Annotation of rpl/lapack/lapack/zlansp.f, revision 1.19
1.11 bertrand 1: *> \brief \b ZLANSP 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 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 ZLANSP + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlansp.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlansp.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlansp.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANSP( NORM, UPLO, N, AP, WORK )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER 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: *> ZLANSP 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: *> complex symmetric matrix A, supplied in packed form.
41: *> \endverbatim
42: *>
43: *> \return ZLANSP
44: *> \verbatim
45: *>
46: *> ZLANSP = ( 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 ZLANSP as described
67: *> above.
68: *> \endverbatim
69: *>
70: *> \param[in] UPLO
71: *> \verbatim
72: *> UPLO is CHARACTER*1
73: *> Specifies whether the upper or lower triangular part of the
74: *> symmetric matrix A is supplied.
75: *> = 'U': Upper triangular part of A is supplied
76: *> = 'L': Lower triangular part of A is supplied
77: *> \endverbatim
78: *>
79: *> \param[in] N
80: *> \verbatim
81: *> N is INTEGER
82: *> The order of the matrix A. N >= 0. When N = 0, ZLANSP is
83: *> set to zero.
84: *> \endverbatim
85: *>
86: *> \param[in] AP
87: *> \verbatim
88: *> AP is COMPLEX*16 array, dimension (N*(N+1)/2)
89: *> The upper or lower triangle of the symmetric matrix A, packed
90: *> columnwise in a linear array. The j-th column of A is stored
91: *> in the array AP as follows:
92: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
93: *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
94: *> \endverbatim
95: *>
96: *> \param[out] WORK
97: *> \verbatim
98: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
99: *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
100: *> WORK is not referenced.
101: *> \endverbatim
102: *
103: * Authors:
104: * ========
105: *
1.15 bertrand 106: *> \author Univ. of Tennessee
107: *> \author Univ. of California Berkeley
108: *> \author Univ. of Colorado Denver
109: *> \author NAG Ltd.
1.8 bertrand 110: *
111: *> \ingroup complex16OTHERauxiliary
112: *
113: * =====================================================================
1.1 bertrand 114: DOUBLE PRECISION FUNCTION ZLANSP( NORM, UPLO, N, AP, WORK )
115: *
1.19 ! bertrand 116: * -- LAPACK auxiliary routine --
1.1 bertrand 117: * -- LAPACK is a software package provided by Univ. of Tennessee, --
118: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119: *
120: * .. Scalar Arguments ..
121: CHARACTER NORM, UPLO
122: INTEGER N
123: * ..
124: * .. Array Arguments ..
125: DOUBLE PRECISION WORK( * )
126: COMPLEX*16 AP( * )
127: * ..
128: *
129: * =====================================================================
130: *
131: * .. Parameters ..
132: DOUBLE PRECISION ONE, ZERO
133: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
134: * ..
135: * .. Local Scalars ..
136: INTEGER I, J, K
1.19 ! bertrand 137: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
1.1 bertrand 138: * ..
139: * .. External Functions ..
1.11 bertrand 140: LOGICAL LSAME, DISNAN
141: EXTERNAL LSAME, DISNAN
1.1 bertrand 142: * ..
143: * .. External Subroutines ..
1.19 ! bertrand 144: EXTERNAL ZLASSQ
1.1 bertrand 145: * ..
146: * .. Intrinsic Functions ..
1.11 bertrand 147: INTRINSIC ABS, DBLE, DIMAG, SQRT
1.1 bertrand 148: * ..
149: * .. Executable Statements ..
150: *
151: IF( N.EQ.0 ) THEN
152: VALUE = ZERO
153: ELSE IF( LSAME( NORM, 'M' ) ) THEN
154: *
155: * Find max(abs(A(i,j))).
