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1.1 bertrand 1: SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, 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, LDA, LDB, N, NRHS
11: * ..
12: * .. Array Arguments ..
13: INTEGER IPIV( * )
14: DOUBLE PRECISION A( LDA, * ), B( LDB, * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * DSYTRS solves a system of linear equations A*X = B with a real
21: * symmetric matrix A using the factorization A = U*D*U**T or
22: * A = L*D*L**T computed by DSYTRF.
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: * NRHS (input) INTEGER
37: * The number of right hand sides, i.e., the number of columns
38: * of the matrix B. NRHS >= 0.
39: *
40: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
41: * The block diagonal matrix D and the multipliers used to
42: * obtain the factor U or L as computed by DSYTRF.
43: *
44: * LDA (input) INTEGER
45: * The leading dimension of the array A. LDA >= max(1,N).
46: *
47: * IPIV (input) INTEGER array, dimension (N)
48: * Details of the interchanges and the block structure of D
49: * as determined by DSYTRF.
50: *
51: * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
52: * On entry, the right hand side matrix B.
53: * On exit, the solution matrix X.
54: *
55: * LDB (input) INTEGER
56: * The leading dimension of the array B. LDB >= max(1,N).
57: *
58: * INFO (output) INTEGER
59: * = 0: successful exit
60: * < 0: if INFO = -i, the i-th argument had an illegal value
61: *
62: * =====================================================================
63: *
64: * .. Parameters ..
65: DOUBLE PRECISION ONE
66: PARAMETER ( ONE = 1.0D+0 )
67: * ..
68: * .. Local Scalars ..
69: LOGICAL UPPER
70: INTEGER J, K, KP
71: DOUBLE PRECISION AK, AKM1, AKM1K, BK, BKM1, DENOM
72: * ..
73: * .. External Functions ..
74: LOGICAL LSAME
75: EXTERNAL LSAME
76: * ..
77: * .. External Subroutines ..
78: EXTERNAL DGEMV, DGER, DSCAL, DSWAP, XERBLA
79: * ..
80: * .. Intrinsic Functions ..
81: INTRINSIC MAX
82: * ..
83: * .. Executable Statements ..
84: *
85: INFO = 0
86: UPPER = LSAME( UPLO, 'U' )
87: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
88: INFO = -1
89: ELSE IF( N.LT.0 ) THEN
90: INFO = -2
91: ELSE IF( NRHS.LT.0 ) THEN
92: INFO = -3
93: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
94: INFO = -5
95: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
96: INFO = -8
97: END IF
98: IF( INFO.NE.0 ) THEN
99: CALL XERBLA( 'DSYTRS', -INFO )
100: RETURN
101: END IF
102: *
103: * Quick return if possible
104: *
105: IF( N.EQ.0 .OR. NRHS.EQ.0 )
106: $ RETURN
107: *
108: IF( UPPER ) THEN
109: *
110: * Solve A*X = B, where A = U*D*U'.
111: *
112: * First solve U*D*X = B, overwriting B with X.
113: *
114: * K is the main loop index, decreasing from N to 1 in steps of
115: * 1 or 2, depending on the size of the diagonal blocks.
116: *
117: K = N
118: 10 CONTINUE
119: *
120: * If K < 1, exit from loop.
121: *
122: IF( K.LT.1 )
123: $ GO TO 30
124: *
125: IF( IPIV( K ).GT.0 ) THEN
126: *
127: * 1 x 1 diagonal block
128: *
129: * Interchange rows K and IPIV(K).
130: *
131: KP = IPIV( K )
132: IF( KP.NE.K )
133: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
134: *
135: * Multiply by inv(U(K)), where U(K) is the transformation
136: * stored in column K of A.
137: *
138: CALL DGER( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
139: $ B( 1, 1 ), LDB )
140: *
141: * Multiply by the inverse of the diagonal block.
142: *
143: CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
144: K = K - 1
145: ELSE
146: *
147: * 2 x 2 diagonal block
148: *
149: * Interchange rows K-1 and -IPIV(K).
150: *
151: KP = -IPIV( K )
152: IF( KP.NE.K-1 )
153: $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
154: *
155: * Multiply by inv(U(K)), where U(K) is the transformation
156: * stored in columns K-1 and K of A.
157: *
158: CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
159: $ B( 1, 1 ), LDB )
160: CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
161: $ LDB, B( 1, 1 ), LDB )
162: *
163: * Multiply by the inverse of the diagonal block.
164: *
165: AKM1K = A( K-1, K )
166: AKM1 = A( K-1, K-1 ) / AKM1K
167: AK = A( K, K ) / AKM1K
168: DENOM = AKM1*AK - ONE
169: DO 20 J = 1, NRHS
170: BKM1 = B( K-1, J ) / AKM1K
171: BK = B( K, J ) / AKM1K
172: B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
173: B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
174: 20 CONTINUE
175: K = K - 2
176: END IF
177: *
178: GO TO 10
179: 30 CONTINUE
180: *
181: * Next solve U'*X = B, overwriting B with X.
182: *
183: * K is the main loop index, increasing from 1 to N in steps of
184: * 1 or 2, depending on the size of the diagonal blocks.
