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1.1 bertrand 1: DOUBLE PRECISION FUNCTION ZLA_HERCOND_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_HERCOND_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 ZHETRF.
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 CHETRF.
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, I, J
80: DOUBLE PRECISION AINVNM, ANORM, TMP
81: LOGICAL UP
82: COMPLEX*16 ZDUM
83: * ..
84: * .. Local Arrays ..
85: INTEGER ISAVE( 3 )
86: * ..
87: * .. External Functions ..
88: LOGICAL LSAME
89: EXTERNAL LSAME
90: * ..
91: * .. External Subroutines ..
92: EXTERNAL ZLACN2, ZHETRS, XERBLA
93: * ..
94: * .. Intrinsic Functions ..
95: INTRINSIC ABS, MAX
96: * ..
97: * .. Statement Functions ..
98: DOUBLE PRECISION CABS1
99: * ..
100: * .. Statement Function Definitions ..
101: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
102: * ..
103: * .. Executable Statements ..
104: *
105: ZLA_HERCOND_C = 0.0D+0
106: *
107: INFO = 0
108: IF( N.LT.0 ) THEN
109: INFO = -2
110: END IF
111: IF( INFO.NE.0 ) THEN
112: CALL XERBLA( 'ZLA_HERCOND_C', -INFO )
113: RETURN
114: END IF
115: UP = .FALSE.
116: IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
117: *
118: * Compute norm of op(A)*op2(C).
119: *
120: ANORM = 0.0D+0
121: IF ( UP ) THEN
122: DO I = 1, N
123: TMP = 0.0D+0
124: IF ( CAPPLY ) THEN
125: DO J = 1, I
126: TMP = TMP + CABS1( A( J, I ) ) / C( J )
127: END DO
128: DO J = I+1, N
129: TMP = TMP + CABS1( A( I, J ) ) / C( J )
130: END DO
131: ELSE
132: DO J = 1, I
133: TMP = TMP + CABS1( A( J, I ) )
134: END DO
135: DO J = I+1, N
136: TMP = TMP + CABS1( A( I, J ) )
137: END DO
138: END IF
139: RWORK( I ) = TMP
140: ANORM = MAX( ANORM, TMP )
141: END DO
142: ELSE
143: DO I = 1, N
144: TMP = 0.0D+0
145: IF ( CAPPLY ) THEN
146: DO J = 1, I
147: TMP = TMP + CABS1( A( I, J ) ) / C( J )
148: END DO
149: DO J = I+1, N
150: TMP = TMP + CABS1( A( J, I ) ) / C( J )
151: END DO
152: ELSE
153: DO J = 1, I
154: TMP = TMP + CABS1( A( I, J ) )
155: END DO
156: DO J = I+1, N
157: TMP = TMP + CABS1( A( J, I ) )
158: END DO
159: END IF
160: RWORK( I ) = TMP
161: ANORM = MAX( ANORM, TMP )
162: END DO
163: END IF
164: *
165: * Quick return if possible.
166: *
167: IF( N.EQ.0 ) THEN
168: ZLA_HERCOND_C = 1.0D+0
169: RETURN
170: ELSE IF( ANORM .EQ. 0.0D+0 ) THEN
171: RETURN
172: END IF
173: *
174: * Estimate the norm of inv(op(A)).
175: *
176: AINVNM = 0.0D+0
177: *
178: KASE = 0
179: 10 CONTINUE
180: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
181: IF( KASE.NE.0 ) THEN
182: IF( KASE.EQ.2 ) THEN
183: *
184: * Multiply by R.
185: *
186: DO I = 1, N
187: WORK( I ) = WORK( I ) * RWORK( I )
188: END DO
189: *
190: IF ( UP ) THEN
191: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
192: $ WORK, N, INFO )
193: ELSE
194: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
195: $ WORK, N, INFO )
196: ENDIF
197: *
198: * Multiply by inv(C).
199: *
200: IF ( CAPPLY ) THEN
201: DO I = 1, N
202: WORK( I ) = WORK( I ) * C( I )
203: END DO
204: END IF
205: ELSE
206: *
207: * Multiply by inv(C').
208: *
209: IF ( CAPPLY ) THEN
210: DO I = 1, N
211: WORK( I ) = WORK( I ) * C( I )
212: END DO
213: END IF
214: *
215: IF ( UP ) THEN
216: CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV,
217: $ WORK, N, INFO )
218: ELSE
219: CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV,
220: $ WORK, N, INFO )
221: END IF
222: *
223: * Multiply by R.
224: *
225: DO I = 1, N
226: WORK( I ) = WORK( I ) * RWORK( I )
227: END DO
228: END IF
229: GO TO 10
230: END IF
231: *
232: * Compute the estimate of the reciprocal condition number.
233: *
234: IF( AINVNM .NE. 0.0D+0 )
235: $ ZLA_HERCOND_C = 1.0D+0 / AINVNM
236: *
237: RETURN
238: *
239: END