lacn2(3)

NAME
lacn2 - lacn2: 1-norm estimate, e.g., || A^{-1} ||_1 in gecon

SYNOPSIS

  Functions
subroutine clacn2 (n, v, x, est, kase, isave)
CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine dlacn2 (n, v, x, isgn, est, kase, isave)
DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine slacn2 (n, v, x, isgn, est, kase, isave)
SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.
subroutine zlacn2 (n, v, x, est, kase, isave)
ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Detailed Description

Function Documentation

  subroutine clacn2 (integer n, complex, dimension( * ) v, complex, dimension( * ) x, real est, integer kase, integer, dimension( 3 ) isave)

CLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

    !>
    !> CLACN2 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 CLACN2 must be
    !>         re-called with all the other parameters unchanged.
    !>

    EST

    !>          EST is REAL
    !>         On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
    !>         unchanged from the previous call to CLACN2.
    !>         On exit, EST is an estimate (a lower bound) for norm(A).
    !>

    KASE

    !>          KASE is INTEGER
    !>         On the initial call to CLACN2, 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 CLACN2, KASE will again be 0.
    !>

    ISAVE

    !>          ISAVE is INTEGER array, dimension (3)
    !>         ISAVE is used to save variables between calls to SLACN2
    !>

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
    !>
    !>  This is a thread safe version of CLACON, which uses the array ISAVE
    !>  in place of a SAVE statement, as follows:
    !>
    !>     CLACON     CLACN2
    !>      JUMP     ISAVE(1)
    !>      J        ISAVE(2)
    !>      ITER     ISAVE(3)
    !>

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 132 of file clacn2.f.

  subroutine dlacn2 (integer n, double precision, dimension( * ) v, double precision, dimension( * ) x, integer, dimension( * ) isgn, double precision est, integer kase, integer, dimension( 3 ) isave)

DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

    !>
    !> DLACN2 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 DLACN2 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 ISAVE(1) = 3, EST should be
    !>         unchanged from the previous call to DLACN2.
    !>         On exit, EST is an estimate (a lower bound) for norm(A).
    !>

    KASE

    !>          KASE is INTEGER
    !>         On the initial call to DLACN2, 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 DLACN2, KASE will again be 0.
    !>

    ISAVE

    !>          ISAVE is INTEGER array, dimension (3)
    !>         ISAVE is used to save variables between calls to DLACN2
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Originally named SONEST, dated March 16, 1988.
    !>
    !>  This is a thread safe version of DLACON, which uses the array ISAVE
    !>  in place of a SAVE statement, as follows:
    !>
    !>     DLACON     DLACN2
    !>      JUMP     ISAVE(1)
    !>      J        ISAVE(2)
    !>      ITER     ISAVE(3)
    !>

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 135 of file dlacn2.f.

  subroutine slacn2 (integer n, real, dimension( * ) v, real, dimension( * ) x, integer, dimension( * ) isgn, real est, integer kase, integer, dimension( 3 ) isave)

SLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

    !>
    !> SLACN2 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 SLACN2 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 ISAVE(1) = 3, EST should be
    !>         unchanged from the previous call to SLACN2.
    !>         On exit, EST is an estimate (a lower bound) for norm(A).
    !>

    KASE

    !>          KASE is INTEGER
    !>         On the initial call to SLACN2, 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 SLACN2, KASE will again be 0.
    !>

    ISAVE

    !>          ISAVE is INTEGER array, dimension (3)
    !>         ISAVE is used to save variables between calls to SLACN2
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  Originally named SONEST, dated March 16, 1988.
    !>
    !>  This is a thread safe version of SLACON, which uses the array ISAVE
    !>  in place of a SAVE statement, as follows:
    !>
    !>     SLACON     SLACN2
    !>      JUMP     ISAVE(1)
    !>      J        ISAVE(2)
    !>      ITER     ISAVE(3)
    !>

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 135 of file slacn2.f.

  subroutine zlacn2 (integer n, complex*16, dimension( * ) v, complex*16, dimension( * ) x, double precision est, integer kase, integer, dimension( 3 ) isave)

ZLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products.

Purpose:

    !>
    !> ZLACN2 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 ZLACN2 must be
    !>         re-called with all the other parameters unchanged.
    !>

    EST

    !>          EST is DOUBLE PRECISION
    !>         On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
    !>         unchanged from the previous call to ZLACN2.
    !>         On exit, EST is an estimate (a lower bound) for norm(A).
    !>

    KASE

    !>          KASE is INTEGER
    !>         On the initial call to ZLACN2, 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 ZLACN2, KASE will again be 0.
    !>

    ISAVE

    !>          ISAVE is INTEGER array, dimension (3)
    !>         ISAVE is used to save variables between calls to ZLACN2
    !>

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
    !>
    !>  This is a thread safe version of ZLACON, which uses the array ISAVE
    !>  in place of a SAVE statement, as follows:
    !>
    !>     ZLACON     ZLACN2
    !>      JUMP     ISAVE(1)
    !>      J        ISAVE(2)
    !>      ITER     ISAVE(3)
    !>

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 132 of file zlacn2.f.

Author

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