1 SUBROUTINE ZTPT01( UPLO, DIAG, N, AP, AINVP, RCOND, RWORK, RESID )
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 RCOND, RESID
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION RWORK( * )
14 COMPLEX*16 AINVP( * ), AP( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZTPT01 computes the residual for a triangular matrix A times its
21 * inverse when A is stored in packed format:
22 * RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
23 * where EPS is the machine epsilon.
24 *
25 * Arguments
26 * ==========
27 *
28 * UPLO (input) CHARACTER*1
29 * Specifies whether the matrix A is upper or lower triangular.
30 * = 'U': Upper triangular
31 * = 'L': Lower triangular
32 *
33 * DIAG (input) CHARACTER*1
34 * Specifies whether or not the matrix A is unit triangular.
35 * = 'N': Non-unit triangular
36 * = 'U': Unit triangular
37 *
38 * N (input) INTEGER
39 * The order of the matrix A. N >= 0.
40 *
41 * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
42 * The original upper or lower triangular matrix A, packed
43 * columnwise in a linear array. The j-th column of A is stored
44 * in the array AP as follows:
45 * if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
46 * if UPLO = 'L',
47 * AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
48 *
49 * AINVP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
50 * On entry, the (triangular) inverse of the matrix A, packed
51 * columnwise in a linear array as in AP.
52 * On exit, the contents of AINVP are destroyed.
53 *
54 * RCOND (output) DOUBLE PRECISION
55 * The reciprocal condition number of A, computed as
56 * 1/(norm(A) * norm(AINV)).
57 *
58 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
59 *
60 * RESID (output) DOUBLE PRECISION
61 * norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
62 *
63 * =====================================================================
64 *
65 * .. Parameters ..
66 DOUBLE PRECISION ZERO, ONE
67 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
68 * ..
69 * .. Local Scalars ..
70 LOGICAL UNITD
71 INTEGER J, JC
72 DOUBLE PRECISION AINVNM, ANORM, EPS
73 * ..
74 * .. External Functions ..
75 LOGICAL LSAME
76 DOUBLE PRECISION DLAMCH, ZLANTP
77 EXTERNAL LSAME, DLAMCH, ZLANTP
78 * ..
79 * .. External Subroutines ..
80 EXTERNAL ZTPMV
81 * ..
82 * .. Intrinsic Functions ..
83 INTRINSIC DBLE
84 * ..
85 * .. Executable Statements ..
86 *
87 * Quick exit if N = 0.
88 *
89 IF( N.LE.0 ) THEN
90 RCOND = ONE
91 RESID = ZERO
92 RETURN
93 END IF
94 *
95 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
96 *
97 EPS = DLAMCH( 'Epsilon' )
98 ANORM = ZLANTP( '1', UPLO, DIAG, N, AP, RWORK )
99 AINVNM = ZLANTP( '1', UPLO, DIAG, N, AINVP, RWORK )
100 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
101 RCOND = ZERO
102 RESID = ONE / EPS
103 RETURN
104 END IF
105 RCOND = ( ONE / ANORM ) / AINVNM
106 *
107 * Compute A * AINV, overwriting AINV.
108 *
109 UNITD = LSAME( DIAG, 'U' )
110 IF( LSAME( UPLO, 'U' ) ) THEN
111 JC = 1
112 DO 10 J = 1, N
113 IF( UNITD )
114 $ AINVP( JC+J-1 ) = ONE
115 *
116 * Form the j-th column of A*AINV.
117 *
118 CALL ZTPMV( 'Upper', 'No transpose', DIAG, J, AP,
119 $ AINVP( JC ), 1 )
120 *
121 * Subtract 1 from the diagonal to form A*AINV - I.
122 *
123 AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE
124 JC = JC + J
125 10 CONTINUE
126 ELSE
127 JC = 1
128 DO 20 J = 1, N
129 IF( UNITD )
130 $ AINVP( JC ) = ONE
131 *
132 * Form the j-th column of A*AINV.
133 *
134 CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ),
135 $ AINVP( JC ), 1 )
136 *
137 * Subtract 1 from the diagonal to form A*AINV - I.
138 *
139 AINVP( JC ) = AINVP( JC ) - ONE
140 JC = JC + N - J + 1
141 20 CONTINUE
142 END IF
143 *
144 * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
145 *
146 RESID = ZLANTP( '1', UPLO, 'Non-unit', N, AINVP, RWORK )
147 *
148 RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
149 *
150 RETURN
151 *
152 * End of ZTPT01
153 *
154 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 RCOND, RESID
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION RWORK( * )
14 COMPLEX*16 AINVP( * ), AP( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZTPT01 computes the residual for a triangular matrix A times its
21 * inverse when A is stored in packed format:
22 * RESID = norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ),
23 * where EPS is the machine epsilon.
