Annotation of rpl/lapack/lapack/zlantp.f, revision 1.18
1.11 bertrand 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.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 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">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER DIAG, NORM, UPLO
25: * INTEGER N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION WORK( * )
29: * COMPLEX*16 AP( * )
30: * ..
1.15 bertrand 31: *
1.8 bertrand 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: *
1.15 bertrand 116: *> \author Univ. of Tennessee
117: *> \author Univ. of California Berkeley
118: *> \author Univ. of Colorado Denver
119: *> \author NAG Ltd.
1.8 bertrand 120: *
1.15 bertrand 121: *> \date December 2016
1.8 bertrand 122: *
123: *> \ingroup complex16OTHERauxiliary
124: *
125: * =====================================================================
1.1 bertrand 126: DOUBLE PRECISION FUNCTION ZLANTP( NORM, UPLO, DIAG, N, AP, WORK )
127: *
1.15 bertrand 128: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 131: * December 2016
1.1 bertrand 132: *
1.18 ! bertrand 133: IMPLICIT NONE
1.1 bertrand 134: * .. Scalar Arguments ..
135: CHARACTER DIAG, NORM, UPLO
136: INTEGER N
137: * ..
138: * .. Array Arguments ..
139: DOUBLE PRECISION WORK( * )
140: COMPLEX*16 AP( * )
141: * ..
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ONE, ZERO
147: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
148: * ..
149: * .. Local Scalars ..
150: LOGICAL UDIAG
151: INTEGER I, J, K
1.18 ! bertrand 152: DOUBLE PRECISION SUM, VALUE
! 153: * ..
! 154: * .. Local Arrays ..
! 155: DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
1.1 bertrand 156: * ..
157: * .. External Functions ..
1.11 bertrand 158: LOGICAL LSAME, DISNAN
159: EXTERNAL LSAME, DISNAN
1.1 bertrand 160: * ..
161: * .. External Subroutines ..
1.18 ! bertrand 162: EXTERNAL ZLASSQ, DCOMBSSQ
1.1 bertrand 163: * ..
164: * .. Intrinsic Functions ..
1.11 bertrand 165: INTRINSIC ABS, SQRT
1.1 bertrand 166: * ..
167: * .. Executable Statements ..
168: *
169: IF( N.EQ.0 ) THEN
170: VALUE = ZERO
171: ELSE IF( LSAME( NORM, 'M' ) ) THEN
172: *
173: * Find max(abs(A(i,j))).
174: *
175: K = 1
176: IF( LSAME( DIAG, 'U' ) ) THEN
177: VALUE = ONE
178: IF( LSAME( UPLO, 'U' ) ) THEN
179: DO 20 J = 1, N
180: DO 10 I = K, K + J - 2
1.11 bertrand 181: SUM = ABS( AP( I ) )
182: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 183: 10 CONTINUE
184: K = K + J
185: 20 CONTINUE
186: ELSE
187: DO 40 J = 1, N
188: DO 30 I = K + 1, K + N - J
1.11 bertrand 189: SUM = ABS( AP( I ) )
190: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 191: 30 CONTINUE
192: K = K + N - J + 1
193: 40 CONTINUE
194: END IF
195: ELSE
196: VALUE = ZERO
197: IF( LSAME( UPLO, 'U' ) ) THEN
198: DO 60 J = 1, N
199: DO 50 I = K, K + J - 1
1.11 bertrand 200: SUM = ABS( AP( I ) )
201: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 202: 50 CONTINUE
203: K = K + J
204: 60 CONTINUE
205: ELSE
206: DO 80 J = 1, N
207: DO 70 I = K, K + N - J
1.11 bertrand 208: SUM = ABS( AP( I ) )
209: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 210: 70 CONTINUE
211: K = K + N - J + 1
212: 80 CONTINUE
213: END IF
214: END IF
215: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
216: *
217: * Find norm1(A).
218: *
219: VALUE = ZERO
220: K = 1
221: UDIAG = LSAME( DIAG, 'U' )
222: IF( LSAME( UPLO, 'U' ) ) THEN
223: DO 110 J = 1, N
224: IF( UDIAG ) THEN
225: SUM = ONE
226: DO 90 I = K, K + J - 2
227: SUM = SUM + ABS( AP( I ) )
228: 90 CONTINUE
229: ELSE
230: SUM = ZERO
231: DO 100 I = K, K + J - 1
232: SUM = SUM + ABS( AP( I ) )
233: 100 CONTINUE
234: END IF
235: K = K + J
1.11 bertrand 236: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 237: 110 CONTINUE
238: ELSE
239: DO 140 J = 1, N
240: IF( UDIAG ) THEN
241: SUM = ONE
242: DO 120 I = K + 1, K + N - J
243: SUM = SUM + ABS( AP( I ) )
244: 120 CONTINUE
245: ELSE
246: SUM = ZERO
247: DO 130 I = K, K + N - J
248: SUM = SUM + ABS( AP( I ) )
249: 130 CONTINUE
250: END IF
251: K = K + N - J + 1
1.11 bertrand 252: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 253: 140 CONTINUE
254: END IF
255: ELSE IF( LSAME( NORM, 'I' ) ) THEN
256: *
257: * Find normI(A).
