Annotation of rpl/lapack/lapack/dppcon.f, revision 1.8
1.1 bertrand 1: SUBROUTINE DPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO )
2: *
1.8 ! bertrand 3: * -- LAPACK routine (version 3.3.1) --
1.1 bertrand 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 6: * -- April 2011 --
1.1 bertrand 7: *
8: * Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
9: *
10: * .. Scalar Arguments ..
11: CHARACTER UPLO
12: INTEGER INFO, N
13: DOUBLE PRECISION ANORM, RCOND
14: * ..
15: * .. Array Arguments ..
16: INTEGER IWORK( * )
17: DOUBLE PRECISION AP( * ), WORK( * )
18: * ..
19: *
20: * Purpose
21: * =======
22: *
23: * DPPCON estimates the reciprocal of the condition number (in the
24: * 1-norm) of a real symmetric positive definite packed matrix using
25: * the Cholesky factorization A = U**T*U or A = L*L**T computed by
26: * DPPTRF.
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: * = 'U': Upper triangle of A is stored;
36: * = 'L': Lower triangle of A is stored.
37: *
38: * N (input) INTEGER
39: * The order of the matrix A. N >= 0.
40: *
41: * AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
42: * The triangular factor U or L from the Cholesky factorization
43: * A = U**T*U or A = L*L**T, packed columnwise in a linear
44: * array. The j-th column of U or L is stored in the array AP
45: * as follows:
46: * if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
47: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
48: *
49: * ANORM (input) DOUBLE PRECISION
50: * The 1-norm (or infinity-norm) of the symmetric matrix A.
51: *
52: * RCOND (output) DOUBLE PRECISION
53: * The reciprocal of the condition number of the matrix A,
54: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
55: * estimate of the 1-norm of inv(A) computed in this routine.
56: *
57: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
58: *
59: * IWORK (workspace) INTEGER array, dimension (N)
60: *
61: * INFO (output) INTEGER
62: * = 0: successful exit
63: * < 0: if INFO = -i, the i-th argument had an illegal value
64: *
65: * =====================================================================
66: *
67: * .. Parameters ..
68: DOUBLE PRECISION ONE, ZERO
69: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
70: * ..
71: * .. Local Scalars ..
72: LOGICAL UPPER
73: CHARACTER NORMIN
74: INTEGER IX, KASE
75: DOUBLE PRECISION AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
76: * ..
77: * .. Local Arrays ..
78: INTEGER ISAVE( 3 )
79: * ..
80: * .. External Functions ..
81: LOGICAL LSAME
82: INTEGER IDAMAX
83: DOUBLE PRECISION DLAMCH
84: EXTERNAL LSAME, IDAMAX, DLAMCH
85: * ..
86: * .. External Subroutines ..
87: EXTERNAL DLACN2, DLATPS, DRSCL, XERBLA
88: * ..
89: * .. Intrinsic Functions ..
90: INTRINSIC ABS
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( ANORM.LT.ZERO ) THEN
103: INFO = -4
104: END IF
105: IF( INFO.NE.0 ) THEN
106: CALL XERBLA( 'DPPCON', -INFO )
107: RETURN
108: END IF
109: *
110: * Quick return if possible
111: *
112: RCOND = ZERO
113: IF( N.EQ.0 ) THEN
114: RCOND = ONE
115: RETURN
116: ELSE IF( ANORM.EQ.ZERO ) THEN
117: RETURN
118: END IF
119: *
120: SMLNUM = DLAMCH( 'Safe minimum' )
121: *
122: * Estimate the 1-norm of the inverse.
123: *
124: KASE = 0
125: NORMIN = 'N'
126: 10 CONTINUE
127: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
128: IF( KASE.NE.0 ) THEN
129: IF( UPPER ) THEN
130: *
1.8 ! bertrand 131: * Multiply by inv(U**T).
1.1 bertrand 132: *
133: CALL DLATPS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
134: $ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO )
135: NORMIN = 'Y'
136: *
137: * Multiply by inv(U).
138: *
139: CALL DLATPS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
140: $ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO )
141: ELSE
142: *
143: * Multiply by inv(L).
144: *
145: CALL DLATPS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
146: $ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO )
147: NORMIN = 'Y'
148: *
1.8 ! bertrand 149: * Multiply by inv(L**T).
1.1 bertrand 150: *
151: CALL DLATPS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
152: $ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO )
153: END IF
154: *
155: * Multiply by 1/SCALE if doing so will not cause overflow.
156: *
157: SCALE = SCALEL*SCALEU
158: IF( SCALE.NE.ONE ) THEN
159: IX = IDAMAX( N, WORK, 1 )
160: IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
161: $ GO TO 20
162: CALL DRSCL( N, SCALE, WORK, 1 )
163: END IF
164: GO TO 10
165: END IF
166: *
167: * Compute the estimate of the reciprocal condition number.
168: *
169: IF( AINVNM.NE.ZERO )
170: $ RCOND = ( ONE / AINVNM ) / ANORM
171: *
172: 20 CONTINUE
173: RETURN
174: *
175: * End of DPPCON
176: *
177: END
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