.TH "gttrf" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gttrf \- gttrf: triangular factor .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgttrf\fP (n, dl, d, du, du2, ipiv, info)" .br .RI "\fBCGTTRF\fP " .ti -1c .RI "subroutine \fBdgttrf\fP (n, dl, d, du, du2, ipiv, info)" .br .RI "\fBDGTTRF\fP " .ti -1c .RI "subroutine \fBsgttrf\fP (n, dl, d, du, du2, ipiv, info)" .br .RI "\fBSGTTRF\fP " .ti -1c .RI "subroutine \fBzgttrf\fP (n, dl, d, du, du2, ipiv, info)" .br .RI "\fBZGTTRF\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgttrf (integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)" .PP \fBCGTTRF\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CGTTRF computes an LU factorization of a complex tridiagonal matrix A !> using elimination with partial pivoting and row interchanges\&. !> !> The factorization has the form !> A = L * U !> where L is a product of permutation and unit lower bidiagonal !> matrices and U is upper triangular with nonzeros in only the main !> diagonal and first two superdiagonals\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. !> .fi .PP .br \fIDL\fP .PP .nf !> DL is COMPLEX array, dimension (N-1) !> On entry, DL must contain the (n-1) sub-diagonal elements of !> A\&. !> !> On exit, DL is overwritten by the (n-1) multipliers that !> define the matrix L from the LU factorization of A\&. !> .fi .PP .br \fID\fP .PP .nf !> D is COMPLEX array, dimension (N) !> On entry, D must contain the diagonal elements of A\&. !> !> On exit, D is overwritten by 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) !> On entry, DU must contain the (n-1) super-diagonal elements !> of A\&. !> !> On exit, DU is overwritten by the (n-1) elements of the first !> super-diagonal of U\&. !> .fi .PP .br \fIDU2\fP .PP .nf !> DU2 is COMPLEX array, dimension (N-2) !> On exit, DU2 is overwritten by the (n-2) elements of the !> second super-diagonal 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 \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -k, the k-th argument had an illegal value !> > 0: if INFO = k, U(k,k) is exactly zero\&. The factorization !> has been completed, but the factor U is exactly !> singular, and division by zero will occur if it is used !> to solve a system of equations\&. !> .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 \fB123\fP of file \fBcgttrf\&.f\fP\&. .SS "subroutine dgttrf (integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)" .PP \fBDGTTRF\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DGTTRF computes an LU factorization of a real tridiagonal matrix A !> using elimination with partial pivoting and row interchanges\&. !> !> The factorization has the form !> A = L * U !> where L is a product of permutation and unit lower bidiagonal !> matrices and U is upper triangular with nonzeros in only the main !> diagonal and first two superdiagonals\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. !> .fi .PP .br \fIDL\fP .PP .nf !> DL is DOUBLE PRECISION array, dimension (N-1) !> On entry, DL must contain the (n-1) sub-diagonal elements of !> A\&. !> !> On exit, DL is overwritten by the (n-1) multipliers that !> define the matrix L from the LU factorization of A\&. !> .fi .PP .br \fID\fP .PP .nf !> D is DOUBLE PRECISION array, dimension (N) !> On entry, D must contain the diagonal elements of A\&. !> !> On exit, D is overwritten by 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) !> On entry, DU must contain the (n-1) super-diagonal elements !> of A\&. !> !> On exit, DU is overwritten by the (n-1) elements of the first !> super-diagonal of U\&. !> .fi .PP .br \fIDU2\fP .PP .nf !> DU2 is DOUBLE PRECISION array, dimension (N-2) !> On exit, DU2 is overwritten by the (n-2) elements of the !> second super-diagonal 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 \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -k, the k-th argument had an illegal value !> > 0: if INFO = k, U(k,k) is exactly zero\&. The factorization !> has been completed, but the factor U is exactly !> singular, and division by zero will occur if it is used !> to solve a system of equations\&. !> .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 \fB123\fP of file \fBdgttrf\&.f\fP\&. .SS "subroutine sgttrf (integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)" .PP \fBSGTTRF\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SGTTRF computes an LU factorization of a real tridiagonal matrix A !> using elimination with partial pivoting and row interchanges\&. !> !> The factorization has the form !> A = L * U !> where L is a product of permutation and unit lower bidiagonal !> matrices and U is upper triangular with nonzeros in only the main !> diagonal and first two superdiagonals\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. !> .fi .PP .br \fIDL\fP .PP .nf !> DL is REAL array, dimension (N-1) !> On entry, DL must contain the (n-1) sub-diagonal elements of !> A\&. !> !> On exit, DL is overwritten by the (n-1) multipliers that !> define the matrix L from the LU factorization of A\&. !> .fi .PP .br \fID\fP .PP .nf !> D is REAL array, dimension (N) !> On entry, D must contain the diagonal elements of A\&. !> !> On exit, D is overwritten by 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) !> On entry, DU must contain the (n-1) super-diagonal elements !> of A\&. !> !> On exit, DU is overwritten by the (n-1) elements of the first !> super-diagonal of U\&. !> .fi .PP .br \fIDU2\fP .PP .nf !> DU2 is REAL array, dimension (N-2) !> On exit, DU2 is overwritten by the (n-2) elements of the !> second super-diagonal 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 \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -k, the k-th argument had an illegal value !> > 0: if INFO = k, U(k,k) is exactly zero\&. The factorization !> has been completed, but the factor U is exactly !> singular, and division by zero will occur if it is used !> to solve a system of equations\&. !> .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 \fB123\fP of file \fBsgttrf\&.f\fP\&. .SS "subroutine zgttrf (integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, integer info)" .PP \fBZGTTRF\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZGTTRF computes an LU factorization of a complex tridiagonal matrix A !> using elimination with partial pivoting and row interchanges\&. !> !> The factorization has the form !> A = L * U !> where L is a product of permutation and unit lower bidiagonal !> matrices and U is upper triangular with nonzeros in only the main !> diagonal and first two superdiagonals\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. !> .fi .PP .br \fIDL\fP .PP .nf !> DL is COMPLEX*16 array, dimension (N-1) !> On entry, DL must contain the (n-1) sub-diagonal elements of !> A\&. !> !> On exit, DL is overwritten by the (n-1) multipliers that !> define the matrix L from the LU factorization of A\&. !> .fi .PP .br \fID\fP .PP .nf !> D is COMPLEX*16 array, dimension (N) !> On entry, D must contain the diagonal elements of A\&. !> !> On exit, D is overwritten by 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) !> On entry, DU must contain the (n-1) super-diagonal elements !> of A\&. !> !> On exit, DU is overwritten by the (n-1) elements of the first !> super-diagonal of U\&. !> .fi .PP .br \fIDU2\fP .PP .nf !> DU2 is COMPLEX*16 array, dimension (N-2) !> On exit, DU2 is overwritten by the (n-2) elements of the !> second super-diagonal 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 \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -k, the k-th argument had an illegal value !> > 0: if INFO = k, U(k,k) is exactly zero\&. The factorization !> has been completed, but the factor U is exactly !> singular, and division by zero will occur if it is used !> to solve a system of equations\&. !> .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 \fB123\fP of file \fBzgttrf\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.