258: *
259: K = 1
260: IF( LSAME( UPLO, 'U' ) ) THEN
261: IF( LSAME( DIAG, 'U' ) ) THEN
262: DO 150 I = 1, N
263: WORK( I ) = ONE
264: 150 CONTINUE
265: DO 170 J = 1, N
266: DO 160 I = 1, J - 1
267: WORK( I ) = WORK( I ) + ABS( AP( K ) )
268: K = K + 1
269: 160 CONTINUE
270: K = K + 1
271: 170 CONTINUE
272: ELSE
273: DO 180 I = 1, N
274: WORK( I ) = ZERO
275: 180 CONTINUE
276: DO 200 J = 1, N
277: DO 190 I = 1, J
278: WORK( I ) = WORK( I ) + ABS( AP( K ) )
279: K = K + 1
280: 190 CONTINUE
281: 200 CONTINUE
282: END IF
283: ELSE
284: IF( LSAME( DIAG, 'U' ) ) THEN
285: DO 210 I = 1, N
286: WORK( I ) = ONE
287: 210 CONTINUE
288: DO 230 J = 1, N
289: K = K + 1
290: DO 220 I = J + 1, N
291: WORK( I ) = WORK( I ) + ABS( AP( K ) )
292: K = K + 1
293: 220 CONTINUE
294: 230 CONTINUE
295: ELSE
296: DO 240 I = 1, N
297: WORK( I ) = ZERO
298: 240 CONTINUE
299: DO 260 J = 1, N
300: DO 250 I = J, N
301: WORK( I ) = WORK( I ) + ABS( AP( K ) )
302: K = K + 1
303: 250 CONTINUE
304: 260 CONTINUE
305: END IF
306: END IF
307: VALUE = ZERO
308: DO 270 I = 1, N
1.11 bertrand 309: SUM = WORK( I )
310: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 311: 270 CONTINUE
312: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
313: *
314: * Find normF(A).
1.18 ! bertrand 315: * SSQ(1) is scale
! 316: * SSQ(2) is sum-of-squares
! 317: * For better accuracy, sum each column separately.
1.1 bertrand 318: *
319: IF( LSAME( UPLO, 'U' ) ) THEN
320: IF( LSAME( DIAG, 'U' ) ) THEN
1.18 ! bertrand 321: SSQ( 1 ) = ONE
! 322: SSQ( 2 ) = N
1.1 bertrand 323: K = 2
324: DO 280 J = 2, N
1.18 ! bertrand 325: COLSSQ( 1 ) = ZERO
! 326: COLSSQ( 2 ) = ONE
! 327: CALL ZLASSQ( J-1, AP( K ), 1,
! 328: $ COLSSQ( 1 ), COLSSQ( 2 ) )
! 329: CALL DCOMBSSQ( SSQ, COLSSQ )
1.1 bertrand 330: K = K + J
331: 280 CONTINUE
332: ELSE
1.18 ! bertrand 333: SSQ( 1 ) = ZERO
! 334: SSQ( 2 ) = ONE
1.1 bertrand 335: K = 1
336: DO 290 J = 1, N
1.18 ! bertrand 337: COLSSQ( 1 ) = ZERO
! 338: COLSSQ( 2 ) = ONE
! 339: CALL ZLASSQ( J, AP( K ), 1,
! 340: $ COLSSQ( 1 ), COLSSQ( 2 ) )
! 341: CALL DCOMBSSQ( SSQ, COLSSQ )
1.1 bertrand 342: K = K + J
343: 290 CONTINUE
344: END IF
345: ELSE
346: IF( LSAME( DIAG, 'U' ) ) THEN
1.18 ! bertrand 347: SSQ( 1 ) = ONE
! 348: SSQ( 2 ) = N
1.1 bertrand 349: K = 2
350: DO 300 J = 1, N - 1
1.18 ! bertrand 351: COLSSQ( 1 ) = ZERO
! 352: COLSSQ( 2 ) = ONE
! 353: CALL ZLASSQ( N-J, AP( K ), 1,
! 354: $ COLSSQ( 1 ), COLSSQ( 2 ) )
! 355: CALL DCOMBSSQ( SSQ, COLSSQ )
1.1 bertrand 356: K = K + N - J + 1
357: 300 CONTINUE
358: ELSE
1.18 ! bertrand 359: SSQ( 1 ) = ZERO
! 360: SSQ( 2 ) = ONE
1.1 bertrand 361: K = 1
362: DO 310 J = 1, N
1.18 ! bertrand 363: COLSSQ( 1 ) = ZERO
! 364: COLSSQ( 2 ) = ONE
! 365: CALL ZLASSQ( N-J+1, AP( K ), 1,
! 366: $ COLSSQ( 1 ), COLSSQ( 2 ) )
! 367: CALL DCOMBSSQ( SSQ, COLSSQ )
1.1 bertrand 368: K = K + N - J + 1
369: 310 CONTINUE
370: END IF
371: END IF
1.18 ! bertrand 372: VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
1.1 bertrand 373: END IF
374: *
375: ZLANTP = VALUE
376: RETURN
377: *
378: * End of ZLANTP
379: *
380: END
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