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: *> \date September 2012
121: *
122: *> \ingroup doubleOTHERauxiliary
123: *
124: * =====================================================================
125: DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
126: *
127: * -- LAPACK auxiliary routine (version 3.4.2) --
128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130: * September 2012
131: *
132: * .. Scalar Arguments ..
133: CHARACTER DIAG, NORM, UPLO
134: INTEGER N
135: * ..
136: * .. Array Arguments ..
137: DOUBLE PRECISION AP( * ), WORK( * )
138: * ..
139: *
140: * =====================================================================
141: *
142: * .. Parameters ..
143: DOUBLE PRECISION ONE, ZERO
144: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
145: * ..
146: * .. Local Scalars ..
147: LOGICAL UDIAG
148: INTEGER I, J, K
149: DOUBLE PRECISION SCALE, SUM, VALUE
150: * ..
151: * .. External Subroutines ..
152: EXTERNAL DLASSQ
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME, DISNAN
156: EXTERNAL LSAME, DISNAN
157: * ..
158: * .. Intrinsic Functions ..
159: INTRINSIC ABS, SQRT
160: * ..
161: * .. Executable Statements ..
162: *
163: IF( N.EQ.0 ) THEN
164: VALUE = ZERO
165: ELSE IF( LSAME( NORM, 'M' ) ) THEN
166: *
167: * Find max(abs(A(i,j))).
168: *
169: K = 1
170: IF( LSAME( DIAG, 'U' ) ) THEN
171: VALUE = ONE
172: IF( LSAME( UPLO, 'U' ) ) THEN
173: DO 20 J = 1, N
174: DO 10 I = K, K + J - 2
175: SUM = ABS( AP( I ) )
176: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
177: 10 CONTINUE
178: K = K + J
179: 20 CONTINUE
180: ELSE
181: DO 40 J = 1, N
182: DO 30 I = K + 1, K + N - J
183: SUM = ABS( AP( I ) )
184: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
185: 30 CONTINUE
186: K = K + N - J + 1
187: 40 CONTINUE
188: END IF
189: ELSE
190: VALUE = ZERO
191: IF( LSAME( UPLO, 'U' ) ) THEN
192: DO 60 J = 1, N
193: DO 50 I = K, K + J - 1
194: SUM = ABS( AP( I ) )
195: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
196: 50 CONTINUE
197: K = K + J
198: 60 CONTINUE
199: ELSE
200: DO 80 J = 1, N
201: DO 70 I = K, K + N - J
202: SUM = ABS( AP( I ) )
203: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
204: 70 CONTINUE
205: K = K + N - J + 1
206: 80 CONTINUE
207: END IF
208: END IF
209: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
210: *
211: * Find norm1(A).
212: *
213: VALUE = ZERO
214: K = 1
215: UDIAG = LSAME( DIAG, 'U' )
216: IF( LSAME( UPLO, 'U' ) ) THEN
217: DO 110 J = 1, N
218: IF( UDIAG ) THEN
219: SUM = ONE
220: DO 90 I = K, K + J - 2
221: SUM = SUM + ABS( AP( I ) )
222: 90 CONTINUE
223: ELSE
224: SUM = ZERO
225: DO 100 I = K, K + J - 1
226: SUM = SUM + ABS( AP( I ) )
227: 100 CONTINUE
228: END IF
229: K = K + J
230: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
231: 110 CONTINUE
232: ELSE
233: DO 140 J = 1, N
234: IF( UDIAG ) THEN
235: SUM = ONE
236: DO 120 I = K + 1, K + N - J
237: SUM = SUM + ABS( AP( I ) )
238: 120 CONTINUE
239: ELSE
240: SUM = ZERO
241: DO 130 I = K, K + N - J
242: SUM = SUM + ABS( AP( I ) )
243: 130 CONTINUE
244: END IF
245: K = K + N - J + 1
246: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
247: 140 CONTINUE
248: END IF
249: ELSE IF( LSAME( NORM, 'I' ) ) THEN
250: *
251: * Find normI(A).
252: *
253: K = 1
254: IF( LSAME( UPLO, 'U' ) ) THEN
255: IF( LSAME( DIAG, 'U' ) ) THEN
256: DO 150 I = 1, N
257: WORK( I ) = ONE
258: 150 CONTINUE
259: DO 170 J = 1, N
260: DO 160 I = 1, J - 1
261: WORK( I ) = WORK( I ) + ABS( AP( K ) )
262: K = K + 1
263: 160 CONTINUE
264: K = K + 1
265: 170 CONTINUE
266: ELSE
267: DO 180 I = 1, N
268: WORK( I ) = ZERO
269: 180 CONTINUE
270: DO 200 J = 1, N
271: DO 190 I = 1, J
272: WORK( I ) = WORK( I ) + ABS( AP( K ) )
273: K = K + 1
274: 190 CONTINUE
275: 200 CONTINUE
276: END IF
277: ELSE
278: IF( LSAME( DIAG, 'U' ) ) THEN
279: DO 210 I = 1, N
280: WORK( I ) = ONE
281: 210 CONTINUE
282: DO 230 J = 1, N
283: K = K + 1
284: DO 220 I = J + 1, N
285: WORK( I ) = WORK( I ) + ABS( AP( K ) )
286: K = K + 1
287: 220 CONTINUE
288: 230 CONTINUE
289: ELSE
290: DO 240 I = 1, N
291: WORK( I ) = ZERO
292: 240 CONTINUE
293: DO 260 J = 1, N
294: DO 250 I = J, N
295: WORK( I ) = WORK( I ) + ABS( AP( K ) )
296: K = K + 1
297: 250 CONTINUE
298: 260 CONTINUE
299: END IF
300: END IF
301: VALUE = ZERO
302: DO 270 I = 1, N
303: SUM = WORK( I )
304: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
305: 270 CONTINUE
306: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
307: *
308: * Find normF(A).
309: *
310: IF( LSAME( UPLO, 'U' ) ) THEN
311: IF( LSAME( DIAG, 'U' ) ) THEN
312: SCALE = ONE
313: SUM = N
314: K = 2
315: DO 280 J = 2, N
316: CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM )
317: K = K + J
318: 280 CONTINUE
319: ELSE
320: SCALE = ZERO
321: SUM = ONE
322: K = 1
323: DO 290 J = 1, N
324: CALL DLASSQ( J, AP( K ), 1, SCALE, SUM )
325: K = K + J
326: 290 CONTINUE
327: END IF
328: ELSE
329: IF( LSAME( DIAG, 'U' ) ) THEN
330: SCALE = ONE
331: SUM = N
332: K = 2
333: DO 300 J = 1, N - 1
334: CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM )
335: K = K + N - J + 1
336: 300 CONTINUE
337: ELSE
338: SCALE = ZERO
339: SUM = ONE
340: K = 1
341: DO 310 J = 1, N
342: CALL DLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
343: K = K + N - J + 1
344: 310 CONTINUE
345: END IF
346: END IF
347: VALUE = SCALE*SQRT( SUM )
348: END IF
349: *
350: DLANTP = VALUE
351: RETURN
352: *
353: * End of DLANTP
354: *
355: END
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