.TH "lacn2" 3 "Tue Jan 28 2025 00:54:31" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lacn2 \- lacn2: 1-norm estimate, e\&.g\&., || A^{-1} ||_1 in gecon
.SH SYNOPSIS
.br
.PP
.SS "Functions"
.in +1c
.ti -1c
.RI "subroutine \fBclacn2\fP (n, v, x, est, kase, isave)"
.br
.RI "\fBCLACN2\fP estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products\&. "
.ti -1c
.RI "subroutine \fBdlacn2\fP (n, v, x, isgn, est, kase, isave)"
.br
.RI "\fBDLACN2\fP estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products\&. "
.ti -1c
.RI "subroutine \fBslacn2\fP (n, v, x, isgn, est, kase, isave)"
.br
.RI "\fBSLACN2\fP estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products\&. "
.ti -1c
.RI "subroutine \fBzlacn2\fP (n, v, x, est, kase, isave)"
.br
.RI "\fBZLACN2\fP estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products\&. "
.in -1c
.SH "Detailed Description"
.PP
.SH "Function Documentation"
.PP
.SS "subroutine clacn2 (integer n, complex, dimension( * ) v, complex, dimension( * ) x, real est, integer kase, integer, dimension( 3 ) isave)"
.PP
\fBCLACN2\fP estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products\&.
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
CLACN2 estimates the 1-norm of a square, complex matrix A\&.
Reverse communication is used for evaluating matrix-vector products\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP
.PP
.nf
N is INTEGER
The order of the matrix\&. N >= 1\&.
.fi
.PP
.br
\fIV\fP
.PP
.nf
V is COMPLEX array, dimension (N)
On the final return, V = A*W, where EST = norm(V)/norm(W)
(W is not returned)\&.
.fi
.PP
.br
\fIX\fP
.PP
.nf
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\&.
.fi
.PP
.br
\fIEST\fP
.PP
.nf
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)\&.
.fi
.PP
.br
\fIKASE\fP
.PP
.nf
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\&.
.fi
.PP
.br
\fIISAVE\fP
.PP
.nf
ISAVE is INTEGER array, dimension (3)
ISAVE is used to save variables between calls to SLACN2
.fi
.PP
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee
.PP
Univ\&. of California Berkeley
.PP
Univ\&. of Colorado Denver
.PP
NAG Ltd\&.
.RE
.PP
\fBFurther Details:\fP
.RS 4
.PP
.nf
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)
.fi
.PP
.RE
.PP
\fBContributors:\fP
.RS 4
Nick Higham, University of Manchester
.RE
.PP
\fBReferences:\fP
.RS 4
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\&.
.RE
.PP
.SS "subroutine dlacn2 (integer n, double precision, dimension( * ) v, double precision, dimension( * ) x, integer, dimension( * ) isgn, double precision est, integer kase, integer, dimension( 3 ) isave)"
.PP
\fBDLACN2\fP estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products\&.
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
DLACN2 estimates the 1-norm of a square, real matrix A\&.
Reverse communication is used for evaluating matrix-vector products\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP
.PP
.nf
N is INTEGER
The order of the matrix\&. N >= 1\&.
.fi
.PP
.br
\fIV\fP
.PP
.nf
V is DOUBLE PRECISION array, dimension (N)
On the final return, V = A*W, where EST = norm(V)/norm(W)
(W is not returned)\&.
.fi
.PP
.br
\fIX\fP
.PP
.nf
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\&.
.fi
.PP
.br
\fIISGN\fP
.PP
.nf
ISGN is INTEGER array, dimension (N)
.fi
.PP
.br
\fIEST\fP
.PP
.nf
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)\&.
.fi
.PP
.br
\fIKASE\fP
.PP
.nf
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\&.
.fi
.PP
.br
\fIISAVE\fP
.PP
.nf
ISAVE is INTEGER array, dimension (3)
ISAVE is used to save variables between calls to DLACN2
.fi
.PP
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee
.PP
Univ\&. of California Berkeley
.PP
Univ\&. of Colorado Denver
.PP
NAG Ltd\&.
