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 December 2016
121: *
122: *> \ingroup doubleOTHERauxiliary
123: *
124: * =====================================================================
125: DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
126: *
127: * -- LAPACK auxiliary routine (version 3.7.0) --
128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130: * December 2016
131: *
132: IMPLICIT NONE
133: * .. Scalar Arguments ..
134: CHARACTER DIAG, NORM, UPLO
135: INTEGER N
136: * ..
137: * .. Array Arguments ..
138: DOUBLE PRECISION AP( * ), WORK( * )
139: * ..
140: *
141: * =====================================================================
142: *
143: * .. Parameters ..
144: DOUBLE PRECISION ONE, ZERO
145: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
146: * ..
147: * .. Local Scalars ..
148: LOGICAL UDIAG
149: INTEGER I, J, K
150: DOUBLE PRECISION SUM, VALUE
151: * ..
152: * .. Local Arrays ..
153: DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
154: * ..
155: * .. External Functions ..
156: LOGICAL LSAME, DISNAN
157: EXTERNAL LSAME, DISNAN
158: * ..
159: * .. External Subroutines ..
160: EXTERNAL DLASSQ, DCOMBSSQ
161: * ..
162: * .. Intrinsic Functions ..
163: INTRINSIC ABS, SQRT
164: * ..
165: * .. Executable Statements ..
166: *
167: IF( N.EQ.0 ) THEN
168: VALUE = ZERO
169: ELSE IF( LSAME( NORM, 'M' ) ) THEN
170: *
171: * Find max(abs(A(i,j))).
172: *
173: K = 1
174: IF( LSAME( DIAG, 'U' ) ) THEN
175: VALUE = ONE
176: IF( LSAME( UPLO, 'U' ) ) THEN
177: DO 20 J = 1, N
178: DO 10 I = K, K + J - 2
179: SUM = ABS( AP( I ) )
180: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
181: 10 CONTINUE
182: K = K + J
183: 20 CONTINUE
184: ELSE
185: DO 40 J = 1, N
186: DO 30 I = K + 1, K + N - J
187: SUM = ABS( AP( I ) )
188: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
189: 30 CONTINUE
190: K = K + N - J + 1
191: 40 CONTINUE
192: END IF
193: ELSE
194: VALUE = ZERO
195: IF( LSAME( UPLO, 'U' ) ) THEN
196: DO 60 J = 1, N
197: DO 50 I = K, K + J - 1
198: SUM = ABS( AP( I ) )
199: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
200: 50 CONTINUE
201: K = K + J
202: 60 CONTINUE
203: ELSE
204: DO 80 J = 1, N
205: DO 70 I = K, K + N - J
206: SUM = ABS( AP( I ) )
207: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
208: 70 CONTINUE
209: K = K + N - J + 1
210: 80 CONTINUE
211: END IF
212: END IF
213: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
214: *
215: * Find norm1(A).
216: *
217: VALUE = ZERO
218: K = 1
219: UDIAG = LSAME( DIAG, 'U' )
220: IF( LSAME( UPLO, 'U' ) ) THEN
221: DO 110 J = 1, N
222: IF( UDIAG ) THEN
223: SUM = ONE
224: DO 90 I = K, K + J - 2
225: SUM = SUM + ABS( AP( I ) )
226: 90 CONTINUE
227: ELSE
228: SUM = ZERO
229: DO 100 I = K, K + J - 1
230: SUM = SUM + ABS( AP( I ) )
231: 100 CONTINUE
232: END IF
233: K = K + J
234: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
235: 110 CONTINUE
236: ELSE
237: DO 140 J = 1, N
238: IF( UDIAG ) THEN
239: SUM = ONE
240: DO 120 I = K + 1, K + N - J
241: SUM = SUM + ABS( AP( I ) )
242: 120 CONTINUE
243: ELSE
244: SUM = ZERO
245: DO 130 I = K, K + N - J
246: SUM = SUM + ABS( AP( I ) )
247: 130 CONTINUE
248: END IF
249: K = K + N - J + 1
250: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
251: 140 CONTINUE
252: END IF
253: ELSE IF( LSAME( NORM, 'I' ) ) THEN
254: *
255: * Find normI(A).
