Annotation of rpl/lapack/lapack/zlansb.f, revision 1.18
1.11 bertrand 1: *> \brief \b ZLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.
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 ZLANSB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlansb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlansb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlansb.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB,
22: * WORK )
1.15 bertrand 23: *
1.8 bertrand 24: * .. Scalar Arguments ..
25: * CHARACTER NORM, UPLO
26: * INTEGER K, LDAB, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION WORK( * )
30: * COMPLEX*16 AB( LDAB, * )
31: * ..
1.15 bertrand 32: *
1.8 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZLANSB returns the value of the one norm, or the Frobenius norm, or
40: *> the infinity norm, or the element of largest absolute value of an
41: *> n by n symmetric band matrix A, with k super-diagonals.
42: *> \endverbatim
43: *>
44: *> \return ZLANSB
45: *> \verbatim
46: *>
47: *> ZLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
48: *> (
49: *> ( norm1(A), NORM = '1', 'O' or 'o'
50: *> (
51: *> ( normI(A), NORM = 'I' or 'i'
52: *> (
53: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
54: *>
55: *> where norm1 denotes the one norm of a matrix (maximum column sum),
56: *> normI denotes the infinity norm of a matrix (maximum row sum) and
57: *> normF denotes the Frobenius norm of a matrix (square root of sum of
58: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
59: *> \endverbatim
60: *
61: * Arguments:
62: * ==========
63: *
64: *> \param[in] NORM
65: *> \verbatim
66: *> NORM is CHARACTER*1
67: *> Specifies the value to be returned in ZLANSB as described
68: *> above.
69: *> \endverbatim
70: *>
71: *> \param[in] UPLO
72: *> \verbatim
73: *> UPLO is CHARACTER*1
74: *> Specifies whether the upper or lower triangular part of the
75: *> band matrix A is supplied.
76: *> = 'U': Upper triangular part is supplied
77: *> = 'L': Lower triangular part is supplied
78: *> \endverbatim
79: *>
80: *> \param[in] N
81: *> \verbatim
82: *> N is INTEGER
83: *> The order of the matrix A. N >= 0. When N = 0, ZLANSB is
84: *> set to zero.
85: *> \endverbatim
86: *>
87: *> \param[in] K
88: *> \verbatim
89: *> K is INTEGER
90: *> The number of super-diagonals or sub-diagonals of the
91: *> band matrix A. K >= 0.
92: *> \endverbatim
93: *>
94: *> \param[in] AB
95: *> \verbatim
96: *> AB is COMPLEX*16 array, dimension (LDAB,N)
97: *> The upper or lower triangle of the symmetric band matrix A,
98: *> stored in the first K+1 rows of AB. The j-th column of A is
99: *> stored in the j-th column of the array AB as follows:
100: *> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
101: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
102: *> \endverbatim
103: *>
104: *> \param[in] LDAB
105: *> \verbatim
106: *> LDAB is INTEGER
107: *> The leading dimension of the array AB. LDAB >= K+1.
108: *> \endverbatim
109: *>
110: *> \param[out] WORK
111: *> \verbatim
112: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
113: *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
114: *> WORK is not referenced.
115: *> \endverbatim
116: *
117: * Authors:
118: * ========
119: *
1.15 bertrand 120: *> \author Univ. of Tennessee
121: *> \author Univ. of California Berkeley
122: *> \author Univ. of Colorado Denver
123: *> \author NAG Ltd.
1.8 bertrand 124: *
1.15 bertrand 125: *> \date December 2016
1.8 bertrand 126: *
127: *> \ingroup complex16OTHERauxiliary
128: *
129: * =====================================================================
1.1 bertrand 130: DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB,
131: $ WORK )
132: *
1.15 bertrand 133: * -- LAPACK auxiliary routine (version 3.7.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 136: * December 2016
1.1 bertrand 137: *
1.18 ! bertrand 138: IMPLICIT NONE
1.1 bertrand 139: * .. Scalar Arguments ..
140: CHARACTER NORM, UPLO
141: INTEGER K, LDAB, N
142: * ..
143: * .. Array Arguments ..
144: DOUBLE PRECISION WORK( * )
145: COMPLEX*16 AB( LDAB, * )
146: * ..
147: *
148: * =====================================================================
149: *
150: * .. Parameters ..
151: DOUBLE PRECISION ONE, ZERO
152: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
153: * ..
154: * .. Local Scalars ..
155: INTEGER I, J, L
1.18 ! bertrand 156: DOUBLE PRECISION ABSA, SUM, VALUE
! 157: * ..
! 158: * .. Local Arrays ..
! 159: DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
1.1 bertrand 160: * ..
161: * .. External Functions ..
1.11 bertrand 162: LOGICAL LSAME, DISNAN
163: EXTERNAL LSAME, DISNAN
1.1 bertrand 164: * ..
