LAPACK  3.9.1
LAPACK: Linear Algebra PACKage

◆ zlagtm()

subroutine zlagtm ( character  TRANS,
integer  N,
integer  NRHS,
double precision  ALPHA,
complex*16, dimension( * )  DL,
complex*16, dimension( * )  D,
complex*16, dimension( * )  DU,
complex*16, dimension( ldx, * )  X,
integer  LDX,
double precision  BETA,
complex*16, dimension( ldb, * )  B,
integer  LDB 
)

ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.

Download ZLAGTM + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZLAGTM performs a matrix-vector product of the form

    B := alpha * A * X + beta * B

 where A is a tridiagonal matrix of order N, B and X are N by NRHS
 matrices, and alpha and beta are real scalars, each of which may be
 0., 1., or -1.
Parameters
[in]TRANS
          TRANS is CHARACTER*1
          Specifies the operation applied to A.
          = 'N':  No transpose, B := alpha * A * X + beta * B
          = 'T':  Transpose,    B := alpha * A**T * X + beta * B
          = 'C':  Conjugate transpose, B := alpha * A**H * X + beta * B
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]NRHS
          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices X and B.
[in]ALPHA
          ALPHA is DOUBLE PRECISION
          The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
          it is assumed to be 0.
[in]DL
          DL is COMPLEX*16 array, dimension (N-1)
          The (n-1) sub-diagonal elements of T.
[in]D
          D is COMPLEX*16 array, dimension (N)
          The diagonal elements of T.
[in]DU
          DU is COMPLEX*16 array, dimension (N-1)
          The (n-1) super-diagonal elements of T.
[in]X
          X is COMPLEX*16 array, dimension (LDX,NRHS)
          The N by NRHS matrix X.
[in]LDX
          LDX is INTEGER
          The leading dimension of the array X.  LDX >= max(N,1).
[in]BETA
          BETA is DOUBLE PRECISION
          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
          it is assumed to be 1.
[in,out]B
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the N by NRHS matrix B.
          On exit, B is overwritten by the matrix expression
          B := alpha * A * X + beta * B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(N,1).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 143 of file zlagtm.f.

