1 SUBROUTINE CPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
2 $ RWORK, RESID )
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 UPLO
10 INTEGER KD, LDA, LDB, LDX, N, NRHS
11 REAL RESID
12 * ..
13 * .. Array Arguments ..
14 REAL RWORK( * )
15 COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * CPBT02 computes the residual for a solution of a Hermitian banded
22 * system of equations A*x = b:
23 * RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
24 * where EPS is the machine precision.
25 *
26 * Arguments
27 * =========
28 *
29 * UPLO (input) CHARACTER*1
30 * Specifies whether the upper or lower triangular part of the
31 * Hermitian matrix A is stored:
32 * = 'U': Upper triangular
33 * = 'L': Lower triangular
34 *
35 * N (input) INTEGER
36 * The number of rows and columns of the matrix A. N >= 0.
37 *
38 * KD (input) INTEGER
39 * The number of super-diagonals of the matrix A if UPLO = 'U',
40 * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
41 *
42 * A (input) COMPLEX array, dimension (LDA,N)
43 * The original Hermitian band matrix A. If UPLO = 'U', the
44 * upper triangular part of A is stored as a band matrix; if
45 * UPLO = 'L', the lower triangular part of A is stored. The
46 * columns of the appropriate triangle are stored in the columns
47 * of A and the diagonals of the triangle are stored in the rows
48 * of A. See CPBTRF for further details.
49 *
50 * LDA (input) INTEGER.
51 * The leading dimension of the array A. LDA >= max(1,KD+1).
52 *
53 * X (input) COMPLEX array, dimension (LDX,NRHS)
54 * The computed solution vectors for the system of linear
55 * equations.
56 *
57 * LDX (input) INTEGER
58 * The leading dimension of the array X. LDX >= max(1,N).
59 *
60 * B (input/output) COMPLEX array, dimension (LDB,NRHS)
61 * On entry, the right hand side vectors for the system of
62 * linear equations.
63 * On exit, B is overwritten with the difference B - A*X.
64 *
65 * LDB (input) INTEGER
66 * The leading dimension of the array B. LDB >= max(1,N).
67 *
68 * RWORK (workspace) REAL array, dimension (N)
69 *
70 * RESID (output) REAL
71 * The maximum over the number of right hand sides of
72 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
73 *
74 * =====================================================================
75 *
76 * .. Parameters ..
77 REAL ZERO, ONE
78 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
79 COMPLEX CONE
80 PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
81 * ..
82 * .. Local Scalars ..
83 INTEGER J
84 REAL ANORM, BNORM, EPS, XNORM
85 * ..
86 * .. External Functions ..
87 REAL CLANHB, SCASUM, SLAMCH
88 EXTERNAL CLANHB, SCASUM, SLAMCH
89 * ..
90 * .. External Subroutines ..
91 EXTERNAL CHBMV
92 * ..
93 * .. Intrinsic Functions ..
94 INTRINSIC MAX
95 * ..
96 * .. Executable Statements ..
97 *
98 * Quick exit if N = 0 or NRHS = 0.
99 *
100 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
101 RESID = ZERO
102 RETURN
103 END IF
104 *
105 * Exit with RESID = 1/EPS if ANORM = 0.
106 *
107 EPS = SLAMCH( 'Epsilon' )
108 ANORM = CLANHB( '1', UPLO, N, KD, A, LDA, RWORK )
109 IF( ANORM.LE.ZERO ) THEN
110 RESID = ONE / EPS
111 RETURN
112 END IF
113 *
114 * Compute B - A*X
115 *
116 DO 10 J = 1, NRHS
117 CALL CHBMV( UPLO, N, KD, -CONE, A, LDA, X( 1, J ), 1, CONE,
118 $ B( 1, J ), 1 )
119 10 CONTINUE
120 *
121 * Compute the maximum over the number of right hand sides of
122 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
123 *
124 RESID = ZERO
125 DO 20 J = 1, NRHS
126 BNORM = SCASUM( N, B( 1, J ), 1 )
127 XNORM = SCASUM( N, X( 1, J ), 1 )
128 IF( XNORM.LE.ZERO ) THEN
129 RESID = ONE / EPS
130 ELSE
131 RESID = MAX( RESID, ( ( BNORM/ANORM )/XNORM )/EPS )
132 END IF
133 20 CONTINUE
134 *
135 RETURN
136 *
137 * End of CPBT02
138 *
139 END
2 $ RWORK, RESID )
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 UPLO
10 INTEGER KD, LDA, LDB, LDX, N, NRHS
11 REAL RESID
12 * ..
