.TH "gtcon" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gtcon \- gtcon: condition number estimate .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgtcon\fP (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)" .br .RI "\fBCGTCON\fP " .ti -1c .RI "subroutine \fBdgtcon\fP (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)" .br .RI "\fBDGTCON\fP " .ti -1c .RI "subroutine \fBsgtcon\fP (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, iwork, info)" .br .RI "\fBSGTCON\fP " .ti -1c .RI "subroutine \fBzgtcon\fP (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work, info)" .br .RI "\fBZGTCON\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgtcon (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)" .PP \fBCGTCON\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * 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 \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIDL\fP .PP .nf DL is COMPLEX array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF\&. .fi .PP .br \fID\fP .PP .nf D is COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A\&. .fi .PP .br \fIDU\fP .PP .nf DU is COMPLEX array, dimension (N-1) The (n-1) elements of the first superdiagonal of U\&. .fi .PP .br \fIDU2\fP .PP .nf DU2 is COMPLEX array, dimension (N-2) The (n-2) elements of the second superdiagonal of U\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i)\&. IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is REAL If NORM = '1' or 'O', the 1-norm of the original matrix A\&. If NORM = 'I', the infinity-norm of the original matrix A\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*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 .SS "subroutine dgtcon (character norm, integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)" .PP \fBDGTCON\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * 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 \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIDL\fP .PP .nf DL is DOUBLE PRECISION array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF\&. .fi .PP .br \fID\fP .PP .nf D is DOUBLE PRECISION array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A\&. .fi .PP .br \fIDU\fP .PP .nf DU is DOUBLE PRECISION array, dimension (N-1) The (n-1) elements of the first superdiagonal of U\&. .fi .PP .br \fIDU2\fP .PP .nf DU2 is DOUBLE PRECISION array, dimension (N-2) The (n-2) elements of the second superdiagonal of U\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i)\&. IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A\&. If NORM = 'I', the infinity-norm of the original matrix A\&. .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/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (2*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 .SS "subroutine sgtcon (character norm, integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)" .PP \fBSGTCON\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * 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 \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIDL\fP .PP .nf DL is REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF\&. .fi .PP .br \fID\fP .PP .nf D is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A\&. .fi .PP .br \fIDU\fP .PP .nf DU is REAL array, dimension (N-1) The (n-1) elements of the first superdiagonal of U\&. .fi .PP .br \fIDU2\fP .PP .nf DU2 is REAL array, dimension (N-2) The (n-2) elements of the second superdiagonal of U\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i)\&. IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is REAL If NORM = '1' or 'O', the 1-norm of the original matrix A\&. If NORM = 'I', the infinity-norm of the original matrix A\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (2*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 .SS "subroutine zgtcon (character norm, integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)" .PP \fBZGTCON\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * 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 \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIDL\fP .PP .nf DL is COMPLEX*16 array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF\&. .fi .PP .br \fID\fP .PP .nf D is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A\&. .fi .PP .br \fIDU\fP .PP .nf DU is COMPLEX*16 array, dimension (N-1) The (n-1) elements of the first superdiagonal of U\&. .fi .PP .br \fIDU2\fP .PP .nf DU2 is COMPLEX*16 array, dimension (N-2) The (n-2) elements of the second superdiagonal of U\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i)\&. IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A\&. If NORM = 'I', the infinity-norm of the original matrix A\&. .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/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.