1 DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
2 $ WORK )
3 *
4 * -- LAPACK auxiliary routine (version 3.2) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * November 2006
8 *
9 * .. Scalar Arguments ..
10 CHARACTER NORM
11 INTEGER KL, KU, LDAB, N
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DLANGB returns the value of the one norm, or the Frobenius norm, or
21 * the infinity norm, or the element of largest absolute value of an
22 * n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
23 *
24 * Description
25 * ===========
26 *
27 * DLANGB returns the value
28 *
29 * DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
30 * (
31 * ( norm1(A), NORM = '1', 'O' or 'o'
32 * (
33 * ( normI(A), NORM = 'I' or 'i'
34 * (
35 * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
36 *
37 * where norm1 denotes the one norm of a matrix (maximum column sum),
38 * normI denotes the infinity norm of a matrix (maximum row sum) and
39 * normF denotes the Frobenius norm of a matrix (square root of sum of
40 * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
41 *
42 * Arguments
43 * =========
44 *
45 * NORM (input) CHARACTER*1
46 * Specifies the value to be returned in DLANGB as described
47 * above.
48 *
49 * N (input) INTEGER
50 * The order of the matrix A. N >= 0. When N = 0, DLANGB is
51 * set to zero.
52 *
53 * KL (input) INTEGER
54 * The number of sub-diagonals of the matrix A. KL >= 0.
55 *
56 * KU (input) INTEGER
57 * The number of super-diagonals of the matrix A. KU >= 0.
58 *
59 * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
60 * The band matrix A, stored in rows 1 to KL+KU+1. The j-th
61 * column of A is stored in the j-th column of the array AB as
62 * follows:
63 * AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
64 *
65 * LDAB (input) INTEGER
66 * The leading dimension of the array AB. LDAB >= KL+KU+1.
67 *
68 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
69 * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
70 * referenced.
71 *
72 * =====================================================================
73 *
74 *
75 * .. Parameters ..
76 DOUBLE PRECISION ONE, ZERO
77 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
78 * ..
79 * .. Local Scalars ..
80 INTEGER I, J, K, L
81 DOUBLE PRECISION SCALE, SUM, VALUE
82 * ..
83 * .. External Subroutines ..
84 EXTERNAL DLASSQ
85 * ..
86 * .. External Functions ..
87 LOGICAL LSAME
88 EXTERNAL LSAME
89 * ..
90 * .. Intrinsic Functions ..
91 INTRINSIC ABS, MAX, MIN, SQRT
92 * ..
93 * .. Executable Statements ..
94 *
95 IF( N.EQ.0 ) THEN
96 VALUE = ZERO
97 ELSE IF( LSAME( NORM, 'M' ) ) THEN
98 *
99 * Find max(abs(A(i,j))).
100 *
101 VALUE = ZERO
102 DO 20 J = 1, N
103 DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
104 VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
105 10 CONTINUE
106 20 CONTINUE
107 ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
108 *
109 * Find norm1(A).
110 *
111 VALUE = ZERO
112 DO 40 J = 1, N
113 SUM = ZERO
114 DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
115 SUM = SUM + ABS( AB( I, J ) )
116 30 CONTINUE
117 VALUE = MAX( VALUE, SUM )
118 40 CONTINUE
119 ELSE IF( LSAME( NORM, 'I' ) ) THEN
120 *
121 * Find normI(A).
122 *
123 DO 50 I = 1, N
124 WORK( I ) = ZERO
125 50 CONTINUE
126 DO 70 J = 1, N
127 K = KU + 1 - J
128 DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
129 WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
130 60 CONTINUE
131 70 CONTINUE
132 VALUE = ZERO
133 DO 80 I = 1, N
134 VALUE = MAX( VALUE, WORK( I ) )
135 80 CONTINUE
136 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
137 *
138 * Find normF(A).
139 *
140 SCALE = ZERO
141 SUM = ONE
142 DO 90 J = 1, N
143 L = MAX( 1, J-KU )
144 K = KU + 1 - J + L
145 CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
146 90 CONTINUE
147 VALUE = SCALE*SQRT( SUM )
148 END IF
149 *
150 DLANGB = VALUE
151 RETURN
152 *
153 * End of DLANGB
154 *
155 END
2 $ WORK )
3 *
4 * -- LAPACK auxiliary routine (version 3.2) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * November 2006
8 *
9 * .. Scalar Arguments ..
