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lacn2(3) Library Functions Manual 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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