![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zlansp.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack|
Return to zlansp.f CVS log | Up to [local] / rpl / lapack / lapack |
1.1 bertrand 1: DOUBLE PRECISION FUNCTION ZLANSP( NORM, UPLO, N, AP, WORK )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER NORM, UPLO
10: INTEGER N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION WORK( * )
14: COMPLEX*16 AP( * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZLANSP returns the value of the one norm, or the Frobenius norm, or
21: * the infinity norm, or the element of largest absolute value of a
22: * complex symmetric matrix A, supplied in packed form.
23: *
24: * Description
25: * ===========
26: *
27: * ZLANSP returns the value
28: *
29: * ZLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
30: * (
31: * ( norm1(A), NORM = '1', 'O' or 'o'
32: * (
33: * ( normI(A), NORM = 'I' or 'i'
34: * (
35: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
36: *
37: * where norm1 denotes the one norm of a matrix (maximum column sum),
38: * normI denotes the infinity norm of a matrix (maximum row sum) and
39: * normF denotes the Frobenius norm of a matrix (square root of sum of
40: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
41: *
42: * Arguments
43: * =========
44: *
45: * NORM (input) CHARACTER*1
46: * Specifies the value to be returned in ZLANSP as described
47: * above.
48: *
49: * UPLO (input) CHARACTER*1
50: * Specifies whether the upper or lower triangular part of the
51: * symmetric matrix A is supplied.
52: * = 'U': Upper triangular part of A is supplied
53: * = 'L': Lower triangular part of A is supplied
54: *
55: * N (input) INTEGER
56: * The order of the matrix A. N >= 0. When N = 0, ZLANSP is
57: * set to zero.
58: *
59: * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
60: * The upper or lower triangle of the symmetric matrix A, packed
61: * columnwise in a linear array. The j-th column of A is stored
62: * in the array AP as follows:
63: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
64: * if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
65: *
66: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
67: * where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
68: * WORK is not referenced.
69: *
70: * =====================================================================
71: *
72: * .. Parameters ..
73: DOUBLE PRECISION ONE, ZERO
74: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
75: * ..
76: * .. Local Scalars ..
77: INTEGER I, J, K
78: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
79: * ..
80: * .. External Functions ..
81: LOGICAL LSAME
82: EXTERNAL LSAME
83: * ..
84: * .. External Subroutines ..
85: EXTERNAL ZLASSQ
86: * ..
87: * .. Intrinsic Functions ..
88: INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT
89: * ..
90: * .. Executable Statements ..
91: *
92: IF( N.EQ.0 ) THEN
93: VALUE = ZERO
94: ELSE IF( LSAME( NORM, 'M' ) ) THEN
95: *
96: * Find max(abs(A(i,j))).
97: *
98: VALUE = ZERO
99: IF( LSAME( UPLO, 'U' ) ) THEN
100: K = 1
101: DO 20 J = 1, N
102: DO 10 I = K, K + J - 1
103: VALUE = MAX( VALUE, ABS( AP( I ) ) )
104: 10 CONTINUE
105: K = K + J
106: 20 CONTINUE
107: ELSE
108: K = 1
109: DO 40 J = 1, N
110: DO 30 I = K, K + N - J
111: VALUE = MAX( VALUE, ABS( AP( I ) ) )
112: 30 CONTINUE
113: K = K + N - J + 1
114: 40 CONTINUE
115: END IF
116: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
117: $ ( NORM.EQ.'1' ) ) THEN
118: *
119: * Find normI(A) ( = norm1(A), since A is symmetric).
120: *
121: VALUE = ZERO
122: K = 1
123: IF( LSAME( UPLO, 'U' ) ) THEN
124: DO 60 J = 1, N
125: SUM = ZERO
126: DO 50 I = 1, J - 1
127: ABSA = ABS( AP( K ) )
128: SUM = SUM + ABSA
129: WORK( I ) = WORK( I ) + ABSA
130: K = K + 1
131: 50 CONTINUE
132: WORK( J ) = SUM + ABS( AP( K ) )
133: K = K + 1
134: 60 CONTINUE
135: DO 70 I = 1, N
136: VALUE = MAX( VALUE, WORK( I ) )
137: 70 CONTINUE
138: ELSE
139: DO 80 I = 1, N
140: WORK( I ) = ZERO
141: 80 CONTINUE
142: DO 100 J = 1, N
143: SUM = WORK( J ) + ABS( AP( K ) )
144: K = K + 1
145: DO 90 I = J + 1, N
146: ABSA = ABS( AP( K ) )
147: SUM = SUM + ABSA
148: WORK( I ) = WORK( I ) + ABSA
149: K = K + 1
150: 90 CONTINUE
151: VALUE = MAX( VALUE, SUM )
152: 100 CONTINUE
153: END IF
154: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
155: *
156: * Find normF(A).
157: *
158: SCALE = ZERO
159: SUM = ONE
160: K = 2
161: IF( LSAME( UPLO, 'U' ) ) THEN
162: DO 110 J = 2, N
163: CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM )
164: K = K + J
165: 110 CONTINUE
166: ELSE
167: DO 120 J = 1, N - 1
168: CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM )
169: K = K + N - J + 1
170: 120 CONTINUE
171: END IF
172: SUM = 2*SUM
173: K = 1
174: DO 130 I = 1, N
175: IF( DBLE( AP( K ) ).NE.ZERO ) THEN
176: ABSA = ABS( DBLE( AP( K ) ) )
177: IF( SCALE.LT.ABSA ) THEN
178: SUM = ONE + SUM*( SCALE / ABSA )**2
179: SCALE = ABSA
180: ELSE
181: SUM = SUM + ( ABSA / SCALE )**2
182: END IF
183: END IF
184: IF( DIMAG( AP( K ) ).NE.ZERO ) THEN
185: ABSA = ABS( DIMAG( AP( K ) ) )
186: IF( SCALE.LT.ABSA ) THEN
187: SUM = ONE + SUM*( SCALE / ABSA )**2
188: SCALE = ABSA
189: ELSE
190: SUM = SUM + ( ABSA / SCALE )**2
191: END IF
192: END IF
193: IF( LSAME( UPLO, 'U' ) ) THEN
194: K = K + I + 1
195: ELSE
196: K = K + N - I + 1
197: END IF
198: 130 CONTINUE
199: VALUE = SCALE*SQRT( SUM )
200: END IF
201: *
202: ZLANSP = VALUE
203: RETURN
204: *
205: * End of ZLANSP
206: *
207: END