.TH "gtts2" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME gtts2 \- gtts2: triangular solve using factor .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcgtts2\fP (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)" .br .RI "\fBCGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. " .ti -1c .RI "subroutine \fBdgtts2\fP (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)" .br .RI "\fBDGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. " .ti -1c .RI "subroutine \fBsgtts2\fP (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)" .br .RI "\fBSGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. " .ti -1c .RI "subroutine \fBzgtts2\fP (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)" .br .RI "\fBZGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cgtts2 (integer itrans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb)" .PP \fBCGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CGTTS2 solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, with a tridiagonal matrix A using the LU factorization computed by CGTTRF\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIITRANS\fP .PP .nf ITRANS is INTEGER Specifies the form of the system of equations\&. = 0: A * X = B (No transpose) = 1: A**T * X = B (Transpose) = 2: A**H * X = B (Conjugate transpose) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. .fi .PP .br \fINRHS\fP .PP .nf NRHS is INTEGER The number of right hand sides, i\&.e\&., the number of columns of the matrix B\&. NRHS >= 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\&. .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 super-diagonal of U\&. .fi .PP .br \fIDU2\fP .PP .nf DU2 is COMPLEX array, dimension (N-2) 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 \fIB\fP .PP .nf B is COMPLEX array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B\&. On exit, B is overwritten by the solution vectors X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,N)\&. .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 dgtts2 (integer itrans, integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb)" .PP \fBDGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DGTTS2 solves one of the systems of equations A*X = B or A**T*X = B, with a tridiagonal matrix A using the LU factorization computed by DGTTRF\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIITRANS\fP .PP .nf ITRANS is INTEGER Specifies the form of the system of equations\&. = 0: A * X = B (No transpose) = 1: A**T* X = B (Transpose) = 2: A**T* X = B (Conjugate transpose = Transpose) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. .fi .PP .br \fINRHS\fP .PP .nf NRHS is INTEGER The number of right hand sides, i\&.e\&., the number of columns of the matrix B\&. NRHS >= 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\&. .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 super-diagonal of U\&. .fi .PP .br \fIDU2\fP .PP .nf DU2 is DOUBLE PRECISION array, dimension (N-2) 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 \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B\&. On exit, B is overwritten by the solution vectors X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,N)\&. .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 sgtts2 (integer itrans, integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb)" .PP \fBSGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SGTTS2 solves one of the systems of equations A*X = B or A**T*X = B, with a tridiagonal matrix A using the LU factorization computed by SGTTRF\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIITRANS\fP .PP .nf ITRANS is INTEGER Specifies the form of the system of equations\&. = 0: A * X = B (No transpose) = 1: A**T* X = B (Transpose) = 2: A**T* X = B (Conjugate transpose = Transpose) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. .fi .PP .br \fINRHS\fP .PP .nf NRHS is INTEGER The number of right hand sides, i\&.e\&., the number of columns of the matrix B\&. NRHS >= 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\&. .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 super-diagonal of U\&. .fi .PP .br \fIDU2\fP .PP .nf DU2 is REAL array, dimension (N-2) 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 \fIB\fP .PP .nf B is REAL array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B\&. On exit, B is overwritten by the solution vectors X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,N)\&. .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 zgtts2 (integer itrans, integer n, integer nrhs, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( * ) du2, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb)" .PP \fBZGTTS2\fP solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZGTTS2 solves one of the systems of equations A * X = B, A**T * X = B, or A**H * X = B, with a tridiagonal matrix A using the LU factorization computed by ZGTTRF\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIITRANS\fP .PP .nf ITRANS is INTEGER Specifies the form of the system of equations\&. = 0: A * X = B (No transpose) = 1: A**T * X = B (Transpose) = 2: A**H * X = B (Conjugate transpose) .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. .fi .PP .br \fINRHS\fP .PP .nf NRHS is INTEGER The number of right hand sides, i\&.e\&., the number of columns of the matrix B\&. NRHS >= 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\&. .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 super-diagonal of U\&. .fi .PP .br \fIDU2\fP .PP .nf DU2 is COMPLEX*16 array, dimension (N-2) 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 \fIB\fP .PP .nf B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the matrix of right hand side vectors B\&. On exit, B is overwritten by the solution vectors X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,N)\&. .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\&.