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