LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ slagtm()

 subroutine slagtm ( character trans, integer n, integer nrhs, real alpha, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( ldx, * ) x, integer ldx, real beta, real, dimension( ldb, * ) b, integer ldb )

SLAGTM 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.

Purpose:
``` SLAGTM performs a matrix-matrix 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'* X + beta * B = 'C': Conjugate transpose = Transpose``` [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 REAL The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise, it is assumed to be 0.``` [in] DL ``` DL is REAL array, dimension (N-1) The (n-1) sub-diagonal elements of T.``` [in] D ``` D is REAL array, dimension (N) The diagonal elements of T.``` [in] DU ``` DU is REAL array, dimension (N-1) The (n-1) super-diagonal elements of T.``` [in] X ``` X is REAL 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 REAL The scalar beta. BETA must be 0., 1., or -1.; otherwise, it is assumed to be 1.``` [in,out] B ``` B is REAL 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).```

Definition at line 143 of file slagtm.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 REAL ALPHA, BETA
154* ..
155* .. Array Arguments ..
156 REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
157 \$ X( LDX, * )
158* ..
159*
160* =====================================================================
161*
162* .. Parameters ..
163 REAL ONE, ZERO
164 parameter( one = 1.0e+0, zero = 0.0e+0 )
165* ..
166* .. Local Scalars ..
167 INTEGER I, J
168* ..
169* .. External Functions ..
170 LOGICAL LSAME
171 EXTERNAL lsame
172* ..
173* .. Executable Statements ..
174*
175 IF( n.EQ.0 )
176 \$ RETURN
177*
178* Multiply B by BETA if BETA.NE.1.
179*
180 IF( beta.EQ.zero ) THEN
181 DO 20 j = 1, nrhs
182 DO 10 i = 1, n
183 b( i, j ) = zero
184 10 CONTINUE
185 20 CONTINUE
186 ELSE IF( beta.EQ.-one ) THEN
187 DO 40 j = 1, nrhs
188 DO 30 i = 1, n
189 b( i, j ) = -b( i, j )
190 30 CONTINUE
191 40 CONTINUE
192 END IF
193*
194 IF( alpha.EQ.one ) THEN
195 IF( lsame( trans, 'N' ) ) THEN
196*
197* Compute B := B + A*X
198*
199 DO 60 j = 1, nrhs
200 IF( n.EQ.1 ) THEN
201 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
202 ELSE
203 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
204 \$ du( 1 )*x( 2, j )
205 b( n, j ) = b( n, j ) + dl( n-1 )*x( n-1, j ) +
206 \$ d( n )*x( n, j )
207 DO 50 i = 2, n - 1
208 b( i, j ) = b( i, j ) + dl( i-1 )*x( i-1, j ) +
209 \$ d( i )*x( i, j ) + du( i )*x( i+1, j )
210 50 CONTINUE
211 END IF
212 60 CONTINUE
213 ELSE
214*
215* Compute B := B + A**T*X
216*
217 DO 80 j = 1, nrhs
218 IF( n.EQ.1 ) THEN
219 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
220 ELSE
221 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
222 \$ dl( 1 )*x( 2, j )
223 b( n, j ) = b( n, j ) + du( n-1 )*x( n-1, j ) +
224 \$ d( n )*x( n, j )
225 DO 70 i = 2, n - 1
226 b( i, j ) = b( i, j ) + du( i-1 )*x( i-1, j ) +
227 \$ d( i )*x( i, j ) + dl( i )*x( i+1, j )
228 70 CONTINUE
229 END IF
230 80 CONTINUE
231 END IF
232 ELSE IF( alpha.EQ.-one ) THEN
233 IF( lsame( trans, 'N' ) ) THEN
234*
235* Compute B := B - A*X
236*
237 DO 100 j = 1, nrhs
238 IF( n.EQ.1 ) THEN
239 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
240 ELSE
241 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
242 \$ du( 1 )*x( 2, j )
243 b( n, j ) = b( n, j ) - dl( n-1 )*x( n-1, j ) -
244 \$ d( n )*x( n, j )
245 DO 90 i = 2, n - 1
246 b( i, j ) = b( i, j ) - dl( i-1 )*x( i-1, j ) -
247 \$ d( i )*x( i, j ) - du( i )*x( i+1, j )
248 90 CONTINUE
249 END IF
250 100 CONTINUE
251 ELSE
252*
253* Compute B := B - A**T*X
254*
255 DO 120 j = 1, nrhs
256 IF( n.EQ.1 ) THEN
257 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
258 ELSE
259 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
260 \$ dl( 1 )*x( 2, j )
261 b( n, j ) = b( n, j ) - du( n-1 )*x( n-1, j ) -
262 \$ d( n )*x( n, j )
263 DO 110 i = 2, n - 1
264 b( i, j ) = b( i, j ) - du( i-1 )*x( i-1, j ) -
265 \$ d( i )*x( i, j ) - dl( i )*x( i+1, j )
266 110 CONTINUE
267 END IF
268 120 CONTINUE
269 END IF
270 END IF
271 RETURN
272*
273* End of SLAGTM
274*
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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