--- name: "la_gbrcond" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/la_gbrcond" --- # la\_gbrcond(3) la\_gbrcond: Skeel condition number estimate ## 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.