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