LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
clascl.f
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1 *> \brief \b CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER TYPE
25 * INTEGER INFO, KL, KU, LDA, M, N
26 * REAL CFROM, CTO
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX A( LDA, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> CLASCL multiplies the M by N complex matrix A by the real scalar
39 *> CTO/CFROM. This is done without over/underflow as long as the final
40 *> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that
41 *> A may be full, upper triangular, lower triangular, upper Hessenberg,
42 *> or banded.
43 *> \endverbatim
44 *
45 * Arguments:
46 * ==========
47 *
48 *> \param[in] TYPE
49 *> \verbatim
50 *> TYPE is CHARACTER*1
51 *> TYPE indices the storage type of the input matrix.
52 *> = 'G': A is a full matrix.
53 *> = 'L': A is a lower triangular matrix.
54 *> = 'U': A is an upper triangular matrix.
55 *> = 'H': A is an upper Hessenberg matrix.
56 *> = 'B': A is a symmetric band matrix with lower bandwidth KL
57 *> and upper bandwidth KU and with the only the lower
58 *> half stored.
59 *> = 'Q': A is a symmetric band matrix with lower bandwidth KL
60 *> and upper bandwidth KU and with the only the upper
61 *> half stored.
62 *> = 'Z': A is a band matrix with lower bandwidth KL and upper
63 *> bandwidth KU. See CGBTRF for storage details.
64 *> \endverbatim
65 *>
66 *> \param[in] KL
67 *> \verbatim
68 *> KL is INTEGER
69 *> The lower bandwidth of A. Referenced only if TYPE = 'B',
70 *> 'Q' or 'Z'.
71 *> \endverbatim
72 *>
73 *> \param[in] KU
74 *> \verbatim
75 *> KU is INTEGER
76 *> The upper bandwidth of A. Referenced only if TYPE = 'B',
77 *> 'Q' or 'Z'.
78 *> \endverbatim
79 *>
80 *> \param[in] CFROM
81 *> \verbatim
82 *> CFROM is REAL
83 *> \endverbatim
84 *>
85 *> \param[in] CTO
86 *> \verbatim
87 *> CTO is REAL
88 *>
89 *> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed
90 *> without over/underflow if the final result CTO*A(I,J)/CFROM
91 *> can be represented without over/underflow. CFROM must be
92 *> nonzero.
93 *> \endverbatim
94 *>
95 *> \param[in] M
96 *> \verbatim
97 *> M is INTEGER
98 *> The number of rows of the matrix A. M >= 0.
99 *> \endverbatim
100 *>
101 *> \param[in] N
102 *> \verbatim
103 *> N is INTEGER
104 *> The number of columns of the matrix A. N >= 0.
105 *> \endverbatim
106 *>
107 *> \param[in,out] A
108 *> \verbatim
109 *> A is COMPLEX array, dimension (LDA,N)
110 *> The matrix to be multiplied by CTO/CFROM. See TYPE for the
111 *> storage type.
112 *> \endverbatim
113 *>
114 *> \param[in] LDA
115 *> \verbatim
116 *> LDA is INTEGER
117 *> The leading dimension of the array A.
118 *> If TYPE = 'G', 'L', 'U', 'H', LDA >= max(1,M);
119 *> TYPE = 'B', LDA >= KL+1;
120 *> TYPE = 'Q', LDA >= KU+1;
121 *> TYPE = 'Z', LDA >= 2*KL+KU+1.
122 *> \endverbatim
123 *>
124 *> \param[out] INFO
125 *> \verbatim
126 *> INFO is INTEGER
127 *> 0 - successful exit
128 *> <0 - if INFO = -i, the i-th argument had an illegal value.
129 *> \endverbatim
130 *
131 * Authors:
132 * ========
133 *
134 *> \author Univ. of Tennessee
135 *> \author Univ. of California Berkeley
136 *> \author Univ. of Colorado Denver
137 *> \author NAG Ltd.
