1: SUBROUTINE DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK,
2: $ IWORK, 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 DLACN2 in place of DLACON, 5 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: INTEGER IWORK( * )
18: DOUBLE PRECISION A( LDA, * ), WORK( * )
19: * ..
20: *
21: * Purpose
22: * =======
23: *
24: * DTRCON 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (3*N)
70: *
71: * IWORK (workspace) INTEGER 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: * ..
89: * .. Local Arrays ..
90: INTEGER ISAVE( 3 )
91: * ..
92: * .. External Functions ..
93: LOGICAL LSAME
94: INTEGER IDAMAX
95: DOUBLE PRECISION DLAMCH, DLANTR
96: EXTERNAL LSAME, IDAMAX, DLAMCH, DLANTR
97: * ..
98: * .. External Subroutines ..
99: EXTERNAL DLACN2, DLATRS, DRSCL, XERBLA
100: * ..
101: * .. Intrinsic Functions ..
102: INTRINSIC ABS, DBLE, MAX
103: * ..
104: * .. Executable Statements ..
105: *
106: * Test the input parameters.
107: *
108: INFO = 0
109: UPPER = LSAME( UPLO, 'U' )
110: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
111: NOUNIT = LSAME( DIAG, 'N' )
112: *
113: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
114: INFO = -1
115: ELSE IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
116: INFO = -2
117: ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
118: INFO = -3
119: ELSE IF( N.LT.0 ) THEN
120: INFO = -4
121: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
122: INFO = -6
123: END IF
124: IF( INFO.NE.0 ) THEN
125: CALL XERBLA( 'DTRCON', -INFO )
126: RETURN
127: END IF
128: *
129: * Quick return if possible
130: *
131: IF( N.EQ.0 ) THEN
132: RCOND = ONE
133: RETURN
134: END IF
135: *
136: RCOND = ZERO
137: SMLNUM = DLAMCH( 'Safe minimum' )*DBLE( MAX( 1, N ) )
138: *
139: * Compute the norm of the triangular matrix A.
140: *
141: ANORM = DLANTR( NORM, UPLO, DIAG, N, N, A, LDA, WORK )
142: *
143: * Continue only if ANORM > 0.
144: *
145: IF( ANORM.GT.ZERO ) THEN
146: *
147: * Estimate the norm of the inverse of A.
148: *
149: AINVNM = ZERO
150: NORMIN = 'N'
151: IF( ONENRM ) THEN
152: KASE1 = 1
153: ELSE
154: KASE1 = 2
155: END IF
156: KASE = 0
157: 10 CONTINUE
158: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
159: IF( KASE.NE.0 ) THEN
160: IF( KASE.EQ.KASE1 ) THEN
161: *
162: * Multiply by inv(A).
163: *
164: CALL DLATRS( UPLO, 'No transpose', DIAG, NORMIN, N, A,
165: $ LDA, WORK, SCALE, WORK( 2*N+1 ), INFO )
166: ELSE
167: *
168: * Multiply by inv(A').
169: *
170: CALL DLATRS( UPLO, 'Transpose', DIAG, NORMIN, N, A, LDA,
171: $ WORK, SCALE, WORK( 2*N+1 ), INFO )
172: END IF
173: NORMIN = 'Y'
174: *
175: * Multiply by 1/SCALE if doing so will not cause overflow.
176: *
177: IF( SCALE.NE.ONE ) THEN
178: IX = IDAMAX( N, WORK, 1 )
179: XNORM = ABS( WORK( IX ) )
180: IF( SCALE.LT.XNORM*SMLNUM .OR. SCALE.EQ.ZERO )
181: $ GO TO 20
182: CALL DRSCL( N, SCALE, WORK, 1 )
183: END IF
184: GO TO 10
185: END IF
186: *
187: * Compute the estimate of the reciprocal condition number.
188: *
189: IF( AINVNM.NE.ZERO )
190: $ RCOND = ( ONE / ANORM ) / AINVNM
191: END IF
192: *
193: 20 CONTINUE
194: RETURN
195: *
196: * End of DTRCON
197: *
198: END
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