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 is INTEGER


         The order of the matrix.  N >= 1.



          V is COMPLEX array, dimension (N)


         On the final return, V = A*W,  where  EST = norm(V)/norm(W)


         (W is not returned).



          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 is INTEGER


         The order of the matrix.  N >= 1.



          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 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 is INTEGER


         The order of the matrix.  N >= 1.



          V is REAL array, dimension (N)


         On the final return, V = A*W,  where  EST = norm(V)/norm(W)


         (W is not returned).



          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, complex16, dimension( ) v, complex16, 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 is INTEGER


         The order of the matrix.  N >= 1.



          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 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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