table of contents
| lacn2(3) | LAPACK | 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 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 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:
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 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
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 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:
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 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
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 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:
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 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 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 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:
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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