156: *
157: VALUE = ZERO
158: IF( LSAME( UPLO, 'U' ) ) THEN
159: K = 1
160: DO 20 J = 1, N
161: DO 10 I = K, K + J - 1
1.11 bertrand 162: SUM = ABS( AP( I ) )
163: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 164: 10 CONTINUE
165: K = K + J
166: 20 CONTINUE
167: ELSE
168: K = 1
169: DO 40 J = 1, N
170: DO 30 I = K, K + N - J
1.11 bertrand 171: SUM = ABS( AP( I ) )
172: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 173: 30 CONTINUE
174: K = K + N - J + 1
175: 40 CONTINUE
176: END IF
177: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
178: $ ( NORM.EQ.'1' ) ) THEN
179: *
180: * Find normI(A) ( = norm1(A), since A is symmetric).
181: *
182: VALUE = ZERO
183: K = 1
184: IF( LSAME( UPLO, 'U' ) ) THEN
185: DO 60 J = 1, N
186: SUM = ZERO
187: DO 50 I = 1, J - 1
188: ABSA = ABS( AP( K ) )
189: SUM = SUM + ABSA
190: WORK( I ) = WORK( I ) + ABSA
191: K = K + 1
192: 50 CONTINUE
193: WORK( J ) = SUM + ABS( AP( K ) )
194: K = K + 1
195: 60 CONTINUE
196: DO 70 I = 1, N
1.11 bertrand 197: SUM = WORK( I )
198: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 199: 70 CONTINUE
200: ELSE
201: DO 80 I = 1, N
202: WORK( I ) = ZERO
203: 80 CONTINUE
204: DO 100 J = 1, N
205: SUM = WORK( J ) + ABS( AP( K ) )
206: K = K + 1
207: DO 90 I = J + 1, N
208: ABSA = ABS( AP( K ) )
209: SUM = SUM + ABSA
210: WORK( I ) = WORK( I ) + ABSA
211: K = K + 1
212: 90 CONTINUE
1.11 bertrand 213: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 214: 100 CONTINUE
215: END IF
216: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
217: *
218: * Find normF(A).
219: *
1.19 ! bertrand 220: SCALE = ZERO
! 221: SUM = ONE
1.1 bertrand 222: K = 2
223: IF( LSAME( UPLO, 'U' ) ) THEN
224: DO 110 J = 2, N
1.19 ! bertrand 225: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
1.1 bertrand 226: K = K + J
227: 110 CONTINUE
228: ELSE
229: DO 120 J = 1, N - 1
1.19 ! bertrand 230: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
1.1 bertrand 231: K = K + N - J + 1
232: 120 CONTINUE
233: END IF
1.19 ! bertrand 234: SUM = 2*SUM
1.1 bertrand 235: K = 1
236: DO 130 I = 1, N
237: IF( DBLE( AP( K ) ).NE.ZERO ) THEN
238: ABSA = ABS( DBLE( AP( K ) ) )
1.19 ! bertrand 239: IF( SCALE.LT.ABSA ) THEN
! 240: SUM = ONE + SUM*( SCALE / ABSA )**2
! 241: SCALE = ABSA
1.1 bertrand 242: ELSE
1.19 ! bertrand 243: SUM = SUM + ( ABSA / SCALE )**2
1.1 bertrand 244: END IF
245: END IF
246: IF( DIMAG( AP( K ) ).NE.ZERO ) THEN
247: ABSA = ABS( DIMAG( AP( K ) ) )
1.19 ! bertrand 248: IF( SCALE.LT.ABSA ) THEN
! 249: SUM = ONE + SUM*( SCALE / ABSA )**2
! 250: SCALE = ABSA
1.1 bertrand 251: ELSE
1.19 ! bertrand 252: SUM = SUM + ( ABSA / SCALE )**2
1.1 bertrand 253: END IF
254: END IF
255: IF( LSAME( UPLO, 'U' ) ) THEN
256: K = K + I + 1
257: ELSE
258: K = K + N - I + 1
259: END IF
260: 130 CONTINUE
1.19 ! bertrand 261: VALUE = SCALE*SQRT( SUM )
1.1 bertrand 262: END IF
263: *
264: ZLANSP = VALUE
265: RETURN
266: *
267: * End of ZLANSP
268: *
269: END
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