165: * .. External Subroutines ..
1.18 ! bertrand 166: EXTERNAL ZLASSQ, DCOMBSSQ
1.1 bertrand 167: * ..
168: * .. Intrinsic Functions ..
169: INTRINSIC ABS, MAX, MIN, SQRT
170: * ..
171: * .. Executable Statements ..
172: *
173: IF( N.EQ.0 ) THEN
174: VALUE = ZERO
175: ELSE IF( LSAME( NORM, 'M' ) ) THEN
176: *
177: * Find max(abs(A(i,j))).
178: *
179: VALUE = ZERO
180: IF( LSAME( UPLO, 'U' ) ) THEN
181: DO 20 J = 1, N
182: DO 10 I = MAX( K+2-J, 1 ), K + 1
1.11 bertrand 183: SUM = ABS( AB( I, J ) )
184: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 185: 10 CONTINUE
186: 20 CONTINUE
187: ELSE
188: DO 40 J = 1, N
189: DO 30 I = 1, MIN( N+1-J, K+1 )
1.11 bertrand 190: SUM = ABS( AB( I, J ) )
191: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 192: 30 CONTINUE
193: 40 CONTINUE
194: END IF
195: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
196: $ ( NORM.EQ.'1' ) ) THEN
197: *
198: * Find normI(A) ( = norm1(A), since A is symmetric).
199: *
200: VALUE = ZERO
201: IF( LSAME( UPLO, 'U' ) ) THEN
202: DO 60 J = 1, N
203: SUM = ZERO
204: L = K + 1 - J
205: DO 50 I = MAX( 1, J-K ), J - 1
206: ABSA = ABS( AB( L+I, J ) )
207: SUM = SUM + ABSA
208: WORK( I ) = WORK( I ) + ABSA
209: 50 CONTINUE
210: WORK( J ) = SUM + ABS( AB( K+1, J ) )
211: 60 CONTINUE
212: DO 70 I = 1, N
1.11 bertrand 213: SUM = WORK( I )
214: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 215: 70 CONTINUE
216: ELSE
217: DO 80 I = 1, N
218: WORK( I ) = ZERO
219: 80 CONTINUE
220: DO 100 J = 1, N
221: SUM = WORK( J ) + ABS( AB( 1, J ) )
222: L = 1 - J
223: DO 90 I = J + 1, MIN( N, J+K )
224: ABSA = ABS( AB( L+I, J ) )
225: SUM = SUM + ABSA
226: WORK( I ) = WORK( I ) + ABSA
227: 90 CONTINUE
1.11 bertrand 228: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 229: 100 CONTINUE
230: END IF
231: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
232: *
233: * Find normF(A).
1.18 ! bertrand 234: * SSQ(1) is scale
! 235: * SSQ(2) is sum-of-squares
! 236: * For better accuracy, sum each column separately.
! 237: *
! 238: SSQ( 1 ) = ZERO
! 239: SSQ( 2 ) = ONE
! 240: *
! 241: * Sum off-diagonals
1.1 bertrand 242: *
243: IF( K.GT.0 ) THEN
244: IF( LSAME( UPLO, 'U' ) ) THEN
245: DO 110 J = 2, N
1.18 ! bertrand 246: COLSSQ( 1 ) = ZERO
! 247: COLSSQ( 2 ) = ONE
1.1 bertrand 248: CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
1.18 ! bertrand 249: $ 1, COLSSQ( 1 ), COLSSQ( 2 ) )
! 250: CALL DCOMBSSQ( SSQ, COLSSQ )
1.1 bertrand 251: 110 CONTINUE
252: L = K + 1
253: ELSE
254: DO 120 J = 1, N - 1
1.18 ! bertrand 255: COLSSQ( 1 ) = ZERO
! 256: COLSSQ( 2 ) = ONE
! 257: CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1,
! 258: $ COLSSQ( 1 ), COLSSQ( 2 ) )
! 259: CALL DCOMBSSQ( SSQ, COLSSQ )
1.1 bertrand 260: 120 CONTINUE
261: L = 1
262: END IF
1.18 ! bertrand 263: SSQ( 2 ) = 2*SSQ( 2 )
1.1 bertrand 264: ELSE
265: L = 1
266: END IF
1.18 ! bertrand 267: *
! 268: * Sum diagonal
! 269: *
! 270: COLSSQ( 1 ) = ZERO
! 271: COLSSQ( 2 ) = ONE
! 272: CALL ZLASSQ( N, AB( L, 1 ), LDAB, COLSSQ( 1 ), COLSSQ( 2 ) )
! 273: CALL DCOMBSSQ( SSQ, COLSSQ )
! 274: VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
1.1 bertrand 275: END IF
276: *
277: ZLANSB = VALUE
278: RETURN
279: *
280: * End of ZLANSB
281: *
282: END
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