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 ofa real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

  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 ofa real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

  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 ofa real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

  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 ofa real or complex matrix, with applications to condition estimation", ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.

Author

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