LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ zlaptm()

 subroutine zlaptm ( character UPLO, integer N, integer NRHS, double precision ALPHA, double precision, dimension( * ) D, complex*16, dimension( * ) E, complex*16, dimension( ldx, * ) X, integer LDX, double precision BETA, complex*16, dimension( ldb, * ) B, integer LDB )

ZLAPTM

Purpose:
``` ZLAPTM 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 DOUBLE PRECISION The scalar alpha. ALPHA must be 1. or -1.; otherwise, it is assumed to be 0.``` [in] D ``` D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the tridiagonal matrix A.``` [in] E ``` E is COMPLEX*16 array, dimension (N-1) The (n-1) subdiagonal or superdiagonal elements of A.``` [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).```
Date
December 2016

Definition at line 131 of file zlaptm.f.

131 *
132 * -- LAPACK test routine (version 3.7.0) --
133 * -- LAPACK is a software package provided by Univ. of Tennessee, --
134 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
135 * December 2016
136 *
137 * .. Scalar Arguments ..
138  CHARACTER uplo
139  INTEGER ldb, ldx, n, nrhs
140  DOUBLE PRECISION alpha, beta
141 * ..
142 * .. Array Arguments ..
143  DOUBLE PRECISION d( * )
144  COMPLEX*16 b( ldb, * ), e( * ), x( ldx, * )
145 * ..
146 *
147 * =====================================================================
148 *
149 * .. Parameters ..
150  DOUBLE PRECISION one, zero
151  parameter( one = 1.0d+0, zero = 0.0d+0 )
152 * ..
153 * .. Local Scalars ..
154  INTEGER i, j
155 * ..
156 * .. External Functions ..
157  LOGICAL lsame
158  EXTERNAL lsame
159 * ..
160 * .. Intrinsic Functions ..
161  INTRINSIC dconjg
162 * ..
163 * .. Executable Statements ..
164 *
165  IF( n.EQ.0 )
166  \$ RETURN
167 *
168  IF( beta.EQ.zero ) THEN
169  DO 20 j = 1, nrhs
170  DO 10 i = 1, n
171  b( i, j ) = zero
172  10 CONTINUE
173  20 CONTINUE
174  ELSE IF( beta.EQ.-one ) THEN
175  DO 40 j = 1, nrhs
176  DO 30 i = 1, n
177  b( i, j ) = -b( i, j )
178  30 CONTINUE
179  40 CONTINUE
180  END IF
181 *
182  IF( alpha.EQ.one ) THEN
183  IF( lsame( uplo, 'U' ) ) THEN
184 *
185 * Compute B := B + A*X, where E is the superdiagonal of A.
186 *
187  DO 60 j = 1, nrhs
188  IF( n.EQ.1 ) THEN
189  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
190  ELSE
191  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
192  \$ e( 1 )*x( 2, j )
193  b( n, j ) = b( n, j ) + dconjg( e( n-1 ) )*
194  \$ x( n-1, j ) + d( n )*x( n, j )
195  DO 50 i = 2, n - 1
196  b( i, j ) = b( i, j ) + dconjg( e( i-1 ) )*
197  \$ x( i-1, j ) + d( i )*x( i, j ) +
198  \$ e( i )*x( i+1, j )
199  50 CONTINUE
200  END IF
201  60 CONTINUE
202  ELSE
203 *
204 * Compute B := B + A*X, where E is the subdiagonal of A.
205 *
206  DO 80 j = 1, nrhs
207  IF( n.EQ.1 ) THEN
208  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
209  ELSE
210  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
211  \$ dconjg( e( 1 ) )*x( 2, j )
212  b( n, j ) = b( n, j ) + e( n-1 )*x( n-1, j ) +
213  \$ d( n )*x( n, j )
214  DO 70 i = 2, n - 1
215  b( i, j ) = b( i, j ) + e( i-1 )*x( i-1, j ) +
216  \$ d( i )*x( i, j ) +
217  \$ dconjg( e( i ) )*x( i+1, j )
218  70 CONTINUE
219  END IF
220  80 CONTINUE
221  END IF
222  ELSE IF( alpha.EQ.-one ) THEN
223  IF( lsame( uplo, 'U' ) ) THEN
224 *
225 * Compute B := B - A*X, where E is the superdiagonal of A.
226 *
227  DO 100 j = 1, nrhs
228  IF( n.EQ.1 ) THEN
229  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
230  ELSE
231  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
232  \$ e( 1 )*x( 2, j )
233  b( n, j ) = b( n, j ) - dconjg( e( n-1 ) )*
234  \$ x( n-1, j ) - d( n )*x( n, j )
235  DO 90 i = 2, n - 1
236  b( i, j ) = b( i, j ) - dconjg( e( i-1 ) )*
237  \$ x( i-1, j ) - d( i )*x( i, j ) -
238  \$ e( i )*x( i+1, j )
239  90 CONTINUE
240  END IF
241  100 CONTINUE
242  ELSE
243 *
244 * Compute B := B - A*X, where E is the subdiagonal of A.
245 *
246  DO 120 j = 1, nrhs
247  IF( n.EQ.1 ) THEN
248  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
249  ELSE
250  b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
251  \$ dconjg( e( 1 ) )*x( 2, j )
252  b( n, j ) = b( n, j ) - e( n-1 )*x( n-1, j ) -
253  \$ d( n )*x( n, j )
254  DO 110 i = 2, n - 1
255  b( i, j ) = b( i, j ) - e( i-1 )*x( i-1, j ) -
256  \$ d( i )*x( i, j ) -
257  \$ dconjg( e( i ) )*x( i+1, j )
258  110 CONTINUE
259  END IF
260  120 CONTINUE
261  END IF
262  END IF
263  RETURN
264 *
265 * End of ZLAPTM
266 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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