185: *
186: K = 1
187: 40 CONTINUE
188: *
189: * If K > N, exit from loop.
190: *
191: IF( K.GT.N )
192: $ GO TO 50
193: *
194: IF( IPIV( K ).GT.0 ) THEN
195: *
196: * 1 x 1 diagonal block
197: *
198: * Multiply by inv(U'(K)), where U(K) is the transformation
199: * stored in column K of A.
200: *
201: CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
202: $ 1, ONE, B( K, 1 ), LDB )
203: *
204: * Interchange rows K and IPIV(K).
205: *
206: KP = IPIV( K )
207: IF( KP.NE.K )
208: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
209: K = K + 1
210: ELSE
211: *
212: * 2 x 2 diagonal block
213: *
214: * Multiply by inv(U'(K+1)), where U(K+1) is the transformation
215: * stored in columns K and K+1 of A.
216: *
217: CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
218: $ 1, ONE, B( K, 1 ), LDB )
219: CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
220: $ A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
221: *
222: * Interchange rows K and -IPIV(K).
223: *
224: KP = -IPIV( K )
225: IF( KP.NE.K )
226: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
227: K = K + 2
228: END IF
229: *
230: GO TO 40
231: 50 CONTINUE
232: *
233: ELSE
234: *
235: * Solve A*X = B, where A = L*D*L'.
236: *
237: * First solve L*D*X = B, overwriting B with X.
238: *
239: * K is the main loop index, increasing from 1 to N in steps of
240: * 1 or 2, depending on the size of the diagonal blocks.
241: *
242: K = 1
243: 60 CONTINUE
244: *
245: * If K > N, exit from loop.
246: *
247: IF( K.GT.N )
248: $ GO TO 80
249: *
250: IF( IPIV( K ).GT.0 ) THEN
251: *
252: * 1 x 1 diagonal block
253: *
254: * Interchange rows K and IPIV(K).
255: *
256: KP = IPIV( K )
257: IF( KP.NE.K )
258: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
259: *
260: * Multiply by inv(L(K)), where L(K) is the transformation
261: * stored in column K of A.
262: *
263: IF( K.LT.N )
264: $ CALL DGER( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
265: $ LDB, B( K+1, 1 ), LDB )
266: *
267: * Multiply by the inverse of the diagonal block.
268: *
269: CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
270: K = K + 1
271: ELSE
272: *
273: * 2 x 2 diagonal block
274: *
275: * Interchange rows K+1 and -IPIV(K).
276: *
277: KP = -IPIV( K )
278: IF( KP.NE.K+1 )
279: $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
280: *
281: * Multiply by inv(L(K)), where L(K) is the transformation
282: * stored in columns K and K+1 of A.
283: *
284: IF( K.LT.N-1 ) THEN
285: CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
286: $ LDB, B( K+2, 1 ), LDB )
287: CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
288: $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
289: END IF
290: *
291: * Multiply by the inverse of the diagonal block.
292: *
293: AKM1K = A( K+1, K )
294: AKM1 = A( K, K ) / AKM1K
295: AK = A( K+1, K+1 ) / AKM1K
296: DENOM = AKM1*AK - ONE
297: DO 70 J = 1, NRHS
298: BKM1 = B( K, J ) / AKM1K
299: BK = B( K+1, J ) / AKM1K
300: B( K, J ) = ( AK*BKM1-BK ) / DENOM
301: B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
302: 70 CONTINUE
303: K = K + 2
304: END IF
305: *
306: GO TO 60
307: 80 CONTINUE
308: *
309: * Next solve L'*X = B, overwriting B with X.
310: *
311: * K is the main loop index, decreasing from N to 1 in steps of
312: * 1 or 2, depending on the size of the diagonal blocks.
313: *
314: K = N
315: 90 CONTINUE
316: *
317: * If K < 1, exit from loop.
318: *
319: IF( K.LT.1 )
320: $ GO TO 100
321: *
322: IF( IPIV( K ).GT.0 ) THEN
323: *
324: * 1 x 1 diagonal block
325: *
326: * Multiply by inv(L'(K)), where L(K) is the transformation
327: * stored in column K of A.
328: *
329: IF( K.LT.N )
330: $ CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
331: $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
332: *
333: * Interchange rows K and IPIV(K).
334: *
335: KP = IPIV( K )
336: IF( KP.NE.K )
337: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
338: K = K - 1
339: ELSE
340: *
341: * 2 x 2 diagonal block
342: *
343: * Multiply by inv(L'(K-1)), where L(K-1) is the transformation
344: * stored in columns K-1 and K of A.
345: *
346: IF( K.LT.N ) THEN
347: CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
348: $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
349: CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
350: $ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
351: $ LDB )
352: END IF
353: *
354: * Interchange rows K and -IPIV(K).
355: *
356: KP = -IPIV( K )
357: IF( KP.NE.K )
358: $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
359: K = K - 2
360: END IF
361: *
362: GO TO 90
363: 100 CONTINUE
364: END IF
365: *
366: RETURN
367: *
368: * End of DSYTRS
369: *
370: END