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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