13 * .. Array Arguments ..
14 REAL RWORK( * )
15 COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
16 * ..
17 *
18 * Purpose
19 * =======
20 *
21 * CPBT02 computes the residual for a solution of a Hermitian banded
22 * system of equations A*x = b:
23 * RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
24 * where EPS is the machine precision.
25 *
26 * Arguments
27 * =========
28 *
29 * UPLO (input) CHARACTER*1
30 * Specifies whether the upper or lower triangular part of the
31 * Hermitian matrix A is stored:
32 * = 'U': Upper triangular
33 * = 'L': Lower triangular
34 *
35 * N (input) INTEGER
36 * The number of rows and columns of the matrix A. N >= 0.
37 *
38 * KD (input) INTEGER
39 * The number of super-diagonals of the matrix A if UPLO = 'U',
40 * or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
41 *
42 * A (input) COMPLEX array, dimension (LDA,N)
43 * The original Hermitian band matrix A. If UPLO = 'U', the
44 * upper triangular part of A is stored as a band matrix; if
45 * UPLO = 'L', the lower triangular part of A is stored. The
46 * columns of the appropriate triangle are stored in the columns
47 * of A and the diagonals of the triangle are stored in the rows
48 * of A. See CPBTRF for further details.
49 *
50 * LDA (input) INTEGER.
51 * The leading dimension of the array A. LDA >= max(1,KD+1).
52 *
53 * X (input) COMPLEX array, dimension (LDX,NRHS)
54 * The computed solution vectors for the system of linear
55 * equations.
56 *
57 * LDX (input) INTEGER
58 * The leading dimension of the array X. LDX >= max(1,N).
59 *
60 * B (input/output) COMPLEX array, dimension (LDB,NRHS)
61 * On entry, the right hand side vectors for the system of
62 * linear equations.
63 * On exit, B is overwritten with the difference B - A*X.
64 *
65 * LDB (input) INTEGER
66 * The leading dimension of the array B. LDB >= max(1,N).
67 *
68 * RWORK (workspace) REAL array, dimension (N)
69 *
70 * RESID (output) REAL
71 * The maximum over the number of right hand sides of
72 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
73 *
74 * =====================================================================
75 *
76 * .. Parameters ..
77 REAL ZERO, ONE
78 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
79 COMPLEX CONE
80 PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
81 * ..
82 * .. Local Scalars ..
83 INTEGER J
84 REAL ANORM, BNORM, EPS, XNORM
85 * ..
86 * .. External Functions ..
87 REAL CLANHB, SCASUM, SLAMCH
88 EXTERNAL CLANHB, SCASUM, SLAMCH
89 * ..
90 * .. External Subroutines ..
91 EXTERNAL CHBMV
92 * ..
93 * .. Intrinsic Functions ..
94 INTRINSIC MAX
95 * ..
96 * .. Executable Statements ..
97 *
98 * Quick exit if N = 0 or NRHS = 0.
99 *
100 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
101 RESID = ZERO
102 RETURN
103 END IF
104 *
105 * Exit with RESID = 1/EPS if ANORM = 0.
106 *
107 EPS = SLAMCH( 'Epsilon' )
108 ANORM = CLANHB( '1', UPLO, N, KD, A, LDA, RWORK )
109 IF( ANORM.LE.ZERO ) THEN
110 RESID = ONE / EPS
111 RETURN
112 END IF
113 *
114 * Compute B - A*X
115 *
116 DO 10 J = 1, NRHS
117 CALL CHBMV( UPLO, N, KD, -CONE, A, LDA, X( 1, J ), 1, CONE,
118 $ B( 1, J ), 1 )
119 10 CONTINUE
120 *
121 * Compute the maximum over the number of right hand sides of
122 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
123 *
124 RESID = ZERO
125 DO 20 J = 1, NRHS
126 BNORM = SCASUM( N, B( 1, J ), 1 )
127 XNORM = SCASUM( N, X( 1, J ), 1 )
128 IF( XNORM.LE.ZERO ) THEN
129 RESID = ONE / EPS
130 ELSE
131 RESID = MAX( RESID, ( ( BNORM/ANORM )/XNORM )/EPS )
132 END IF
133 20 CONTINUE
134 *
135 RETURN
136 *
137 * End of CPBT02
138 *
139 END