1 DOUBLE PRECISION FUNCTION ZLANHP( 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 * ZLANHP 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 hermitian matrix A, supplied in packed form.
23 *
24 * Description
25 * ===========
26 *
27 * ZLANHP returns the value
28 *
29 * ZLANHP = ( 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 ZLANHP as described
47 * above.
48 *
49 * UPLO (input) CHARACTER*1
50 * Specifies whether the upper or lower triangular part of the
51 * hermitian 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, ZLANHP 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 hermitian 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 * Note that the imaginary parts of the diagonal elements need
66 * not be set and are assumed to be zero.
67 *
68 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
69 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
70 * WORK is not referenced.
71 *
72 * =====================================================================
73 *
74 * .. Parameters ..
75 DOUBLE PRECISION ONE, ZERO
76 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
77 * ..
78 * .. Local Scalars ..
79 INTEGER I, J, K
80 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
81 * ..
82 * .. External Functions ..
83 LOGICAL LSAME
84 EXTERNAL LSAME
85 * ..
86 * .. External Subroutines ..
87 EXTERNAL ZLASSQ
88 * ..
89 * .. Intrinsic Functions ..
90 INTRINSIC ABS, DBLE, MAX, SQRT
91 * ..
92 * .. Executable Statements ..
93 *
94 IF( N.EQ.0 ) THEN
95 VALUE = ZERO
96 ELSE IF( LSAME( NORM, 'M' ) ) THEN
97 *
98 * Find max(abs(A(i,j))).
99 *
100 VALUE = ZERO
101 IF( LSAME( UPLO, 'U' ) ) THEN
102 K = 0
103 DO 20 J = 1, N
104 DO 10 I = K + 1, K + J - 1
105 VALUE = MAX( VALUE, ABS( AP( I ) ) )
106 10 CONTINUE
107 K = K + J
108 VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) )
109 20 CONTINUE
110 ELSE
111 K = 1
112 DO 40 J = 1, N
113 VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) )
114 DO 30 I = K + 1, K + N - J
115 VALUE = MAX( VALUE, ABS( AP( I ) ) )
116 30 CONTINUE
117 K = K + N - J + 1
118 40 CONTINUE
119 END IF
120 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
121 $ ( NORM.EQ.'1' ) ) THEN
122 *
123 * Find normI(A) ( = norm1(A), since A is hermitian).
124 *
125 VALUE = ZERO
126 K = 1
127 IF( LSAME( UPLO, 'U' ) ) THEN
128 DO 60 J = 1, N
129 SUM = ZERO
130 DO 50 I = 1, J - 1
131 ABSA = ABS( AP( K ) )
132 SUM = SUM + ABSA
133 WORK( I ) = WORK( I ) + ABSA
134 K = K + 1
135 50 CONTINUE
136 WORK( J ) = SUM + ABS( DBLE( AP( K ) ) )
137 K = K + 1
138 60 CONTINUE
139 DO 70 I = 1, N
140 VALUE = MAX( VALUE, WORK( I ) )
141 70 CONTINUE
142 ELSE
143 DO 80 I = 1, N
144 WORK( I ) = ZERO
145 80 CONTINUE
146 DO 100 J = 1, N
147 SUM = WORK( J ) + ABS( DBLE( AP( K ) ) )
148 K = K + 1
149 DO 90 I = J + 1, N
150 ABSA = ABS( AP( K ) )
151 SUM = SUM + ABSA
152 WORK( I ) = WORK( I ) + ABSA
153 K = K + 1
154 90 CONTINUE
155 VALUE = MAX( VALUE, SUM )
156 100 CONTINUE
157 END IF
158 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
159 *
160 * Find normF(A).
161 *
162 SCALE = ZERO
163 SUM = ONE
164 K = 2
165 IF( LSAME( UPLO, 'U' ) ) THEN
166 DO 110 J = 2, N
167 CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
168 K = K + J
169 110 CONTINUE
170 ELSE
171 DO 120 J = 1, N - 1
172 CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
173 K = K + N - J + 1
174 120 CONTINUE
175 END IF
176 SUM = 2*SUM
177 K = 1
178 DO 130 I = 1, N
179 IF( DBLE( AP( K ) ).NE.ZERO ) THEN
180 ABSA = ABS( DBLE( AP( K ) ) )
181 IF( SCALE.LT.ABSA ) THEN
182 SUM = ONE + SUM*( SCALE / ABSA )**2
183 SCALE = ABSA
184 ELSE
185 SUM = SUM + ( ABSA / SCALE )**2
186 END IF
187 END IF
188 IF( LSAME( UPLO, 'U' ) ) THEN
189 K = K + I + 1
190 ELSE
191 K = K + N - I + 1
192 END IF
193 130 CONTINUE
194 VALUE = SCALE*SQRT( SUM )
195 END IF
196 *
197 ZLANHP = VALUE
198 RETURN
199 *
200 * End of ZLANHP
201 *
202 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 * ZLANHP 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 hermitian matrix A, supplied in packed form.
