1 DOUBLE PRECISION FUNCTION ZLANSP( NORM, UPLO, N, AP, 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 N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION WORK( * )
14 COMPLEX*16 AP( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZLANSP 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, supplied in packed form.
23 *
24 * Description
25 * ===========
26 *
27 * ZLANSP returns the value
28 *
29 * ZLANSP = ( 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 ZLANSP 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 supplied.
52 * = 'U': Upper triangular part of A is supplied
53 * = 'L': Lower triangular part of A is supplied
54 *
55 * N (input) INTEGER
56 * The order of the matrix A. N >= 0. When N = 0, ZLANSP is
57 * set to zero.
58 *
59 * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
60 * The upper or lower triangle of the symmetric matrix A, packed
61 * columnwise in a linear array. The j-th column of A is stored
62 * in the array AP as follows:
63 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
64 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
65 *
66 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
67 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
68 * WORK is not referenced.
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 DOUBLE PRECISION ONE, ZERO
74 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
75 * ..
76 * .. Local Scalars ..
77 INTEGER I, J, K
78 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
79 * ..
80 * .. External Functions ..
81 LOGICAL LSAME
82 EXTERNAL LSAME
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL ZLASSQ
86 * ..
87 * .. Intrinsic Functions ..
88 INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT
89 * ..
90 * .. Executable Statements ..
91 *
92 IF( N.EQ.0 ) THEN
93 VALUE = ZERO
94 ELSE IF( LSAME( NORM, 'M' ) ) THEN
95 *
96 * Find max(abs(A(i,j))).
97 *
98 VALUE = ZERO
99 IF( LSAME( UPLO, 'U' ) ) THEN
100 K = 1
101 DO 20 J = 1, N
102 DO 10 I = K, K + J - 1
103 VALUE = MAX( VALUE, ABS( AP( I ) ) )
104 10 CONTINUE
105 K = K + J
106 20 CONTINUE
107 ELSE
108 K = 1
109 DO 40 J = 1, N
110 DO 30 I = K, K + N - J
111 VALUE = MAX( VALUE, ABS( AP( I ) ) )
112 30 CONTINUE
113 K = K + N - J + 1
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 K = 1
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( AP( K ) )
128 SUM = SUM + ABSA
129 WORK( I ) = WORK( I ) + ABSA
130 K = K + 1
131 50 CONTINUE
132 WORK( J ) = SUM + ABS( AP( K ) )
133 K = K + 1
134 60 CONTINUE
135 DO 70 I = 1, N
136 VALUE = MAX( VALUE, WORK( I ) )
137 70 CONTINUE
138 ELSE
139 DO 80 I = 1, N
140 WORK( I ) = ZERO
141 80 CONTINUE
142 DO 100 J = 1, N
143 SUM = WORK( J ) + ABS( AP( K ) )
144 K = K + 1
145 DO 90 I = J + 1, N
146 ABSA = ABS( AP( K ) )
147 SUM = SUM + ABSA
148 WORK( I ) = WORK( I ) + ABSA
149 K = K + 1
150 90 CONTINUE
151 VALUE = MAX( VALUE, SUM )
152 100 CONTINUE
153 END IF
154 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
155 *
156 * Find normF(A).
157 *
158 SCALE = ZERO
159 SUM = ONE
160 K = 2
161 IF( LSAME( UPLO, 'U' ) ) THEN
162 DO 110 J = 2, N
163 CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
164 K = K + J
165 110 CONTINUE
166 ELSE
167 DO 120 J = 1, N - 1
168 CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
169 K = K + N - J + 1
170 120 CONTINUE
171 END IF
172 SUM = 2*SUM
173 K = 1
174 DO 130 I = 1, N
175 IF( DBLE( AP( K ) ).NE.ZERO ) THEN
176 ABSA = ABS( DBLE( AP( K ) ) )
177 IF( SCALE.LT.ABSA ) THEN
178 SUM = ONE + SUM*( SCALE / ABSA )**2
179 SCALE = ABSA
180 ELSE
181 SUM = SUM + ( ABSA / SCALE )**2
182 END IF
183 END IF
184 IF( DIMAG( AP( K ) ).NE.ZERO ) THEN
185 ABSA = ABS( DIMAG( AP( K ) ) )
186 IF( SCALE.LT.ABSA ) THEN
187 SUM = ONE + SUM*( SCALE / ABSA )**2
188 SCALE = ABSA
189 ELSE
190 SUM = SUM + ( ABSA / SCALE )**2
191 END IF
192 END IF
193 IF( LSAME( UPLO, 'U' ) ) THEN
194 K = K + I + 1
195 ELSE
196 K = K + N - I + 1
197 END IF
198 130 CONTINUE
199 VALUE = SCALE*SQRT( SUM )
200 END IF
201 *
202 ZLANSP = VALUE
203 RETURN
204 *
205 * End of ZLANSP
206 *
207 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 N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION WORK( * )
14 COMPLEX*16 AP( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZLANSP 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, supplied in packed form.
