 10 20 30 40 50
161: * -- -- -- -- -- -- -- -- --
162: * 03 13 23 33 11 33 11 21 31 41 51
163: * -- -- -- -- -- -- -- -- --
164: * 04 14 24 34 44 43 44 22 32 42 52
165: *
166: * =====================================================================
167: *
168: * .. Parameters ..
169: DOUBLE PRECISION ONE
170: COMPLEX*16 CONE
171: PARAMETER ( ONE = 1.D0, CONE = ( 1.D0, 0.D0 ) )
172: * ..
173: * .. Local Scalars ..
174: LOGICAL LOWER, NISODD, NORMALTRANSR
175: INTEGER N1, N2, K
176: * ..
177: * .. External Functions ..
178: LOGICAL LSAME
179: EXTERNAL LSAME
180: * ..
181: * .. External Subroutines ..
182: EXTERNAL XERBLA, ZTFTRI, ZLAUUM, ZTRMM, ZHERK
183: * ..
184: * .. Intrinsic Functions ..
185: INTRINSIC MOD
186: * ..
187: * .. Executable Statements ..
188: *
189: * Test the input parameters.
190: *
191: INFO = 0
192: NORMALTRANSR = LSAME( TRANSR, 'N' )
193: LOWER = LSAME( UPLO, 'L' )
194: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'C' ) ) THEN
195: INFO = -1
196: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
197: INFO = -2
198: ELSE IF( N.LT.0 ) THEN
199: INFO = -3
200: END IF
201: IF( INFO.NE.0 ) THEN
202: CALL XERBLA( 'ZPFTRI', -INFO )
203: RETURN
204: END IF
205: *
206: * Quick return if possible
207: *
208: IF( N.EQ.0 )
209: + RETURN
210: *
211: * Invert the triangular Cholesky factor U or L.
212: *
213: CALL ZTFTRI( TRANSR, UPLO, 'N', N, A, INFO )
214: IF( INFO.GT.0 )
215: + RETURN
216: *
217: * If N is odd, set NISODD = .TRUE.
218: * If N is even, set K = N/2 and NISODD = .FALSE.
219: *
220: IF( MOD( N, 2 ).EQ.0 ) THEN
221: K = N / 2
222: NISODD = .FALSE.
223: ELSE
224: NISODD = .TRUE.
225: END IF
226: *
227: * Set N1 and N2 depending on LOWER
228: *
229: IF( LOWER ) THEN
230: N2 = N / 2
231: N1 = N - N2
232: ELSE
233: N1 = N / 2
234: N2 = N - N1
235: END IF
236: *
237: * Start execution of triangular matrix multiply: inv(U)*inv(U)^C or
238: * inv(L)^C*inv(L). There are eight cases.
239: *
240: IF( NISODD ) THEN
241: *
242: * N is odd
243: *
244: IF( NORMALTRANSR ) THEN
245: *
246: * N is odd and TRANSR = 'N'
247: *
248: IF( LOWER ) THEN
249: *
250: * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:N1-1) )
251: * T1 -> a(0,0), T2 -> a(0,1), S -> a(N1,0)
252: * T1 -> a(0), T2 -> a(n), S -> a(N1)
253: *
254: CALL ZLAUUM( 'L', N1, A( 0 ), N, INFO )
255: CALL ZHERK( 'L', 'C', N1, N2, ONE, A( N1 ), N, ONE,
256: + A( 0 ), N )
257: CALL ZTRMM( 'L', 'U', 'N', 'N', N2, N1, CONE, A( N ), N,
258: + A( N1 ), N )
259: CALL ZLAUUM( 'U', N2, A( N ), N, INFO )
260: *
261: ELSE
262: *
263: * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:N2-1)
264: * T1 -> a(N1+1,0), T2 -> a(N1,0), S -> a(0,0)
265: * T1 -> a(N2), T2 -> a(N1), S -> a(0)
266: *
267: CALL ZLAUUM( 'L', N1, A( N2 ), N, INFO )
268: CALL ZHERK( 'L', 'N', N1, N2, ONE, A( 0 ), N, ONE,
269: + A( N2 ), N )
270: CALL ZTRMM( 'R', 'U', 'C', 'N', N1, N2, CONE, A( N1 ), N,
271: + A( 0 ), N )
272: CALL ZLAUUM( 'U', N2, A( N1 ), N, INFO )
273: *
274: END IF
275: *
276: ELSE
277: *
278: * N is odd and TRANSR = 'C'
279: *
280: IF( LOWER ) THEN
281: *
