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1.1 bertrand 1: DOUBLE PRECISION FUNCTION DLANGE( NORM, M, N, A, LDA, 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
10: INTEGER LDA, M, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION A( LDA, * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DLANGE 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 matrix A.
22: *
23: * Description
24: * ===========
25: *
26: * DLANGE returns the value
27: *
28: * DLANGE = ( 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 DLANGE as described
46: * above.
47: *
48: * M (input) INTEGER
49: * The number of rows of the matrix A. M >= 0. When M = 0,
50: * DLANGE is set to zero.
51: *
52: * N (input) INTEGER
53: * The number of columns of the matrix A. N >= 0. When N = 0,
54: * DLANGE is set to zero.
55: *
56: * A (input) DOUBLE PRECISION array, dimension (LDA,N)
57: * The m by n matrix A.
58: *
59: * LDA (input) INTEGER
60: * The leading dimension of the array A. LDA >= max(M,1).
61: *
62: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
63: * where LWORK >= M when NORM = 'I'; otherwise, WORK is not
64: * referenced.
65: *
66: * =====================================================================
67: *
68: * .. Parameters ..
69: DOUBLE PRECISION ONE, ZERO
70: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
71: * ..
72: * .. Local Scalars ..
73: INTEGER I, J
74: DOUBLE PRECISION SCALE, SUM, VALUE
75: * ..
76: * .. External Subroutines ..
77: EXTERNAL DLASSQ
78: * ..
79: * .. External Functions ..
80: LOGICAL LSAME
81: EXTERNAL LSAME
82: * ..
83: * .. Intrinsic Functions ..
84: INTRINSIC ABS, MAX, MIN, SQRT
85: * ..
86: * .. Executable Statements ..
87: *
88: IF( MIN( M, N ).EQ.0 ) THEN
89: VALUE = ZERO
90: ELSE IF( LSAME( NORM, 'M' ) ) THEN
91: *
92: * Find max(abs(A(i,j))).
93: *
94: VALUE = ZERO
95: DO 20 J = 1, N
96: DO 10 I = 1, M
97: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
98: 10 CONTINUE
99: 20 CONTINUE
100: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
101: *
102: * Find norm1(A).
103: *
104: VALUE = ZERO
105: DO 40 J = 1, N
106: SUM = ZERO
107: DO 30 I = 1, M
108: SUM = SUM + ABS( A( I, J ) )
109: 30 CONTINUE
110: VALUE = MAX( VALUE, SUM )
111: 40 CONTINUE
112: ELSE IF( LSAME( NORM, 'I' ) ) THEN
113: *
114: * Find normI(A).
115: *
116: DO 50 I = 1, M
117: WORK( I ) = ZERO
118: 50 CONTINUE
119: DO 70 J = 1, N
120: DO 60 I = 1, M
121: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
122: 60 CONTINUE
123: 70 CONTINUE
124: VALUE = ZERO
125: DO 80 I = 1, M
126: VALUE = MAX( VALUE, WORK( I ) )
127: 80 CONTINUE
128: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
129: *
130: * Find normF(A).
131: *
132: SCALE = ZERO
133: SUM = ONE
134: DO 90 J = 1, N
135: CALL DLASSQ( M, A( 1, J ), 1, SCALE, SUM )
136: 90 CONTINUE
137: VALUE = SCALE*SQRT( SUM )
138: END IF
139: *
140: DLANGE = VALUE
141: RETURN
142: *
143: * End of DLANGE
144: *
145: END