LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
sgbt01.f
Go to the documentation of this file.
1 *> \brief \b SGBT01
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE SGBT01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
12 * RESID )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER KL, KU, LDA, LDAFAC, M, N
16 * REAL RESID
17 * ..
18 * .. Array Arguments ..
19 * INTEGER IPIV( * )
20 * REAL A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> SGBT01 reconstructs a band matrix A from its L*U factorization and
30 *> computes the residual:
31 *> norm(L*U - A) / ( N * norm(A) * EPS ),
32 *> where EPS is the machine epsilon.
33 *>
34 *> The expression L*U - A is computed one column at a time, so A and
35 *> AFAC are not modified.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] M
42 *> \verbatim
43 *> M is INTEGER
44 *> The number of rows of the matrix A. M >= 0.
45 *> \endverbatim
46 *>
47 *> \param[in] N
48 *> \verbatim
49 *> N is INTEGER
50 *> The number of columns of the matrix A. N >= 0.
51 *> \endverbatim
52 *>
53 *> \param[in] KL
54 *> \verbatim
55 *> KL is INTEGER
56 *> The number of subdiagonals within the band of A. KL >= 0.
57 *> \endverbatim
58 *>
59 *> \param[in] KU
60 *> \verbatim
61 *> KU is INTEGER
62 *> The number of superdiagonals within the band of A. KU >= 0.
63 *> \endverbatim
64 *>
65 *> \param[in,out] A
66 *> \verbatim
67 *> A is REAL array, dimension (LDA,N)
68 *> The original matrix A in band storage, stored in rows 1 to
69 *> KL+KU+1.
70 *> \endverbatim
71 *>
72 *> \param[in] LDA
73 *> \verbatim
74 *> LDA is INTEGER.
75 *> The leading dimension of the array A. LDA >= max(1,KL+KU+1).
76 *> \endverbatim
77 *>
78 *> \param[in] AFAC
79 *> \verbatim
80 *> AFAC is REAL array, dimension (LDAFAC,N)
81 *> The factored form of the matrix A. AFAC contains the banded
82 *> factors L and U from the L*U factorization, as computed by
83 *> SGBTRF. U is stored as an upper triangular band matrix with
84 *> KL+KU superdiagonals in rows 1 to KL+KU+1, and the
85 *> multipliers used during the factorization are stored in rows
86 *> KL+KU+2 to 2*KL+KU+1. See SGBTRF for further details.
87 *> \endverbatim
88 *>
89 *> \param[in] LDAFAC
90 *> \verbatim
91 *> LDAFAC is INTEGER
92 *> The leading dimension of the array AFAC.
93 *> LDAFAC >= max(1,2*KL*KU+1).
94 *> \endverbatim
95 *>
96 *> \param[in] IPIV
97 *> \verbatim
98 *> IPIV is INTEGER array, dimension (min(M,N))
99 *> The pivot indices from SGBTRF.
100 *> \endverbatim
101 *>
102 *> \param[out] WORK
103 *> \verbatim
104 *> WORK is REAL array, dimension (2*KL+KU+1)
105 *> \endverbatim
106 *>
107 *> \param[out] RESID
108 *> \verbatim
109 *> RESID is REAL
110 *> norm(L*U - A) / ( N * norm(A) * EPS )
111 *> \endverbatim
112 *
113 * Authors:
114 * ========
115 *
116 *> \author Univ. of Tennessee
117 *> \author Univ. of California Berkeley
118 *> \author Univ. of Colorado Denver
119 *> \author NAG Ltd.
120 *
121 *> \ingroup single_lin
122 *
123 * =====================================================================
124  SUBROUTINE sgbt01( M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK,
125  \$ RESID )
126 *
127 * -- LAPACK test routine --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 *
131 * .. Scalar Arguments ..
132  INTEGER KL, KU, LDA, LDAFAC, M, N
133  REAL RESID
134 * ..
135 * .. Array Arguments ..
136  INTEGER IPIV( * )
137  REAL A( LDA, * ), AFAC( LDAFAC, * ), WORK( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  REAL ZERO, ONE
144  parameter( zero = 0.0e+0, one = 1.0e+0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER I, I1, I2, IL, IP, IW, J, JL, JU, JUA, KD, LENJ
148  REAL ANORM, EPS, T
149 * ..
150 * .. External Functions ..
151  REAL SASUM, SLAMCH
152  EXTERNAL sasum, slamch
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL saxpy, scopy
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max, min, real
159 * ..
160 * .. Executable Statements ..
161 *
162 * Quick exit if M = 0 or N = 0.
163 *
164  resid = zero
165  IF( m.LE.0 .OR. n.LE.0 )
166  \$ RETURN
167 *
168 * Determine EPS and the norm of A.
169 *
170  eps = slamch( 'Epsilon' )
171  kd = ku + 1
172  anorm = zero
173  DO 10 j = 1, n
174  i1 = max( kd+1-j, 1 )
175  i2 = min( kd+m-j, kl+kd )
176  IF( i2.GE.i1 )
177  \$ anorm = max( anorm, sasum( i2-i1+1, a( i1, j ), 1 ) )
178  10 CONTINUE
179 *
180 * Compute one column at a time of L*U - A.
181 *
182  kd = kl + ku + 1
183  DO 40 j = 1, n
184 *
185 * Copy the J-th column of U to WORK.
186 *
187  ju = min( kl+ku, j-1 )
188  jl = min( kl, m-j )
189  lenj = min( m, j ) - j + ju + 1
190  IF( lenj.GT.0 ) THEN
191  CALL scopy( lenj, afac( kd-ju, j ), 1, work, 1 )
192  DO 20 i = lenj + 1, ju + jl + 1
193  work( i ) = zero
194  20 CONTINUE
195 *
196 * Multiply by the unit lower triangular matrix L. Note that L
197 * is stored as a product of transformations and permutations.
198 *
199  DO 30 i = min( m-1, j ), j - ju, -1
200  il = min( kl, m-i )
201  IF( il.GT.0 ) THEN
202  iw = i - j + ju + 1
203  t = work( iw )
204  CALL saxpy( il, t, afac( kd+1, i ), 1, work( iw+1 ),
205  \$ 1 )
206  ip = ipiv( i )
207  IF( i.NE.ip ) THEN
208  ip = ip - j + ju + 1
209  work( iw ) = work( ip )
210  work( ip ) = t
211  END IF
212  END IF
213  30 CONTINUE
214 *
215 * Subtract the corresponding column of A.
216 *
217  jua = min( ju, ku )
218  IF( jua+jl+1.GT.0 )
219  \$ CALL saxpy( jua+jl+1, -one, a( ku+1-jua, j ), 1,
220  \$ work( ju+1-jua ), 1 )
221 *
222 * Compute the 1-norm of the column.
223 *
224  resid = max( resid, sasum( ju+jl+1, work, 1 ) )
225  END IF
226  40 CONTINUE
227 *
228 * Compute norm(L*U - A) / ( N * norm(A) * EPS )
229 *
230  IF( anorm.LE.zero ) THEN
231  IF( resid.NE.zero )
232  \$ resid = one / eps
233  ELSE
234  resid = ( ( resid / real( n ) ) / anorm ) / eps
235  END IF
236 *
237  RETURN
238 *
239 * End of SGBT01
240 *
241  END
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
subroutine sgbt01(M, N, KL, KU, A, LDA, AFAC, LDAFAC, IPIV, WORK, RESID)
SGBT01
Definition: sgbt01.f:126