1: *> \brief \b ZLANTP 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 ZLANTP + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlantp.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlantp.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlantp.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANTP( 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 WORK( * )
29: * COMPLEX*16 AP( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZLANTP returns the value of the one norm, or the Frobenius norm, or
39: *> the infinity norm, or the element of largest absolute value of a
40: *> triangular matrix A, supplied in packed form.
41: *> \endverbatim
42: *>
43: *> \return ZLANTP
44: *> \verbatim
45: *>
46: *> ZLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
47: *> (
48: *> ( norm1(A), NORM = '1', 'O' or 'o'
49: *> (
50: *> ( normI(A), NORM = 'I' or 'i'
51: *> (
52: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
53: *>
54: *> where norm1 denotes the one norm of a matrix (maximum column sum),
55: *> normI denotes the infinity norm of a matrix (maximum row sum) and
56: *> normF denotes the Frobenius norm of a matrix (square root of sum of
57: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
58: *> \endverbatim
59: *
60: * Arguments:
61: * ==========
62: *
63: *> \param[in] NORM
64: *> \verbatim
65: *> NORM is CHARACTER*1
66: *> Specifies the value to be returned in ZLANTP as described
67: *> above.
68: *> \endverbatim
69: *>
70: *> \param[in] UPLO
71: *> \verbatim
72: *> UPLO is CHARACTER*1
73: *> Specifies whether the matrix A is upper or lower triangular.
74: *> = 'U': Upper triangular
75: *> = 'L': Lower triangular
76: *> \endverbatim
77: *>
78: *> \param[in] DIAG
79: *> \verbatim
80: *> DIAG is CHARACTER*1
81: *> Specifies whether or not the matrix A is unit triangular.
82: *> = 'N': Non-unit triangular
83: *> = 'U': Unit triangular
84: *> \endverbatim
85: *>
86: *> \param[in] N
87: *> \verbatim
88: *> N is INTEGER
89: *> The order of the matrix A. N >= 0. When N = 0, ZLANTP is
90: *> set to zero.
91: *> \endverbatim
92: *>
93: *> \param[in] AP
94: *> \verbatim
95: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
96: *> The upper or lower triangular matrix A, packed columnwise in
97: *> a linear array. The j-th column of A is stored in the array
98: *> AP as follows:
99: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
100: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
101: *> Note that when DIAG = 'U', the elements of the array AP
102: *> corresponding to the diagonal elements of the matrix A are
103: *> not referenced, but are assumed to be one.
104: *> \endverbatim
105: *>
106: *> \param[out] WORK
107: *> \verbatim
108: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
109: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
110: *> referenced.
111: *> \endverbatim
112: *
113: * Authors:
114: * ========
115: *
116: *> \author Univ. of Tennessee
117: *> \author Univ. of California Berkeley
118: *> \author Univ. of Colorado Denver
119: *> \author NAG Ltd.
120: *
121: *> \ingroup complex16OTHERauxiliary
122: *
123: * =====================================================================
124: DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
125: *
126: * -- LAPACK auxiliary routine --
127: * -- LAPACK is a software package provided by Univ. of Tennessee, --
128: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129: *
130: * .. Scalar Arguments ..
131: CHARACTER DIAG, NORM, UPLO
132: INTEGER N
133: * ..
134: * .. Array Arguments ..
135: DOUBLE PRECISION WORK( * )
136: COMPLEX*16 AP( * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: DOUBLE PRECISION ONE, ZERO
143: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
144: * ..
145: * .. Local Scalars ..
146: LOGICAL UDIAG
147: INTEGER I, J, K
148: DOUBLE PRECISION SCALE, SUM, VALUE
149: * ..
150: * .. External Functions ..
151: LOGICAL LSAME, DISNAN
152: EXTERNAL LSAME, DISNAN
153: * ..
154: * .. External Subroutines ..
155: EXTERNAL ZLASSQ
156: * ..
157: * .. Intrinsic Functions ..
158: INTRINSIC ABS, SQRT
159: * ..
160: * .. Executable Statements ..
161: *
162: IF( N.EQ.0 ) THEN
163: VALUE = ZERO
164: ELSE IF( LSAME( NORM, 'M' ) ) THEN
165: *
166: * Find max(abs(A(i,j))).
167: *
168: K = 1
169: IF( LSAME( DIAG, 'U' ) ) THEN
170: VALUE = ONE
171: IF( LSAME( UPLO, 'U' ) ) THEN
172: DO 20 J = 1, N
173: DO 10 I = K, K + J - 2
174: SUM = ABS( AP( I ) )
175: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
176: 10 CONTINUE
177: K = K + J
178: 20 CONTINUE
179: ELSE
180: DO 40 J = 1, N
181: DO 30 I = K + 1, K + N - J
182: SUM = ABS( AP( I ) )
183: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
184: 30 CONTINUE
185: K = K + N - J + 1
186: 40 CONTINUE
187: END IF
188: ELSE
189: VALUE = ZERO
190: IF( LSAME( UPLO, 'U' ) ) THEN
191: DO 60 J = 1, N
192: DO 50 I = K, K + J - 1
193: SUM = ABS( AP( I ) )
194: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
195: 50 CONTINUE
196: K = K + J
197: 60 CONTINUE
198: ELSE
199: DO 80 J = 1, N
200: DO 70 I = K, K + N - J
201: SUM = ABS( AP( I ) )
202: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
203: 70 CONTINUE
204: K = K + N - J + 1
205: 80 CONTINUE
206: END IF
207: END IF
208: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
209: *
210: * Find norm1(A).
