1: SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, 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, ITYPE, LDA, LDB, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION A( LDA, * ), B( LDB, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DSYGS2 reduces a real symmetric-definite generalized eigenproblem
20: * to standard form.
21: *
22: * If ITYPE = 1, the problem is A*x = lambda*B*x,
23: * and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')
24: *
25: * If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
26: * B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.
27: *
28: * B must have been previously factorized as U'*U or L*L' by DPOTRF.
29: *
30: * Arguments
31: * =========
32: *
33: * ITYPE (input) INTEGER
34: * = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
35: * = 2 or 3: compute U*A*U' or L'*A*L.
36: *
37: * UPLO (input) CHARACTER*1
38: * Specifies whether the upper or lower triangular part of the
39: * symmetric matrix A is stored, and how B has been factorized.
40: * = 'U': Upper triangular
41: * = 'L': Lower triangular
42: *
43: * N (input) INTEGER
44: * The order of the matrices A and B. N >= 0.
45: *
46: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
47: * On entry, the symmetric matrix A. If UPLO = 'U', the leading
48: * n by n upper triangular part of A contains the upper
49: * triangular part of the matrix A, and the strictly lower
50: * triangular part of A is not referenced. If UPLO = 'L', the
51: * leading n by n lower triangular part of A contains the lower
52: * triangular part of the matrix A, and the strictly upper
53: * triangular part of A is not referenced.
54: *
55: * On exit, if INFO = 0, the transformed matrix, stored in the
56: * same format as A.
57: *
58: * LDA (input) INTEGER
59: * The leading dimension of the array A. LDA >= max(1,N).
60: *
61: * B (input) DOUBLE PRECISION array, dimension (LDB,N)
62: * The triangular factor from the Cholesky factorization of B,
63: * as returned by DPOTRF.
64: *
65: * LDB (input) INTEGER
66: * The leading dimension of the array B. LDB >= max(1,N).
67: *
68: * INFO (output) INTEGER
69: * = 0: successful exit.
70: * < 0: if INFO = -i, the i-th argument had an illegal value.
71: *
72: * =====================================================================
73: *
74: * .. Parameters ..
75: DOUBLE PRECISION ONE, HALF
76: PARAMETER ( ONE = 1.0D0, HALF = 0.5D0 )
77: * ..
78: * .. Local Scalars ..
79: LOGICAL UPPER
80: INTEGER K
81: DOUBLE PRECISION AKK, BKK, CT
82: * ..
83: * .. External Subroutines ..
84: EXTERNAL DAXPY, DSCAL, DSYR2, DTRMV, DTRSV, XERBLA
85: * ..
86: * .. Intrinsic Functions ..
87: INTRINSIC MAX
88: * ..
89: * .. External Functions ..
90: LOGICAL LSAME
91: EXTERNAL LSAME
92: * ..
93: * .. Executable Statements ..
94: *
95: * Test the input parameters.
96: *
97: INFO = 0
98: UPPER = LSAME( UPLO, 'U' )
99: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
100: INFO = -1
101: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
102: INFO = -2
103: ELSE IF( N.LT.0 ) THEN
104: INFO = -3
105: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
106: INFO = -5
107: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
108: INFO = -7
109: END IF
110: IF( INFO.NE.0 ) THEN
111: CALL XERBLA( 'DSYGS2', -INFO )
112: RETURN
113: END IF
114: *
115: IF( ITYPE.EQ.1 ) THEN
116: IF( UPPER ) THEN
117: *
118: * Compute inv(U')*A*inv(U)
119: *
120: DO 10 K = 1, N
121: *
122: * Update the upper triangle of A(k:n,k:n)
123: *
124: AKK = A( K, K )
125: BKK = B( K, K )
126: AKK = AKK / BKK**2
127: A( K, K ) = AKK
128: IF( K.LT.N ) THEN
129: CALL DSCAL( N-K, ONE / BKK, A( K, K+1 ), LDA )
130: CT = -HALF*AKK
131: CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ),
132: $ LDA )
133: CALL DSYR2( UPLO, N-K, -ONE, A( K, K+1 ), LDA,
134: $ B( K, K+1 ), LDB, A( K+1, K+1 ), LDA )
135: CALL DAXPY( N-K, CT, B( K, K+1 ), LDB, A( K, K+1 ),
136: $ LDA )
137: CALL DTRSV( UPLO, 'Transpose', 'Non-unit', N-K,
138: $ B( K+1, K+1 ), LDB, A( K, K+1 ), LDA )
139: END IF
140: 10 CONTINUE
141: ELSE
142: *
143: * Compute inv(L)*A*inv(L')
144: *
145: DO 20 K = 1, N
146: *
147: * Update the lower triangle of A(k:n,k:n)
148: *
149: AKK = A( K, K )
150: BKK = B( K, K )
151: AKK = AKK / BKK**2
152: A( K, K ) = AKK
153: IF( K.LT.N ) THEN
154: CALL DSCAL( N-K, ONE / BKK, A( K+1, K ), 1 )
155: CT = -HALF*AKK
156: CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 )
157: CALL DSYR2( UPLO, N-K, -ONE, A( K+1, K ), 1,
158: $ B( K+1, K ), 1, A( K+1, K+1 ), LDA )
159: CALL DAXPY( N-K, CT, B( K+1, K ), 1, A( K+1, K ), 1 )
160: CALL DTRSV( UPLO, 'No transpose', 'Non-unit', N-K,
161: $ B( K+1, K+1 ), LDB, A( K+1, K ), 1 )
162: END IF
163: 20 CONTINUE
164: END IF
165: ELSE
166: IF( UPPER ) THEN
167: *
168: * Compute U*A*U'
169: *
170: DO 30 K = 1, N
171: *
172: * Update the upper triangle of A(1:k,1:k)
173: *
174: AKK = A( K, K )
175: BKK = B( K, K )
176: CALL DTRMV( UPLO, 'No transpose', 'Non-unit', K-1, B,
177: $ LDB, A( 1, K ), 1 )
178: CT = HALF*AKK
179: CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 )
180: CALL DSYR2( UPLO, K-1, ONE, A( 1, K ), 1, B( 1, K ), 1,
181: $ A, LDA )
182: CALL DAXPY( K-1, CT, B( 1, K ), 1, A( 1, K ), 1 )
183: CALL DSCAL( K-1, BKK, A( 1, K ), 1 )
184: A( K, K ) = AKK*BKK**2
185: 30 CONTINUE
186: ELSE
187: *
188: * Compute L'*A*L
189: *
190: DO 40 K = 1, N
191: *
192: * Update the lower triangle of A(1:k,1:k)
193: *
194: AKK = A( K, K )
195: BKK = B( K, K )
196: CALL DTRMV( UPLO, 'Transpose', 'Non-unit', K-1, B, LDB,
197: $ A( K, 1 ), LDA )
198: CT = HALF*AKK
199: CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA )
200: CALL DSYR2( UPLO, K-1, ONE, A( K, 1 ), LDA, B( K, 1 ),
201: $ LDB, A, LDA )
202: CALL DAXPY( K-1, CT, B( K, 1 ), LDB, A( K, 1 ), LDA )
203: CALL DSCAL( K-1, BKK, A( K, 1 ), LDA )
204: A( K, K ) = AKK*BKK**2
205: 40 CONTINUE
206: END IF
207: END IF
208: RETURN
209: *
210: * End of DSYGS2
211: *
212: END
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