.TH "la_gbrpvgrw" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME la_gbrpvgrw \- la_gbrpvgrw: reciprocal pivot growth .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "real function \fBcla_gbrpvgrw\fP (n, kl, ku, ncols, ab, ldab, afb, ldafb)" .br .RI "\fBCLA_GBRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix\&. " .ti -1c .RI "double precision function \fBdla_gbrpvgrw\fP (n, kl, ku, ncols, ab, ldab, afb, ldafb)" .br .RI "\fBDLA_GBRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix\&. " .ti -1c .RI "real function \fBsla_gbrpvgrw\fP (n, kl, ku, ncols, ab, ldab, afb, ldafb)" .br .RI "\fBSLA_GBRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix\&. " .ti -1c .RI "double precision function \fBzla_gbrpvgrw\fP (n, kl, ku, ncols, ab, ldab, afb, ldafb)" .br .RI "\fBZLA_GBRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "real function cla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb)" .PP \fBCLA_GBRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U)\&. The 'max absolute element' norm is used\&. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor\&. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 \fINCOLS\fP .PP .nf NCOLS is INTEGER The number of columns of the matrix A\&. NCOLS >= 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 .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_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb)" .PP \fBDLA_GBRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U)\&. The 'max absolute element' norm is used\&. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor\&. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 \fINCOLS\fP .PP .nf NCOLS is INTEGER The number of columns of the matrix A\&. NCOLS >= 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 .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_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb)" .PP \fBSLA_GBRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U)\&. The 'max absolute element' norm is used\&. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor\&. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 \fINCOLS\fP .PP .nf NCOLS is INTEGER The number of columns of the matrix A\&. NCOLS >= 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 .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_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldafb, * ) afb, integer ldafb)" .PP \fBZLA_GBRPVGRW\fP computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U)\&. The 'max absolute element' norm is used\&. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor\&. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \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 \fINCOLS\fP .PP .nf NCOLS is INTEGER The number of columns of the matrix A\&. NCOLS >= 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 .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\&.