LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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).```

Definition at line 115 of file dlaptm.f.

116*
117* -- LAPACK test routine --
118* -- LAPACK is a software package provided by Univ. of Tennessee, --
119* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120*
121* .. Scalar Arguments ..
122 INTEGER LDB, LDX, N, NRHS
123 DOUBLE PRECISION ALPHA, BETA
124* ..
125* .. Array Arguments ..
126 DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), X( LDX, * )
127* ..
128*
129* =====================================================================
130*
131* .. Parameters ..
132 DOUBLE PRECISION ONE, ZERO
133 parameter( one = 1.0d+0, zero = 0.0d+0 )
134* ..
135* .. Local Scalars ..
136 INTEGER I, J
137* ..
138* .. Executable Statements ..
139*
140 IF( n.EQ.0 )
141 \$ RETURN
142*
143* Multiply B by BETA if BETA.NE.1.
144*
145 IF( beta.EQ.zero ) THEN
146 DO 20 j = 1, nrhs
147 DO 10 i = 1, n
148 b( i, j ) = zero
149 10 CONTINUE
150 20 CONTINUE
151 ELSE IF( beta.EQ.-one ) THEN
152 DO 40 j = 1, nrhs
153 DO 30 i = 1, n
154 b( i, j ) = -b( i, j )
155 30 CONTINUE
156 40 CONTINUE
157 END IF
158*
159 IF( alpha.EQ.one ) THEN
160*
161* Compute B := B + A*X
162*
163 DO 60 j = 1, nrhs
164 IF( n.EQ.1 ) THEN
165 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j )
166 ELSE
167 b( 1, j ) = b( 1, j ) + d( 1 )*x( 1, j ) +
168 \$ e( 1 )*x( 2, j )
169 b( n, j ) = b( n, j ) + e( n-1 )*x( n-1, j ) +
170 \$ d( n )*x( n, j )
171 DO 50 i = 2, n - 1
172 b( i, j ) = b( i, j ) + e( i-1 )*x( i-1, j ) +
173 \$ d( i )*x( i, j ) + e( i )*x( i+1, j )
174 50 CONTINUE
175 END IF
176 60 CONTINUE
177 ELSE IF( alpha.EQ.-one ) THEN
178*
179* Compute B := B - A*X
180*
181 DO 80 j = 1, nrhs
182 IF( n.EQ.1 ) THEN
183 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j )
184 ELSE
185 b( 1, j ) = b( 1, j ) - d( 1 )*x( 1, j ) -
186 \$ e( 1 )*x( 2, j )
187 b( n, j ) = b( n, j ) - e( n-1 )*x( n-1, j ) -
188 \$ d( n )*x( n, j )
189 DO 70 i = 2, n - 1
190 b( i, j ) = b( i, j ) - e( i-1 )*x( i-1, j ) -
191 \$ d( i )*x( i, j ) - e( i )*x( i+1, j )
192 70 CONTINUE
193 END IF
194 80 CONTINUE
195 END IF
196 RETURN
197*
198* End of DLAPTM
199*
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