211: *
212: VALUE = ZERO
213: K = 1
214: UDIAG = LSAME( DIAG, 'U' )
215: IF( LSAME( UPLO, 'U' ) ) THEN
216: DO 110 J = 1, N
217: IF( UDIAG ) THEN
218: SUM = ONE
219: DO 90 I = K, K + J - 2
220: SUM = SUM + ABS( AP( I ) )
221: 90 CONTINUE
222: ELSE
223: SUM = ZERO
224: DO 100 I = K, K + J - 1
225: SUM = SUM + ABS( AP( I ) )
226: 100 CONTINUE
227: END IF
228: K = K + J
229: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
230: 110 CONTINUE
231: ELSE
232: DO 140 J = 1, N
233: IF( UDIAG ) THEN
234: SUM = ONE
235: DO 120 I = K + 1, K + N - J
236: SUM = SUM + ABS( AP( I ) )
237: 120 CONTINUE
238: ELSE
239: SUM = ZERO
240: DO 130 I = K, K + N - J
241: SUM = SUM + ABS( AP( I ) )
242: 130 CONTINUE
243: END IF
244: K = K + N - J + 1
245: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
246: 140 CONTINUE
247: END IF
248: ELSE IF( LSAME( NORM, 'I' ) ) THEN
249: *
250: * Find normI(A).
251: *
252: K = 1
253: IF( LSAME( UPLO, 'U' ) ) THEN
254: IF( LSAME( DIAG, 'U' ) ) THEN
255: DO 150 I = 1, N
256: WORK( I ) = ONE
257: 150 CONTINUE
258: DO 170 J = 1, N
259: DO 160 I = 1, J - 1
260: WORK( I ) = WORK( I ) + ABS( AP( K ) )
261: K = K + 1
262: 160 CONTINUE
263: K = K + 1
264: 170 CONTINUE
265: ELSE
266: DO 180 I = 1, N
267: WORK( I ) = ZERO
268: 180 CONTINUE
269: DO 200 J = 1, N
270: DO 190 I = 1, J
271: WORK( I ) = WORK( I ) + ABS( AP( K ) )
272: K = K + 1
273: 190 CONTINUE
274: 200 CONTINUE
275: END IF
276: ELSE
277: IF( LSAME( DIAG, 'U' ) ) THEN
278: DO 210 I = 1, N
279: WORK( I ) = ONE
280: 210 CONTINUE
281: DO 230 J = 1, N
282: K = K + 1
283: DO 220 I = J + 1, N
284: WORK( I ) = WORK( I ) + ABS( AP( K ) )
285: K = K + 1
286: 220 CONTINUE
287: 230 CONTINUE
288: ELSE
289: DO 240 I = 1, N
290: WORK( I ) = ZERO
291: 240 CONTINUE
292: DO 260 J = 1, N
293: DO 250 I = J, N
294: WORK( I ) = WORK( I ) + ABS( AP( K ) )
295: K = K + 1
296: 250 CONTINUE
297: 260 CONTINUE
298: END IF
299: END IF
300: VALUE = ZERO
301: DO 270 I = 1, N
302: SUM = WORK( I )
303: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
304: 270 CONTINUE
305: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
306: *
307: * Find normF(A).
308: *
309: IF( LSAME( UPLO, 'U' ) ) THEN
310: IF( LSAME( DIAG, 'U' ) ) THEN
311: SCALE = ONE
312: SUM = N
313: K = 2
314: DO 280 J = 2, N
315: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
316: K = K + J
317: 280 CONTINUE
318: ELSE
319: SCALE = ZERO
320: SUM = ONE
321: K = 1
322: DO 290 J = 1, N
323: CALL ZLASSQ( J, AP( K ), 1, SCALE, SUM )
324: K = K + J
325: 290 CONTINUE
326: END IF
327: ELSE
328: IF( LSAME( DIAG, 'U' ) ) THEN
329: SCALE = ONE
330: SUM = N
331: K = 2
332: DO 300 J = 1, N - 1
333: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
334: K = K + N - J + 1
335: 300 CONTINUE
336: ELSE
337: SCALE = ZERO
338: SUM = ONE
339: K = 1
340: DO 310 J = 1, N
341: CALL ZLASSQ( N-J+1, AP( K ), 1, SCALE, SUM )
342: K = K + N - J + 1
343: 310 CONTINUE
344: END IF
345: END IF
346: VALUE = SCALE*SQRT( SUM )
347: END IF
348: *
349: ZLANTP = VALUE
350: RETURN
351: *
352: * End of ZLANTP
353: *
354: END
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