lacn2(3) LAPACK lacn2(3)

lacn2 - lacn2: 1-norm estimate, e.g., || A^{-1} ||_1 in gecon


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.

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.

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.

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.

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.

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