256: *
257: K = 1
258: IF( LSAME( UPLO, 'U' ) ) THEN
259: IF( LSAME( DIAG, 'U' ) ) THEN
260: DO 150 I = 1, N
261: WORK( I ) = ONE
262: 150 CONTINUE
263: DO 170 J = 1, N
264: DO 160 I = 1, J - 1
265: WORK( I ) = WORK( I ) + ABS( AP( K ) )
266: K = K + 1
267: 160 CONTINUE
268: K = K + 1
269: 170 CONTINUE
270: ELSE
271: DO 180 I = 1, N
272: WORK( I ) = ZERO
273: 180 CONTINUE
274: DO 200 J = 1, N
275: DO 190 I = 1, J
276: WORK( I ) = WORK( I ) + ABS( AP( K ) )
277: K = K + 1
278: 190 CONTINUE
279: 200 CONTINUE
280: END IF
281: ELSE
282: IF( LSAME( DIAG, 'U' ) ) THEN
283: DO 210 I = 1, N
284: WORK( I ) = ONE
285: 210 CONTINUE
286: DO 230 J = 1, N
287: K = K + 1
288: DO 220 I = J + 1, N
289: WORK( I ) = WORK( I ) + ABS( AP( K ) )
290: K = K + 1
291: 220 CONTINUE
292: 230 CONTINUE
293: ELSE
294: DO 240 I = 1, N
295: WORK( I ) = ZERO
296: 240 CONTINUE
297: DO 260 J = 1, N
298: DO 250 I = J, N
299: WORK( I ) = WORK( I ) + ABS( AP( K ) )
300: K = K + 1
301: 250 CONTINUE
302: 260 CONTINUE
303: END IF
304: END IF
305: VALUE = ZERO
306: DO 270 I = 1, N
307: SUM = WORK( I )
308: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
309: 270 CONTINUE
310: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
311: *
312: * Find normF(A).
313: * SSQ(1) is scale
314: * SSQ(2) is sum-of-squares
315: * For better accuracy, sum each column separately.
316: *
317: IF( LSAME( UPLO, 'U' ) ) THEN
318: IF( LSAME( DIAG, 'U' ) ) THEN
319: SSQ( 1 ) = ONE
320: SSQ( 2 ) = N
321: K = 2
322: DO 280 J = 2, N
323: COLSSQ( 1 ) = ZERO
324: COLSSQ( 2 ) = ONE
325: CALL DLASSQ( J-1, AP( K ), 1,
326: $ COLSSQ( 1 ), COLSSQ( 2 ) )
327: CALL DCOMBSSQ( SSQ, COLSSQ )
328: K = K + J
329: 280 CONTINUE
330: ELSE
331: SSQ( 1 ) = ZERO
332: SSQ( 2 ) = ONE
333: K = 1
334: DO 290 J = 1, N
335: COLSSQ( 1 ) = ZERO
336: COLSSQ( 2 ) = ONE
337: CALL DLASSQ( J, AP( K ), 1,
338: $ COLSSQ( 1 ), COLSSQ( 2 ) )
339: CALL DCOMBSSQ( SSQ, COLSSQ )
340: K = K + J
341: 290 CONTINUE
342: END IF
343: ELSE
344: IF( LSAME( DIAG, 'U' ) ) THEN
345: SSQ( 1 ) = ONE
346: SSQ( 2 ) = N
347: K = 2
348: DO 300 J = 1, N - 1
349: COLSSQ( 1 ) = ZERO
350: COLSSQ( 2 ) = ONE
351: CALL DLASSQ( N-J, AP( K ), 1,
352: $ COLSSQ( 1 ), COLSSQ( 2 ) )
353: CALL DCOMBSSQ( SSQ, COLSSQ )
354: K = K + N - J + 1
355: 300 CONTINUE
356: ELSE
357: SSQ( 1 ) = ZERO
358: SSQ( 2 ) = ONE
359: K = 1
360: DO 310 J = 1, N
361: COLSSQ( 1 ) = ZERO
362: COLSSQ( 2 ) = ONE
363: CALL DLASSQ( N-J+1, AP( K ), 1,
364: $ COLSSQ( 1 ), COLSSQ( 2 ) )
365: CALL DCOMBSSQ( SSQ, COLSSQ )
366: K = K + N - J + 1
367: 310 CONTINUE
368: END IF
369: END IF
370: VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
371: END IF
372: *
373: DLANTP = VALUE
374: RETURN
375: *
376: * End of DLANTP
377: *
378: END
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