.TH "la_gbrcond" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME la_gbrcond \- la_gbrcond: Skeel condition number estimate .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "real function \fBcla_gbrcond_c\fP (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)" .br .RI "\fBCLA_GBRCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices\&. " .ti -1c .RI "real function \fBcla_gbrcond_x\fP (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)" .br .RI "\fBCLA_GBRCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for general banded matrices\&. " .ti -1c .RI "double precision function \fBdla_gbrcond\fP (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork)" .br .RI "\fBDLA_GBRCOND\fP estimates the Skeel condition number for a general banded matrix\&. " .ti -1c .RI "real function \fBsla_gbrcond\fP (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork)" .br .RI "\fBSLA_GBRCOND\fP estimates the Skeel condition number for a general banded matrix\&. " .ti -1c .RI "double precision function \fBzla_gbrcond_c\fP (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork)" .br .RI "\fBZLA_GBRCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices\&. " .ti -1c .RI "double precision function \fBzla_gbrcond_x\fP (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork)" .br .RI "\fBZLA_GBRCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for general banded matrices\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "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)" .PP \fBCLA_GBRCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLA_GBRCOND_C Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf 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) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of linear equations, i\&.e\&., the order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKL\fP .PP .nf KL is INTEGER The number of subdiagonals within the band of A\&. KL >= 0\&. .fi .PP .br \fIKU\fP .PP .nf KU is INTEGER The number of superdiagonals within the band of A\&. KU >= 0\&. .fi .PP .br \fIAB\fP .PP .nf 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) .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KL+KU+1\&. .fi .PP .br \fIAFB\fP .PP .nf 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\&. .fi .PP .br \fILDAFB\fP .PP .nf LDAFB is INTEGER The leading dimension of the array AFB\&. LDAFB >= 2*KL+KU+1\&. .fi .PP .br \fIIPIV\fP .PP .nf 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)\&. .fi .PP .br \fIC\fP .PP .nf C is REAL array, dimension (N) The vector C in the formula op(A) * inv(diag(C))\&. .fi .PP .br \fICAPPLY\fP .PP .nf CAPPLY is LOGICAL If \&.TRUE\&. then access the vector C in the formula above\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: Successful exit\&. i > 0: The ith argument is invalid\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*N)\&. Workspace\&. .fi .PP .br \fIRWORK\fP .PP .nf RWORK is REAL array, dimension (N)\&. Workspace\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBCLA_GBRCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for general banded matrices\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLA_GBRCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX vector\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf 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) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of linear equations, i\&.e\&., the order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKL\fP .PP .nf KL is INTEGER The number of subdiagonals within the band of A\&. KL >= 0\&. .fi .PP .br \fIKU\fP .PP .nf KU is INTEGER The number of superdiagonals within the band of A\&. KU >= 0\&. .fi .PP .br \fIAB\fP .PP .nf 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) .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KL+KU+1\&. .fi .PP .br \fIAFB\fP .PP .nf 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\&. .fi .PP .br \fILDAFB\fP .PP .nf LDAFB is INTEGER The leading dimension of the array AFB\&. LDAFB >= 2*KL+KU+1\&. .fi .PP .br \fIIPIV\fP .PP .nf 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)\&. .fi .PP .br \fIX\fP .PP .nf X is COMPLEX array, dimension (N) The vector X in the formula op(A) * diag(X)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: Successful exit\&. i > 0: The ith argument is invalid\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*N)\&. Workspace\&. .fi .PP .br \fIRWORK\fP .PP .nf RWORK is REAL array, dimension (N)\&. Workspace\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBDLA_GBRCOND\fP estimates the Skeel condition number for a general banded matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf 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) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of linear equations, i\&.e\&., the order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKL\fP .PP .nf KL is INTEGER The number of subdiagonals within the band of A\&. KL >= 0\&. .fi .PP .br \fIKU\fP .PP .nf KU is INTEGER The number of superdiagonals within the band of A\&. KU >= 0\&. .fi .PP .br \fIAB\fP .PP .nf 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) .