1 DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
2 *
3 * -- LAPACK auxiliary routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER NORM, UPLO
10 INTEGER LDA, N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION A( LDA, * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DLANSY returns the value of the one norm, or the Frobenius norm, or
20 * the infinity norm, or the element of largest absolute value of a
21 * real symmetric matrix A.
22 *
23 * Description
24 * ===========
25 *
26 * DLANSY returns the value
27 *
28 * DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
29 * (
30 * ( norm1(A), NORM = '1', 'O' or 'o'
31 * (
32 * ( normI(A), NORM = 'I' or 'i'
33 * (
34 * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
35 *
36 * where norm1 denotes the one norm of a matrix (maximum column sum),
37 * normI denotes the infinity norm of a matrix (maximum row sum) and
38 * normF denotes the Frobenius norm of a matrix (square root of sum of
39 * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
40 *
41 * Arguments
42 * =========
43 *
44 * NORM (input) CHARACTER*1
45 * Specifies the value to be returned in DLANSY as described
46 * above.
47 *
48 * UPLO (input) CHARACTER*1
49 * Specifies whether the upper or lower triangular part of the
50 * symmetric matrix A is to be referenced.
51 * = 'U': Upper triangular part of A is referenced
52 * = 'L': Lower triangular part of A is referenced
53 *
54 * N (input) INTEGER
55 * The order of the matrix A. N >= 0. When N = 0, DLANSY is
56 * set to zero.
57 *
58 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
59 * The symmetric matrix A. If UPLO = 'U', the leading n by n
60 * upper triangular part of A contains the upper triangular part
61 * of the matrix A, and the strictly lower triangular part of A
62 * is not referenced. If UPLO = 'L', the leading n by n lower
63 * triangular part of A contains the lower triangular part of
64 * the matrix A, and the strictly upper triangular part of A is
65 * not referenced.
66 *
67 * LDA (input) INTEGER
68 * The leading dimension of the array A. LDA >= max(N,1).
69 *
70 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
71 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
72 * WORK is not referenced.
73 *
74 * =====================================================================
75 *
76 * .. Parameters ..
77 DOUBLE PRECISION ONE, ZERO
78 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
79 * ..
80 * .. Local Scalars ..
81 INTEGER I, J
82 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL DLASSQ
86 * ..
87 * .. External Functions ..
88 LOGICAL LSAME
89 EXTERNAL LSAME
90 * ..
91 * .. Intrinsic Functions ..
92 INTRINSIC ABS, MAX, SQRT
93 * ..
94 * .. Executable Statements ..
95 *
96 IF( N.EQ.0 ) THEN
97 VALUE = ZERO
98 ELSE IF( LSAME( NORM, 'M' ) ) THEN
99 *
100 * Find max(abs(A(i,j))).
101 *
102 VALUE = ZERO
103 IF( LSAME( UPLO, 'U' ) ) THEN
104 DO 20 J = 1, N
105 DO 10 I = 1, J
106 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
107 10 CONTINUE
108 20 CONTINUE
109 ELSE
110 DO 40 J = 1, N
111 DO 30 I = J, N
112 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
113 30 CONTINUE
114 40 CONTINUE
115 END IF
116 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
117 $ ( NORM.EQ.'1' ) ) THEN
118 *
119 * Find normI(A) ( = norm1(A), since A is symmetric).
120 *
121 VALUE = ZERO
122 IF( LSAME( UPLO, 'U' ) ) THEN
123 DO 60 J = 1, N
124 SUM = ZERO
125 DO 50 I = 1, J - 1
126 ABSA = ABS( A( I, J ) )
127 SUM = SUM + ABSA
128 WORK( I ) = WORK( I ) + ABSA
129 50 CONTINUE
130 WORK( J ) = SUM + ABS( A( J, J ) )
131 60 CONTINUE
132 DO 70 I = 1, N
133 VALUE = MAX( VALUE, WORK( I ) )
134 70 CONTINUE
135 ELSE
136 DO 80 I = 1, N
137 WORK( I ) = ZERO
138 80 CONTINUE
139 DO 100 J = 1, N
140 SUM = WORK( J ) + ABS( A( J, J ) )
141 DO 90 I = J + 1, N
142 ABSA = ABS( A( I, J ) )
143 SUM = SUM + ABSA
144 WORK( I ) = WORK( I ) + ABSA
145 90 CONTINUE
146 VALUE = MAX( VALUE, SUM )
147 100 CONTINUE
148 END IF
149 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
150 *
151 * Find normF(A).
152 *
153 SCALE = ZERO
154 SUM = ONE
155 IF( LSAME( UPLO, 'U' ) ) THEN
156 DO 110 J = 2, N
157 CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
158 110 CONTINUE
159 ELSE
160 DO 120 J = 1, N - 1
161 CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
162 120 CONTINUE
163 END IF
164 SUM = 2*SUM
165 CALL DLASSQ( N, A, LDA+1, SCALE, SUM )
166 VALUE = SCALE*SQRT( SUM )
167 END IF
168 *
169 DLANSY = VALUE
170 RETURN
171 *
172 * End of DLANSY
173 *
174 END
2 *
3 * -- LAPACK auxiliary routine (version 3.2) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * November 2006
7 *
8 * .. Scalar Arguments ..
