--- name: "gtts2" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/gtts2" --- # gtts2(3) gtts2: triangular solve using factor ## NAME gtts2 - gtts2: triangular solve using factor ## SYNOPSIS ### Functions subroutine **cgtts2** (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)\ **CGTTS2** solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. subroutine **dgtts2** (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)\ **DGTTS2** solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. subroutine **sgtts2** (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)\ **SGTTS2** solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. subroutine **zgtts2** (itrans, n, nrhs, dl, d, du, du2, ipiv, b, ldb)\ **ZGTTS2** solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. ## Detailed Description ## Function Documentation ### 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) **CGTTS2** solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. **Purpose:** ``` !> !> 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. !> ``` **Parameters** *ITRANS* ``` !> 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) !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. !> ``` *NRHS* ``` !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> ``` *DL* ``` !> DL is COMPLEX array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A. !> ``` *D* ``` !> D is COMPLEX array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !> ``` *DU* ``` !> DU is COMPLEX array, dimension (N-1) !> The (n-1) elements of the first super-diagonal of U. !> ``` *DU2* ``` !> DU2 is COMPLEX array, dimension (N-2) !> The (n-2) elements of the second super-diagonal of U. !> ``` *IPIV* ``` !> 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. !> ``` *B* ``` !> 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. !> ``` *LDB* ``` !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **127** of file **cgtts2.f**. ### 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) **DGTTS2** solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. **Purpose:** ``` !> !> 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. !> ``` **Parameters** *ITRANS* ``` !> 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) !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. !> ``` *NRHS* ``` !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> ``` *DL* ``` !> DL is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A. !> ``` *D* ``` !> D is DOUBLE PRECISION array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !> ``` *DU* ``` !> DU is DOUBLE PRECISION array, dimension (N-1) !> The (n-1) elements of the first super-diagonal of U. !> ``` *DU2* ``` !> DU2 is DOUBLE PRECISION array, dimension (N-2) !> The (n-2) elements of the second super-diagonal of U. !> ``` *IPIV* ``` !> 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. !> ``` *B* ``` !> 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. !> ``` *LDB* ``` !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **127** of file **dgtts2.f**. ### 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) **SGTTS2** solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. **Purpose:** ``` !> !> 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. !> ``` **Parameters** *ITRANS* ``` !> 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) !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. !> ``` *NRHS* ``` !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> ``` *DL* ``` !> DL is REAL array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A. !> ``` *D* ``` !> D is REAL array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !> ``` *DU* ``` !> DU is REAL array, dimension (N-1) !> The (n-1) elements of the first super-diagonal of U. !> ``` *DU2* ``` !> DU2 is REAL array, dimension (N-2) !> The (n-2) elements of the second super-diagonal of U. !> ``` *IPIV* ``` !> 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. !> ``` *B* ``` !> 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. !> ``` *LDB* ``` !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **127** of file **sgtts2.f**. ### 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) **ZGTTS2** solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf. **Purpose:** ``` !> !> 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. !> ``` **Parameters** *ITRANS* ``` !> 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) !> ``` *N* ``` !> N is INTEGER !> The order of the matrix A. !> ``` *NRHS* ``` !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> ``` *DL* ``` !> DL is COMPLEX*16 array, dimension (N-1) !> The (n-1) multipliers that define the matrix L from the !> LU factorization of A. !> ``` *D* ``` !> D is COMPLEX*16 array, dimension (N) !> The n diagonal elements of the upper triangular matrix U from !> the LU factorization of A. !> ``` *DU* ``` !> DU is COMPLEX*16 array, dimension (N-1) !> The (n-1) elements of the first super-diagonal of U. !> ``` *DU2* ``` !> DU2 is COMPLEX*16 array, dimension (N-2) !> The (n-2) elements of the second super-diagonal of U. !> ``` *IPIV* ``` !> 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. !> ``` *B* ``` !> 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. !> ``` *LDB* ``` !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> ``` **Author** Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line **127** of file **zgtts2.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.