la_gbrcond - la_gbrcond: Skeel condition number estimate

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 la_gbrcond(3)

realfunctioncla_gbrcond_c(charactertrans,integern,integerkl,integerku,complex,dimension(ldab,*)ab,integerldab,complex,dimension(ldafb,*)afb,integerldafb,integer,dimension(*)ipiv,real,dimension(*)c,logicalcapply,integerinfo,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. ParametersTRANS 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. realfunctioncla_gbrcond_x(charactertrans,integern,integerkl,integerku,complex,dimension(ldab,*)ab,integerldab,complex,dimension(ldafb,*)afb,integerldafb,integer,dimension(*)ipiv,complex,dimension(*)x,integerinfo,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. ParametersTRANS 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. doubleprecisionfunctiondla_gbrcond(charactertrans,integern,integerkl,integerku,doubleprecision,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(ldafb,*)afb,integerldafb,integer,dimension(*)ipiv,integercmode,doubleprecision,dimension(*)c,integerinfo,doubleprecision,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. ParametersTRANS 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. realfunctionsla_gbrcond(charactertrans,integern,integerkl,integerku,real,dimension(ldab,*)ab,integerldab,real,dimension(ldafb,*)afb,integerldafb,integer,dimension(*)ipiv,integercmode,real,dimension(*)c,integerinfo,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. ParametersTRANS 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. doubleprecisionfunctionzla_gbrcond_c(charactertrans,integern,integerkl,integerku,complex*16,dimension(ldab,*)ab,integerldab,complex*16,dimension(ldafb,*)afb,integerldafb,integer,dimension(*)ipiv,doubleprecision,dimension(*)c,logicalcapply,integerinfo,complex*16,dimension(*)work,doubleprecision,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. ParametersTRANS 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. doubleprecisionfunctionzla_gbrcond_x(charactertrans,integern,integerkl,integerku,complex*16,dimension(ldab,*)ab,integerldab,complex*16,dimension(ldafb,*)afb,integerldafb,integer,dimension(*)ipiv,complex*16,dimension(*)x,integerinfo,complex*16,dimension(*)work,doubleprecision,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. ParametersTRANS 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.

la_gbrcond - la_gbrcond: Skeel condition number estimate

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.