9 CHARACTER NORM, UPLO
10 INTEGER LDA, N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION A( LDA, * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DLANSY returns the value of the one norm, or the Frobenius norm, or
20 * the infinity norm, or the element of largest absolute value of a
21 * real symmetric matrix A.
22 *
23 * Description
24 * ===========
25 *
26 * DLANSY returns the value
27 *
28 * DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
29 * (
30 * ( norm1(A), NORM = '1', 'O' or 'o'
31 * (
32 * ( normI(A), NORM = 'I' or 'i'
33 * (
34 * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
35 *
36 * where norm1 denotes the one norm of a matrix (maximum column sum),
37 * normI denotes the infinity norm of a matrix (maximum row sum) and
38 * normF denotes the Frobenius norm of a matrix (square root of sum of
39 * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
40 *
41 * Arguments
42 * =========
43 *
44 * NORM (input) CHARACTER*1
45 * Specifies the value to be returned in DLANSY as described
46 * above.
47 *
48 * UPLO (input) CHARACTER*1
49 * Specifies whether the upper or lower triangular part of the
50 * symmetric matrix A is to be referenced.
51 * = 'U': Upper triangular part of A is referenced
52 * = 'L': Lower triangular part of A is referenced
53 *
54 * N (input) INTEGER
55 * The order of the matrix A. N >= 0. When N = 0, DLANSY is
56 * set to zero.
57 *
58 * A (input) DOUBLE PRECISION array, dimension (LDA,N)
59 * The symmetric matrix A. If UPLO = 'U', the leading n by n
60 * upper triangular part of A contains the upper triangular part
61 * of the matrix A, and the strictly lower triangular part of A
62 * is not referenced. If UPLO = 'L', the leading n by n lower
63 * triangular part of A contains the lower triangular part of
64 * the matrix A, and the strictly upper triangular part of A is
65 * not referenced.
66 *
67 * LDA (input) INTEGER
68 * The leading dimension of the array A. LDA >= max(N,1).
69 *
70 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
71 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
72 * WORK is not referenced.
73 *
74 * =====================================================================
75 *
76 * .. Parameters ..
77 DOUBLE PRECISION ONE, ZERO
78 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
79 * ..
80 * .. Local Scalars ..
81 INTEGER I, J
82 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL DLASSQ
86 * ..
87 * .. External Functions ..
88 LOGICAL LSAME
89 EXTERNAL LSAME
90 * ..
91 * .. Intrinsic Functions ..
92 INTRINSIC ABS, MAX, SQRT
93 * ..
94 * .. Executable Statements ..
95 *
96 IF( N.EQ.0 ) THEN
97 VALUE = ZERO
98 ELSE IF( LSAME( NORM, 'M' ) ) THEN
99 *
100 * Find max(abs(A(i,j))).
101 *
102 VALUE = ZERO
103 IF( LSAME( UPLO, 'U' ) ) THEN
104 DO 20 J = 1, N
105 DO 10 I = 1, J
106 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
107 10 CONTINUE
108 20 CONTINUE
109 ELSE
110 DO 40 J = 1, N
111 DO 30 I = J, N
112 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
113 30 CONTINUE
114 40 CONTINUE
115 END IF
116 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
117 $ ( NORM.EQ.'1' ) ) THEN
118 *
119 * Find normI(A) ( = norm1(A), since A is symmetric).
120 *
121 VALUE = ZERO
122 IF( LSAME( UPLO, 'U' ) ) THEN
123 DO 60 J = 1, N
124 SUM = ZERO
125 DO 50 I = 1, J - 1
126 ABSA = ABS( A( I, J ) )
127 SUM = SUM + ABSA
128 WORK( I ) = WORK( I ) + ABSA
129 50 CONTINUE
130 WORK( J ) = SUM + ABS( A( J, J ) )
131 60 CONTINUE
132 DO 70 I = 1, N
133 VALUE = MAX( VALUE, WORK( I ) )
134 70 CONTINUE
135 ELSE
136 DO 80 I = 1, N
137 WORK( I ) = ZERO
138 80 CONTINUE
139 DO 100 J = 1, N
140 SUM = WORK( J ) + ABS( A( J, J ) )
141 DO 90 I = J + 1, N
142 ABSA = ABS( A( I, J ) )
143 SUM = SUM + ABSA
144 WORK( I ) = WORK( I ) + ABSA
145 90 CONTINUE
146 VALUE = MAX( VALUE, SUM )
147 100 CONTINUE
148 END IF
149 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
150 *
151 * Find normF(A).
152 *
153 SCALE = ZERO
154 SUM = ONE
155 IF( LSAME( UPLO, 'U' ) ) THEN
156 DO 110 J = 2, N
157 CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
158 110 CONTINUE
159 ELSE
160 DO 120 J = 1, N - 1
161 CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
162 120 CONTINUE
163 END IF
164 SUM = 2*SUM
165 CALL DLASSQ( N, A, LDA+1, SCALE, SUM )
166 VALUE = SCALE*SQRT( SUM )
167 END IF
168 *
169 DLANSY = VALUE
170 RETURN
171 *
172 * End of DLANSY
173 *
174 END