.RE
.PP
\fBFurther Details:\fP
.RS 4
.PP
.nf
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)
.fi
.PP
.RE
.PP
\fBContributors:\fP
.RS 4
Nick Higham, University of Manchester
.RE
.PP
\fBReferences:\fP
.RS 4
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\&.
.RE
.PP
.SS "subroutine slacn2 (integer n, real, dimension( * ) v, real, dimension( * ) x, integer, dimension( * ) isgn, real est, integer kase, integer, dimension( 3 ) isave)"
.PP
\fBSLACN2\fP estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products\&.
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
SLACN2 estimates the 1-norm of a square, real matrix A\&.
Reverse communication is used for evaluating matrix-vector products\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP
.PP
.nf
N is INTEGER
The order of the matrix\&. N >= 1\&.
.fi
.PP
.br
\fIV\fP
.PP
.nf
V is REAL array, dimension (N)
On the final return, V = A*W, where EST = norm(V)/norm(W)
(W is not returned)\&.
.fi
.PP
.br
\fIX\fP
.PP
.nf
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\&.
.fi
.PP
.br
\fIISGN\fP
.PP
.nf
ISGN is INTEGER array, dimension (N)
.fi
.PP
.br
\fIEST\fP
.PP
.nf
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)\&.
.fi
.PP
.br
\fIKASE\fP
.PP
.nf
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\&.
.fi
.PP
.br
\fIISAVE\fP
.PP
.nf
ISAVE is INTEGER array, dimension (3)
ISAVE is used to save variables between calls to SLACN2
.fi
.PP
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee
.PP
Univ\&. of California Berkeley
.PP
Univ\&. of Colorado Denver
.PP
NAG Ltd\&.
.RE
.PP
\fBFurther Details:\fP
.RS 4
.PP
.nf
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)
.fi
.PP
.RE
.PP
\fBContributors:\fP
.RS 4
Nick Higham, University of Manchester
.RE
.PP
\fBReferences:\fP
.RS 4
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\&.
.RE
.PP
.SS "subroutine zlacn2 (integer n, complex*16, dimension( * ) v, complex*16, dimension( * ) x, double precision est, integer kase, integer, dimension( 3 ) isave)"
.PP
\fBZLACN2\fP estimates the 1-norm of a square matrix, using reverse communication for evaluating matrix-vector products\&.
.PP
\fBPurpose:\fP
.RS 4
.PP
.nf
ZLACN2 estimates the 1-norm of a square, complex matrix A\&.
Reverse communication is used for evaluating matrix-vector products\&.
.fi
.PP
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP
.PP
.nf
N is INTEGER
The order of the matrix\&. N >= 1\&.
.fi
.PP
.br
\fIV\fP
.PP
.nf
V is COMPLEX*16 array, dimension (N)
On the final return, V = A*W, where EST = norm(V)/norm(W)
(W is not returned)\&.
.fi
.PP
.br
\fIX\fP
.PP
.nf
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\&.
.fi
.PP
.br
\fIEST\fP
.PP
.nf
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)\&.
.fi
.PP
.br
\fIKASE\fP
.PP
.nf
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\&.
.fi
.PP
.br
\fIISAVE\fP
.PP
.nf
ISAVE is INTEGER array, dimension (3)
ISAVE is used to save variables between calls to ZLACN2
.fi
.PP
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee
.PP
Univ\&. of California Berkeley
.PP
Univ\&. of Colorado Denver
.PP
NAG Ltd\&.
.RE
.PP
\fBFurther Details:\fP
.RS 4
.PP
.nf
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)
.fi
.PP
.RE
.PP
\fBContributors:\fP
.RS 4
Nick Higham, University of Manchester
.RE
.PP
\fBReferences:\fP
.RS 4
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\&.
.RE
.PP
.SH "Author"
.PP
Generated automatically by Doxygen for LAPACK from the source code\&.