1: SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
2: *
3: * -- LAPACK routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER UPLO
10: INTEGER INFO, N
11: * ..
12: * .. Array Arguments ..
13: INTEGER IPIV( * )
14: COMPLEX*16 AP( * ), WORK( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZSPTRI computes the inverse of a complex symmetric indefinite matrix
21: * A in packed storage using the factorization A = U*D*U**T or
22: * A = L*D*L**T computed by ZSPTRF.
23: *
24: * Arguments
25: * =========
26: *
27: * UPLO (input) CHARACTER*1
28: * Specifies whether the details of the factorization are stored
29: * as an upper or lower triangular matrix.
30: * = 'U': Upper triangular, form is A = U*D*U**T;
31: * = 'L': Lower triangular, form is A = L*D*L**T.
32: *
33: * N (input) INTEGER
34: * The order of the matrix A. N >= 0.
35: *
36: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
37: * On entry, the block diagonal matrix D and the multipliers
38: * used to obtain the factor U or L as computed by ZSPTRF,
39: * stored as a packed triangular matrix.
40: *
41: * On exit, if INFO = 0, the (symmetric) inverse of the original
42: * matrix, stored as a packed triangular matrix. The j-th column
43: * of inv(A) is stored in the array AP as follows:
44: * if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
45: * if UPLO = 'L',
46: * AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
47: *
48: * IPIV (input) INTEGER array, dimension (N)
49: * Details of the interchanges and the block structure of D
50: * as determined by ZSPTRF.
51: *
52: * WORK (workspace) COMPLEX*16 array, dimension (N)
53: *
54: * INFO (output) INTEGER
55: * = 0: successful exit
56: * < 0: if INFO = -i, the i-th argument had an illegal value
57: * > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
58: * inverse could not be computed.
59: *
60: * =====================================================================
61: *
62: * .. Parameters ..
63: COMPLEX*16 ONE, ZERO
64: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
65: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
66: * ..
67: * .. Local Scalars ..
68: LOGICAL UPPER
69: INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
70: COMPLEX*16 AK, AKKP1, AKP1, D, T, TEMP
71: * ..
72: * .. External Functions ..
73: LOGICAL LSAME
74: COMPLEX*16 ZDOTU
75: EXTERNAL LSAME, ZDOTU
76: * ..
77: * .. External Subroutines ..
78: EXTERNAL XERBLA, ZCOPY, ZSPMV, ZSWAP
79: * ..
80: * .. Intrinsic Functions ..
81: INTRINSIC ABS
82: * ..
83: * .. Executable Statements ..
84: *
85: * Test the input parameters.
86: *
87: INFO = 0
88: UPPER = LSAME( UPLO, 'U' )
89: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
90: INFO = -1
91: ELSE IF( N.LT.0 ) THEN
92: INFO = -2
93: END IF
94: IF( INFO.NE.0 ) THEN
95: CALL XERBLA( 'ZSPTRI', -INFO )
96: RETURN
97: END IF
98: *
99: * Quick return if possible
100: *
101: IF( N.EQ.0 )
102: $ RETURN
103: *
104: * Check that the diagonal matrix D is nonsingular.
105: *
106: IF( UPPER ) THEN
107: *
108: * Upper triangular storage: examine D from bottom to top
109: *
110: KP = N*( N+1 ) / 2
111: DO 10 INFO = N, 1, -1
112: IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
113: $ RETURN
114: KP = KP - INFO
115: 10 CONTINUE
116: ELSE
117: *
118: * Lower triangular storage: examine D from top to bottom.
119: *
120: KP = 1
121: DO 20 INFO = 1, N
122: IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
123: $ RETURN
124: KP = KP + N - INFO + 1
125: 20 CONTINUE
126: END IF
127: INFO = 0
128: *
129: IF( UPPER ) THEN
130: *
131: * Compute inv(A) from the factorization A = U*D*U'.
132: *
133: * K is the main loop index, increasing from 1 to N in steps of
134: * 1 or 2, depending on the size of the diagonal blocks.
135: *
136: K = 1
137: KC = 1
138: 30 CONTINUE
139: *
140: * If K > N, exit from loop.
141: *
142: IF( K.GT.N )
143: $ GO TO 50
144: *
145: KCNEXT = KC + K
146: IF( IPIV( K ).GT.0 ) THEN
147: *
148: * 1 x 1 diagonal block
149: *
150: * Invert the diagonal block.
151: *
152: AP( KC+K-1 ) = ONE / AP( KC+K-1 )
153: *
154: * Compute column K of the inverse.
155: *
156: IF( K.GT.1 ) THEN
157: CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
158: CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
159: $ 1 )
160: AP( KC+K-1 ) = AP( KC+K-1 ) -
161: $ ZDOTU( K-1, WORK, 1, AP( KC ), 1 )
162: END IF
163: KSTEP = 1
164: ELSE
165: *
166: * 2 x 2 diagonal block
167: *
168: * Invert the diagonal block.
169: *
170: T = AP( KCNEXT+K-1 )
171: AK = AP( KC+K-1 ) / T
172: AKP1 = AP( KCNEXT+K ) / T
173: AKKP1 = AP( KCNEXT+K-1 ) / T
174: D = T*( AK*AKP1-ONE )
175: AP( KC+K-1 ) = AKP1 / D
176: AP( KCNEXT+K ) = AK / D
177: AP( KCNEXT+K-1 ) = -AKKP1 / D
178: *
179: * Compute columns K and K+1 of the inverse.
