Annotation of rpl/lapack/lapack/dgttrf.f, revision 1.1.1.1
1.1 bertrand 1: SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
2: *
3: * -- LAPACK 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, N
10: * ..
11: * .. Array Arguments ..
12: INTEGER IPIV( * )
13: DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DGTTRF computes an LU factorization of a real tridiagonal matrix A
20: * using elimination with partial pivoting and row interchanges.
21: *
22: * The factorization has the form
23: * A = L * U
24: * where L is a product of permutation and unit lower bidiagonal
25: * matrices and U is upper triangular with nonzeros in only the main
26: * diagonal and first two superdiagonals.
27: *
28: * Arguments
29: * =========
30: *
31: * N (input) INTEGER
32: * The order of the matrix A.
33: *
34: * DL (input/output) DOUBLE PRECISION array, dimension (N-1)
35: * On entry, DL must contain the (n-1) sub-diagonal elements of
36: * A.
37: *
38: * On exit, DL is overwritten by the (n-1) multipliers that
39: * define the matrix L from the LU factorization of A.
40: *
41: * D (input/output) DOUBLE PRECISION array, dimension (N)
42: * On entry, D must contain the diagonal elements of A.
43: *
44: * On exit, D is overwritten by the n diagonal elements of the
45: * upper triangular matrix U from the LU factorization of A.
46: *
47: * DU (input/output) DOUBLE PRECISION array, dimension (N-1)
48: * On entry, DU must contain the (n-1) super-diagonal elements
49: * of A.
50: *
51: * On exit, DU is overwritten by the (n-1) elements of the first
52: * super-diagonal of U.
53: *
54: * DU2 (output) DOUBLE PRECISION array, dimension (N-2)
55: * On exit, DU2 is overwritten by the (n-2) elements of the
56: * second super-diagonal of U.
57: *
58: * IPIV (output) INTEGER array, dimension (N)
59: * The pivot indices; for 1 <= i <= n, row i of the matrix was
60: * interchanged with row IPIV(i). IPIV(i) will always be either
61: * i or i+1; IPIV(i) = i indicates a row interchange was not
62: * required.
63: *
64: * INFO (output) INTEGER
65: * = 0: successful exit
66: * < 0: if INFO = -k, the k-th argument had an illegal value
67: * > 0: if INFO = k, U(k,k) is exactly zero. The factorization
68: * has been completed, but the factor U is exactly
69: * singular, and division by zero will occur if it is used
70: * to solve a system of equations.
71: *
72: * =====================================================================
73: *
74: * .. Parameters ..
75: DOUBLE PRECISION ZERO
76: PARAMETER ( ZERO = 0.0D+0 )
77: * ..
78: * .. Local Scalars ..
79: INTEGER I
80: DOUBLE PRECISION FACT, TEMP
81: * ..
82: * .. Intrinsic Functions ..
83: INTRINSIC ABS
84: * ..
85: * .. External Subroutines ..
86: EXTERNAL XERBLA
87: * ..
88: * .. Executable Statements ..
89: *
90: INFO = 0
91: IF( N.LT.0 ) THEN
92: INFO = -1
93: CALL XERBLA( 'DGTTRF', -INFO )
94: RETURN
95: END IF
96: *
97: * Quick return if possible
98: *
99: IF( N.EQ.0 )
100: $ RETURN
101: *
102: * Initialize IPIV(i) = i and DU2(I) = 0
103: *
104: DO 10 I = 1, N
105: IPIV( I ) = I
106: 10 CONTINUE
107: DO 20 I = 1, N - 2
108: DU2( I ) = ZERO
109: 20 CONTINUE
110: *
111: DO 30 I = 1, N - 2
112: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
113: *
114: * No row interchange required, eliminate DL(I)
115: *
116: IF( D( I ).NE.ZERO ) THEN
117: FACT = DL( I ) / D( I )
118: DL( I ) = FACT
119: D( I+1 ) = D( I+1 ) - FACT*DU( I )
120: END IF
121: ELSE
122: *
123: * Interchange rows I and I+1, eliminate DL(I)
124: *
125: FACT = D( I ) / DL( I )
126: D( I ) = DL( I )
127: DL( I ) = FACT
128: TEMP = DU( I )
129: DU( I ) = D( I+1 )
130: D( I+1 ) = TEMP - FACT*D( I+1 )
131: DU2( I ) = DU( I+1 )
132: DU( I+1 ) = -FACT*DU( I+1 )
133: IPIV( I ) = I + 1
134: END IF
135: 30 CONTINUE
136: IF( N.GT.1 ) THEN
137: I = N - 1
138: IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
139: IF( D( I ).NE.ZERO ) THEN
140: FACT = DL( I ) / D( I )
141: DL( I ) = FACT
142: D( I+1 ) = D( I+1 ) - FACT*DU( I )
143: END IF
144: ELSE
145: FACT = D( I ) / DL( I )
146: D( I ) = DL( I )
147: DL( I ) = FACT
148: TEMP = DU( I )
149: DU( I ) = D( I+1 )
150: D( I+1 ) = TEMP - FACT*D( I+1 )
151: IPIV( I ) = I + 1
152: END IF
153: END IF
154: *
155: * Check for a zero on the diagonal of U.
156: *
157: DO 40 I = 1, N
158: IF( D( I ).EQ.ZERO ) THEN
159: INFO = I
160: GO TO 50
161: END IF
162: 40 CONTINUE
163: 50 CONTINUE
164: *
165: RETURN
166: *
167: * End of DGTTRF
168: *
169: END
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