1: SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
2: $ RWORK, INFO )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
10: *
11: * .. Scalar Arguments ..
12: CHARACTER DIAG, NORM, UPLO
13: INTEGER INFO, LDA, N
14: DOUBLE PRECISION RCOND
15: * ..
16: * .. Array Arguments ..
17: DOUBLE PRECISION RWORK( * )
18: COMPLEX*16 A( LDA, * ), WORK( * )
19: * ..
20: *
21: * Purpose
22: * =======
23: *
24: * ZTRCON estimates the reciprocal of the condition number of a
25: * triangular matrix A, in either the 1-norm or the infinity-norm.
26: *
27: * The norm of A is computed and an estimate is obtained for
28: * norm(inv(A)), then the reciprocal of the condition number is
29: * computed as
30: * RCOND = 1 / ( norm(A) * norm(inv(A)) ).
31: *
32: * Arguments
33: * =========
34: *
35: * NORM (input) CHARACTER*1
36: * Specifies whether the 1-norm condition number or the
37: * infinity-norm condition number is required:
38: * = '1' or 'O': 1-norm;
39: * = 'I': Infinity-norm.
40: *
41: * UPLO (input) CHARACTER*1
42: * = 'U': A is upper triangular;
43: * = 'L': A is lower triangular.
44: *
45: * DIAG (input) CHARACTER*1
46: * = 'N': A is non-unit triangular;
47: * = 'U': A is unit triangular.
48: *
49: * N (input) INTEGER
50: * The order of the matrix A. N >= 0.
51: *
52: * A (input) COMPLEX*16 array, dimension (LDA,N)
53: * The triangular matrix A. If UPLO = 'U', the leading N-by-N
54: * upper triangular part of the array A contains the upper
55: * triangular matrix, and the strictly lower triangular part of
56: * A is not referenced. If UPLO = 'L', the leading N-by-N lower
57: * triangular part of the array A contains the lower triangular
58: * matrix, and the strictly upper triangular part of A is not
59: * referenced. If DIAG = 'U', the diagonal elements of A are
60: * also not referenced and are assumed to be 1.
61: *
62: * LDA (input) INTEGER
63: * The leading dimension of the array A. LDA >= max(1,N).
64: *
65: * RCOND (output) DOUBLE PRECISION
66: * The reciprocal of the condition number of the matrix A,
67: * computed as RCOND = 1/(norm(A) * norm(inv(A))).
68: *
69: * WORK (workspace) COMPLEX*16 array, dimension (2*N)
70: *
71: * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
72: *
73: * INFO (output) INTEGER
74: * = 0: successful exit
75: * < 0: if INFO = -i, the i-th argument had an illegal value
76: *
77: * =====================================================================
78: *
79: * .. Parameters ..
80: DOUBLE PRECISION ONE, ZERO
81: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
82: * ..
83: * .. Local Scalars ..
84: LOGICAL NOUNIT, ONENRM, UPPER
85: CHARACTER NORMIN
86: INTEGER IX, KASE, KASE1
87: DOUBLE PRECISION AINVNM, ANORM, SCALE, SMLNUM, XNORM
88: COMPLEX*16 ZDUM
89: * ..
90: * .. Local Arrays ..
91: INTEGER ISAVE( 3 )
92: * ..
93: * .. External Functions ..
94: LOGICAL LSAME
95: INTEGER IZAMAX
96: DOUBLE PRECISION DLAMCH, ZLANTR
97: EXTERNAL LSAME, IZAMAX, DLAMCH, ZLANTR
98: * ..
99: * .. External Subroutines ..
100: EXTERNAL XERBLA, ZDRSCL, ZLACN2, ZLATRS
101: * ..
102: * .. Intrinsic Functions ..
103: INTRINSIC ABS, DBLE, DIMAG, MAX
104: * ..
105: * .. Statement Functions ..
106: DOUBLE PRECISION CABS1
107: * ..
108: * .. Statement Function definitions ..
109: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
110: * ..
111: * .. Executable Statements ..
112: *
113: * Test the input parameters.
114: *
115: INFO = 0
116: UPPER = LSAME( UPLO, 'U' )
117: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
118: NOUNIT = LSAME( DIAG, 'N' )
119: *
120: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
121: INFO = -1
122: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
123: INFO = -2
124: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
125: INFO = -3
126: ELSE IF( N.LT.0 ) THEN
127: INFO = -4
128: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
129: INFO = -6
130: END IF
131: IF( INFO.NE.0 ) THEN
132: CALL XERBLA( 'ZTRCON', -INFO )
133: RETURN
134: END IF
135: *
136: * Quick return if possible
137: *
138: IF( N.EQ.0 ) THEN
139: RCOND = ONE
140: RETURN
141: END IF
142: *
143: RCOND = ZERO
144: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
145: *
146: * Compute the norm of the triangular matrix A.
147: *
148: ANORM = ZLANTR( NORM, UPLO, DIAG, N, N, A, LDA, RWORK )
149: *
150: * Continue only if ANORM > 0.
151: *
152: IF( ANORM.GT.ZERO ) THEN
153: *
154: * Estimate the norm of the inverse of A.
155: *
156: AINVNM = ZERO
157: NORMIN = 'N'
158: IF( ONENRM ) THEN
159: KASE1 = 1
160: ELSE
161: KASE1 = 2
162: END IF
163: KASE = 0
164: 10 CONTINUE
165: CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
166: IF( KASE.NE.0 ) THEN
167: IF( KASE.EQ.KASE1 ) THEN
168: *
169: * Multiply by inv(A).
170: *
171: CALL ZLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
172: $ LDA, WORK, SCALE, RWORK, INFO )
173: ELSE
174: *
175: * Multiply by inv(A').
176: *
177: CALL ZLATRS( UPLO, 'Conjugate transpose', DIAG, NORMIN,
178: $ N, A, LDA, WORK, SCALE, RWORK, INFO )
179: END IF
180: NORMIN = 'Y'
181: *
182: * Multiply by 1/SCALE if doing so will not cause overflow.
183: *
184: IF( SCALE.NE.ONE ) THEN
185: IX = IZAMAX( N, WORK, 1 )
186: XNORM = CABS1( WORK( IX ) )
187: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
188: $ GO TO 20
189: CALL ZDRSCL( N, SCALE, WORK, 1 )
190: END IF
191: GO TO 10
192: END IF
193: *
194: * Compute the estimate of the reciprocal condition number.
195: *
196: IF( AINVNM.NE.ZERO )
197: $ RCOND = ( ONE / ANORM ) / AINVNM
198: END IF
199: *
200: 20 CONTINUE
201: RETURN
202: *
203: * End of ZTRCON
204: *
205: END
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