23 *
24 * Description
25 * ===========
26 *
27 * ZLANSP returns the value
28 *
29 * ZLANSP = ( 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 ZLANSP 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 supplied.
52 * = 'U': Upper triangular part of A is supplied
53 * = 'L': Lower triangular part of A is supplied
54 *
55 * N (input) INTEGER
56 * The order of the matrix A. N >= 0. When N = 0, ZLANSP is
57 * set to zero.
58 *
59 * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
60 * The upper or lower triangle of the symmetric matrix A, packed
61 * columnwise in a linear array. The j-th column of A is stored
62 * in the array AP as follows:
63 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
64 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
65 *
66 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
67 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
68 * WORK is not referenced.
69 *
70 * =====================================================================
71 *
72 * .. Parameters ..
73 DOUBLE PRECISION ONE, ZERO
74 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
75 * ..
76 * .. Local Scalars ..
77 INTEGER I, J, K
78 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
79 * ..
80 * .. External Functions ..
81 LOGICAL LSAME
82 EXTERNAL LSAME
83 * ..
84 * .. External Subroutines ..
85 EXTERNAL ZLASSQ
86 * ..
87 * .. Intrinsic Functions ..
88 INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT
89 * ..
90 * .. Executable Statements ..
91 *
92 IF( N.EQ.0 ) THEN
93 VALUE = ZERO
94 ELSE IF( LSAME( NORM, 'M' ) ) THEN
95 *
96 * Find max(abs(A(i,j))).
97 *
98 VALUE = ZERO
99 IF( LSAME( UPLO, 'U' ) ) THEN
100 K = 1
101 DO 20 J = 1, N
102 DO 10 I = K, K + J - 1
103 VALUE = MAX( VALUE, ABS( AP( I ) ) )
104 10 CONTINUE
105 K = K + J
106 20 CONTINUE
107 ELSE
108 K = 1
109 DO 40 J = 1, N
110 DO 30 I = K, K + N - J
111 VALUE = MAX( VALUE, ABS( AP( I ) ) )
112 30 CONTINUE
113 K = K + N - J + 1
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 K = 1
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( AP( K ) )
128 SUM = SUM + ABSA
129 WORK( I ) = WORK( I ) + ABSA
130 K = K + 1
131 50 CONTINUE
132 WORK( J ) = SUM + ABS( AP( K ) )
133 K = K + 1
134 60 CONTINUE
135 DO 70 I = 1, N
136 VALUE = MAX( VALUE, WORK( I ) )
137 70 CONTINUE
138 ELSE
139 DO 80 I = 1, N
140 WORK( I ) = ZERO
141 80 CONTINUE
142 DO 100 J = 1, N
143 SUM = WORK( J ) + ABS( AP( K ) )
144 K = K + 1
145 DO 90 I = J + 1, N
146 ABSA = ABS( AP( K ) )
147 SUM = SUM + ABSA
148 WORK( I ) = WORK( I ) + ABSA
149 K = K + 1
150 90 CONTINUE
151 VALUE = MAX( VALUE, SUM )
152 100 CONTINUE
153 END IF
154 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
155 *
156 * Find normF(A).
157 *
158 SCALE = ZERO
159 SUM = ONE
160 K = 2
161 IF( LSAME( UPLO, 'U' ) ) THEN
162 DO 110 J = 2, N
163 CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
164 K = K + J
165 110 CONTINUE
166 ELSE
167 DO 120 J = 1, N - 1
168 CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
169 K = K + N - J + 1
170 120 CONTINUE
171 END IF
172 SUM = 2*SUM
173 K = 1
174 DO 130 I = 1, N
175 IF( DBLE( AP( K ) ).NE.ZERO ) THEN
176 ABSA = ABS( DBLE( AP( K ) ) )
177 IF( SCALE.LT.ABSA ) THEN
178 SUM = ONE + SUM*( SCALE / ABSA )**2
179 SCALE = ABSA
180 ELSE
181 SUM = SUM + ( ABSA / SCALE )**2
182 END IF
183 END IF
184 IF( DIMAG( AP( K ) ).NE.ZERO ) THEN
185 ABSA = ABS( DIMAG( AP( K ) ) )
186 IF( SCALE.LT.ABSA ) THEN
187 SUM = ONE + SUM*( SCALE / ABSA )**2
188 SCALE = ABSA
189 ELSE
190 SUM = SUM + ( ABSA / SCALE )**2
191 END IF
192 END IF
193 IF( LSAME( UPLO, 'U' ) ) THEN
194 K = K + I + 1
195 ELSE
196 K = K + N - I + 1
197 END IF
198 130 CONTINUE
199 VALUE = SCALE*SQRT( SUM )
200 END IF
201 *
202 ZLANSP = VALUE
203 RETURN
204 *
205 * End of ZLANSP
206 *
207 END