10 CHARACTER NORM
11 INTEGER KL, KU, LDAB, N
12 * ..
13 * .. Array Arguments ..
14 DOUBLE PRECISION AB( LDAB, * ), WORK( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * DLANGB returns the value of the one norm, or the Frobenius norm, or
21 * the infinity norm, or the element of largest absolute value of an
22 * n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
23 *
24 * Description
25 * ===========
26 *
27 * DLANGB returns the value
28 *
29 * DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
30 * (
31 * ( norm1(A), NORM = '1', 'O' or 'o'
32 * (
33 * ( normI(A), NORM = 'I' or 'i'
34 * (
35 * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
36 *
37 * where norm1 denotes the one norm of a matrix (maximum column sum),
38 * normI denotes the infinity norm of a matrix (maximum row sum) and
39 * normF denotes the Frobenius norm of a matrix (square root of sum of
40 * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
41 *
42 * Arguments
43 * =========
44 *
45 * NORM (input) CHARACTER*1
46 * Specifies the value to be returned in DLANGB as described
47 * above.
48 *
49 * N (input) INTEGER
50 * The order of the matrix A. N >= 0. When N = 0, DLANGB is
51 * set to zero.
52 *
53 * KL (input) INTEGER
54 * The number of sub-diagonals of the matrix A. KL >= 0.
55 *
56 * KU (input) INTEGER
57 * The number of super-diagonals of the matrix A. KU >= 0.
58 *
59 * AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
60 * The band matrix A, stored in rows 1 to KL+KU+1. The j-th
61 * column of A is stored in the j-th column of the array AB as
62 * follows:
63 * AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
64 *
65 * LDAB (input) INTEGER
66 * The leading dimension of the array AB. LDAB >= KL+KU+1.
67 *
68 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
69 * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
70 * referenced.
71 *
72 * =====================================================================
73 *
74 *
75 * .. Parameters ..
76 DOUBLE PRECISION ONE, ZERO
77 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
78 * ..
79 * .. Local Scalars ..
80 INTEGER I, J, K, L
81 DOUBLE PRECISION SCALE, SUM, VALUE
82 * ..
83 * .. External Subroutines ..
84 EXTERNAL DLASSQ
85 * ..
86 * .. External Functions ..
87 LOGICAL LSAME
88 EXTERNAL LSAME
89 * ..
90 * .. Intrinsic Functions ..
91 INTRINSIC ABS, MAX, MIN, SQRT
92 * ..
93 * .. Executable Statements ..
94 *
95 IF( N.EQ.0 ) THEN
96 VALUE = ZERO
97 ELSE IF( LSAME( NORM, 'M' ) ) THEN
98 *
99 * Find max(abs(A(i,j))).
100 *
101 VALUE = ZERO
102 DO 20 J = 1, N
103 DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
104 VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
105 10 CONTINUE
106 20 CONTINUE
107 ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
108 *
109 * Find norm1(A).
110 *
111 VALUE = ZERO
112 DO 40 J = 1, N
113 SUM = ZERO
114 DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
115 SUM = SUM + ABS( AB( I, J ) )
116 30 CONTINUE
117 VALUE = MAX( VALUE, SUM )
118 40 CONTINUE
119 ELSE IF( LSAME( NORM, 'I' ) ) THEN
120 *
121 * Find normI(A).
122 *
123 DO 50 I = 1, N
124 WORK( I ) = ZERO
125 50 CONTINUE
126 DO 70 J = 1, N
127 K = KU + 1 - J
128 DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
129 WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
130 60 CONTINUE
131 70 CONTINUE
132 VALUE = ZERO
133 DO 80 I = 1, N
134 VALUE = MAX( VALUE, WORK( I ) )
135 80 CONTINUE
136 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
137 *
138 * Find normF(A).
139 *
140 SCALE = ZERO
141 SUM = ONE
142 DO 90 J = 1, N
143 L = MAX( 1, J-KU )
144 K = KU + 1 - J + L
145 CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
146 90 CONTINUE
147 VALUE = SCALE*SQRT( SUM )
148 END IF
149 *
150 DLANGB = VALUE
151 RETURN
152 *
153 * End of DLANGB
154 *
155 END