Annotation of rpl/lapack/lapack/zsycon.f, revision 1.8
1.1 bertrand 1: SUBROUTINE ZSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
2: $ INFO )
3: *
1.8 ! bertrand 4: * -- LAPACK routine (version 3.3.1) --
1.1 bertrand 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 7: * -- April 2011 --
1.1 bertrand 8: *
9: * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
10: *
11: * .. Scalar Arguments ..
12: CHARACTER UPLO
13: INTEGER INFO, LDA, N
14: DOUBLE PRECISION ANORM, RCOND
15: * ..
16: * .. Array Arguments ..
17: INTEGER IPIV( * )
18: COMPLEX*16 A( LDA, * ), WORK( * )
19: * ..
20: *
21: * Purpose
22: * =======
23: *
24: * ZSYCON estimates the reciprocal of the condition number (in the
25: * 1-norm) of a complex symmetric matrix A using the factorization
26: * A = U*D*U**T or A = L*D*L**T computed by ZSYTRF.
27: *
28: * An estimate is obtained for norm(inv(A)), and the reciprocal of the
29: * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
30: *
31: * Arguments
32: * =========
33: *
34: * UPLO (input) CHARACTER*1
35: * Specifies whether the details of the factorization are stored
36: * as an upper or lower triangular matrix.
37: * = 'U': Upper triangular, form is A = U*D*U**T;
38: * = 'L': Lower triangular, form is A = L*D*L**T.
39: *
40: * N (input) INTEGER
41: * The order of the matrix A. N >= 0.
42: *
43: * A (input) COMPLEX*16 array, dimension (LDA,N)
44: * The block diagonal matrix D and the multipliers used to
45: * obtain the factor U or L as computed by ZSYTRF.
46: *
47: * LDA (input) INTEGER
48: * The leading dimension of the array A. LDA >= max(1,N).
49: *
50: * IPIV (input) INTEGER array, dimension (N)
51: * Details of the interchanges and the block structure of D
52: * as determined by ZSYTRF.
53: *
54: * ANORM (input) DOUBLE PRECISION
55: * The 1-norm of the original matrix A.
56: *
57: * RCOND (output) DOUBLE PRECISION
58: * The reciprocal of the condition number of the matrix A,
59: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
60: * estimate of the 1-norm of inv(A) computed in this routine.
61: *
62: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
63: *
64: * INFO (output) INTEGER
65: * = 0: successful exit
66: * < 0: if INFO = -i, the i-th argument had an illegal value
67: *
68: * =====================================================================
69: *
70: * .. Parameters ..
71: DOUBLE PRECISION ONE, ZERO
72: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
73: * ..
74: * .. Local Scalars ..
75: LOGICAL UPPER
76: INTEGER I, KASE
77: DOUBLE PRECISION AINVNM
78: * ..
79: * .. Local Arrays ..
80: INTEGER ISAVE( 3 )
81: * ..
82: * .. External Functions ..
83: LOGICAL LSAME
84: EXTERNAL LSAME
85: * ..
86: * .. External Subroutines ..
87: EXTERNAL XERBLA, ZLACN2, ZSYTRS
88: * ..
89: * .. Intrinsic Functions ..
90: INTRINSIC MAX
91: * ..
92: * .. Executable Statements ..
93: *
94: * Test the input parameters.
95: *
96: INFO = 0
97: UPPER = LSAME( UPLO, 'U' )
98: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
99: INFO = -1
100: ELSE IF( N.LT.0 ) THEN
101: INFO = -2
102: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
103: INFO = -4
104: ELSE IF( ANORM.LT.ZERO ) THEN
105: INFO = -6
106: END IF
107: IF( INFO.NE.0 ) THEN
108: CALL XERBLA( 'ZSYCON', -INFO )
109: RETURN
110: END IF
111: *
112: * Quick return if possible
113: *
114: RCOND = ZERO
115: IF( N.EQ.0 ) THEN
116: RCOND = ONE
117: RETURN
118: ELSE IF( ANORM.LE.ZERO ) THEN
119: RETURN
120: END IF
121: *
122: * Check that the diagonal matrix D is nonsingular.
123: *
124: IF( UPPER ) THEN
125: *
126: * Upper triangular storage: examine D from bottom to top
127: *
128: DO 10 I = N, 1, -1
129: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
130: $ RETURN
131: 10 CONTINUE
132: ELSE
133: *
134: * Lower triangular storage: examine D from top to bottom.
135: *
136: DO 20 I = 1, N
137: IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
138: $ RETURN
139: 20 CONTINUE
140: END IF
141: *
142: * Estimate the 1-norm of the inverse.
143: *
144: KASE = 0
145: 30 CONTINUE
146: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
147: IF( KASE.NE.0 ) THEN
148: *
1.8 ! bertrand 149: * Multiply by inv(L*D*L**T) or inv(U*D*U**T).
1.1 bertrand 150: *
151: CALL ZSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
152: GO TO 30
153: END IF
154: *
155: * Compute the estimate of the reciprocal condition number.
156: *
157: IF( AINVNM.NE.ZERO )
158: $ RCOND = ( ONE / AINVNM ) / ANORM
159: *
160: RETURN
161: *
162: * End of ZSYCON
163: *
164: END
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