la_gbrcond(3) Library Functions Manual la_gbrcond(3) NAME la_gbrcond - la_gbrcond: Skeel condition number estimate SYNOPSIS Functions real function cla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork) CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices. real function cla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork) CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices. double precision function dla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork) DLA_GBRCOND estimates the Skeel condition number for a general banded matrix. real function sla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork) SLA_GBRCOND estimates the Skeel condition number for a general banded matrix. double precision function zla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork) ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices. double precision function zla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork) ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices. Detailed Description Function Documentation real function cla_gbrcond_c (character trans, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, real, dimension( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork) CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices. Purpose: !> !> CLA_GBRCOND_C Computes the infinity norm condition number of !> op(A) * inv(diag(C)) where C is a REAL vector. !> Parameters TRANS !> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate Transpose = Transpose) !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> AB !> AB is COMPLEX array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is COMPLEX array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by CGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> IPIV !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by CGBTRF; row i of the matrix was interchanged !> with row IPIV(i). !> 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 158 of file cla_gbrcond_c.f. real function cla_gbrcond_x (character trans, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork) CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices. Purpose: !> !> CLA_GBRCOND_X Computes the infinity norm condition number of !> op(A) * diag(X) where X is a COMPLEX vector. !> Parameters TRANS !> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate Transpose = Transpose) !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> AB !> AB is COMPLEX array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is COMPLEX array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by CGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> IPIV !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by CGBTRF; row i of the matrix was interchanged !> with row IPIV(i). !> 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 151 of file cla_gbrcond_x.f. double precision function dla_gbrcond (character trans, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, double precision, dimension( * ) c, integer info, double precision, dimension( * ) work, integer, dimension( * ) iwork) DLA_GBRCOND estimates the Skeel condition number for a general banded matrix. Purpose: !> !> DLA_GBRCOND 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 TRANS !> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate Transpose = Transpose) !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> AB !> AB is DOUBLE PRECISION array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by DGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> IPIV !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by DGBTRF; row i of the matrix was interchanged !> with row IPIV(i). !> 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 (5*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 167 of file dla_gbrcond.f. real function sla_gbrcond (character trans, integer n, integer kl, integer ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c, integer info, real, dimension( * ) work, integer, dimension( * ) iwork) SLA_GBRCOND estimates the Skeel condition number for a general banded matrix. Purpose: !> !> SLA_GBRCOND 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 TRANS !> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate Transpose = Transpose) !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> AB !> AB is REAL array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is REAL array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by SGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> IPIV !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by SGBTRF; row i of the matrix was interchanged !> with row IPIV(i). !> 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 (5*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 166 of file sla_gbrcond.f. double precision function zla_gbrcond_c (character trans, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, double precision, dimension( * ) c, logical capply, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork) ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices. Purpose: !> !> ZLA_GBRCOND_C Computes the infinity norm condition number of !> op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. !> Parameters TRANS !> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate Transpose = Transpose) !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> AB !> AB is COMPLEX*16 array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is COMPLEX*16 array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by ZGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> IPIV !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by ZGBTRF; row i of the matrix was interchanged !> with row IPIV(i). !> 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 159 of file zla_gbrcond_c.f. double precision function zla_gbrcond_x (character trans, integer n, integer kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, complex*16, dimension( * ) x, integer info, complex*16, dimension( * ) work, double precision, dimension( * ) rwork) ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices. Purpose: !> !> ZLA_GBRCOND_X Computes the infinity norm condition number of !> op(A) * diag(X) where X is a COMPLEX*16 vector. !> Parameters TRANS !> TRANS is CHARACTER*1 !> Specifies the form of the system of equations: !> = 'N': A * X = B (No transpose) !> = 'T': A**T * X = B (Transpose) !> = 'C': A**H * X = B (Conjugate Transpose = Transpose) !> N !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> KL !> KL is INTEGER !> The number of subdiagonals within the band of A. KL >= 0. !> KU !> KU is INTEGER !> The number of superdiagonals within the band of A. KU >= 0. !> AB !> AB is COMPLEX*16 array, dimension (LDAB,N) !> On entry, the matrix A in band storage, in rows 1 to KL+KU+1. !> The j-th column of A is stored in the j-th column of the !> array AB as follows: !> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) !> LDAB !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KL+KU+1. !> AFB !> AFB is COMPLEX*16 array, dimension (LDAFB,N) !> Details of the LU factorization of the band matrix A, as !> computed by ZGBTRF. U is stored as an upper triangular !> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, !> and the multipliers used during the factorization are stored !> in rows KL+KU+2 to 2*KL+KU+1. !> LDAFB !> LDAFB is INTEGER !> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. !> IPIV !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by ZGBTRF; row i of the matrix was interchanged !> with row IPIV(i). !> 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 152 of file zla_gbrcond_x.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 la_gbrcond(3)