282: * SRPA for LOWER, TRANSPOSE, and N is odd
283: * T1 -> a(0), T2 -> a(1), S -> a(0+N1*N1)
284: *
285: CALL ZLAUUM( 'U', N1, A( 0 ), N1, INFO )
286: CALL ZHERK( 'U', 'N', N1, N2, ONE, A( N1*N1 ), N1, ONE,
287: + A( 0 ), N1 )
288: CALL ZTRMM( 'R', 'L', 'N', 'N', N1, N2, CONE, A( 1 ), N1,
289: + A( N1*N1 ), N1 )
290: CALL ZLAUUM( 'L', N2, A( 1 ), N1, INFO )
291: *
292: ELSE
293: *
294: * SRPA for UPPER, TRANSPOSE, and N is odd
295: * T1 -> a(0+N2*N2), T2 -> a(0+N1*N2), S -> a(0)
296: *
297: CALL ZLAUUM( 'U', N1, A( N2*N2 ), N2, INFO )
298: CALL ZHERK( 'U', 'C', N1, N2, ONE, A( 0 ), N2, ONE,
299: + A( N2*N2 ), N2 )
300: CALL ZTRMM( 'L', 'L', 'C', 'N', N2, N1, CONE, A( N1*N2 ),
301: + N2, A( 0 ), N2 )
302: CALL ZLAUUM( 'L', N2, A( N1*N2 ), N2, INFO )
303: *
304: END IF
305: *
306: END IF
307: *
308: ELSE
309: *
310: * N is even
311: *
312: IF( NORMALTRANSR ) THEN
313: *
314: * N is even and TRANSR = 'N'
315: *
316: IF( LOWER ) THEN
317: *
318: * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) )
319: * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0)
320: * T1 -> a(1), T2 -> a(0), S -> a(k+1)
321: *
322: CALL ZLAUUM( 'L', K, A( 1 ), N+1, INFO )
323: CALL ZHERK( 'L', 'C', K, K, ONE, A( K+1 ), N+1, ONE,
324: + A( 1 ), N+1 )
325: CALL ZTRMM( 'L', 'U', 'N', 'N', K, K, CONE, A( 0 ), N+1,
326: + A( K+1 ), N+1 )
327: CALL ZLAUUM( 'U', K, A( 0 ), N+1, INFO )
328: *
329: ELSE
330: *
331: * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) )
332: * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0)
333: * T1 -> a(k+1), T2 -> a(k), S -> a(0)
334: *
335: CALL ZLAUUM( 'L', K, A( K+1 ), N+1, INFO )
336: CALL ZHERK( 'L', 'N', K, K, ONE, A( 0 ), N+1, ONE,
337: + A( K+1 ), N+1 )
338: CALL ZTRMM( 'R', 'U', 'C', 'N', K, K, CONE, A( K ), N+1,
339: + A( 0 ), N+1 )
340: CALL ZLAUUM( 'U', K, A( K ), N+1, INFO )
341: *
342: END IF
343: *
344: ELSE
345: *
346: * N is even and TRANSR = 'C'
347: *
348: IF( LOWER ) THEN
349: *
350: * SRPA for LOWER, TRANSPOSE, and N is even (see paper)
351: * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1),
352: * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k
353: *
354: CALL ZLAUUM( 'U', K, A( K ), K, INFO )
355: CALL ZHERK( 'U', 'N', K, K, ONE, A( K*( K+1 ) ), K, ONE,
356: + A( K ), K )
357: CALL ZTRMM( 'R', 'L', 'N', 'N', K, K, CONE, A( 0 ), K,
358: + A( K*( K+1 ) ), K )
359: CALL ZLAUUM( 'L', K, A( 0 ), K, INFO )
360: *
361: ELSE
362: *
363: * SRPA for UPPER, TRANSPOSE, and N is even (see paper)
364: * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0),
365: * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k
366: *
367: CALL ZLAUUM( 'U', K, A( K*( K+1 ) ), K, INFO )
368: CALL ZHERK( 'U', 'C', K, K, ONE, A( 0 ), K, ONE,
369: + A( K*( K+1 ) ), K )
370: CALL ZTRMM( 'L', 'L', 'C', 'N', K, K, CONE, A( K*K ), K,
371: + A( 0 ), K )
372: CALL ZLAUUM( 'L', K, A( K*K ), K, INFO )
373: *
374: END IF
375: *
376: END IF
377: *
378: END IF
379: *
380: RETURN
381: *
382: * End of ZPFTRI
383: *
384: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zpftri.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack