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NAME DSBTRD - reduce a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transforma- tion SYNOPSIS SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO ) CHARACTER UPLO, VECT INTEGER INFO, KD, LDAB, LDQ, N DOUBLE PRECISION AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ), WORK( * ) PURPOSE DSBTRD reduces a real symmetric band matrix A to symmetric tridiagonal form T by an orthogonal similarity transforma- tion: Q**T * A * Q = T. ARGUMENTS VECT (input) CHARACTER*1 = 'N': do not form Q; = 'V': form Q. UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) On entry, the upper or lower triangle of the sym- metric band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, the diagonal elements of A are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the offdiagonal elements of T; the rest of A is overwritten by values generated during the reduc- tion. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. D (output) DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T. E (output) DOUBLE PRECISION array, dimension (N-1) The off-diagonal elements of the tridiagonal matrix T: E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. Q (output) DOUBLE PRECISION array, dimension (LDQ,N) If VECT = 'V', the N-by-N orthogonal matrix Q. If VECT = 'N', the array Q is not referenced. LDQ (input) INTEGER The leading dimension of the array Q. LDQ >= max(1,N) if VECT = 'V'. WORK (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value