1 SUBROUTINE ZTPT06( RCOND, RCONDC, UPLO, DIAG, N, AP, RWORK, RAT )
2 *
3 * -- LAPACK test routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 CHARACTER DIAG, UPLO
9 INTEGER N
10 DOUBLE PRECISION RAT, RCOND, RCONDC
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION RWORK( * )
14 COMPLEX*16 AP( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZTPT06 computes a test ratio comparing RCOND (the reciprocal
21 * condition number of the triangular matrix A) and RCONDC, the estimate
22 * computed by ZTPCON. Information about the triangular matrix is used
23 * 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 * ZTPCON.
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 * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
52 * The upper or lower triangular matrix A, packed columnwise in
53 * a linear array. The j-th column of A is stored in the array
54 * AP as follows:
55 * if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
56 * if UPLO = 'L',
57 * AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
58 *
59 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
60 *
61 * RAT (output) DOUBLE PRECISION
62 * The test ratio. If both RCOND and RCONDC are nonzero,
63 * RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
64 * If RAT = 0, the two estimates are exactly the same.
65 *
66 * =====================================================================
67 *
68 * .. Parameters ..
69 DOUBLE PRECISION ZERO, ONE
70 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
71 * ..
72 * .. Local Scalars ..
73 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN
74 * ..
75 * .. External Functions ..
76 DOUBLE PRECISION DLAMCH, ZLANTP
77 EXTERNAL DLAMCH, ZLANTP
78 * ..
79 * .. Intrinsic Functions ..
80 INTRINSIC MAX, MIN
81 * ..
82 * .. Executable Statements ..
83 *
84 EPS = DLAMCH( 'Epsilon' )
85 RMAX = MAX( RCOND, RCONDC )
86 RMIN = MIN( RCOND, RCONDC )
87 *
88 * Do the easy cases first.
89 *
90 IF( RMIN.LT.ZERO ) THEN
91 *
92 * Invalid value for RCOND or RCONDC, return 1/EPS.
93 *
94 RAT = ONE / EPS
95 *
96 ELSE IF( RMIN.GT.ZERO ) THEN
97 *
98 * Both estimates are positive, return RMAX/RMIN - 1.
99 *
100 RAT = RMAX / RMIN - ONE
101 *
102 ELSE IF( RMAX.EQ.ZERO ) THEN
103 *
104 * Both estimates zero.
105 *
106 RAT = ZERO
107 *
108 ELSE
109 *
110 * One estimate is zero, the other is non-zero. If the matrix is
111 * ill-conditioned, return the nonzero estimate multiplied by
112 * 1/EPS; if the matrix is badly scaled, return the nonzero
113 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
114 * element in absolute value in A.
115 *
116 BIGNUM = ONE / DLAMCH( 'Safe minimum' )
117 ANORM = ZLANTP( 'M', UPLO, DIAG, N, AP, RWORK )
118 *
119 RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
120 END IF
121 *
122 RETURN
123 *
124 * End of ZTPT06
125 *
126 END
2 *
3 * -- LAPACK test routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 CHARACTER DIAG, UPLO
9 INTEGER N
10 DOUBLE PRECISION RAT, RCOND, RCONDC
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION RWORK( * )
14 COMPLEX*16 AP( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZTPT06 computes a test ratio comparing RCOND (the reciprocal
21 * condition number of the triangular matrix A) and RCONDC, the estimate
22 * computed by ZTPCON. Information about the triangular matrix is used
23 * 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 * ZTPCON.
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 * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
52 * The upper or lower triangular matrix A, packed columnwise in
53 * a linear array. The j-th column of A is stored in the array
54 * AP as follows:
55 * if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
56 * if UPLO = 'L',
57 * AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
58 *
59 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
60 *
61 * RAT (output) DOUBLE PRECISION
62 * The test ratio. If both RCOND and RCONDC are nonzero,
63 * RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
64 * If RAT = 0, the two estimates are exactly the same.
65 *
66 * =====================================================================
67 *
68 * .. Parameters ..
69 DOUBLE PRECISION ZERO, ONE
70 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
71 * ..
72 * .. Local Scalars ..
73 DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN
74 * ..
75 * .. External Functions ..
76 DOUBLE PRECISION DLAMCH, ZLANTP
77 EXTERNAL DLAMCH, ZLANTP
78 * ..
79 * .. Intrinsic Functions ..
80 INTRINSIC MAX, MIN
81 * ..
82 * .. Executable Statements ..
83 *
84 EPS = DLAMCH( 'Epsilon' )
85 RMAX = MAX( RCOND, RCONDC )
86 RMIN = MIN( RCOND, RCONDC )
87 *
88 * Do the easy cases first.
89 *
90 IF( RMIN.LT.ZERO ) THEN
91 *
92 * Invalid value for RCOND or RCONDC, return 1/EPS.
93 *
94 RAT = ONE / EPS
95 *
96 ELSE IF( RMIN.GT.ZERO ) THEN
97 *
98 * Both estimates are positive, return RMAX/RMIN - 1.
99 *
100 RAT = RMAX / RMIN - ONE
101 *
102 ELSE IF( RMAX.EQ.ZERO ) THEN
103 *
104 * Both estimates zero.
105 *
106 RAT = ZERO
107 *
108 ELSE
109 *
110 * One estimate is zero, the other is non-zero. If the matrix is
111 * ill-conditioned, return the nonzero estimate multiplied by
112 * 1/EPS; if the matrix is badly scaled, return the nonzero
113 * estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
114 * element in absolute value in A.
115 *
116 BIGNUM = ONE / DLAMCH( 'Safe minimum' )
117 ANORM = ZLANTP( 'M', UPLO, DIAG, N, AP, RWORK )
118 *
119 RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
120 END IF
121 *
122 RETURN
123 *
124 * End of ZTPT06
125 *
126 END