1: *> \brief \b DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLANTP + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlantp.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlantp.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlantp.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER DIAG, NORM, UPLO
25: * INTEGER N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION AP( * ), WORK( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DLANTP returns the value of the one norm, or the Frobenius norm, or
38: *> the infinity norm, or the element of largest absolute value of a
39: *> triangular matrix A, supplied in packed form.
40: *> \endverbatim
41: *>
42: *> \return DLANTP
43: *> \verbatim
44: *>
45: *> DLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
46: *> (
47: *> ( norm1(A), NORM = '1', 'O' or 'o'
48: *> (
49: *> ( normI(A), NORM = 'I' or 'i'
50: *> (
51: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
52: *>
53: *> where norm1 denotes the one norm of a matrix (maximum column sum),
54: *> normI denotes the infinity norm of a matrix (maximum row sum) and
55: *> normF denotes the Frobenius norm of a matrix (square root of sum of
56: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
57: *> \endverbatim
58: *
59: * Arguments:
60: * ==========
61: *
62: *> \param[in] NORM
63: *> \verbatim
64: *> NORM is CHARACTER*1
65: *> Specifies the value to be returned in DLANTP as described
66: *> above.
67: *> \endverbatim
68: *>
69: *> \param[in] UPLO
70: *> \verbatim
71: *> UPLO is CHARACTER*1
72: *> Specifies whether the matrix A is upper or lower triangular.
73: *> = 'U': Upper triangular
74: *> = 'L': Lower triangular
75: *> \endverbatim
76: *>
77: *> \param[in] DIAG
78: *> \verbatim
79: *> DIAG is CHARACTER*1
80: *> Specifies whether or not the matrix A is unit triangular.
81: *> = 'N': Non-unit triangular
82: *> = 'U': Unit triangular
83: *> \endverbatim
84: *>
85: *> \param[in] N
86: *> \verbatim
87: *> N is INTEGER
88: *> The order of the matrix A. N >= 0. When N = 0, DLANTP is
89: *> set to zero.
90: *> \endverbatim
91: *>
92: *> \param[in] AP
93: *> \verbatim
94: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
95: *> The upper or lower triangular matrix A, packed columnwise in
96: *> a linear array. The j-th column of A is stored in the array
97: *> AP as follows:
98: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
99: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
100: *> Note that when DIAG = 'U', the elements of the array AP
101: *> corresponding to the diagonal elements of the matrix A are
102: *> not referenced, but are assumed to be one.
103: *> \endverbatim
104: *>
105: *> \param[out] WORK
106: *> \verbatim
107: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
108: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
109: *> referenced.
110: *> \endverbatim
111: *
112: * Authors:
113: * ========
114: *
115: *> \author Univ. of Tennessee
116: *> \author Univ. of California Berkeley
117: *> \author Univ. of Colorado Denver
118: *> \author NAG Ltd.
119: *
120: *> \ingroup doubleOTHERauxiliary
121: *
122: * =====================================================================
123: DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
124: *
125: * -- LAPACK auxiliary routine --
126: * -- LAPACK is a software package provided by Univ. of Tennessee, --
127: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128: *
129: * .. Scalar Arguments ..
130: CHARACTER DIAG, NORM, UPLO
131: INTEGER N
132: * ..
133: * .. Array Arguments ..
134: DOUBLE PRECISION AP( * ), WORK( * )
135: * ..
136: *
137: * =====================================================================
138: *
139: * .. Parameters ..
140: DOUBLE PRECISION ONE, ZERO
141: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
142: * ..
143: * .. Local Scalars ..
144: LOGICAL UDIAG
145: INTEGER I, J, K
146: DOUBLE PRECISION SCALE, SUM, VALUE
147: * ..
148: * .. External Subroutines ..
149: EXTERNAL DLASSQ
150: * ..
151: * .. External Functions ..
152: LOGICAL LSAME, DISNAN
153: EXTERNAL LSAME, DISNAN
154: * ..
155: * .. Intrinsic Functions ..
156: INTRINSIC ABS, SQRT
157: * ..
158: * .. Executable Statements ..
159: *
160: IF( N.EQ.0 ) THEN
161: VALUE = ZERO
162: ELSE IF( LSAME( NORM, 'M' ) ) THEN
163: *
164: * Find max(abs(A(i,j))).
165: *
166: K = 1
167: IF( LSAME( DIAG, 'U' ) ) THEN
168: VALUE = ONE
169: IF( LSAME( UPLO, 'U' ) ) THEN
170: DO 20 J = 1, N
171: DO 10 I = K, K + J - 2
172: SUM = ABS( AP( I ) )
173: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
174: 10 CONTINUE
175: K = K + J
176: 20 CONTINUE
177: ELSE
178: DO 40 J = 1, N
179: DO 30 I = K + 1, K + N - J
180: SUM = ABS( AP( I ) )
181: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
182: 30 CONTINUE
183: K = K + N - J + 1
184: 40 CONTINUE
185: END IF
186: ELSE
187: VALUE = ZERO
188: IF( LSAME( UPLO, 'U' ) ) THEN
189: DO 60 J = 1, N
190: DO 50 I = K, K + J - 1
191: SUM = ABS( AP( I ) )
192: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
193: 50 CONTINUE
194: K = K + J
195: 60 CONTINUE
196: ELSE
197: DO 80 J = 1, N
198: DO 70 I = K, K + N - J
199: SUM = ABS( AP( I ) )
200: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
201: 70 CONTINUE
202: K = K + N - J + 1
203: 80 CONTINUE
204: END IF
205: END IF
206: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
207: *
208: * Find norm1(A).
