table of contents
| 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Last modified: April, 1999
Contributors:
References:
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Originally named SONEST, dated March 16, 1988.
References:
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Originally named SONEST, dated March 16, 1988.
References:
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
Last modified: April, 1999
Contributors:
References:
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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