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SUBROUTINE CLAPTM( UPLO, N, NRHS, ALPHA, D, E, X, LDX, BETA, B,
$ LDB )
*
* -- LAPACK auxiliary routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* February 29, 1992
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDB, LDX, N, NRHS
REAL ALPHA, BETA
* ..
* .. Array Arguments ..
REAL D( * )
COMPLEX B( LDB, * ), E( * ), X( LDX, * )
* ..
*
* 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.
*
* Arguments
* =========
*
* UPLO (input) 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.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrices X and B.
*
* ALPHA (input) REAL
* The scalar alpha. ALPHA must be 1. or -1.; otherwise,
* it is assumed to be 0.
*
* D (input) REAL array, dimension (N)
* The n diagonal elements of the tridiagonal matrix A.
*
* E (input) COMPLEX array, dimension (N-1)
* The (n-1) subdiagonal or superdiagonal elements of A.
*
* X (input) COMPLEX array, dimension (LDX,NRHS)
* The N by NRHS matrix X.
*
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(N,1).
*
* BETA (input) REAL
* The scalar beta. BETA must be 0., 1., or -1.; otherwise,
* it is assumed to be 1.
*
* B (input/output) 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.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(N,1).
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG
* ..
* .. Executable Statements ..
*
IF( N.EQ.0 )
$ RETURN
*
IF( BETA.EQ.ZERO ) THEN
DO 20 J = 1, NRHS
DO 10 I = 1, N
B( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
ELSE IF( BETA.EQ.-ONE ) THEN
DO 40 J = 1, NRHS
DO 30 I = 1, N
B( I, J ) = -B( I, J )
30 CONTINUE
40 CONTINUE
END IF
*
IF( ALPHA.EQ.ONE ) THEN
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Compute B := B + A*X, where E is the superdiagonal of A.
*
DO 60 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
$ E( 1 )*X( 2, J )
B( N, J ) = B( N, J ) + CONJG( E( N-1 ) )*
$ X( N-1, J ) + D( N )*X( N, J )
DO 50 I = 2, N - 1
B( I, J ) = B( I, J ) + CONJG( E( I-1 ) )*
$ X( I-1, J ) + D( I )*X( I, J ) +
$ E( I )*X( I+1, J )
50 CONTINUE
END IF
60 CONTINUE
ELSE
*
* Compute B := B + A*X, where E is the subdiagonal of A.
*
DO 80 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
$ CONJG( E( 1 ) )*X( 2, J )
B( N, J ) = B( N, J ) + E( N-1 )*X( N-1, J ) +
$ D( N )*X( N, J )
DO 70 I = 2, N - 1
B( I, J ) = B( I, J ) + E( I-1 )*X( I-1, J ) +
$ D( I )*X( I, J ) +
$ CONJG( E( I ) )*X( I+1, J )
70 CONTINUE
END IF
80 CONTINUE
END IF
ELSE IF( ALPHA.EQ.-ONE ) THEN
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Compute B := B - A*X, where E is the superdiagonal of A.
*
DO 100 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
$ E( 1 )*X( 2, J )
B( N, J ) = B( N, J ) - CONJG( E( N-1 ) )*
$ X( N-1, J ) - D( N )*X( N, J )
DO 90 I = 2, N - 1
B( I, J ) = B( I, J ) - CONJG( E( I-1 ) )*
$ X( I-1, J ) - D( I )*X( I, J ) -
$ E( I )*X( I+1, J )
90 CONTINUE
END IF
100 CONTINUE
ELSE
*
* Compute B := B - A*X, where E is the subdiagonal of A.
*
DO 120 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
$ CONJG( E( 1 ) )*X( 2, J )
B( N, J ) = B( N, J ) - E( N-1 )*X( N-1, J ) -
$ D( N )*X( N, J )
DO 110 I = 2, N - 1
B( I, J ) = B( I, J ) - E( I-1 )*X( I-1, J ) -
$ D( I )*X( I, J ) -
$ CONJG( E( I ) )*X( I+1, J )
110 CONTINUE
END IF
120 CONTINUE
END IF
END IF
RETURN
*
* End of CLAPTM
*
END
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