1: DOUBLE PRECISION FUNCTION ZLA_SYRCOND_C( UPLO, N, A, LDA, AF,
2: $ LDAF, IPIV, C, CAPPLY,
3: $ INFO, WORK, RWORK )
4: *
5: * -- LAPACK routine (version 3.2.1) --
6: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
7: * -- Jason Riedy of Univ. of California Berkeley. --
8: * -- April 2009 --
9: *
10: * -- LAPACK is a software package provided by Univ. of Tennessee, --
11: * -- Univ. of California Berkeley and NAG Ltd. --
12: *
13: IMPLICIT NONE
14: * ..
15: * .. Scalar Arguments ..
16: CHARACTER UPLO
17: LOGICAL CAPPLY
18: INTEGER N, LDA, LDAF, INFO
19: * ..
20: * .. Array Arguments ..
21: INTEGER IPIV( * )
22: COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * )
23: DOUBLE PRECISION C( * ), RWORK( * )
24: * ..
25: *
26: * Purpose
27: * =======
28: *
29: * ZLA_SYRCOND_C Computes the infinity norm condition number of
30: * op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
31: *
32: * Arguments
33: * =========
34: *
35: * UPLO (input) CHARACTER*1
36: * = 'U': Upper triangle of A is stored;
37: * = 'L': Lower triangle of A is stored.
38: *
39: * N (input) INTEGER
40: * The number of linear equations, i.e., the order of the
41: * matrix A. N >= 0.
42: *
43: * A (input) COMPLEX*16 array, dimension (LDA,N)
44: * On entry, the N-by-N matrix A
45: *
46: * LDA (input) INTEGER
47: * The leading dimension of the array A. LDA >= max(1,N).
48: *
49: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
50: * The block diagonal matrix D and the multipliers used to
51: * obtain the factor U or L as computed by ZSYTRF.
52: *
53: * LDAF (input) INTEGER
54: * The leading dimension of the array AF. LDAF >= max(1,N).
55: *
56: * IPIV (input) INTEGER array, dimension (N)
57: * Details of the interchanges and the block structure of D
58: * as determined by ZSYTRF.
59: *
60: * C (input) DOUBLE PRECISION array, dimension (N)
61: * The vector C in the formula op(A) * inv(diag(C)).
62: *
63: * CAPPLY (input) LOGICAL
64: * If .TRUE. then access the vector C in the formula above.
65: *
66: * INFO (output) INTEGER
67: * = 0: Successful exit.
68: * i > 0: The ith argument is invalid.
69: *
70: * WORK (input) COMPLEX*16 array, dimension (2*N).
71: * Workspace.
72: *
73: * RWORK (input) DOUBLE PRECISION array, dimension (N).
74: * Workspace.
75: *
76: * =====================================================================
77: *
78: * .. Local Scalars ..
79: INTEGER KASE
80: DOUBLE PRECISION AINVNM, ANORM, TMP
81: INTEGER I, J
82: LOGICAL UP
83: COMPLEX*16 ZDUM
84: * ..
85: * .. Local Arrays ..
86: INTEGER ISAVE( 3 )
87: * ..
88: * .. External Functions ..
89: LOGICAL LSAME
90: EXTERNAL LSAME
91: * ..
92: * .. External Subroutines ..
93: EXTERNAL ZLACN2, ZSYTRS, XERBLA
94: * ..
95: * .. Intrinsic Functions ..
96: INTRINSIC ABS, MAX
97: * ..
98: * .. Statement Functions ..
99: DOUBLE PRECISION CABS1
100: * ..
101: * .. Statement Function Definitions ..
102: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
103: * ..
104: * .. Executable Statements ..
105: *
106: ZLA_SYRCOND_C = 0.0D+0
107: *
108: INFO = 0
109: IF( N.LT.0 ) THEN
110: INFO = -2
111: END IF
112: IF( INFO.NE.0 ) THEN
113: CALL XERBLA( 'ZLA_SYRCOND_C', -INFO )
114: RETURN
115: END IF
116: UP = .FALSE.
117: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
118: *
119: * Compute norm of op(A)*op2(C).
120: *
121: ANORM = 0.0D+0
122: IF ( UP ) THEN
123: DO I = 1, N
124: TMP = 0.0D+0
125: IF ( CAPPLY ) THEN
126: DO J = 1, I
127: TMP = TMP + CABS1( A( J, I ) ) / C( J )
128: END DO
129: DO J = I+1, N
130: TMP = TMP + CABS1( A( I, J ) ) / C( J )
131: END DO
132: ELSE
133: DO J = 1, I
134: TMP = TMP + CABS1( A( J, I ) )
135: END DO
136: DO J = I+1, N
137: TMP = TMP + CABS1( A( I, J ) )
138: END DO
139: END IF
140: RWORK( I ) = TMP
141: ANORM = MAX( ANORM, TMP )
142: END DO
143: ELSE
144: DO I = 1, N
145: TMP = 0.0D+0
146: IF ( CAPPLY ) THEN
147: DO J = 1, I
148: TMP = TMP + CABS1( A( I, J ) ) / C( J )
149: END DO
150: DO J = I+1, N
151: TMP = TMP + CABS1( A( J, I ) ) / C( J )
152: END DO
153: ELSE
154: DO J = 1, I
155: TMP = TMP + CABS1( A( I, J ) )
156: END DO
157: DO J = I+1, N
158: TMP = TMP + CABS1( A( J, I ) )
159: END DO
160: END IF
161: RWORK( I ) = TMP
162: ANORM = MAX( ANORM, TMP )
163: END DO
164: END IF
165: *
166: * Quick return if possible.
167: *
168: IF( N.EQ.0 ) THEN
169: ZLA_SYRCOND_C = 1.0D+0
170: RETURN
171: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
172: RETURN
173: END IF
174: *
175: * Estimate the norm of inv(op(A)).
176: *
177: AINVNM = 0.0D+0
178: *
179: KASE = 0
180: 10 CONTINUE
181: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
182: IF( KASE.NE.0 ) THEN
183: IF( KASE.EQ.2 ) THEN
184: *
185: * Multiply by R.
186: *
187: DO I = 1, N
188: WORK( I ) = WORK( I ) * RWORK( I )
189: END DO
190: *
191: IF ( UP ) THEN
192: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
193: $ WORK, N, INFO )
194: ELSE
195: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
196: $ WORK, N, INFO )
197: ENDIF
198: *
199: * Multiply by inv(C).
200: *
201: IF ( CAPPLY ) THEN
202: DO I = 1, N
203: WORK( I ) = WORK( I ) * C( I )
204: END DO
205: END IF
206: ELSE
207: *
208: * Multiply by inv(C**T).
209: *
210: IF ( CAPPLY ) THEN
211: DO I = 1, N
212: WORK( I ) = WORK( I ) * C( I )
213: END DO
214: END IF
215: *
216: IF ( UP ) THEN
217: CALL ZSYTRS( 'U', N, 1, AF, LDAF, IPIV,
218: $ WORK, N, INFO )
219: ELSE
220: CALL ZSYTRS( 'L', N, 1, AF, LDAF, IPIV,
221: $ WORK, N, INFO )
222: END IF
223: *
224: * Multiply by R.
225: *
226: DO I = 1, N
227: WORK( I ) = WORK( I ) * RWORK( I )
228: END DO
229: END IF
230: GO TO 10
231: END IF
232: *
233: * Compute the estimate of the reciprocal condition number.
234: *
235: IF( AINVNM .NE. 0.0D+0 )
236: $ ZLA_SYRCOND_C = 1.0D+0 / AINVNM
237: *
238: RETURN
239: *
240: END
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