1 DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, 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 DIAG, NORM, UPLO
10 INTEGER N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION AP( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DLANTP 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 * triangular matrix A, supplied in packed form.
22 *
23 * Description
24 * ===========
25 *
26 * DLANTP returns the value
27 *
28 * DLANTP = ( 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 DLANTP as described
46 * above.
47 *
48 * UPLO (input) CHARACTER*1
49 * Specifies whether the matrix A is upper or lower triangular.
50 * = 'U': Upper triangular
51 * = 'L': Lower triangular
52 *
53 * DIAG (input) CHARACTER*1
54 * Specifies whether or not the matrix A is unit triangular.
55 * = 'N': Non-unit triangular
56 * = 'U': Unit triangular
57 *
58 * N (input) INTEGER
59 * The order of the matrix A. N >= 0. When N = 0, DLANTP is
60 * set to zero.
61 *
62 * AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
63 * The upper or lower triangular matrix A, packed columnwise in
64 * a linear array. The j-th column of A is stored in the array
65 * AP as follows:
66 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
67 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
68 * Note that when DIAG = 'U', the elements of the array AP
69 * corresponding to the diagonal elements of the matrix A are
70 * not referenced, but are assumed to be one.
71 *
72 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
73 * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
74 * referenced.
75 *
76 * =====================================================================
77 *
78 * .. Parameters ..
79 DOUBLE PRECISION ONE, ZERO
80 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
81 * ..
82 * .. Local Scalars ..
83 LOGICAL UDIAG
84 INTEGER I, J, K
85 DOUBLE PRECISION SCALE, SUM, VALUE
86 * ..
87 * .. External Subroutines ..
88 EXTERNAL DLASSQ
89 * ..
90 * .. External Functions ..
91 LOGICAL LSAME
92 EXTERNAL LSAME
93 * ..
94 * .. Intrinsic Functions ..
95 INTRINSIC ABS, MAX, SQRT
96 * ..
97 * .. Executable Statements ..
98 *
99 IF( N.EQ.0 ) THEN
100 VALUE = ZERO
101 ELSE IF( LSAME( NORM, 'M' ) ) THEN
102 *
103 * Find max(abs(A(i,j))).
104 *
105 K = 1
106 IF( LSAME( DIAG, 'U' ) ) THEN
107 VALUE = ONE
108 IF( LSAME( UPLO, 'U' ) ) THEN
109 DO 20 J = 1, N
110 DO 10 I = K, K + J - 2
111 VALUE = MAX( VALUE, ABS( AP( I ) ) )
112 10 CONTINUE
113 K = K + J
114 20 CONTINUE
115 ELSE
116 DO 40 J = 1, N
117 DO 30 I = K + 1, K + N - J
118 VALUE = MAX( VALUE, ABS( AP( I ) ) )
119 30 CONTINUE
120 K = K + N - J + 1
121 40 CONTINUE
122 END IF
123 ELSE
124 VALUE = ZERO
125 IF( LSAME( UPLO, 'U' ) ) THEN
126 DO 60 J = 1, N
127 DO 50 I = K, K + J - 1
128 VALUE = MAX( VALUE, ABS( AP( I ) ) )
129 50 CONTINUE
130 K = K + J
131 60 CONTINUE
132 ELSE
133 DO 80 J = 1, N
134 DO 70 I = K, K + N - J
135 VALUE = MAX( VALUE, ABS( AP( I ) ) )
136 70 CONTINUE
137 K = K + N - J + 1
138 80 CONTINUE
139 END IF
140 END IF
141 ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
142 *
143 * Find norm1(A).