138 *
139 *> \date June 2016
140 *
141 *> \ingroup complexOTHERauxiliary
142 *
143 * =====================================================================
144  SUBROUTINE clascl( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO )
145 *
146 * -- LAPACK auxiliary routine (version 3.6.1) --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 * June 2016
150 *
151 * .. Scalar Arguments ..
152  CHARACTER TYPE
153  INTEGER INFO, KL, KU, LDA, M, N
154  REAL CFROM, CTO
155 * ..
156 * .. Array Arguments ..
157  COMPLEX A( lda, * )
158 * ..
159 *
160 * =====================================================================
161 *
162 * .. Parameters ..
163  REAL ZERO, ONE
164  parameter ( zero = 0.0e0, one = 1.0e0 )
165 * ..
166 * .. Local Scalars ..
167  LOGICAL DONE
168  INTEGER I, ITYPE, J, K1, K2, K3, K4
169  REAL BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME, SISNAN
173  REAL SLAMCH
174  EXTERNAL lsame, slamch, sisnan
175 * ..
176 * .. Intrinsic Functions ..
177  INTRINSIC abs, max, min
178 * ..
179 * .. External Subroutines ..
180  EXTERNAL xerbla
181 * ..
182 * .. Executable Statements ..
183 *
184 * Test the input arguments
185 *
186  info = 0
187 *
188  IF( lsame( TYPE, 'G' ) ) then
189  itype = 0
190  ELSE IF( lsame( TYPE, 'L' ) ) then
191  itype = 1
192  ELSE IF( lsame( TYPE, 'U' ) ) then
193  itype = 2
194  ELSE IF( lsame( TYPE, 'H' ) ) then
195  itype = 3
196  ELSE IF( lsame( TYPE, 'B' ) ) then
197  itype = 4
198  ELSE IF( lsame( TYPE, 'Q' ) ) then
199  itype = 5
200  ELSE IF( lsame( TYPE, 'Z' ) ) then
201  itype = 6
202  ELSE
203  itype = -1
204  END IF
205 *
206  IF( itype.EQ.-1 ) THEN
207  info = -1
208  ELSE IF( cfrom.EQ.zero .OR. sisnan(cfrom) ) THEN
209  info = -4
210  ELSE IF( sisnan(cto) ) THEN
211  info = -5
212  ELSE IF( m.LT.0 ) THEN
213  info = -6
214  ELSE IF( n.LT.0 .OR. ( itype.EQ.4 .AND. n.NE.m ) .OR.
215  \$ ( itype.EQ.5 .AND. n.NE.m ) ) THEN
216  info = -7
217  ELSE IF( itype.LE.3 .AND. lda.LT.max( 1, m ) ) THEN
218  info = -9
219  ELSE IF( itype.GE.4 ) THEN
220  IF( kl.LT.0 .OR. kl.GT.max( m-1, 0 ) ) THEN
221  info = -2
222  ELSE IF( ku.LT.0 .OR. ku.GT.max( n-1, 0 ) .OR.
223  \$ ( ( itype.EQ.4 .OR. itype.EQ.5 ) .AND. kl.NE.ku ) )
224  \$ THEN
225  info = -3
226  ELSE IF( ( itype.EQ.4 .AND. lda.LT.kl+1 ) .OR.
227  \$ ( itype.EQ.5 .AND. lda.LT.ku+1 ) .OR.
228  \$ ( itype.EQ.6 .AND. lda.LT.2*kl+ku+1 ) ) THEN
229  info = -9
230  END IF
231  END IF
232 *
233  IF( info.NE.0 ) THEN
234  CALL xerbla( 'CLASCL', -info )
235  RETURN
236  END IF
237 *
238 * Quick return if possible
239 *
240  IF( n.EQ.0 .OR. m.EQ.0 )
241  \$ RETURN
242 *
243 * Get machine parameters
244 *
245  smlnum = slamch( 'S' )
246  bignum = one / smlnum
247 *
248  cfromc = cfrom
249  ctoc = cto
250 *
251  10 CONTINUE
252  cfrom1 = cfromc*smlnum
253  IF( cfrom1.EQ.cfromc ) THEN
254 ! CFROMC is an inf. Multiply by a correctly signed zero for
255 ! finite CTOC, or a NaN if CTOC is infinite.
