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lacon(3) LAPACK 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.

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.

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.

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.

Author

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