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KL+KU+1\&. .fi .PP .br \fIAFB\fP .PP .nf 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\&. .fi .PP .br \fILDAFB\fP .PP .nf LDAFB is INTEGER The leading dimension of the array AFB\&. LDAFB >= 2*KL+KU+1\&. .fi .PP .br \fIIPIV\fP .PP .nf 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)\&. .fi .PP .br \fICMODE\fP .PP .nf 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) .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension (N) The vector C in the formula op(A) * op2(C)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: Successful exit\&. i > 0: The ith argument is invalid\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (5*N)\&. Workspace\&. .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (N)\&. Workspace\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBSLA_GBRCOND\fP estimates the Skeel condition number for a general banded matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf 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) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of linear equations, i\&.e\&., the order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKL\fP .PP .nf KL is INTEGER The number of subdiagonals within the band of A\&. KL >= 0\&. .fi .PP .br \fIKU\fP .PP .nf KU is INTEGER The number of superdiagonals within the band of A\&. KU >= 0\&. .fi .PP .br \fIAB\fP .PP .nf 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) .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KL+KU+1\&. .fi .PP .br \fIAFB\fP .PP .nf 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\&. .fi .PP .br \fILDAFB\fP .PP .nf LDAFB is INTEGER The leading dimension of the array AFB\&. LDAFB >= 2*KL+KU+1\&. .fi .PP .br \fIIPIV\fP .PP .nf 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)\&. .fi .PP .br \fICMODE\fP .PP .nf 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) .fi .PP .br \fIC\fP .PP .nf C is REAL array, dimension (N) The vector C in the formula op(A) * op2(C)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: Successful exit\&. i > 0: The ith argument is invalid\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (5*N)\&. Workspace\&. .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (N)\&. Workspace\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBZLA_GBRCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLA_GBRCOND_C Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf 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) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of linear equations, i\&.e\&., the order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKL\fP .PP .nf KL is INTEGER The number of subdiagonals within the band of A\&. KL >= 0\&. .fi .PP .br \fIKU\fP .PP .nf KU is INTEGER The number of superdiagonals within the band of A\&. KU >= 0\&. .fi .PP .br \fIAB\fP .PP .nf 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) .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KL+KU+1\&. .fi .PP .br \fIAFB\fP .PP .nf 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\&. .fi .PP .br \fILDAFB\fP .PP .nf LDAFB is INTEGER The leading dimension of the array AFB\&. LDAFB >= 2*KL+KU+1\&. .fi .PP .br \fIIPIV\fP .PP .nf 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)\&. .fi .PP .br \fIC\fP .PP .nf C is DOUBLE PRECISION array, dimension (N) The vector C in the formula op(A) * inv(diag(C))\&. .fi .PP .br \fICAPPLY\fP .PP .nf CAPPLY is LOGICAL If \&.TRUE\&. then access the vector C in the formula above\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: Successful exit\&. i > 0: The ith argument is invalid\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N)\&. Workspace\&. .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION array, dimension (N)\&. Workspace\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "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)" .PP \fBZLA_GBRCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for general banded matrices\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLA_GBRCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fITRANS\fP .PP .nf 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) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of linear equations, i\&.e\&., the order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKL\fP .PP .nf KL is INTEGER The number of subdiagonals within the band of A\&. KL >= 0\&. .fi .PP .br \fIKU\fP .PP .nf KU is INTEGER The number of superdiagonals within the band of A\&. KU >= 0\&. .fi .PP .br \fIAB\fP .PP .nf 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) .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KL+KU+1\&. .fi .PP .br \fIAFB\fP .PP .nf 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\&. .fi .PP .br \fILDAFB\fP .PP .nf LDAFB is INTEGER The leading dimension of the array AFB\&. LDAFB >= 2*KL+KU+1\&. .fi .PP .br \fIIPIV\fP .PP .nf 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)\&. .fi .PP .br \fIX\fP .PP .nf X is COMPLEX*16 array, dimension (N) The vector X in the formula op(A) * diag(X)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: Successful exit\&. i > 0: The ith argument is invalid\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N)\&. Workspace\&. .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION array, dimension (N)\&. Workspace\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.