LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cbdt01.f
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1 *> \brief \b CBDT01
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 CBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
12 * RWORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER KD, LDA, LDPT, LDQ, M, N
16 * REAL RESID
17 * ..
18 * .. Array Arguments ..
19 * REAL D( * ), E( * ), RWORK( * )
20 * COMPLEX A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
21 * $ WORK( * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> CBDT01 reconstructs a general matrix A from its bidiagonal form
31 *> A = Q * B * P**H
32 *> where Q (m by min(m,n)) and P**H (min(m,n) by n) are unitary
33 *> matrices and B is bidiagonal.
34 *>
35 *> The test ratio to test the reduction is
36 *> RESID = norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
37 *> where EPS is the machine precision.
38 *> \endverbatim
39 *
40 * Arguments:
41 * ==========
42 *
43 *> \param[in] M
44 *> \verbatim
45 *> M is INTEGER
46 *> The number of rows of the matrices A and Q.
47 *> \endverbatim
48 *>
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The number of columns of the matrices A and P**H.
53 *> \endverbatim
54 *>
55 *> \param[in] KD
56 *> \verbatim
57 *> KD is INTEGER
58 *> If KD = 0, B is diagonal and the array E is not referenced.
59 *> If KD = 1, the reduction was performed by xGEBRD; B is upper
60 *> bidiagonal if M >= N, and lower bidiagonal if M < N.
61 *> If KD = -1, the reduction was performed by xGBBRD; B is
62 *> always upper bidiagonal.
63 *> \endverbatim
64 *>
65 *> \param[in] A
66 *> \verbatim
67 *> A is COMPLEX array, dimension (LDA,N)
68 *> The m by n matrix A.
69 *> \endverbatim
70 *>
71 *> \param[in] LDA
72 *> \verbatim
73 *> LDA is INTEGER
74 *> The leading dimension of the array A. LDA >= max(1,M).
75 *> \endverbatim
76 *>
77 *> \param[in] Q
78 *> \verbatim
79 *> Q is COMPLEX array, dimension (LDQ,N)
80 *> The m by min(m,n) unitary matrix Q in the reduction
81 *> A = Q * B * P**H.
82 *> \endverbatim
83 *>
84 *> \param[in] LDQ
85 *> \verbatim
86 *> LDQ is INTEGER
87 *> The leading dimension of the array Q. LDQ >= max(1,M).
88 *> \endverbatim
89 *>
90 *> \param[in] D
91 *> \verbatim
92 *> D is REAL array, dimension (min(M,N))
93 *> The diagonal elements of the bidiagonal matrix B.
94 *> \endverbatim
95 *>
96 *> \param[in] E
97 *> \verbatim
98 *> E is REAL array, dimension (min(M,N)-1)
99 *> The superdiagonal elements of the bidiagonal matrix B if
100 *> m >= n, or the subdiagonal elements of B if m < n.
101 *> \endverbatim
102 *>
103 *> \param[in] PT
104 *> \verbatim
105 *> PT is COMPLEX array, dimension (LDPT,N)
106 *> The min(m,n) by n unitary matrix P**H in the reduction
107 *> A = Q * B * P**H.
108 *> \endverbatim
109 *>
110 *> \param[in] LDPT
111 *> \verbatim
112 *> LDPT is INTEGER
113 *> The leading dimension of the array PT.
114 *> LDPT >= max(1,min(M,N)).
115 *> \endverbatim
116 *>
117 *> \param[out] WORK
118 *> \verbatim
119 *> WORK is COMPLEX array, dimension (M+N)
120 *> \endverbatim
121 *>
122 *> \param[out] RWORK
123 *> \verbatim
124 *> RWORK is REAL array, dimension (M)
125 *> \endverbatim
126 *>
127 *> \param[out] RESID
128 *> \verbatim
129 *> RESID is REAL
130 *> The test ratio:
131 *> norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
132 *> \endverbatim
133 *
134 * Authors:
135 * ========
136 *
137 *> \author Univ. of Tennessee
138 *> \author Univ. of California Berkeley
139 *> \author Univ. of Colorado Denver
140 *> \author NAG Ltd.
141 *
142 *> \ingroup complex_eig
143 *
144 * =====================================================================
145  SUBROUTINE cbdt01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
146  $ RWORK, RESID )
147 *
148 * -- LAPACK test routine --
149 * -- LAPACK is a software package provided by Univ. of Tennessee, --
150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151 *
152 * .. Scalar Arguments ..
153  INTEGER KD, LDA, LDPT, LDQ, M, N
154  REAL RESID
155 * ..
156 * .. Array Arguments ..
157  REAL D( * ), E( * ), RWORK( * )
158  COMPLEX A( LDA, * ), PT( LDPT, * ), Q( LDQ, * ),
159  $ work( * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  REAL ZERO, ONE
166  parameter( zero = 0.0e+0, one = 1.0e+0 )
167 * ..
168 * .. Local Scalars ..
169  INTEGER I, J
170  REAL ANORM, EPS
171 * ..
