la_hercond(3) Library Functions Manual la_hercond(3) NAME la_hercond - la_hercond: Skeel condition number estimate SYNOPSIS Functions real function cla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork) CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices. real function cla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) CLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices. real function cla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork) CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices. real function cla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices. double precision function dla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork) DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix. real function sla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork) SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix. double precision function zla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork) ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices. double precision function zla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices. double precision function zla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork) ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices. double precision function zla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices. Detailed Description Function Documentation real function cla_hercond_c (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension ( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork) CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices. Purpose: !> !> CLA_HERCOND_C computes the infinity norm condition number of !> op(A) * inv(diag(C)) where C is a REAL vector. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is COMPLEX array, dimension (LDA,N) !> On entry, the N-by-N matrix A !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is COMPLEX array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CHETRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CHETRF. !> C !> C is REAL array, dimension (N) !> The vector C in the formula op(A) * inv(diag(C)). !> CAPPLY !> CAPPLY is LOGICAL !> If .TRUE. then access the vector C in the formula above. !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is COMPLEX array, dimension (2*N). !> Workspace. !> RWORK !> RWORK is REAL array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 136 of file cla_hercond_c.f. real function cla_hercond_x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork) CLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices. Purpose: !> !> CLA_HERCOND_X computes the infinity norm condition number of !> op(A) * diag(X) where X is a COMPLEX vector. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is COMPLEX array, dimension (LDA,N) !> On entry, the N-by-N matrix A. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is COMPLEX array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CHETRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CHETRF. !> X !> X is COMPLEX array, dimension (N) !> The vector X in the formula op(A) * diag(X). !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is COMPLEX array, dimension (2*N). !> Workspace. !> RWORK !> RWORK is REAL array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 129 of file cla_hercond_x.f. real function cla_syrcond_c (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, real, dimension( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork) CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices. Purpose: !> !> CLA_SYRCOND_C Computes the infinity norm condition number of !> op(A) * inv(diag(C)) where C is a REAL vector. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is COMPLEX array, dimension (LDA,N) !> On entry, the N-by-N matrix A !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is COMPLEX array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CSYTRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CSYTRF. !> C !> C is REAL array, dimension (N) !> The vector C in the formula op(A) * inv(diag(C)). !> CAPPLY !> CAPPLY is LOGICAL !> If .TRUE. then access the vector C in the formula above. !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is COMPLEX array, dimension (2*N). !> Workspace. !> RWORK !> RWORK is REAL array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 136 of file cla_syrcond_c.f. real function cla_syrcond_x (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork) CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices. Purpose: !> !> CLA_SYRCOND_X Computes the infinity norm condition number of !> op(A) * diag(X) where X is a COMPLEX vector. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is COMPLEX array, dimension (LDA,N) !> On entry, the N-by-N matrix A. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is COMPLEX array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CSYTRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CSYTRF. !> X !> X is COMPLEX array, dimension (N) !> The vector X in the formula op(A) * diag(X). !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is COMPLEX array, dimension (2*N). !> Workspace. !> RWORK !> RWORK is REAL array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 129 of file cla_syrcond_x.f. double precision function dla_syrcond (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, integer cmode, double precision, dimension( * ) c, integer info, double precision, dimension( * ) work, integer, dimension( * ) iwork) DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix. Purpose: !> !> DLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C) !> where op2 is determined by CMODE as follows !> CMODE = 1 op2(C) = C !> CMODE = 0 op2(C) = I !> CMODE = -1 op2(C) = inv(C) !> The Skeel condition number cond(A) = norminf( |inv(A)||A| ) !> is computed by computing scaling factors R such that !> diag(R)*A*op2(C) is row equilibrated and computing the standard !> infinity-norm condition number. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the N-by-N matrix A. