LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ claptm()

subroutine claptm ( character  UPLO,
integer  N,
integer  NRHS,
real  ALPHA,
real, dimension( * )  D,
complex, dimension( * )  E,
complex, dimension( ldx, * )  X,
integer  LDX,
real  BETA,
complex, dimension( ldb, * )  B,
integer  LDB 
)

CLAPTM

Purpose:
 CLAPTM multiplies an N by NRHS matrix X by a Hermitian tridiagonal
 matrix A and stores the result in a matrix B.  The operation has the
 form

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

 where alpha may be either 1. or -1. and beta may be 0., 1., or -1.
Parameters
[in]UPLO
          UPLO is CHARACTER
          Specifies whether the superdiagonal or the subdiagonal of the
          tridiagonal matrix A is stored.
          = 'U':  Upper, E is the superdiagonal of A.
          = 'L':  Lower, E is the subdiagonal of A.
[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 1. or -1.; otherwise,
          it is assumed to be 0.
[in]D
          D is REAL array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.
[in]E
          E is COMPLEX array, dimension (N-1)
          The (n-1) subdiagonal or superdiagonal elements of A.
[in]X
          X is COMPLEX 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 COMPLEX 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 127 of file claptm.f.

129*
130* -- LAPACK test routine --
131* -- LAPACK is a software package provided by Univ. of Tennessee, --
132* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
133*
134* .. Scalar Arguments ..
135 CHARACTER UPLO
136 INTEGER LDB, LDX, N, NRHS
137 REAL ALPHA, BETA
138* ..
139* .. Array Arguments ..
140 REAL D( * )
141 COMPLEX B( LDB, * ), E( * ), X( LDX, * )
142* ..
143*
144* =====================================================================
145*
146* .. Parameters ..
147 REAL ONE, ZERO
148 parameter( one = 1.0e+0, zero = 0.0e+0 )
149* ..
150* .. Local Scalars ..
151 INTEGER I, J
152* ..
153* .. External Functions ..
154 LOGICAL LSAME
155 EXTERNAL lsame
156* ..
157* .. Intrinsic Functions ..
158 INTRINSIC conjg
159* ..
160* .. Executable Statements ..
161*
162 IF( n.EQ.0 )
163 $ RETURN
164*
165 IF( beta.EQ.zero ) THEN
166 DO 20 j = 1, nrhs
167 DO 10 i = 1, n
168 b( i, j ) = zero
169 10 CONTINUE
170 20 CONTINUE
171 ELSE IF( beta.EQ.-one ) THEN
172 DO 40 j = 1, nrhs
173 DO 30 i = 1, n
174 b( i, j ) = -b( i, j )
175 30 CONTINUE
176 40 CONTINUE
177 END IF
178*
179 IF( alpha.EQ.one ) THEN
180 IF( lsame( uplo, 'U' ) ) THEN
181*
182* Compute B := B + A*X, where E is the superdiagonal of A.
183*
184 DO 60 j = 1, nrhs
185 IF( n.EQ.1 ) THEN
186 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
187 ELSE
188 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
189 $ e( 1 )*x( 2, j )
190 b( n, j ) = b( n, j ) + conjg( e( n-1 ) )*
191 $ x( n-1, j ) + d( n )*x( n, j )
192 DO 50 i = 2, n - 1
193 b( i, j ) = b( i, j ) + conjg( e( i-1 ) )*
194 $ x( i-1, j ) + d( i )*x( i, j ) +
195 $ e( i )*x( i+1, j )
196 50 CONTINUE
197 END IF
198 60 CONTINUE
199 ELSE
200*
201* Compute B := B + A*X, where E is the subdiagonal of A.
202*
203 DO 80 j = 1, nrhs
204 IF( n.EQ.1 ) THEN
205 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
206 ELSE
207 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
208 $ conjg( e( 1 ) )*x( 2, j )
209 b( n, j ) = b( n, j ) + e( n-1 )*x( n-1, j ) +
210 $ d( n )*x( n, j )
211 DO 70 i = 2, n - 1
212 b( i, j ) = b( i, j ) + e( i-1 )*x( i-1, j ) +
213 $ d( i )*x( i, j ) +
214 $ conjg( e( i ) )*x( i+1, j )
215 70 CONTINUE
216 END IF
217 80 CONTINUE
218 END IF
219 ELSE IF( alpha.EQ.-one ) THEN
220 IF( lsame( uplo, 'U' ) ) THEN
221*
222* Compute B := B - A*X, where E is the superdiagonal of A.
223*
224 DO 100 j = 1, nrhs
225 IF( n.EQ.1 ) THEN
226 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
227 ELSE
228 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
229 $ e( 1 )*x( 2, j )
230 b( n, j ) = b( n, j ) - conjg( e( n-1 ) )*
231 $ x( n-1, j ) - d( n )*x( n, j )
232 DO 90 i = 2, n - 1
233 b( i, j ) = b( i, j ) - conjg( e( i-1 ) )*
234 $ x( i-1, j ) - d( i )*x( i, j ) -
235 $ e( i )*x( i+1, j )
236 90 CONTINUE
237 END IF
238 100 CONTINUE
239 ELSE
240*
241* Compute B := B - A*X, where E is the subdiagonal of A.
242*
243 DO 120 j = 1, nrhs
244 IF( n.EQ.1 ) THEN
245 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
246 ELSE
247 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
248 $ conjg( e( 1 ) )*x( 2, j )
249 b( n, j ) = b( n, j ) - e( n-1 )*x( n-1, j ) -
250 $ d( n )*x( n, j )
251 DO 110 i = 2, n - 1
252 b( i, j ) = b( i, j ) - e( i-1 )*x( i-1, j ) -
253 $ d( i )*x( i, j ) -
254 $ conjg( e( i ) )*x( i+1, j )
255 110 CONTINUE
256 END IF
257 120 CONTINUE
258 END IF
259 END IF
260 RETURN
261*
262* End of CLAPTM
263*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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