1 SUBROUTINE DTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
2 $ WORK, RAT )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER DIAG, UPLO
10 INTEGER KD, LDAB, N
11 DOUBLE PRECISION RAT, RCOND, RCONDC
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DTBT06 computes a test ratio comparing RCOND (the reciprocal
21 * condition number of a triangular matrix A) and RCONDC, the estimate
22 * computed by DTBCON. Information about the triangular matrix A is
23 * used if one estimate is zero and the other is non-zero to decide if
24 * underflow in the estimate is justified.
25 *
26 * Arguments
27 * =========
28 *
29 * RCOND (input) DOUBLE PRECISION
30 * The estimate of the reciprocal condition number obtained by
31 * forming the explicit inverse of the matrix A and computing
32 * RCOND = 1/( norm(A) * norm(inv(A)) ).
33 *
34 * RCONDC (input) DOUBLE PRECISION
35 * The estimate of the reciprocal condition number computed by
36 * DTBCON.
37 *
38 * UPLO (input) CHARACTER
39 * Specifies whether the matrix A is upper or lower triangular.
40 * = 'U': Upper triangular
41 * = 'L': Lower triangular
42 *
43 * DIAG (input) CHARACTER
44 * Specifies whether or not the matrix A is unit triangular.
45 * = 'N': Non-unit triangular
46 * = 'U': Unit triangular
47 *
48 * N (input) INTEGER
49 * The order of the matrix A. N >= 0.
50 *
51 * KD (input) INTEGER
52 * The number of superdiagonals or subdiagonals of the
53 * triangular band matrix A. KD >= 0.
54 *
55 * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
56 * The upper or lower triangular band matrix A, stored in the
57 * first kd+1 rows of the array. The j-th column of A is stored
58 * in the j-th column of the array AB as follows:
59 * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
60 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
61 *
62 * LDAB (input) INTEGER
63 * The leading dimension of the array AB. LDAB >= KD+1.
64 *
65 * WORK (workspace) DOUBLE PRECISION array, dimension (N)
66 *
67 * RAT (output) DOUBLE PRECISION
68 * The test ratio. If both RCOND and RCONDC are nonzero,
69 * RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
70 * If RAT = 0, the two estimates are exactly the same.
71 *
72 * =====================================================================
73 *
74 * .. Parameters ..
75 DOUBLE PRECISION ZERO, ONE
76 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
77 * ..
78 * .. Local Scalars ..
79 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
80 * ..
81 * .. External Functions ..
82 DOUBLE PRECISION DLAMCH, DLANTB
83 EXTERNAL DLAMCH, DLANTB
84 * ..
85 * .. Intrinsic Functions ..
86 INTRINSIC MAX, MIN
87 * ..
88 * .. External Subroutines ..
89 EXTERNAL DLABAD
90 * ..
91 * .. Executable Statements ..
92 *
93 EPS = DLAMCH( 'Epsilon' )
94 RMAX = MAX( RCOND, RCONDC )
95 RMIN = MIN( RCOND, RCONDC )
96 *
97 * Do the easy cases first.
98 *
99 IF( RMIN.LT.ZERO ) THEN
100 *
101 * Invalid value for RCOND or RCONDC, return 1/EPS.
102 *
103 RAT = ONE / EPS
104 *
105 ELSE IF( RMIN.GT.ZERO ) THEN
106 *
107 * Both estimates are positive, return RMAX/RMIN - 1.
108 *
109 RAT = RMAX / RMIN - ONE
110 *
111 ELSE IF( RMAX.EQ.ZERO ) THEN
112 *
113 * Both estimates zero.
114 *
115 RAT = ZERO
116 *
117 ELSE
118 *
119 * One estimate is zero, the other is non-zero. If the matrix is
120 * ill-conditioned, return the nonzero estimate multiplied by
121 * 1/EPS; if the matrix is badly scaled, return the nonzero
122 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
123 * element in absolute value in A.