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is DOUBLE PRECISION array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by DSYTRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by DSYTRF. !> CMODE !> CMODE is INTEGER !> Determines op2(C) in the formula op(A) * op2(C) as follows: !> CMODE = 1 op2(C) = C !> CMODE = 0 op2(C) = I !> CMODE = -1 op2(C) = inv(C) !> C !> C is DOUBLE PRECISION array, dimension (N) !> The vector C in the formula op(A) * op2(C). !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is DOUBLE PRECISION array, dimension (3*N). !> Workspace. !> IWORK !> IWORK is INTEGER array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 145 of file dla_syrcond.f. real function sla_syrcond (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork) SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix. Purpose: !> !> SLA_SYRCOND estimates the Skeel condition number of op(A) * op2(C) !> where op2 is determined by CMODE as follows !> CMODE = 1 op2(C) = C !> CMODE = 0 op2(C) = I !> CMODE = -1 op2(C) = inv(C) !> The Skeel condition number cond(A) = norminf( |inv(A)||A| ) !> is computed by computing scaling factors R such that !> diag(R)*A*op2(C) is row equilibrated and computing the standard !> infinity-norm condition number. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is REAL array, dimension (LDA,N) !> On entry, the N-by-N matrix A. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is REAL array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by SSYTRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by SSYTRF. !> CMODE !> CMODE is INTEGER !> Determines op2(C) in the formula op(A) * op2(C) as follows: !> CMODE = 1 op2(C) = C !> CMODE = 0 op2(C) = I !> CMODE = -1 op2(C) = inv(C) !> C !> C is REAL array, dimension (N) !> The vector C in the formula op(A) * op2(C). !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is REAL array, dimension (3*N). !> Workspace. !> IWORK !> IWORK is INTEGER array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 144 of file sla_syrcond.f. double precision function zla_hercond_c (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension ( * ) c, logical capply, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork) ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices. Purpose: !> !> ZLA_HERCOND_C computes the infinity norm condition number of !> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the N-by-N matrix A !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is COMPLEX*16 array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by ZHETRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CHETRF. !> C !> C is DOUBLE PRECISION array, dimension (N) !> The vector C in the formula op(A) * inv(diag(C)). !> CAPPLY !> CAPPLY is LOGICAL !> If .TRUE. then access the vector C in the formula above. !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is COMPLEX*16 array, dimension (2*N). !> Workspace. !> RWORK !> RWORK is DOUBLE PRECISION array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 137 of file zla_hercond_c.f. double precision function zla_hercond_x (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork) ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices. Purpose: !> !> ZLA_HERCOND_X computes the infinity norm condition number of !> op(A) * diag(X) where X is a COMPLEX*16 vector. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the N-by-N matrix A. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is COMPLEX*16 array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by ZHETRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CHETRF. !> X !> X is COMPLEX*16 array, dimension (N) !> The vector X in the formula op(A) * diag(X). !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is COMPLEX*16 array, dimension (2*N). !> Workspace. !> RWORK !> RWORK is DOUBLE PRECISION array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 130 of file zla_hercond_x.f. double precision function zla_syrcond_c (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension( * ) c, logical capply, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork) ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices. Purpose: !> !> ZLA_SYRCOND_C Computes the infinity norm condition number of !> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the N-by-N matrix A !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is COMPLEX*16 array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by ZSYTRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by ZSYTRF. !> C !> C is DOUBLE PRECISION array, dimension (N) !> The vector C in the formula op(A) * inv(diag(C)). !> CAPPLY !> CAPPLY is LOGICAL !> If .TRUE. then access the vector C in the formula above. !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is COMPLEX*16 array, dimension (2*N). !> Workspace. !> RWORK !> RWORK is DOUBLE PRECISION array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 137 of file zla_syrcond_c.f. double precision function zla_syrcond_x (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork) ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices. Purpose: !> !> ZLA_SYRCOND_X Computes the infinity norm condition number of !> op(A) * diag(X) where X is a COMPLEX*16 vector. !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the N-by-N matrix A. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> AF !> AF is COMPLEX*16 array, dimension (LDAF,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by ZSYTRF. !> LDAF !> LDAF is INTEGER !> The leading dimension of the array AF. LDAF >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by ZSYTRF. !> X !> X is COMPLEX*16 array, dimension (N) !> The vector X in the formula op(A) * diag(X). !> INFO !> INFO is INTEGER !> = 0: Successful exit. !> i > 0: The ith argument is invalid. !> WORK !> WORK is COMPLEX*16 array, dimension (2*N). !> Workspace. !> RWORK !> RWORK is DOUBLE PRECISION array, dimension (N). !> Workspace. !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 130 of file zla_syrcond_x.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 la_hercond(3)