23 *
24 * Description
25 * ===========
26 *
27 * ZLANHP returns the value
28 *
29 * ZLANHP = ( 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 ZLANHP as described
47 * above.
48 *
49 * UPLO (input) CHARACTER*1
50 * Specifies whether the upper or lower triangular part of the
51 * hermitian 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, ZLANHP 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 hermitian 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 * Note that the imaginary parts of the diagonal elements need
66 * not be set and are assumed to be zero.
67 *
68 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
69 * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
70 * WORK is not referenced.
71 *
72 * =====================================================================
73 *
74 * .. Parameters ..
75 DOUBLE PRECISION ONE, ZERO
76 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
77 * ..
78 * .. Local Scalars ..
79 INTEGER I, J, K
80 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
81 * ..
82 * .. External Functions ..
83 LOGICAL LSAME
84 EXTERNAL LSAME
85 * ..
86 * .. External Subroutines ..
87 EXTERNAL ZLASSQ
88 * ..
89 * .. Intrinsic Functions ..
90 INTRINSIC ABS, DBLE, MAX, SQRT
91 * ..
92 * .. Executable Statements ..
93 *
94 IF( N.EQ.0 ) THEN
95 VALUE = ZERO
96 ELSE IF( LSAME( NORM, 'M' ) ) THEN
97 *
98 * Find max(abs(A(i,j))).
99 *
100 VALUE = ZERO
101 IF( LSAME( UPLO, 'U' ) ) THEN
102 K = 0
103 DO 20 J = 1, N
104 DO 10 I = K + 1, K + J - 1
105 VALUE = MAX( VALUE, ABS( AP( I ) ) )
106 10 CONTINUE
107 K = K + J
108 VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) )
109 20 CONTINUE
110 ELSE
111 K = 1
112 DO 40 J = 1, N
113 VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) )
114 DO 30 I = K + 1, K + N - J
115 VALUE = MAX( VALUE, ABS( AP( I ) ) )
116 30 CONTINUE
117 K = K + N - J + 1
118 40 CONTINUE
119 END IF
120 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
121 $ ( NORM.EQ.'1' ) ) THEN
122 *
123 * Find normI(A) ( = norm1(A), since A is hermitian).
124 *
125 VALUE = ZERO
126 K = 1
127 IF( LSAME( UPLO, 'U' ) ) THEN
128 DO 60 J = 1, N
129 SUM = ZERO
130 DO 50 I = 1, J - 1
131 ABSA = ABS( AP( K ) )
132 SUM = SUM + ABSA
133 WORK( I ) = WORK( I ) + ABSA
134 K = K + 1
135 50 CONTINUE
136 WORK( J ) = SUM + ABS( DBLE( AP( K ) ) )
137 K = K + 1
138 60 CONTINUE
139 DO 70 I = 1, N
140 VALUE = MAX( VALUE, WORK( I ) )
141 70 CONTINUE
142 ELSE
143 DO 80 I = 1, N
144 WORK( I ) = ZERO
145 80 CONTINUE
146 DO 100 J = 1, N
147 SUM = WORK( J ) + ABS( DBLE( AP( K ) ) )
148 K = K + 1
149 DO 90 I = J + 1, N
150 ABSA = ABS( AP( K ) )
151 SUM = SUM + ABSA
152 WORK( I ) = WORK( I ) + ABSA
153 K = K + 1
154 90 CONTINUE
155 VALUE = MAX( VALUE, SUM )
156 100 CONTINUE
157 END IF
158 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
159 *
160 * Find normF(A).
161 *
162 SCALE = ZERO
163 SUM = ONE
164 K = 2
165 IF( LSAME( UPLO, 'U' ) ) THEN
166 DO 110 J = 2, N
167 CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
168 K = K + J
169 110 CONTINUE
170 ELSE
171 DO 120 J = 1, N - 1
172 CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
173 K = K + N - J + 1
174 120 CONTINUE
175 END IF
176 SUM = 2*SUM
177 K = 1
178 DO 130 I = 1, N
179 IF( DBLE( AP( K ) ).NE.ZERO ) THEN
180 ABSA = ABS( DBLE( AP( K ) ) )
181 IF( SCALE.LT.ABSA ) THEN
182 SUM = ONE + SUM*( SCALE / ABSA )**2
183 SCALE = ABSA
184 ELSE
185 SUM = SUM + ( ABSA / SCALE )**2
186 END IF
187 END IF
188 IF( LSAME( UPLO, 'U' ) ) THEN
189 K = K + I + 1
190 ELSE
191 K = K + N - I + 1
192 END IF
193 130 CONTINUE
194 VALUE = SCALE*SQRT( SUM )
195 END IF
196 *
197 ZLANHP = VALUE
198 RETURN
199 *
200 * End of ZLANHP
201 *
202 END