1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
|
SUBROUTINE CPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, KD, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX AB( LDAB, * ), B( LDB, * )
* ..
*
* Purpose
* =======
*
* CPBTRS solves a system of linear equations A*X = B with a Hermitian
* positive definite band matrix A using the Cholesky factorization
* A = U**H*U or A = L*L**H computed by CPBTRF.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangular factor stored in AB;
* = 'L': Lower triangular factor stored in AB.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KD (input) INTEGER
* The number of superdiagonals of the matrix A if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* AB (input) COMPLEX array, dimension (LDAB,N)
* The triangular factor U or L from the Cholesky factorization
* A = U**H*U or A = L*L**H of the band matrix A, stored in the
* first KD+1 rows of the array. The j-th column of U or L is
* stored in the j-th column of the array AB as follows:
* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KD+1.
*
* B (input/output) COMPLEX array, dimension (LDB,NRHS)
* On entry, the right hand side matrix B.
* On exit, the solution matrix X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CTBSV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( KD.LT.0 ) THEN
INFO = -3
ELSE IF( NRHS.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -6
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CPBTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Solve A*X = B where A = U'*U.
*
DO 10 J = 1, NRHS
*
* Solve U'*X = B, overwriting B with X.
*
CALL CTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
$ KD, AB, LDAB, B( 1, J ), 1 )
*
* Solve U*X = B, overwriting B with X.
*
CALL CTBSV( 'Upper', 'No transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
10 CONTINUE
ELSE
*
* Solve A*X = B where A = L*L'.
*
DO 20 J = 1, NRHS
*
* Solve L*X = B, overwriting B with X.
*
CALL CTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
$ LDAB, B( 1, J ), 1 )
*
* Solve L'*X = B, overwriting B with X.
*
CALL CTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
$ KD, AB, LDAB, B( 1, J ), 1 )
20 CONTINUE
END IF
*
RETURN
*
* End of CPBTRS
*
END
|
