.TH "gttrs" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
gttrs \- gttrs: triangular solve using factor
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcgttrs\fP (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)"
.br
.RI "\fBCGTTRS\fP "
.ti -1c
.RI "subroutine \fBdgttrs\fP (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)"
.br
.RI "\fBDGTTRS\fP "
.ti -1c
.RI "subroutine \fBsgttrs\fP (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)"
.br
.RI "\fBSGTTRS\fP "
.ti -1c
.RI "subroutine \fBzgttrs\fP (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)"
.br
.RI "\fBZGTTRS\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgttrs (character trans, 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, integer info)"

.PP
\fBCGTTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CGTTRS 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
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations\&.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  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
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -k, the k-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 dgttrs (character trans, 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, integer info)"

.PP
\fBDGTTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DGTTRS 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
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations\&.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T* X = B  (Transpose)
          = 'C':  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
.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 sgttrs (character trans, 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, integer info)"

.PP
\fBSGTTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SGTTRS 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
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations\&.
          = 'N':  A * X = B  (No transpose)
          = 'T':  A**T* X = B  (Transpose)
          = 'C':  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
.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 zgttrs (character trans, 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, integer info)"

.PP
\fBZGTTRS\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZGTTRS 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
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
          Specifies the form of the system of equations\&.
          = 'N':  A * X = B     (No transpose)
          = 'T':  A**T * X = B  (Transpose)
          = 'C':  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
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -k, the k-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\&.