124 *
125 SMLNUM = DLAMCH( 'Safe minimum' )
126 BIGNUM = ONE / SMLNUM
127 CALL DLABAD( SMLNUM, BIGNUM )
128 ANORM = DLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, WORK )
129 *
130 RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
131 END IF
132 *
133 RETURN
134 *
135 * End of DTBT06
136 *
137 END
2 $ WORK, RAT )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER DIAG, UPLO
10 INTEGER KD, LDAB, N
11 DOUBLE PRECISION RAT, RCOND, RCONDC
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DTBT06 computes a test ratio comparing RCOND (the reciprocal
21 * condition number of a triangular matrix A) and RCONDC, the estimate
22 * computed by DTBCON. Information about the triangular matrix A is
23 * used if one estimate is zero and the other is non-zero to decide if
24 * underflow in the estimate is justified.
25 *
26 * Arguments
27 * =========
28 *
29 * RCOND (input) DOUBLE PRECISION
30 * The estimate of the reciprocal condition number obtained by
31 * forming the explicit inverse of the matrix A and computing
32 * RCOND = 1/( norm(A) * norm(inv(A)) ).
33 *
34 * RCONDC (input) DOUBLE PRECISION
35 * The estimate of the reciprocal condition number computed by
36 * DTBCON.
37 *
38 * UPLO (input) CHARACTER
39 * Specifies whether the matrix A is upper or lower triangular.
40 * = 'U': Upper triangular
41 * = 'L': Lower triangular
42 *
43 * DIAG (input) CHARACTER
44 * Specifies whether or not the matrix A is unit triangular.
45 * = 'N': Non-unit triangular
46 * = 'U': Unit triangular
47 *
48 * N (input) INTEGER
49 * The order of the matrix A. N >= 0.
50 *
51 * KD (input) INTEGER
52 * The number of superdiagonals or subdiagonals of the
53 * triangular band matrix A. KD >= 0.
54 *
55 * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
56 * The upper or lower triangular band matrix A, stored in the
57 * first kd+1 rows of the array. The j-th column of A is stored
58 * in the j-th column of the array AB as follows:
59 * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
60 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
61 *
62 * LDAB (input) INTEGER
63 * The leading dimension of the array AB. LDAB >= KD+1.
64 *
65 * WORK (workspace) DOUBLE PRECISION array, dimension (N)
66 *
67 * RAT (output) DOUBLE PRECISION
68 * The test ratio. If both RCOND and RCONDC are nonzero,
69 * RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
70 * If RAT = 0, the two estimates are exactly the same.
71 *
72 * =====================================================================
73 *
74 * .. Parameters ..
75 DOUBLE PRECISION ZERO, ONE
76 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
77 * ..
78 * .. Local Scalars ..
79 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
80 * ..
81 * .. External Functions ..
82 DOUBLE PRECISION DLAMCH, DLANTB
83 EXTERNAL DLAMCH, DLANTB
84 * ..
85 * .. Intrinsic Functions ..
86 INTRINSIC MAX, MIN
87 * ..
88 * .. External Subroutines ..
89 EXTERNAL DLABAD
90 * ..
91 * .. Executable Statements ..
92 *
93 EPS = DLAMCH( 'Epsilon' )
94 RMAX = MAX( RCOND, RCONDC )
95 RMIN = MIN( RCOND, RCONDC )
96 *
97 * Do the easy cases first.
98 *
99 IF( RMIN.LT.ZERO ) THEN
100 *
101 * Invalid value for RCOND or RCONDC, return 1/EPS.
102 *
103 RAT = ONE / EPS
104 *
105 ELSE IF( RMIN.GT.ZERO ) THEN
106 *
107 * Both estimates are positive, return RMAX/RMIN - 1.
108 *
109 RAT = RMAX / RMIN - ONE
110 *
111 ELSE IF( RMAX.EQ.ZERO ) THEN
112 *
113 * Both estimates zero.
114 *
115 RAT = ZERO
116 *
117 ELSE
118 *
119 * One estimate is zero, the other is non-zero. If the matrix is
120 * ill-conditioned, return the nonzero estimate multiplied by
121 * 1/EPS; if the matrix is badly scaled, return the nonzero
122 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
123 * element in absolute value in A.
124 *
125 SMLNUM = DLAMCH( 'Safe minimum' )
126 BIGNUM = ONE / SMLNUM
127 CALL DLABAD( SMLNUM, BIGNUM )
128 ANORM = DLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, WORK )
129 *
130 RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
131 END IF
132 *
133 RETURN
134 *
135 * End of DTBT06
136 *
137 END