LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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sgttrf.f
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1*> \brief \b SGTTRF
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgttrf.f">
11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgttrf.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
22*
23* .. Scalar Arguments ..
24* INTEGER INFO, N
25* ..
26* .. Array Arguments ..
27* INTEGER IPIV( * )
28* REAL D( * ), DL( * ), DU( * ), DU2( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> SGTTRF computes an LU factorization of a real tridiagonal matrix A
38*> using elimination with partial pivoting and row interchanges.
39*>
40*> The factorization has the form
41*> A = L * U
42*> where L is a product of permutation and unit lower bidiagonal
43*> matrices and U is upper triangular with nonzeros in only the main
44*> diagonal and first two superdiagonals.
45*> \endverbatim
46*
47* Arguments:
48* ==========
49*
50*> \param[in] N
51*> \verbatim
52*> N is INTEGER
53*> The order of the matrix A.
54*> \endverbatim
55*>
56*> \param[in,out] DL
57*> \verbatim
58*> DL is REAL array, dimension (N-1)
59*> On entry, DL must contain the (n-1) sub-diagonal elements of
60*> A.
61*>
62*> On exit, DL is overwritten by the (n-1) multipliers that
63*> define the matrix L from the LU factorization of A.
64*> \endverbatim
65*>
66*> \param[in,out] D
67*> \verbatim
68*> D is REAL array, dimension (N)
69*> On entry, D must contain the diagonal elements of A.
70*>
71*> On exit, D is overwritten by the n diagonal elements of the
72*> upper triangular matrix U from the LU factorization of A.
73*> \endverbatim
74*>
75*> \param[in,out] DU
76*> \verbatim
77*> DU is REAL array, dimension (N-1)
78*> On entry, DU must contain the (n-1) super-diagonal elements
79*> of A.
80*>
81*> On exit, DU is overwritten by the (n-1) elements of the first
82*> super-diagonal of U.
83*> \endverbatim
84*>
85*> \param[out] DU2
86*> \verbatim
87*> DU2 is REAL array, dimension (N-2)
88*> On exit, DU2 is overwritten by the (n-2) elements of the
89*> second super-diagonal of U.
90*> \endverbatim
91*>
92*> \param[out] IPIV
93*> \verbatim
94*> IPIV is INTEGER array, dimension (N)
95*> The pivot indices; for 1 <= i <= n, row i of the matrix was
96*> interchanged with row IPIV(i). IPIV(i) will always be either
97*> i or i+1; IPIV(i) = i indicates a row interchange was not
98*> required.
99*> \endverbatim
100*>
101*> \param[out] INFO
102*> \verbatim
103*> INFO is INTEGER
104*> = 0: successful exit
105*> < 0: if INFO = -k, the k-th argument had an illegal value
106*> > 0: if INFO = k, U(k,k) is exactly zero. The factorization
107*> has been completed, but the factor U is exactly
108*> singular, and division by zero will occur if it is used
109*> to solve a system of equations.
110*> \endverbatim
111*
112* Authors:
113* ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \ingroup gttrf
121*
122* =====================================================================
123 SUBROUTINE sgttrf( N, DL, D, DU, DU2, IPIV, INFO )
124*
125* -- LAPACK computational routine --
126* -- LAPACK is a software package provided by Univ. of Tennessee, --
127* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128*
129* .. Scalar Arguments ..
130 INTEGER INFO, N
131* ..
132* .. Array Arguments ..
133 INTEGER IPIV( * )
134 REAL D( * ), DL( * ), DU( * ), DU2( * )
135* ..
136*
137* =====================================================================
138*
139* .. Parameters ..
140 REAL ZERO
141 parameter( zero = 0.0e+0 )
142* ..
143* .. Local Scalars ..
144 INTEGER I
145 REAL FACT, TEMP
146* ..
147* .. Intrinsic Functions ..
148 INTRINSIC abs
149* ..
150* .. External Subroutines ..
151 EXTERNAL xerbla
152* ..
153* .. Executable Statements ..
154*
155 info = 0
156 IF( n.LT.0 ) THEN
157 info = -1
158 CALL xerbla( 'SGTTRF', -info )
159 RETURN
160 END IF
161*
162* Quick return if possible
163*
164 IF( n.EQ.0 )
165 \$ RETURN
166*
167* Initialize IPIV(i) = i and DU2(I) = 0
168*
169 DO 10 i = 1, n
170 ipiv( i ) = i
171 10 CONTINUE
172 DO 20 i = 1, n - 2
173 du2( i ) = zero
174 20 CONTINUE
175*
176 DO 30 i = 1, n - 2
177 IF( abs( d( i ) ).GE.abs( dl( i ) ) ) THEN
178*
179* No row interchange required, eliminate DL(I)
180*
181 IF( d( i ).NE.zero ) THEN
182 fact = dl( i ) / d( i )
183 dl( i ) = fact
184 d( i+1 ) = d( i+1 ) - fact*du( i )
185 END IF
186 ELSE
187*
188* Interchange rows I and I+1, eliminate DL(I)
189*
190 fact = d( i ) / dl( i )
191 d( i ) = dl( i )
192 dl( i ) = fact
193 temp = du( i )
194 du( i ) = d( i+1 )
195 d( i+1 ) = temp - fact*d( i+1 )
196 du2( i ) = du( i+1 )
197 du( i+1 ) = -fact*du( i+1 )
198 ipiv( i ) = i + 1
199 END IF
200 30 CONTINUE
201 IF( n.GT.1 ) THEN
202 i = n - 1
203 IF( abs( d( i ) ).GE.abs( dl( i ) ) ) THEN
204 IF( d( i ).NE.zero ) THEN
205 fact = dl( i ) / d( i )
206 dl( i ) = fact
207 d( i+1 ) = d( i+1 ) - fact*du( i )
208 END IF
209 ELSE
210 fact = d( i ) / dl( i )
211 d( i ) = dl( i )
212 dl( i ) = fact
213 temp = du( i )
214 du( i ) = d( i+1 )
215 d( i+1 ) = temp - fact*d( i+1 )
216 ipiv( i ) = i + 1
217 END IF
218 END IF
219*
220* Check for a zero on the diagonal of U.
221*
222 DO 40 i = 1, n
223 IF( d( i ).EQ.zero ) THEN
224 info = i
225 GO TO 50
226 END IF
227 40 CONTINUE
228 50 CONTINUE
229*
230 RETURN
231*
232* End of SGTTRF
233*
234 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine sgttrf(n, dl, d, du, du2, ipiv, info)
SGTTRF
Definition sgttrf.f:124