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SUBROUTINE CPTTRS( UPLO, N, NRHS, D, E, B, LDB, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL D( * )
COMPLEX B( LDB, * ), E( * )
* ..
*
* Purpose
* =======
*
* CPTTRS solves a system of linear equations A * X = B with a
* Hermitian positive definite tridiagonal matrix A using the
* factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* Specifies whether the superdiagonal or the subdiagonal
* of the tridiagonal matrix A is stored and the form of the
* factorization:
* = 'U': E is the superdiagonal of U, and A = U'*D*U;
* = 'L': E is the subdiagonal of L, and A = L*D*L'.
* (The two forms are equivalent if A is real.)
*
* N (input) INTEGER
* The order of the tridiagonal matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrix B. NRHS >= 0.
*
* D (input) REAL array, dimension (N)
* The n diagonal elements of the diagonal matrix D from the
* factorization computed by CPTTRF.
*
* E (input) COMPLEX array, dimension (N-1)
* The (n-1) off-diagonal elements of the unit bidiagonal
* factor U or L from the factorization computed by CPTTRF
* (see UPLO).
*
* B (input/output) REAL array, dimension (LDB,NRHS)
* On entry, the right hand side matrix B.
* On exit, the solution matrix X.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX
* ..
* .. Executable Statements ..
*
* Test the input arguments.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CPTTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( UPPER ) THEN
*
* Solve A * X = B using the factorization A = U'*D*U,
* overwriting each right hand side vector with its solution.
*
DO 30 J = 1, NRHS
*
* Solve U' * x = b.
*
DO 10 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
10 CONTINUE
*
* Solve D * U * x = b.
*
B( N, J ) = B( N, J ) / D( N )
DO 20 I = N - 1, 1, -1
B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
20 CONTINUE
30 CONTINUE
ELSE
*
* Solve A * X = B using the factorization A = L*D*L',
* overwriting each right hand side vector with its solution.
*
DO 60 J = 1, NRHS
*
* Solve L * x = b.
*
DO 40 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
40 CONTINUE
*
* Solve D * L' * x = b.
*
B( N, J ) = B( N, J ) / D( N )
DO 50 I = N - 1, 1, -1
B( I, J ) = B( I, J ) / D( I ) -
$ B( I+1, J )*CONJG( E( I ) )
50 CONTINUE
60 CONTINUE
END IF
*
RETURN
*
* End of CPTTRS
*
END
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