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lacon(3) Library Functions Manual 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

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