180: *
181: IF( K.GT.1 ) THEN
182: CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
183: CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
184: $ 1 )
185: AP( KC+K-1 ) = AP( KC+K-1 ) -
186: $ ZDOTU( K-1, WORK, 1, AP( KC ), 1 )
187: AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
188: $ ZDOTU( K-1, AP( KC ), 1, AP( KCNEXT ),
189: $ 1 )
190: CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
191: CALL ZSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO,
192: $ AP( KCNEXT ), 1 )
193: AP( KCNEXT+K ) = AP( KCNEXT+K ) -
194: $ ZDOTU( K-1, WORK, 1, AP( KCNEXT ), 1 )
195: END IF
196: KSTEP = 2
197: KCNEXT = KCNEXT + K + 1
198: END IF
199: *
200: KP = ABS( IPIV( K ) )
201: IF( KP.NE.K ) THEN
202: *
203: * Interchange rows and columns K and KP in the leading
204: * submatrix A(1:k+1,1:k+1)
205: *
206: KPC = ( KP-1 )*KP / 2 + 1
207: CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
208: KX = KPC + KP - 1
209: DO 40 J = KP + 1, K - 1
210: KX = KX + J - 1
211: TEMP = AP( KC+J-1 )
212: AP( KC+J-1 ) = AP( KX )
213: AP( KX ) = TEMP
214: 40 CONTINUE
215: TEMP = AP( KC+K-1 )
216: AP( KC+K-1 ) = AP( KPC+KP-1 )
217: AP( KPC+KP-1 ) = TEMP
218: IF( KSTEP.EQ.2 ) THEN
219: TEMP = AP( KC+K+K-1 )
220: AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
221: AP( KC+K+KP-1 ) = TEMP
222: END IF
223: END IF
224: *
225: K = K + KSTEP
226: KC = KCNEXT
227: GO TO 30
228: 50 CONTINUE
229: *
230: ELSE
231: *
232: * Compute inv(A) from the factorization A = L*D*L'.
233: *
234: * K is the main loop index, increasing from 1 to N in steps of
235: * 1 or 2, depending on the size of the diagonal blocks.
236: *
237: NPP = N*( N+1 ) / 2
238: K = N
239: KC = NPP
240: 60 CONTINUE
241: *
242: * If K < 1, exit from loop.
243: *
244: IF( K.LT.1 )
245: $ GO TO 80
246: *
247: KCNEXT = KC - ( N-K+2 )
248: IF( IPIV( K ).GT.0 ) THEN
249: *
250: * 1 x 1 diagonal block
251: *
252: * Invert the diagonal block.
253: *
254: AP( KC ) = ONE / AP( KC )
255: *
256: * Compute column K of the inverse.
257: *
258: IF( K.LT.N ) THEN
259: CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
260: CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+N-K+1 ), WORK, 1,
261: $ ZERO, AP( KC+1 ), 1 )
262: AP( KC ) = AP( KC ) - ZDOTU( N-K, WORK, 1, AP( KC+1 ),
263: $ 1 )
264: END IF
265: KSTEP = 1
266: ELSE
267: *
268: * 2 x 2 diagonal block
269: *
270: * Invert the diagonal block.
271: *
272: T = AP( KCNEXT+1 )
273: AK = AP( KCNEXT ) / T
274: AKP1 = AP( KC ) / T
275: AKKP1 = AP( KCNEXT+1 ) / T
276: D = T*( AK*AKP1-ONE )
277: AP( KCNEXT ) = AKP1 / D
278: AP( KC ) = AK / D
279: AP( KCNEXT+1 ) = -AKKP1 / D
280: *
281: * Compute columns K-1 and K of the inverse.
282: *
283: IF( K.LT.N ) THEN
284: CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
285: CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
286: $ ZERO, AP( KC+1 ), 1 )
287: AP( KC ) = AP( KC ) - ZDOTU( N-K, WORK, 1, AP( KC+1 ),
288: $ 1 )
289: AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
290: $ ZDOTU( N-K, AP( KC+1 ), 1,
291: $ AP( KCNEXT+2 ), 1 )
292: CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
293: CALL ZSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
294: $ ZERO, AP( KCNEXT+2 ), 1 )
295: AP( KCNEXT ) = AP( KCNEXT ) -
296: $ ZDOTU( N-K, WORK, 1, AP( KCNEXT+2 ), 1 )
297: END IF
298: KSTEP = 2
299: KCNEXT = KCNEXT - ( N-K+3 )
300: END IF
301: *
302: KP = ABS( IPIV( K ) )
303: IF( KP.NE.K ) THEN
304: *
305: * Interchange rows and columns K and KP in the trailing
306: * submatrix A(k-1:n,k-1:n)
307: *
308: KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
309: IF( KP.LT.N )
310: $ CALL ZSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
311: KX = KC + KP - K
312: DO 70 J = K + 1, KP - 1
313: KX = KX + N - J + 1
314: TEMP = AP( KC+J-K )
315: AP( KC+J-K ) = AP( KX )
316: AP( KX ) = TEMP
317: 70 CONTINUE
318: TEMP = AP( KC )
319: AP( KC ) = AP( KPC )
320: AP( KPC ) = TEMP
321: IF( KSTEP.EQ.2 ) THEN
322: TEMP = AP( KC-N+K-1 )
323: AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
324: AP( KC-N+KP-1 ) = TEMP
325: END IF
326: END IF
327: *
328: K = K - KSTEP
329: KC = KCNEXT
330: GO TO 60
331: 80 CONTINUE
332: END IF
333: *
334: RETURN
335: *
336: * End of ZSPTRI
337: *
338: END
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