144 *
145 VALUE = ZERO
146 K = 1
147 UDIAG = LSAME( DIAG, 'U' )
148 IF( LSAME( UPLO, 'U' ) ) THEN
149 DO 110 J = 1, N
150 IF( UDIAG ) THEN
151 SUM = ONE
152 DO 90 I = K, K + J - 2
153 SUM = SUM + ABS( AP( I ) )
154 90 CONTINUE
155 ELSE
156 SUM = ZERO
157 DO 100 I = K, K + J - 1
158 SUM = SUM + ABS( AP( I ) )
159 100 CONTINUE
160 END IF
161 K = K + J
162 VALUE = MAX( VALUE, SUM )
163 110 CONTINUE
164 ELSE
165 DO 140 J = 1, N
166 IF( UDIAG ) THEN
167 SUM = ONE
168 DO 120 I = K + 1, K + N - J
169 SUM = SUM + ABS( AP( I ) )
170 120 CONTINUE
171 ELSE
172 SUM = ZERO
173 DO 130 I = K, K + N - J
174 SUM = SUM + ABS( AP( I ) )
175 130 CONTINUE
176 END IF
177 K = K + N - J + 1
178 VALUE = MAX( VALUE, SUM )
179 140 CONTINUE
180 END IF
181 ELSE IF( LSAME( NORM, 'I' ) ) THEN
182 *
183 * Find normI(A).
184 *
185 K = 1
186 IF( LSAME( UPLO, 'U' ) ) THEN
187 IF( LSAME( DIAG, 'U' ) ) THEN
188 DO 150 I = 1, N
189 WORK( I ) = ONE
190 150 CONTINUE
191 DO 170 J = 1, N
192 DO 160 I = 1, J - 1
193 WORK( I ) = WORK( I ) + ABS( AP( K ) )
194 K = K + 1
195 160 CONTINUE
196 K = K + 1
197 170 CONTINUE
198 ELSE
199 DO 180 I = 1, N
200 WORK( I ) = ZERO
201 180 CONTINUE
202 DO 200 J = 1, N
203 DO 190 I = 1, J
204 WORK( I ) = WORK( I ) + ABS( AP( K ) )
205 K = K + 1
206 190 CONTINUE
207 200 CONTINUE
208 END IF
209 ELSE
210 IF( LSAME( DIAG, 'U' ) ) THEN
211 DO 210 I = 1, N
212 WORK( I ) = ONE
213 210 CONTINUE
214 DO 230 J = 1, N
215 K = K + 1
216 DO 220 I = J + 1, N
217 WORK( I ) = WORK( I ) + ABS( AP( K ) )
218 K = K + 1
219 220 CONTINUE
220 230 CONTINUE
221 ELSE
222 DO 240 I = 1, N
223 WORK( I ) = ZERO
224 240 CONTINUE
225 DO 260 J = 1, N
226 DO 250 I = J, N
227 WORK( I ) = WORK( I ) + ABS( AP( K ) )
228 K = K + 1
229 250 CONTINUE
230 260 CONTINUE
231 END IF
232 END IF
233 VALUE = ZERO
234 DO 270 I = 1, N
235 VALUE = MAX( VALUE, WORK( I ) )
236 270 CONTINUE
237 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
238 *
239 * Find normF(A).
240 *
241 IF( LSAME( UPLO, 'U' ) ) THEN
242 IF( LSAME( DIAG, 'U' ) ) THEN
243 SCALE = ONE
244 SUM = N
245 K = 2
246 DO 280 J = 2, N
247 CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
248 K = K + J
249 280 CONTINUE
250 ELSE
251 SCALE = ZERO
252 SUM = ONE
253 K = 1
254 DO 290 J = 1, N
255 CALL DLASSQ( J, AP( K ), 1, SCALE, SUM )
256 K = K + J
257 290 CONTINUE
258 END IF
259 ELSE
260 IF( LSAME( DIAG, 'U' ) ) THEN
261 SCALE = ONE
262 SUM = N
263 K = 2
264 DO 300 J = 1, N - 1
265 CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
266 K = K + N - J + 1
267 300 CONTINUE
268 ELSE
269 SCALE = ZERO
270 SUM = ONE
271 K = 1
272 DO 310 J = 1, N
273 CALL DLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
274 K = K + N - J + 1
275 310 CONTINUE
276 END IF
277 END IF
278 VALUE = SCALE*SQRT( SUM )
279 END IF
280 *
281 DLANTP = VALUE
282 RETURN
283 *
284 * End of DLANTP
285 *
286 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 DIAG, NORM, UPLO
10 INTEGER N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION AP( * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * DLANTP 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 * triangular matrix A, supplied in packed form.
