1 DOUBLE PRECISION FUNCTION ZLANSY( 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 WORK( * )
14 COMPLEX*16 A( LDA, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZLANSY returns the value of the one norm, or the Frobenius norm, or
21 * the infinity norm, or the element of largest absolute value of a
22 * complex symmetric matrix A.
23 *
24 * Description
25 * ===========
26 *
27 * ZLANSY returns the value
28 *
29 * ZLANSY = ( 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 ZLANSY as described
47 * above.
48 *
49 * UPLO (input) CHARACTER*1
50 * Specifies whether the upper or lower triangular part of the
51 * symmetric matrix A is to be referenced.
52 * = 'U': Upper triangular part of A is referenced
53 * = 'L': Lower triangular part of A is referenced
54 *
55 * N (input) INTEGER
56 * The order of the matrix A. N >= 0. When N = 0, ZLANSY is
57 * set to zero.
58 *
59 * A (input) COMPLEX*16 array, dimension (LDA,N)
60 * The symmetric matrix A. If UPLO = 'U', the leading n by n
61 * upper triangular part of A contains the upper triangular part
62 * of the matrix A, and the strictly lower triangular part of A
63 * is not referenced. If UPLO = 'L', the leading n by n lower
64 * triangular part of A contains the lower triangular part of
65 * the matrix A, and the strictly upper triangular part of A is
66 * not referenced.
67 *
68 * LDA (input) INTEGER
69 * The leading dimension of the array A. LDA >= max(N,1).
70 *
71 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
72 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
73 * WORK is not referenced.
74 *
75 * =====================================================================
76 *
77 * .. Parameters ..
78 DOUBLE PRECISION ONE, ZERO
79 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
80 * ..
81 * .. Local Scalars ..
82 INTEGER I, J
83 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
84 * ..
85 * .. External Functions ..
86 LOGICAL LSAME
87 EXTERNAL LSAME
88 * ..
89 * .. External Subroutines ..
90 EXTERNAL ZLASSQ
91 * ..
92 * .. Intrinsic Functions ..
93 INTRINSIC ABS, MAX, SQRT
94 * ..
95 * .. Executable Statements ..
96 *
97 IF( N.EQ.0 ) THEN
98 VALUE = ZERO
99 ELSE IF( LSAME( NORM, 'M' ) ) THEN
100 *
101 * Find max(abs(A(i,j))).
102 *
103 VALUE = ZERO
104 IF( LSAME( UPLO, 'U' ) ) THEN
105 DO 20 J = 1, N
106 DO 10 I = 1, J
107 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
108 10 CONTINUE
109 20 CONTINUE
110 ELSE
111 DO 40 J = 1, N
112 DO 30 I = J, N
113 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
114 30 CONTINUE
115 40 CONTINUE
116 END IF
117 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
118 $ ( NORM.EQ.'1' ) ) THEN
119 *
120 * Find normI(A) ( = norm1(A), since A is symmetric).
121 *
122 VALUE = ZERO
123 IF( LSAME( UPLO, 'U' ) ) THEN
124 DO 60 J = 1, N
125 SUM = ZERO
126 DO 50 I = 1, J - 1
127 ABSA = ABS( A( I, J ) )
128 SUM = SUM + ABSA
129 WORK( I ) = WORK( I ) + ABSA
130 50 CONTINUE
131 WORK( J ) = SUM + ABS( A( J, J ) )
132 60 CONTINUE
133 DO 70 I = 1, N
134 VALUE = MAX( VALUE, WORK( I ) )
135 70 CONTINUE
136 ELSE
137 DO 80 I = 1, N
138 WORK( I ) = ZERO
139 80 CONTINUE
140 DO 100 J = 1, N
141 SUM = WORK( J ) + ABS( A( J, J ) )
142 DO 90 I = J + 1, N
143 ABSA = ABS( A( I, J ) )
144 SUM = SUM + ABSA
145 WORK( I ) = WORK( I ) + ABSA
146 90 CONTINUE
147 VALUE = MAX( VALUE, SUM )
148 100 CONTINUE
149 END IF
150 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
151 *
152 * Find normF(A).
153 *
154 SCALE = ZERO
155 SUM = ONE
156 IF( LSAME( UPLO, 'U' ) ) THEN
157 DO 110 J = 2, N
158 CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
159 110 CONTINUE
160 ELSE
161 DO 120 J = 1, N - 1
162 CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
163 120 CONTINUE
164 END IF
165 SUM = 2*SUM
166 CALL ZLASSQ( N, A, LDA+1, SCALE, SUM )
167 VALUE = SCALE*SQRT( SUM )
168 END IF
169 *
170 ZLANSY = VALUE
171 RETURN
172 *
173 * End of ZLANSY
174 *
175 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 WORK( * )
14 COMPLEX*16 A( LDA, * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZLANSY returns the value of the one norm, or the Frobenius norm, or
21 * the infinity norm, or the element of largest absolute value of a
22 * complex symmetric matrix A.
