DLAGTF factorizes the matrix (T - lambda*I), where T is an n by n


 tridiagonal matrix and lambda is a scalar, as


    T - lambda*I = PLU,


 where P is a permutation matrix, L is a unit lower tridiagonal matrix


 with at most one non-zero sub-diagonal elements per column and U is


 an upper triangular matrix with at most two non-zero super-diagonal


 elements per column.


 The factorization is obtained by Gaussian elimination with partial


 pivoting and implicit row scaling.


 The parameter LAMBDA is included in the routine so that DLAGTF may


 be used, in conjunction with DLAGTS, to obtain eigenvectors of T by


 inverse iteration.

N

          N is INTEGER


          The order of the matrix T.

A

          A is DOUBLE PRECISION array, dimension (N)


          On entry, A must contain the diagonal elements of T.


          On exit, A is overwritten by the n diagonal elements of the


          upper triangular matrix U of the factorization of T.

LAMBDA

          LAMBDA is DOUBLE PRECISION


          On entry, the scalar lambda.

B

          B is DOUBLE PRECISION array, dimension (N-1)


          On entry, B must contain the (n-1) super-diagonal elements of


          T.


          On exit, B is overwritten by the (n-1) super-diagonal


          elements of the matrix U of the factorization of T.

C

          C is DOUBLE PRECISION array, dimension (N-1)


          On entry, C must contain the (n-1) sub-diagonal elements of


          T.


          On exit, C is overwritten by the (n-1) sub-diagonal elements


          of the matrix L of the factorization of T.

TOL

          TOL is DOUBLE PRECISION


          On entry, a relative tolerance used to indicate whether or


          not the matrix (T - lambda*I) is nearly singular. TOL should


          normally be chose as approximately the largest relative error


          in the elements of T. For example, if the elements of T are


          correct to about 4 significant figures, then TOL should be


          set to about 5*10**(-4). If TOL is supplied as less than eps,


          where eps is the relative machine precision, then the value


          eps is used in place of TOL.

D

          D is DOUBLE PRECISION array, dimension (N-2)


          On exit, D is overwritten by the (n-2) second super-diagonal


          elements of the matrix U of the factorization of T.

IN

          IN is INTEGER array, dimension (N)


          On exit, IN contains details of the permutation matrix P. If


          an interchange occurred at the kth step of the elimination,


          then IN(k) = 1, otherwise IN(k) = 0. The element IN(n)


          returns the smallest positive integer j such that


             abs( u(j,j) ) <= norm( (T - lambda*I)(j) )*TOL,


          where norm( A(j) ) denotes the sum of the absolute values of


          the jth row of the matrix A. If no such j exists then IN(n)


          is returned as zero. If IN(n) is returned as positive, then a


          diagonal element of U is small, indicating that


          (T - lambda*I) is singular or nearly singular,

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -k, the kth argument had an illegal value

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 SLAGTF factorizes the matrix (T - lambda*I), where T is an n by n


 tridiagonal matrix and lambda is a scalar, as


    T - lambda*I = PLU,


 where P is a permutation matrix, L is a unit lower tridiagonal matrix


 with at most one non-zero sub-diagonal elements per column and U is


 an upper triangular matrix with at most two non-zero super-diagonal


 elements per column.


 The factorization is obtained by Gaussian elimination with partial


 pivoting and implicit row scaling.


 The parameter LAMBDA is included in the routine so that SLAGTF may


 be used, in conjunction with SLAGTS, to obtain eigenvectors of T by


 inverse iteration.

N

          N is INTEGER


          The order of the matrix T.

A

          A is REAL array, dimension (N)


          On entry, A must contain the diagonal elements of T.


          On exit, A is overwritten by the n diagonal elements of the


          upper triangular matrix U of the factorization of T.

LAMBDA

          LAMBDA is REAL


          On entry, the scalar lambda.

B

          B is REAL array, dimension (N-1)


          On entry, B must contain the (n-1) super-diagonal elements of


          T.


          On exit, B is overwritten by the (n-1) super-diagonal


          elements of the matrix U of the factorization of T.

C

          C is REAL array, dimension (N-1)


          On entry, C must contain the (n-1) sub-diagonal elements of


          T.


          On exit, C is overwritten by the (n-1) sub-diagonal elements


          of the matrix L of the factorization of T.

TOL

          TOL is REAL


          On entry, a relative tolerance used to indicate whether or


          not the matrix (T - lambda*I) is nearly singular. TOL should


          normally be chose as approximately the largest relative error


          in the elements of T. For example, if the elements of T are


          correct to about 4 significant figures, then TOL should be


          set to about 5*10**(-4). If TOL is supplied as less than eps,


          where eps is the relative machine precision, then the value


          eps is used in place of TOL.

D

          D is REAL array, dimension (N-2)


          On exit, D is overwritten by the (n-2) second super-diagonal


          elements of the matrix U of the factorization of T.

IN

          IN is INTEGER array, dimension (N)


          On exit, IN contains details of the permutation matrix P. If


          an interchange occurred at the kth step of the elimination,


          then IN(k) = 1, otherwise IN(k) = 0. The element IN(n)


          returns the smallest positive integer j such that


             abs( u(j,j) ) <= norm( (T - lambda*I)(j) )*TOL,


          where norm( A(j) ) denotes the sum of the absolute values of


          the jth row of the matrix A. If no such j exists then IN(n)


          is returned as zero. If IN(n) is returned as positive, then a


          diagonal element of U is small, indicating that


          (T - lambda*I) is singular or nearly singular,

INFO

          INFO is INTEGER


          = 0: successful exit


          < 0: if INFO = -k, the kth argument had an illegal value

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.