.TH "tbcon" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME tbcon \- tbcon: condition number estimate .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBctbcon\fP (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)" .br .RI "\fBCTBCON\fP " .ti -1c .RI "subroutine \fBdtbcon\fP (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)" .br .RI "\fBDTBCON\fP " .ti -1c .RI "subroutine \fBstbcon\fP (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)" .br .RI "\fBSTBCON\fP " .ti -1c .RI "subroutine \fBztbcon\fP (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)" .br .RI "\fBZTBCON\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine ctbcon (character norm, character uplo, character diag, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)" .PP \fBCTBCON\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm\&. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) )\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fINORM\fP .PP .nf NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKD\fP .PP .nf KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is COMPLEX array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+1\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A)))\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*N) .fi .PP .br \fIRWORK\fP .PP .nf RWORK is REAL array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 .PP Definition at line \fB141\fP of file \fBctbcon\&.f\fP\&. .SS "subroutine dtbcon (character norm, character uplo, character diag, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)" .PP \fBDTBCON\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm\&. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) )\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fINORM\fP .PP .nf NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKD\fP .PP .nf KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+1\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A)))\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (3*N) .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 .PP Definition at line \fB141\fP of file \fBdtbcon\&.f\fP\&. .SS "subroutine stbcon (character norm, character uplo, character diag, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)" .PP \fBSTBCON\fP .PP \fBPurpose:\fP .RS 4 .PP .nf STBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm\&. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) )\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fINORM\fP .PP .nf NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKD\fP .PP .nf KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is REAL array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+1\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A)))\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (3*N) .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 .PP Definition at line \fB141\fP of file \fBstbcon\&.f\fP\&. .SS "subroutine ztbcon (character norm, character uplo, character diag, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)" .PP \fBZTBCON\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm\&. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) )\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fINORM\fP .PP .nf NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': A is upper triangular; = 'L': A is lower triangular\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 = 'N': A is non-unit triangular; = 'U': A is unit triangular\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIKD\fP .PP .nf KD is INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A\&. KD >= 0\&. .fi .PP .br \fIAB\fP .PP .nf AB is COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array\&. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd)\&. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1\&. .fi .PP .br \fILDAB\fP .PP .nf LDAB is INTEGER The leading dimension of the array AB\&. LDAB >= KD+1\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A)))\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N) .fi .PP .br \fIRWORK\fP .PP .nf RWORK is DOUBLE PRECISION array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 .PP Definition at line \fB141\fP of file \fBztbcon\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.