24 *
25 * Arguments
26 * ==========
27 *
28 * UPLO (input) CHARACTER*1
29 * Specifies whether the matrix A is upper or lower triangular.
30 * = 'U': Upper triangular
31 * = 'L': Lower triangular
32 *
33 * DIAG (input) CHARACTER*1
34 * Specifies whether or not the matrix A is unit triangular.
35 * = 'N': Non-unit triangular
36 * = 'U': Unit triangular
37 *
38 * N (input) INTEGER
39 * The order of the matrix A. N >= 0.
40 *
41 * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
42 * The original upper or lower triangular matrix A, packed
43 * columnwise in a linear array. The j-th column of A is stored
44 * in the array AP as follows:
45 * if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
46 * if UPLO = 'L',
47 * AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
48 *
49 * AINVP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
50 * On entry, the (triangular) inverse of the matrix A, packed
51 * columnwise in a linear array as in AP.
52 * On exit, the contents of AINVP are destroyed.
53 *
54 * RCOND (output) DOUBLE PRECISION
55 * The reciprocal condition number of A, computed as
56 * 1/(norm(A) * norm(AINV)).
57 *
58 * RWORK (workspace) DOUBLE PRECISION array, dimension (N)
59 *
60 * RESID (output) DOUBLE PRECISION
61 * norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
62 *
63 * =====================================================================
64 *
65 * .. Parameters ..
66 DOUBLE PRECISION ZERO, ONE
67 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
68 * ..
69 * .. Local Scalars ..
70 LOGICAL UNITD
71 INTEGER J, JC
72 DOUBLE PRECISION AINVNM, ANORM, EPS
73 * ..
74 * .. External Functions ..
75 LOGICAL LSAME
76 DOUBLE PRECISION DLAMCH, ZLANTP
77 EXTERNAL LSAME, DLAMCH, ZLANTP
78 * ..
79 * .. External Subroutines ..
80 EXTERNAL ZTPMV
81 * ..
82 * .. Intrinsic Functions ..
83 INTRINSIC DBLE
84 * ..
85 * .. Executable Statements ..
86 *
87 * Quick exit if N = 0.
88 *
89 IF( N.LE.0 ) THEN
90 RCOND = ONE
91 RESID = ZERO
92 RETURN
93 END IF
94 *
95 * Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
96 *
97 EPS = DLAMCH( 'Epsilon' )
98 ANORM = ZLANTP( '1', UPLO, DIAG, N, AP, RWORK )
99 AINVNM = ZLANTP( '1', UPLO, DIAG, N, AINVP, RWORK )
100 IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
101 RCOND = ZERO
102 RESID = ONE / EPS
103 RETURN
104 END IF
105 RCOND = ( ONE / ANORM ) / AINVNM
106 *
107 * Compute A * AINV, overwriting AINV.
108 *
109 UNITD = LSAME( DIAG, 'U' )
110 IF( LSAME( UPLO, 'U' ) ) THEN
111 JC = 1
112 DO 10 J = 1, N
113 IF( UNITD )
114 $ AINVP( JC+J-1 ) = ONE
115 *
116 * Form the j-th column of A*AINV.
117 *
118 CALL ZTPMV( 'Upper', 'No transpose', DIAG, J, AP,
119 $ AINVP( JC ), 1 )
120 *
121 * Subtract 1 from the diagonal to form A*AINV - I.
122 *
123 AINVP( JC+J-1 ) = AINVP( JC+J-1 ) - ONE
124 JC = JC + J
125 10 CONTINUE
126 ELSE
127 JC = 1
128 DO 20 J = 1, N
129 IF( UNITD )
130 $ AINVP( JC ) = ONE
131 *
132 * Form the j-th column of A*AINV.
133 *
134 CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J+1, AP( JC ),
135 $ AINVP( JC ), 1 )
136 *
137 * Subtract 1 from the diagonal to form A*AINV - I.
138 *
139 AINVP( JC ) = AINVP( JC ) - ONE
140 JC = JC + N - J + 1
141 20 CONTINUE
142 END IF
143 *
144 * Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
145 *
146 RESID = ZLANTP( '1', UPLO, 'Non-unit', N, AINVP, RWORK )
147 *
148 RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
149 *
150 RETURN
151 *
152 * End of ZTPT01
153 *
154 END