256  mul = ctoc / cfromc
257  done = .true.
258  cto1 = ctoc
259  ELSE
260  cto1 = ctoc / bignum
261  IF( cto1.EQ.ctoc ) THEN
262 ! CTOC is either 0 or an inf. In both cases, CTOC itself
263 ! serves as the correct multiplication factor.
264  mul = ctoc
265  done = .true.
266  cfromc = one
267  ELSE IF( abs( cfrom1 ).GT.abs( ctoc ) .AND. ctoc.NE.zero ) THEN
268  mul = smlnum
269  done = .false.
270  cfromc = cfrom1
271  ELSE IF( abs( cto1 ).GT.abs( cfromc ) ) THEN
272  mul = bignum
273  done = .false.
274  ctoc = cto1
275  ELSE
276  mul = ctoc / cfromc
277  done = .true.
278  END IF
279  END IF
280 *
281  IF( itype.EQ.0 ) THEN
282 *
283 * Full matrix
284 *
285  DO 30 j = 1, n
286  DO 20 i = 1, m
287  a( i, j ) = a( i, j )*mul
288  20 CONTINUE
289  30 CONTINUE
290 *
291  ELSE IF( itype.EQ.1 ) THEN
292 *
293 * Lower triangular matrix
294 *
295  DO 50 j = 1, n
296  DO 40 i = j, m
297  a( i, j ) = a( i, j )*mul
298  40 CONTINUE
299  50 CONTINUE
300 *
301  ELSE IF( itype.EQ.2 ) THEN
302 *
303 * Upper triangular matrix
304 *
305  DO 70 j = 1, n
306  DO 60 i = 1, min( j, m )
307  a( i, j ) = a( i, j )*mul
308  60 CONTINUE
309  70 CONTINUE
310 *
311  ELSE IF( itype.EQ.3 ) THEN
312 *
313 * Upper Hessenberg matrix
314 *
315  DO 90 j = 1, n
316  DO 80 i = 1, min( j+1, m )
317  a( i, j ) = a( i, j )*mul
318  80 CONTINUE
319  90 CONTINUE
320 *
321  ELSE IF( itype.EQ.4 ) THEN
322 *
323 * Lower half of a symmetric band matrix
324 *
325  k3 = kl + 1
326  k4 = n + 1
327  DO 110 j = 1, n
328  DO 100 i = 1, min( k3, k4-j )
329  a( i, j ) = a( i, j )*mul
330  100 CONTINUE
331  110 CONTINUE
332 *
333  ELSE IF( itype.EQ.5 ) THEN
334 *
335 * Upper half of a symmetric band matrix
336 *
337  k1 = ku + 2
338  k3 = ku + 1
339  DO 130 j = 1, n
340  DO 120 i = max( k1-j, 1 ), k3
341  a( i, j ) = a( i, j )*mul
342  120 CONTINUE
343  130 CONTINUE
344 *
345  ELSE IF( itype.EQ.6 ) THEN
346 *
347 * Band matrix
348 *
349  k1 = kl + ku + 2
350  k2 = kl + 1
351  k3 = 2*kl + ku + 1
352  k4 = kl + ku + 1 + m
353  DO 150 j = 1, n
354  DO 140 i = max( k1-j, k2 ), min( k3, k4-j )
355  a( i, j ) = a( i, j )*mul
356  140 CONTINUE
357  150 CONTINUE
358 *
359  END IF
360 *
361  IF( .NOT.done )
362  \$ GO TO 10
363 *
364  RETURN
365 *
366 * End of CLASCL
367 *
368  END
subroutine clascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: clascl.f:145
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62