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
|
SUBROUTINE ZPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO )
*
* -- LAPACK routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* June 30, 1999
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * )
COMPLEX*16 B( LDB, * ), E( * )
* ..
*
* Purpose
* =======
*
* ZPTTRS solves a tridiagonal system of the form
* A * X = B
* using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF.
* D is a diagonal matrix specified in the vector D, U (or L) is a unit
* bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
* the vector E, and X and B are N by NRHS matrices.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies the form of the factorization and whether the
* vector E is the superdiagonal of the upper bidiagonal factor
* U or the subdiagonal of the lower bidiagonal factor L.
* = 'U': A = U'*D*U, E is the superdiagonal of U
* = 'L': A = L*D*L', E is the subdiagonal of L
*
* N (input) INTEGER
* The order of the tridiagonal matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* D (input) DOUBLE PRECISION array, dimension (N)
* The n diagonal elements of the diagonal matrix D from the
* factorization A = U'*D*U or A = L*D*L'.
*
* E (input) COMPLEX*16 array, dimension (N-1)
* If UPLO = 'U', the (n-1) superdiagonal elements of the unit
* bidiagonal factor U from the factorization A = U'*D*U.
* If UPLO = 'L', the (n-1) subdiagonal elements of the unit
* bidiagonal factor L from the factorization A = L*D*L'.
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
* On entry, the right hand side vectors B for the system of
* linear equations.
* On exit, the solution vectors, X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -k, the k-th argument had an illegal value
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL UPPER
INTEGER IUPLO, J, JB, NB
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZPTTS2
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input arguments.
*
INFO = 0
UPPER = ( UPLO.EQ.'U' .OR. UPLO.EQ.'u' )
IF( .NOT.UPPER .AND. .NOT.( UPLO.EQ.'L' .OR. UPLO.EQ.'l' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZPTTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
* Determine the number of right-hand sides to solve at a time.
*
IF( NRHS.EQ.1 ) THEN
NB = 1
ELSE
NB = MAX( 1, ILAENV( 1, 'ZPTTRS', UPLO, N, NRHS, -1, -1 ) )
END IF
*
* Decode UPLO
*
IF( UPPER ) THEN
IUPLO = 1
ELSE
IUPLO = 0
END IF
*
IF( NB.GE.NRHS ) THEN
CALL ZPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
ELSE
DO 10 J = 1, NRHS, NB
JB = MIN( NRHS-J+1, NB )
CALL ZPTTS2( IUPLO, N, JB, D, E, B( 1, J ), LDB )
10 CONTINUE
END IF
*
RETURN
*
* End of ZPTTRS
*
END
|