22 *
23 * Description
24 * ===========
25 *
26 * DLANTP returns the value
27 *
28 * DLANTP = ( 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 DLANTP as described
46 * above.
47 *
48 * UPLO (input) CHARACTER*1
49 * Specifies whether the matrix A is upper or lower triangular.
50 * = 'U': Upper triangular
51 * = 'L': Lower triangular
52 *
53 * DIAG (input) CHARACTER*1
54 * Specifies whether or not the matrix A is unit triangular.
55 * = 'N': Non-unit triangular
56 * = 'U': Unit triangular
57 *
58 * N (input) INTEGER
59 * The order of the matrix A. N >= 0. When N = 0, DLANTP is
60 * set to zero.
61 *
62 * AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
63 * The upper or lower triangular matrix A, packed columnwise in
64 * a linear array. The j-th column of A is stored in the array
65 * AP as follows:
66 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
67 * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
68 * Note that when DIAG = 'U', the elements of the array AP
69 * corresponding to the diagonal elements of the matrix A are
70 * not referenced, but are assumed to be one.
71 *
72 * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
73 * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
74 * referenced.
75 *
76 * =====================================================================
77 *
78 * .. Parameters ..
79 DOUBLE PRECISION ONE, ZERO
80 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
81 * ..
82 * .. Local Scalars ..
83 LOGICAL UDIAG
84 INTEGER I, J, K
85 DOUBLE PRECISION SCALE, SUM, VALUE
86 * ..
87 * .. External Subroutines ..
88 EXTERNAL DLASSQ
89 * ..
90 * .. External Functions ..
91 LOGICAL LSAME
92 EXTERNAL LSAME
93 * ..
94 * .. Intrinsic Functions ..
95 INTRINSIC ABS, MAX, SQRT
96 * ..
97 * .. Executable Statements ..
98 *
99 IF( N.EQ.0 ) THEN
100 VALUE = ZERO
101 ELSE IF( LSAME( NORM, 'M' ) ) THEN
102 *
103 * Find max(abs(A(i,j))).
104 *
105 K = 1
106 IF( LSAME( DIAG, 'U' ) ) THEN
107 VALUE = ONE
108 IF( LSAME( UPLO, 'U' ) ) THEN
109 DO 20 J = 1, N
110 DO 10 I = K, K + J - 2
111 VALUE = MAX( VALUE, ABS( AP( I ) ) )
112 10 CONTINUE
113 K = K + J
114 20 CONTINUE
115 ELSE
116 DO 40 J = 1, N
117 DO 30 I = K + 1, K + N - J
118 VALUE = MAX( VALUE, ABS( AP( I ) ) )
119 30 CONTINUE
120 K = K + N - J + 1
121 40 CONTINUE
122 END IF
123 ELSE
124 VALUE = ZERO
125 IF( LSAME( UPLO, 'U' ) ) THEN
126 DO 60 J = 1, N
127 DO 50 I = K, K + J - 1
128 VALUE = MAX( VALUE, ABS( AP( I ) ) )
129 50 CONTINUE
130 K = K + J
131 60 CONTINUE
132 ELSE
133 DO 80 J = 1, N
134 DO 70 I = K, K + N - J
135 VALUE = MAX( VALUE, ABS( AP( I ) ) )
136 70 CONTINUE
137 K = K + N - J + 1
138 80 CONTINUE
139 END IF
140 END IF
141 ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
142 *
143 * Find norm1(A).
