Annotation of rpl/lapack/lapack/zlangb.f, revision 1.6
1.1 bertrand 1: DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
2: $ WORK )
3: *
4: * -- LAPACK auxiliary routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: CHARACTER NORM
11: INTEGER KL, KU, LDAB, N
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION WORK( * )
15: COMPLEX*16 AB( LDAB, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZLANGB returns the value of the one norm, or the Frobenius norm, or
22: * the infinity norm, or the element of largest absolute value of an
23: * n by n band matrix A, with kl sub-diagonals and ku super-diagonals.
24: *
25: * Description
26: * ===========
27: *
28: * ZLANGB returns the value
29: *
30: * ZLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
31: * (
32: * ( norm1(A), NORM = '1', 'O' or 'o'
33: * (
34: * ( normI(A), NORM = 'I' or 'i'
35: * (
36: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
37: *
38: * where norm1 denotes the one norm of a matrix (maximum column sum),
39: * normI denotes the infinity norm of a matrix (maximum row sum) and
40: * normF denotes the Frobenius norm of a matrix (square root of sum of
41: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
42: *
43: * Arguments
44: * =========
45: *
46: * NORM (input) CHARACTER*1
47: * Specifies the value to be returned in ZLANGB as described
48: * above.
49: *
50: * N (input) INTEGER
51: * The order of the matrix A. N >= 0. When N = 0, ZLANGB is
52: * set to zero.
53: *
54: * KL (input) INTEGER
55: * The number of sub-diagonals of the matrix A. KL >= 0.
56: *
57: * KU (input) INTEGER
58: * The number of super-diagonals of the matrix A. KU >= 0.
59: *
60: * AB (input) COMPLEX*16 array, dimension (LDAB,N)
61: * The band matrix A, stored in rows 1 to KL+KU+1. The j-th
62: * column of A is stored in the j-th column of the array AB as
63: * follows:
64: * AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
65: *
66: * LDAB (input) INTEGER
67: * The leading dimension of the array AB. LDAB >= KL+KU+1.
68: *
69: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
70: * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
71: * referenced.
72: *
73: * =====================================================================
74: *
75: * .. Parameters ..
76: DOUBLE PRECISION ONE, ZERO
77: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
78: * ..
79: * .. Local Scalars ..
80: INTEGER I, J, K, L
81: DOUBLE PRECISION SCALE, SUM, VALUE
82: * ..
83: * .. External Functions ..
84: LOGICAL LSAME
85: EXTERNAL LSAME
86: * ..
87: * .. External Subroutines ..
88: EXTERNAL ZLASSQ
89: * ..
90: * .. Intrinsic Functions ..
91: INTRINSIC ABS, MAX, MIN, SQRT
92: * ..
93: * .. Executable Statements ..
94: *
95: IF( N.EQ.0 ) THEN
96: VALUE = ZERO
97: ELSE IF( LSAME( NORM, 'M' ) ) THEN
98: *
99: * Find max(abs(A(i,j))).
100: *
101: VALUE = ZERO
102: DO 20 J = 1, N
103: DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
104: VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
105: 10 CONTINUE
106: 20 CONTINUE
107: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
108: *
109: * Find norm1(A).
110: *
111: VALUE = ZERO
112: DO 40 J = 1, N
113: SUM = ZERO
114: DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
115: SUM = SUM + ABS( AB( I, J ) )
116: 30 CONTINUE
117: VALUE = MAX( VALUE, SUM )
118: 40 CONTINUE
119: ELSE IF( LSAME( NORM, 'I' ) ) THEN
120: *
121: * Find normI(A).
122: *
123: DO 50 I = 1, N
124: WORK( I ) = ZERO
125: 50 CONTINUE
126: DO 70 J = 1, N
127: K = KU + 1 - J
128: DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
129: WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
130: 60 CONTINUE
131: 70 CONTINUE
132: VALUE = ZERO
133: DO 80 I = 1, N
134: VALUE = MAX( VALUE, WORK( I ) )
135: 80 CONTINUE
136: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
137: *
138: * Find normF(A).
139: *
140: SCALE = ZERO
141: SUM = ONE
142: DO 90 J = 1, N
143: L = MAX( 1, J-KU )
144: K = KU + 1 - J + L
145: CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
146: 90 CONTINUE
147: VALUE = SCALE*SQRT( SUM )
148: END IF
149: *
150: ZLANGB = VALUE
151: RETURN
152: *
153: * End of ZLANGB
154: *
155: END
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