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zgbsv.f
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Tue Dec 21 13:53:42 2010 UTC (13 years, 6 months ago) by
bertrand
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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
2: *
3: * -- LAPACK driver 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: INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
10: * ..
11: * .. Array Arguments ..
12: INTEGER IPIV( * )
13: COMPLEX*16 AB( LDAB, * ), B( LDB, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * ZGBSV computes the solution to a complex system of linear equations
20: * A * X = B, where A is a band matrix of order N with KL subdiagonals
21: * and KU superdiagonals, and X and B are N-by-NRHS matrices.
22: *
23: * The LU decomposition with partial pivoting and row interchanges is
24: * used to factor A as A = L * U, where L is a product of permutation
25: * and unit lower triangular matrices with KL subdiagonals, and U is
26: * upper triangular with KL+KU superdiagonals. The factored form of A
27: * is then used to solve the system of equations A * X = B.
28: *
29: * Arguments
30: * =========
31: *
32: * N (input) INTEGER
33: * The number of linear equations, i.e., the order of the
34: * matrix A. N >= 0.
35: *
36: * KL (input) INTEGER
37: * The number of subdiagonals within the band of A. KL >= 0.
38: *
39: * KU (input) INTEGER
40: * The number of superdiagonals within the band of A. KU >= 0.
41: *
42: * NRHS (input) INTEGER
43: * The number of right hand sides, i.e., the number of columns
44: * of the matrix B. NRHS >= 0.
45: *
46: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
47: * On entry, the matrix A in band storage, in rows KL+1 to
48: * 2*KL+KU+1; rows 1 to KL of the array need not be set.
49: * The j-th column of A is stored in the j-th column of the
50: * array AB as follows:
51: * AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
52: * On exit, details of the factorization: U is stored as an
53: * upper triangular band matrix with KL+KU superdiagonals in
54: * rows 1 to KL+KU+1, and the multipliers used during the
55: * factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
56: * See below for further details.
57: *
58: * LDAB (input) INTEGER
59: * The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
60: *
61: * IPIV (output) INTEGER array, dimension (N)
62: * The pivot indices that define the permutation matrix P;
63: * row i of the matrix was interchanged with row IPIV(i).
64: *
65: * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
66: * On entry, the N-by-NRHS right hand side matrix B.
67: * On exit, if INFO = 0, the N-by-NRHS solution matrix X.
68: *
69: * LDB (input) INTEGER
70: * The leading dimension of the array B. LDB >= max(1,N).
71: *
72: * INFO (output) INTEGER
73: * = 0: successful exit
74: * < 0: if INFO = -i, the i-th argument had an illegal value
75: * > 0: if INFO = i, U(i,i) is exactly zero. The factorization
76: * has been completed, but the factor U is exactly
77: * singular, and the solution has not been computed.
78: *
79: * Further Details
80: * ===============
81: *
82: * The band storage scheme is illustrated by the following example, when
83: * M = N = 6, KL = 2, KU = 1:
84: *
85: * On entry: On exit:
86: *
87: * * * * + + + * * * u14 u25 u36
88: * * * + + + + * * u13 u24 u35 u46
89: * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
90: * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
91: * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
92: * a31 a42 a53 a64 * * m31 m42 m53 m64 * *
93: *
94: * Array elements marked * are not used by the routine; elements marked
95: * + need not be set on entry, but are required by the routine to store
96: * elements of U because of fill-in resulting from the row interchanges.
97: *
98: * =====================================================================
99: *
100: * .. External Subroutines ..
101: EXTERNAL XERBLA, ZGBTRF, ZGBTRS
102: * ..
103: * .. Intrinsic Functions ..
104: INTRINSIC MAX
105: * ..
106: * .. Executable Statements ..
107: *
108: * Test the input parameters.
109: *
110: INFO = 0
111: IF( N.LT.0 ) THEN
112: INFO = -1
113: ELSE IF( KL.LT.0 ) THEN
114: INFO = -2
115: ELSE IF( KU.LT.0 ) THEN
116: INFO = -3
117: ELSE IF( NRHS.LT.0 ) THEN
118: INFO = -4
119: ELSE IF( LDAB.LT.2*KL+KU+1 ) THEN
120: INFO = -6
121: ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
122: INFO = -9
123: END IF
124: IF( INFO.NE.0 ) THEN
125: CALL XERBLA( 'ZGBSV ', -INFO )
126: RETURN
127: END IF
128: *
129: * Compute the LU factorization of the band matrix A.
130: *
131: CALL ZGBTRF( N, N, KL, KU, AB, LDAB, IPIV, INFO )
132: IF( INFO.EQ.0 ) THEN
133: *
134: * Solve the system A*X = B, overwriting B with X.
135: *
136: CALL ZGBTRS( 'No transpose', N, KL, KU, NRHS, AB, LDAB, IPIV,
137: $ B, LDB, INFO )
138: END IF
139: RETURN
140: *
141: * End of ZGBSV
142: *
143: END
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