lacn2(3) Library Functions Manual 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 !> 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. Definition at line 132 of file clacn2.f. 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 !> 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. Definition at line 135 of file dlacn2.f. 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 !> 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. Definition at line 135 of file slacn2.f. 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 !> 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. Definition at line 132 of file zlacn2.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 lacn2(3)