144 *
145 VALUE = ZERO
146 K = 1
147 UDIAG = LSAME( DIAG, 'U' )
148 IF( LSAME( UPLO, 'U' ) ) THEN
149 DO 110 J = 1, N
150 IF( UDIAG ) THEN
151 SUM = ONE
152 DO 90 I = K, K + J - 2
153 SUM = SUM + ABS( AP( I ) )
154 90 CONTINUE
155 ELSE
156 SUM = ZERO
157 DO 100 I = K, K + J - 1
158 SUM = SUM + ABS( AP( I ) )
159 100 CONTINUE
160 END IF
161 K = K + J
162 VALUE = MAX( VALUE, SUM )
163 110 CONTINUE
164 ELSE
165 DO 140 J = 1, N
166 IF( UDIAG ) THEN
167 SUM = ONE
168 DO 120 I = K + 1, K + N - J
169 SUM = SUM + ABS( AP( I ) )
170 120 CONTINUE
171 ELSE
172 SUM = ZERO
173 DO 130 I = K, K + N - J
174 SUM = SUM + ABS( AP( I ) )
175 130 CONTINUE
176 END IF
177 K = K + N - J + 1
178 VALUE = MAX( VALUE, SUM )
179 140 CONTINUE
180 END IF
181 ELSE IF( LSAME( NORM, 'I' ) ) THEN
182 *
183 * Find normI(A).
184 *
185 K = 1
186 IF( LSAME( UPLO, 'U' ) ) THEN
187 IF( LSAME( DIAG, 'U' ) ) THEN
188 DO 150 I = 1, N
189 WORK( I ) = ONE
190 150 CONTINUE
191 DO 170 J = 1, N
192 DO 160 I = 1, J - 1
193 WORK( I ) = WORK( I ) + ABS( AP( K ) )
194 K = K + 1
195 160 CONTINUE
196 K = K + 1
197 170 CONTINUE
198 ELSE
199 DO 180 I = 1, N
200 WORK( I ) = ZERO
201 180 CONTINUE
202 DO 200 J = 1, N
203 DO 190 I = 1, J
204 WORK( I ) = WORK( I ) + ABS( AP( K ) )
205 K = K + 1
206 190 CONTINUE
207 200 CONTINUE
208 END IF
209 ELSE
210 IF( LSAME( DIAG, 'U' ) ) THEN
211 DO 210 I = 1, N
212 WORK( I ) = ONE
213 210 CONTINUE
214 DO 230 J = 1, N
215 K = K + 1
216 DO 220 I = J + 1, N
217 WORK( I ) = WORK( I ) + ABS( AP( K ) )
218 K = K + 1
219 220 CONTINUE
220 230 CONTINUE
221 ELSE
222 DO 240 I = 1, N
223 WORK( I ) = ZERO
224 240 CONTINUE
225 DO 260 J = 1, N
226 DO 250 I = J, N
227 WORK( I ) = WORK( I ) + ABS( AP( K ) )
228 K = K + 1
229 250 CONTINUE
230 260 CONTINUE
231 END IF
232 END IF
233 VALUE = ZERO
234 DO 270 I = 1, N
235 VALUE = MAX( VALUE, WORK( I ) )
236 270 CONTINUE
237 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
238 *
239 * Find normF(A).
240 *
241 IF( LSAME( UPLO, 'U' ) ) THEN
242 IF( LSAME( DIAG, 'U' ) ) THEN
243 SCALE = ONE
244 SUM = N
245 K = 2
246 DO 280 J = 2, N
247 CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
248 K = K + J
249 280 CONTINUE
250 ELSE
251 SCALE = ZERO
252 SUM = ONE
253 K = 1
254 DO 290 J = 1, N
255 CALL DLASSQ( J, AP( K ), 1, SCALE, SUM )
256 K = K + J
257 290 CONTINUE
258 END IF
259 ELSE
260 IF( LSAME( DIAG, 'U' ) ) THEN
261 SCALE = ONE
262 SUM = N
263 K = 2
264 DO 300 J = 1, N - 1
265 CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
266 K = K + N - J + 1
267 300 CONTINUE
268 ELSE
269 SCALE = ZERO
270 SUM = ONE
271 K = 1
272 DO 310 J = 1, N
273 CALL DLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
274 K = K + N - J + 1
275 310 CONTINUE
276 END IF
277 END IF
278 VALUE = SCALE*SQRT( SUM )
279 END IF
280 *
281 DLANTP = VALUE
282 RETURN
283 *
284 * End of DLANTP
285 *
286 END