LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dlaptm()

 subroutine dlaptm ( integer N, integer NRHS, double precision ALPHA, double precision, dimension( * ) D, double precision, dimension( * ) E, double precision, dimension( ldx, * ) X, integer LDX, double precision BETA, double precision, dimension( ldb, * ) B, integer LDB )

DLAPTM

Purpose:
``` DLAPTM multiplies an N by NRHS matrix X by a symmetric 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] 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 DOUBLE PRECISION array, dimension (N-1) The (n-1) subdiagonal or superdiagonal elements of A.``` [in] X ``` X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 118 of file dlaptm.f.

118 *
119 * -- LAPACK test routine (version 3.7.0) --
120 * -- LAPACK is a software package provided by Univ. of Tennessee, --
121 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
122 * December 2016
123 *
124 * .. Scalar Arguments ..
125  INTEGER ldb, ldx, n, nrhs
126  DOUBLE PRECISION alpha, beta
127 * ..
128 * .. Array Arguments ..
129  DOUBLE PRECISION b( ldb, * ), d( * ), e( * ), x( ldx, * )
130 * ..
131 *
132 * =====================================================================
133 *
134 * .. Parameters ..
135  DOUBLE PRECISION one, zero
136  parameter( one = 1.0d+0, zero = 0.0d+0 )
137 * ..
138 * .. Local Scalars ..
139  INTEGER i, j
140 * ..
141 * .. Executable Statements ..
142 *
143  IF( n.EQ.0 )
144  \$ RETURN
145 *
146 * Multiply B by BETA if BETA.NE.1.
147 *
148  IF( beta.EQ.zero ) THEN
149  DO 20 j = 1, nrhs
150  DO 10 i = 1, n
151  b( i, j ) = zero
152  10 CONTINUE
153  20 CONTINUE
154  ELSE IF( beta.EQ.-one ) THEN
155  DO 40 j = 1, nrhs
156  DO 30 i = 1, n
157  b( i, j ) = -b( i, j )
158  30 CONTINUE
159  40 CONTINUE
160  END IF
161 *
162  IF( alpha.EQ.one ) THEN
163 *
164 * Compute B := B + A*X
165 *
166  DO 60 j = 1, nrhs
167  IF( n.EQ.1 ) THEN
168  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
169  ELSE
170  b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
171  \$ e( 1 )*x( 2, j )
172  b( n, j ) = b( n, j ) + e( n-1 )*x( n-1, j ) +
173  \$ d( n )*x( n, j )
174  DO 50 i = 2, n - 1
175  b( i, j ) = b( i, j ) + e( i-1 )*x( i-1, j ) +
176  \$ d( i )*x( i, j ) + e( i )*x( i+1, j )
177  50 CONTINUE
178  END IF
179  60 CONTINUE
180  ELSE IF( alpha.EQ.-one ) THEN
181 *
182 * Compute B := B - A*X
183 *
184  DO 80 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 ) - e( n-1 )*x( n-1, j ) -
191  \$ d( n )*x( n, j )
192  DO 70 i = 2, n - 1
193  b( i, j ) = b( i, j ) - e( i-1 )*x( i-1, j ) -
194  \$ d( i )*x( i, j ) - e( i )*x( i+1, j )
195  70 CONTINUE
196  END IF
197  80 CONTINUE
198  END IF
199  RETURN
200 *
201 * End of DLAPTM
202 *
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