lacon(3)

NAME
lacon - lacon: 1-norm estimate, e.g., || A^{-1} ||_1 in gecon, old

SYNOPSIS

  Functions
subroutine clacon (n, v, x, est, kase)
CLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine dlacon (n, v, x, isgn, est, kase)
DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine slacon (n, v, x, isgn, est, kase)
SLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine zlacon (n, v, x, est, kase)
ZLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Detailed Description

Function Documentation

  subroutine clacon (integer n, complex, dimension( n ) v, complex, dimension( n ) x, real est, integer kase)

CLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

     CLACON estimates the 1-norm of a square, complex matrix A.
     Reverse communication is used for evaluating matrix-vector products.

Parameters
    N

              N is INTEGER
             The order of the matrix.  N >= 1.

    V

              V is COMPLEX array, dimension (N)
             On the final return, V = A*W,  where  EST = norm(V)/norm(W)
             (W is not returned).

    X

              X is COMPLEX array, dimension (N)
             On an intermediate return, X should be overwritten by
                   A * X,   if KASE=1,
                   A**H * X,  if KASE=2,
             where A**H is the conjugate transpose of A, and CLACON must be
             re-called with all the other parameters unchanged.

    EST

              EST is REAL
             On entry with KASE = 1 or 2 and JUMP = 3, EST should be
             unchanged from the previous call to CLACON.
             On exit, EST is an estimate (a lower bound) for norm(A).

    KASE

              KASE is INTEGER
             On the initial call to CLACON, KASE should be 0.
             On an intermediate return, KASE will be 1 or 2, indicating
             whether X should be overwritten by A * X  or A**H * X.
             On the final return from CLACON, KASE will again be 0.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:
    Originally named CONEST, dated March 16, 1988.
     Last modified: April, 1999

Contributors:
    Nick Higham, University of Manchester

References:
    N.J. Higham, 'FORTRAN codes for estimating the one-norm of
      a real or complex matrix, with applications to condition estimation', ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 113 of file clacon.f.

  subroutine dlacon (integer n, double precision, dimension( * ) v, double precision, dimension( * ) x, integer, dimension( * ) isgn, double precision est, integer kase)

DLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

     DLACON estimates the 1-norm of a square, real matrix A.
     Reverse communication is used for evaluating matrix-vector products.

Parameters
    N

              N is INTEGER
             The order of the matrix.  N >= 1.

    V

              V is DOUBLE PRECISION array, dimension (N)
             On the final return, V = A*W,  where  EST = norm(V)/norm(W)
             (W is not returned).

    X

              X is DOUBLE PRECISION array, dimension (N)
             On an intermediate return, X should be overwritten by
                   A * X,   if KASE=1,
                   A**T * X,  if KASE=2,
             and DLACON must be re-called with all the other parameters
             unchanged.

    ISGN

              ISGN is INTEGER array, dimension (N)

    EST

              EST is DOUBLE PRECISION
             On entry with KASE = 1 or 2 and JUMP = 3, EST should be
             unchanged from the previous call to DLACON.
             On exit, EST is an estimate (a lower bound) for norm(A).

    KASE

              KASE is INTEGER
             On the initial call to DLACON, KASE should be 0.
             On an intermediate return, KASE will be 1 or 2, indicating
             whether X should be overwritten by A * X  or A**T * X.
             On the final return from DLACON, KASE will again be 0.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Nick Higham, University of Manchester.
     Originally named SONEST, dated March 16, 1988.

References:
    N.J. Higham, 'FORTRAN codes for estimating the one-norm of
      a real or complex matrix, with applications to condition estimation', ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 114 of file dlacon.f.

  subroutine slacon (integer n, real, dimension( * ) v, real, dimension( * ) x, integer, dimension( * ) isgn, real est, integer kase)

SLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

     SLACON estimates the 1-norm of a square, real matrix A.
     Reverse communication is used for evaluating matrix-vector products.

Parameters
    N

              N is INTEGER
             The order of the matrix.  N >= 1.

    V

              V is REAL array, dimension (N)
             On the final return, V = A*W,  where  EST = norm(V)/norm(W)
             (W is not returned).

    X

              X is REAL array, dimension (N)
             On an intermediate return, X should be overwritten by
                   A * X,   if KASE=1,
                   A**T * X,  if KASE=2,
             and SLACON must be re-called with all the other parameters
             unchanged.

    ISGN

              ISGN is INTEGER array, dimension (N)

    EST

              EST is REAL
             On entry with KASE = 1 or 2 and JUMP = 3, EST should be
             unchanged from the previous call to SLACON.
             On exit, EST is an estimate (a lower bound) for norm(A).

    KASE

              KASE is INTEGER
             On the initial call to SLACON, KASE should be 0.
             On an intermediate return, KASE will be 1 or 2, indicating
             whether X should be overwritten by A * X  or A**T * X.
             On the final return from SLACON, KASE will again be 0.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Nick Higham, University of Manchester.
     Originally named SONEST, dated March 16, 1988.

References:
    N.J. Higham, 'FORTRAN codes for estimating the one-norm of
      a real or complex matrix, with applications to condition estimation', ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 114 of file slacon.f.

  subroutine zlacon (integer n, complex*16, dimension( n ) v, complex*16, dimension( n ) x, double precision est, integer kase)

ZLACON estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

     ZLACON estimates the 1-norm of a square, complex matrix A.
     Reverse communication is used for evaluating matrix-vector products.

Parameters
    N

              N is INTEGER
             The order of the matrix.  N >= 1.

    V

              V is COMPLEX*16 array, dimension (N)
             On the final return, V = A*W,  where  EST = norm(V)/norm(W)
             (W is not returned).

    X

              X is COMPLEX*16 array, dimension (N)
             On an intermediate return, X should be overwritten by
                   A * X,   if KASE=1,
                   A**H * X,  if KASE=2,
             where A**H is the conjugate transpose of A, and ZLACON must be
             re-called with all the other parameters unchanged.

    EST

              EST is DOUBLE PRECISION
             On entry with KASE = 1 or 2 and JUMP = 3, EST should be
             unchanged from the previous call to ZLACON.
             On exit, EST is an estimate (a lower bound) for norm(A).

    KASE

              KASE is INTEGER
             On the initial call to ZLACON, KASE should be 0.
             On an intermediate return, KASE will be 1 or 2, indicating
             whether X should be overwritten by A * X  or A**H * X.
             On the final return from ZLACON, KASE will again be 0.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:
    Originally named CONEST, dated March 16, 1988.
     Last modified: April, 1999

Contributors:
    Nick Higham, University of Manchester

References:
    N.J. Higham, 'FORTRAN codes for estimating the one-norm of
      a real or complex matrix, with applications to condition estimation', ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Definition at line 113 of file zlacon.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.