145 *
146 * -- LAPACK auxiliary routine --
147 * -- LAPACK is a software package provided by Univ. of Tennessee, --
148 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149 *
150 * .. Scalar Arguments ..
151  CHARACTER TRANS
152  INTEGER LDB, LDX, N, NRHS
153  DOUBLE PRECISION ALPHA, BETA
154 * ..
155 * .. Array Arguments ..
156  COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
157  $ X( LDX, * )
158 * ..
159 *
160 * =====================================================================
161 *
162 * .. Parameters ..
163  DOUBLE PRECISION ONE, ZERO
164  parameter( one = 1.0d+0, zero = 0.0d+0 )
165 * ..
166 * .. Local Scalars ..
167  INTEGER I, J
168 * ..
169 * .. External Functions ..
170  LOGICAL LSAME
171  EXTERNAL lsame
172 * ..
173 * .. Intrinsic Functions ..
174  INTRINSIC dconjg
175 * ..
176 * .. Executable Statements ..
177 *
178  IF( n.EQ.0 )
179  $ RETURN
180 *
181 * Multiply B by BETA if BETA.NE.1.
182 *
183  IF( beta.EQ.zero ) THEN
184  DO 20 j = 1, nrhs
185  DO 10 i = 1, n
186  b( i, j ) = zero
187  10 CONTINUE
188  20 CONTINUE
189  ELSE IF( beta.EQ.-one ) THEN
190  DO 40 j = 1, nrhs
191  DO 30 i = 1, n
192  b( i, j ) = -b( i, j )
193  30 CONTINUE
194  40 CONTINUE
195  END IF
196 *
197  IF( alpha.EQ.one ) THEN
198  IF( lsame( trans, 'N' ) ) THEN
199 *
200 * Compute B := B + A*X
201 *
202  DO 60 j = 1, nrhs
203  IF( n.EQ.1 ) THEN
204  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
205  ELSE
206  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
207  $ du( 1 )*x( 2, j )
208  b( n, j ) = b( n, j ) + dl( n-1 )*x( n-1, j ) +
209  $ d( n )*x( n, j )
210  DO 50 i = 2, n - 1
211  b( i, j ) = b( i, j ) + dl( i-1 )*x( i-1, j ) +
212  $ d( i )*x( i, j ) + du( i )*x( i+1, j )
213  50 CONTINUE
214  END IF
215  60 CONTINUE
216  ELSE IF( lsame( trans, 'T' ) ) THEN
217 *
218 * Compute B := B + A**T * X
219 *
220  DO 80 j = 1, nrhs
221  IF( n.EQ.1 ) THEN
222  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
223  ELSE
224  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
225  $ dl( 1 )*x( 2, j )
226  b( n, j ) = b( n, j ) + du( n-1 )*x( n-1, j ) +
227  $ d( n )*x( n, j )
228  DO 70 i = 2, n - 1
229  b( i, j ) = b( i, j ) + du( i-1 )*x( i-1, j ) +
230  $ d( i )*x( i, j ) + dl( i )*x( i+1, j )
231  70 CONTINUE
232  END IF
233  80 CONTINUE
234  ELSE IF( lsame( trans, 'C' ) ) THEN
235 *
236 * Compute B := B + A**H * X
237 *
238  DO 100 j = 1, nrhs
239  IF( n.EQ.1 ) THEN
240  b( 1, j ) = b( 1, j ) + dconjg( d( 1 ) )*x( 1, j )
241  ELSE
242  b( 1, j ) = b( 1, j ) + dconjg( d( 1 ) )*x( 1, j ) +
243  $ dconjg( dl( 1 ) )*x( 2, j )
244  b( n, j ) = b( n, j ) + dconjg( du( n-1 ) )*
245  $ x( n-1, j ) + dconjg( d( n ) )*x( n, j )
246  DO 90 i = 2, n - 1
247  b( i, j ) = b( i, j ) + dconjg( du( i-1 ) )*
248  $ x( i-1, j ) + dconjg( d( i ) )*
249  $ x( i, j ) + dconjg( dl( i ) )*
250  $ x( i+1, j )
251  90 CONTINUE
252  END IF
253  100 CONTINUE
254  END IF
255  ELSE IF( alpha.EQ.-one ) THEN
256  IF( lsame( trans, 'N' ) ) THEN
257 *
258 * Compute B := B - A*X
259 *
260  DO 120 j = 1, nrhs
261  IF( n.EQ.1 ) THEN
262  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
263  ELSE
264  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
265  $ du( 1 )*x( 2, j )
266  b( n, j ) = b( n, j ) - dl( n-1 )*x( n-1, j ) -
267  $ d( n )*x( n, j )
268  DO 110 i = 2, n - 1
269  b( i, j ) = b( i, j ) - dl( i-1 )*x( i-1, j ) -
270  $ d( i )*x( i, j ) - du( i )*x( i+1, j )
271  110 CONTINUE
272  END IF
273  120 CONTINUE
274  ELSE IF( lsame( trans, 'T' ) ) THEN
275 *
276 * Compute B := B - A**T *X
277 *
278  DO 140 j = 1, nrhs
279  IF( n.EQ.1 ) THEN
280  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
281  ELSE
282  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
283  $ dl( 1 )*x( 2, j )
284  b( n, j ) = b( n, j ) - du( n-1 )*x( n-1, j ) -
285  $ d( n )*x( n, j )
286  DO 130 i = 2, n - 1
287  b( i, j ) = b( i, j ) - du( i-1 )*x( i-1, j ) -
288  $ d( i )*x( i, j ) - dl( i )*x( i+1, j )
289  130 CONTINUE
290  END IF
291  140 CONTINUE
292  ELSE IF( lsame( trans, 'C' ) ) THEN
293 *
294 * Compute B := B - A**H *X
295 *
296  DO 160 j = 1, nrhs
297  IF( n.EQ.1 ) THEN
298  b( 1, j ) = b( 1, j ) - dconjg( d( 1 ) )*x( 1, j )
299  ELSE
300  b( 1, j ) = b( 1, j ) - dconjg( d( 1 ) )*x( 1, j ) -
301  $ dconjg( dl( 1 ) )*x( 2, j )
302  b( n, j ) = b( n, j ) - dconjg( du( n-1 ) )*
303  $ x( n-1, j ) - dconjg( d( n ) )*x( n, j )
304  DO 150 i = 2, n - 1
305  b( i, j ) = b( i, j ) - dconjg( du( i-1 ) )*
306  $ x( i-1, j ) - dconjg( d( i ) )*
307  $ x( i, j ) - dconjg( dl( i ) )*
308  $ x( i+1, j )
309  150 CONTINUE
310  END IF
311  160 CONTINUE
312  END IF
313  END IF
314  RETURN
315 *
316 * End of ZLAGTM
317 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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