23 *
24 * Description
25 * ===========
26 *
27 * ZLANSY returns the value
28 *
29 * ZLANSY = ( 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 ZLANSY as described
47 * above.
48 *
49 * UPLO (input) CHARACTER*1
50 * Specifies whether the upper or lower triangular part of the
51 * symmetric matrix A is to be referenced.
52 * = 'U': Upper triangular part of A is referenced
53 * = 'L': Lower triangular part of A is referenced
54 *
55 * N (input) INTEGER
56 * The order of the matrix A. N >= 0. When N = 0, ZLANSY is
57 * set to zero.
58 *
59 * A (input) COMPLEX*16 array, dimension (LDA,N)
60 * The symmetric matrix A. If UPLO = 'U', the leading n by n
61 * upper triangular part of A contains the upper triangular part
62 * of the matrix A, and the strictly lower triangular part of A
63 * is not referenced. If UPLO = 'L', the leading n by n lower
64 * triangular part of A contains the lower triangular part of
65 * the matrix A, and the strictly upper triangular part of A is
66 * not referenced.
67 *
68 * LDA (input) INTEGER
69 * The leading dimension of the array A. LDA >= max(N,1).
70 *
71 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
72 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
73 * WORK is not referenced.
74 *
75 * =====================================================================
76 *
77 * .. Parameters ..
78 DOUBLE PRECISION ONE, ZERO
79 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
80 * ..
81 * .. Local Scalars ..
82 INTEGER I, J
83 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
84 * ..
85 * .. External Functions ..
86 LOGICAL LSAME
87 EXTERNAL LSAME
88 * ..
89 * .. External Subroutines ..
90 EXTERNAL ZLASSQ
91 * ..
92 * .. Intrinsic Functions ..
93 INTRINSIC ABS, MAX, SQRT
94 * ..
95 * .. Executable Statements ..
96 *
97 IF( N.EQ.0 ) THEN
98 VALUE = ZERO
99 ELSE IF( LSAME( NORM, 'M' ) ) THEN
100 *
101 * Find max(abs(A(i,j))).
102 *
103 VALUE = ZERO
104 IF( LSAME( UPLO, 'U' ) ) THEN
105 DO 20 J = 1, N
106 DO 10 I = 1, J
107 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
108 10 CONTINUE
109 20 CONTINUE
110 ELSE
111 DO 40 J = 1, N
112 DO 30 I = J, N
113 VALUE = MAX( VALUE, ABS( A( I, J ) ) )
114 30 CONTINUE
115 40 CONTINUE
116 END IF
117 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
118 $ ( NORM.EQ.'1' ) ) THEN
119 *
120 * Find normI(A) ( = norm1(A), since A is symmetric).
121 *
122 VALUE = ZERO
123 IF( LSAME( UPLO, 'U' ) ) THEN
124 DO 60 J = 1, N
125 SUM = ZERO
126 DO 50 I = 1, J - 1
127 ABSA = ABS( A( I, J ) )
128 SUM = SUM + ABSA
129 WORK( I ) = WORK( I ) + ABSA
130 50 CONTINUE
131 WORK( J ) = SUM + ABS( A( J, J ) )
132 60 CONTINUE
133 DO 70 I = 1, N
134 VALUE = MAX( VALUE, WORK( I ) )
135 70 CONTINUE
136 ELSE
137 DO 80 I = 1, N
138 WORK( I ) = ZERO
139 80 CONTINUE
140 DO 100 J = 1, N
141 SUM = WORK( J ) + ABS( A( J, J ) )
142 DO 90 I = J + 1, N
143 ABSA = ABS( A( I, J ) )
144 SUM = SUM + ABSA
145 WORK( I ) = WORK( I ) + ABSA
146 90 CONTINUE
147 VALUE = MAX( VALUE, SUM )
148 100 CONTINUE
149 END IF
150 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
151 *
152 * Find normF(A).
153 *
154 SCALE = ZERO
155 SUM = ONE
156 IF( LSAME( UPLO, 'U' ) ) THEN
157 DO 110 J = 2, N
158 CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
159 110 CONTINUE
160 ELSE
161 DO 120 J = 1, N - 1
162 CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
163 120 CONTINUE
164 END IF
165 SUM = 2*SUM
166 CALL ZLASSQ( N, A, LDA+1, SCALE, SUM )
167 VALUE = SCALE*SQRT( SUM )
168 END IF
169 *
170 ZLANSY = VALUE
171 RETURN
172 *
173 * End of ZLANSY
174 *
175 END