209: *
210: VALUE = ZERO
211: K = 1
212: UDIAG = LSAME( DIAG, 'U' )
213: IF( LSAME( UPLO, 'U' ) ) THEN
214: DO 110 J = 1, N
215: IF( UDIAG ) THEN
216: SUM = ONE
217: DO 90 I = K, K + J - 2
218: SUM = SUM + ABS( AP( I ) )
219: 90 CONTINUE
220: ELSE
221: SUM = ZERO
222: DO 100 I = K, K + J - 1
223: SUM = SUM + ABS( AP( I ) )
224: 100 CONTINUE
225: END IF
226: K = K + J
227: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
228: 110 CONTINUE
229: ELSE
230: DO 140 J = 1, N
231: IF( UDIAG ) THEN
232: SUM = ONE
233: DO 120 I = K + 1, K + N - J
234: SUM = SUM + ABS( AP( I ) )
235: 120 CONTINUE
236: ELSE
237: SUM = ZERO
238: DO 130 I = K, K + N - J
239: SUM = SUM + ABS( AP( I ) )
240: 130 CONTINUE
241: END IF
242: K = K + N - J + 1
243: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
244: 140 CONTINUE
245: END IF
246: ELSE IF( LSAME( NORM, 'I' ) ) THEN
247: *
248: * Find normI(A).
249: *
250: K = 1
251: IF( LSAME( UPLO, 'U' ) ) THEN
252: IF( LSAME( DIAG, 'U' ) ) THEN
253: DO 150 I = 1, N
254: WORK( I ) = ONE
255: 150 CONTINUE
256: DO 170 J = 1, N
257: DO 160 I = 1, J - 1
258: WORK( I ) = WORK( I ) + ABS( AP( K ) )
259: K = K + 1
260: 160 CONTINUE
261: K = K + 1
262: 170 CONTINUE
263: ELSE
264: DO 180 I = 1, N
265: WORK( I ) = ZERO
266: 180 CONTINUE
267: DO 200 J = 1, N
268: DO 190 I = 1, J
269: WORK( I ) = WORK( I ) + ABS( AP( K ) )
270: K = K + 1
271: 190 CONTINUE
272: 200 CONTINUE
273: END IF
274: ELSE
275: IF( LSAME( DIAG, 'U' ) ) THEN
276: DO 210 I = 1, N
277: WORK( I ) = ONE
278: 210 CONTINUE
279: DO 230 J = 1, N
280: K = K + 1
281: DO 220 I = J + 1, N
282: WORK( I ) = WORK( I ) + ABS( AP( K ) )
283: K = K + 1
284: 220 CONTINUE
285: 230 CONTINUE
286: ELSE
287: DO 240 I = 1, N
288: WORK( I ) = ZERO
289: 240 CONTINUE
290: DO 260 J = 1, N
291: DO 250 I = J, N
292: WORK( I ) = WORK( I ) + ABS( AP( K ) )
293: K = K + 1
294: 250 CONTINUE
295: 260 CONTINUE
296: END IF
297: END IF
298: VALUE = ZERO
299: DO 270 I = 1, N
300: SUM = WORK( I )
301: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
302: 270 CONTINUE
303: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
304: *
305: * Find normF(A).
306: *
307: IF( LSAME( UPLO, 'U' ) ) THEN
308: IF( LSAME( DIAG, 'U' ) ) THEN
309: SCALE = ONE
310: SUM = N
311: K = 2
312: DO 280 J = 2, N
313: CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
314: K = K + J
315: 280 CONTINUE
316: ELSE
317: SCALE = ZERO
318: SUM = ONE
319: K = 1
320: DO 290 J = 1, N
321: CALL DLASSQ( J, AP( K ), 1, SCALE, SUM )
322: K = K + J
323: 290 CONTINUE
324: END IF
325: ELSE
326: IF( LSAME( DIAG, 'U' ) ) THEN
327: SCALE = ONE
328: SUM = N
329: K = 2
330: DO 300 J = 1, N - 1
331: CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
332: K = K + N - J + 1
333: 300 CONTINUE
334: ELSE
335: SCALE = ZERO
336: SUM = ONE
337: K = 1
338: DO 310 J = 1, N
339: CALL DLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
340: K = K + N - J + 1
341: 310 CONTINUE
342: END IF
343: END IF
344: VALUE = SCALE*SQRT( SUM )
345: END IF
346: *
347: DLANTP = VALUE
348: RETURN
349: *
350: * End of DLANTP
351: *
352: END
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