.TH "lacn2" 3 "Wed Feb 7 2024 11:30:40" "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\&.