172 * .. External Functions ..
173  REAL CLANGE, SCASUM, SLAMCH
174  EXTERNAL clange, scasum, slamch
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL ccopy, cgemv
178 * ..
179 * .. Intrinsic Functions ..
180  INTRINSIC cmplx, max, min, real
181 * ..
182 * .. Executable Statements ..
183 *
184 * Quick return if possible
185 *
186  IF( m.LE.0 .OR. n.LE.0 ) THEN
187  resid = zero
188  RETURN
189  END IF
190 *
191 * Compute A - Q * B * P**H one column at a time.
192 *
193  resid = zero
194  IF( kd.NE.0 ) THEN
195 *
196 * B is bidiagonal.
197 *
198  IF( kd.NE.0 .AND. m.GE.n ) THEN
199 *
200 * B is upper bidiagonal and M >= N.
201 *
202  DO 20 j = 1, n
203  CALL ccopy( m, a( 1, j ), 1, work, 1 )
204  DO 10 i = 1, n - 1
205  work( m+i ) = d( i )*pt( i, j ) + e( i )*pt( i+1, j )
206  10 CONTINUE
207  work( m+n ) = d( n )*pt( n, j )
208  CALL cgemv( 'No transpose', m, n, -cmplx( one ), q, ldq,
209  $ work( m+1 ), 1, cmplx( one ), work, 1 )
210  resid = max( resid, scasum( m, work, 1 ) )
211  20 CONTINUE
212  ELSE IF( kd.LT.0 ) THEN
213 *
214 * B is upper bidiagonal and M < N.
215 *
216  DO 40 j = 1, n
217  CALL ccopy( m, a( 1, j ), 1, work, 1 )
218  DO 30 i = 1, m - 1
219  work( m+i ) = d( i )*pt( i, j ) + e( i )*pt( i+1, j )
220  30 CONTINUE
221  work( m+m ) = d( m )*pt( m, j )
222  CALL cgemv( 'No transpose', m, m, -cmplx( one ), q, ldq,
223  $ work( m+1 ), 1, cmplx( one ), work, 1 )
224  resid = max( resid, scasum( m, work, 1 ) )
225  40 CONTINUE
226  ELSE
227 *
228 * B is lower bidiagonal.
229 *
230  DO 60 j = 1, n
231  CALL ccopy( m, a( 1, j ), 1, work, 1 )
232  work( m+1 ) = d( 1 )*pt( 1, j )
233  DO 50 i = 2, m
234  work( m+i ) = e( i-1 )*pt( i-1, j ) +
235  $ d( i )*pt( i, j )
236  50 CONTINUE
237  CALL cgemv( 'No transpose', m, m, -cmplx( one ), q, ldq,
238  $ work( m+1 ), 1, cmplx( one ), work, 1 )
239  resid = max( resid, scasum( m, work, 1 ) )
240  60 CONTINUE
241  END IF
242  ELSE
243 *
244 * B is diagonal.
245 *
246  IF( m.GE.n ) THEN
247  DO 80 j = 1, n
248  CALL ccopy( m, a( 1, j ), 1, work, 1 )
249  DO 70 i = 1, n
250  work( m+i ) = d( i )*pt( i, j )
251  70 CONTINUE
252  CALL cgemv( 'No transpose', m, n, -cmplx( one ), q, ldq,
253  $ work( m+1 ), 1, cmplx( one ), work, 1 )
254  resid = max( resid, scasum( m, work, 1 ) )
255  80 CONTINUE
256  ELSE
257  DO 100 j = 1, n
258  CALL ccopy( m, a( 1, j ), 1, work, 1 )
259  DO 90 i = 1, m
260  work( m+i ) = d( i )*pt( i, j )
261  90 CONTINUE
262  CALL cgemv( 'No transpose', m, m, -cmplx( one ), q, ldq,
263  $ work( m+1 ), 1, cmplx( one ), work, 1 )
264  resid = max( resid, scasum( m, work, 1 ) )
265  100 CONTINUE
266  END IF
267  END IF
268 *
269 * Compute norm(A - Q * B * P**H) / ( n * norm(A) * EPS )
270 *
271  anorm = clange( '1', m, n, a, lda, rwork )
272  eps = slamch( 'Precision' )
273 *
274  IF( anorm.LE.zero ) THEN
275  IF( resid.NE.zero )
276  $ resid = one / eps
277  ELSE
278  IF( anorm.GE.resid ) THEN
279  resid = ( resid / anorm ) / ( real( n )*eps )
280  ELSE
281  IF( anorm.LT.one ) THEN
282  resid = ( min( resid, real( n )*anorm ) / anorm ) /
283  $ ( real( n )*eps )
284  ELSE
285  resid = min( resid / anorm, real( n ) ) /
286  $ ( real( n )*eps )
287  END IF
288  END IF
289  END IF
290 *
291  RETURN
292 *
293 * End of CBDT01
294 *
295  END
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
subroutine cbdt01(M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK, RWORK, RESID)
CBDT01
Definition: cbdt01.f:147