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

.in +1c
.ti -1c
.RI "subroutine \fBcpttrs\fP (uplo, n, nrhs, d, e, b, ldb, info)"
.br
.RI "\fBCPTTRS\fP "
.ti -1c
.RI "subroutine \fBdpttrs\fP (n, nrhs, d, e, b, ldb, info)"
.br
.RI "\fBDPTTRS\fP "
.ti -1c
.RI "subroutine \fBspttrs\fP (n, nrhs, d, e, b, ldb, info)"
.br
.RI "\fBSPTTRS\fP "
.ti -1c
.RI "subroutine \fBzpttrs\fP (uplo, n, nrhs, d, e, b, ldb, info)"
.br
.RI "\fBZPTTRS\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cpttrs (character uplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 CPTTRS solves a tridiagonal system of the form
    A * X = B
 using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF\&.
 D is a diagonal matrix specified in the vector D, U (or L) is a unit
 bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
 the vector E, and X and B are N by NRHS matrices\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies the form of the factorization and whether the
          vector E is the superdiagonal of the upper bidiagonal factor
          U or the subdiagonal of the lower bidiagonal factor L\&.
          = 'U':  A = U**H*D*U, E is the superdiagonal of U
          = 'L':  A = L*D*L**H, E is the subdiagonal of L
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the tridiagonal matrix A\&.  N >= 0\&.
.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
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization A = U**H*D*U or A = L*D*L**H\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is COMPLEX array, dimension (N-1)
          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
          bidiagonal factor U from the factorization A = U**H*D*U\&.
          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
          bidiagonal factor L from the factorization A = L*D*L**H\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors B for the system of
          linear equations\&.
          On exit, 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 dpttrs (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 DPTTRS solves a tridiagonal system of the form
    A * X = B
 using the L*D*L**T factorization of A computed by DPTTRF\&.  D is a
 diagonal matrix specified in the vector D, L is a unit bidiagonal
 matrix whose subdiagonal is specified in the vector E, and X and B
 are N by NRHS matrices\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the tridiagonal matrix A\&.  N >= 0\&.
.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
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          L*D*L**T factorization of A\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal elements of the unit bidiagonal factor
          L from the L*D*L**T factorization of A\&.  E can also be regarded
          as the superdiagonal of the unit bidiagonal factor U from the
          factorization A = U**T*D*U\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors B for the system of
          linear equations\&.
          On exit, 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 spttrs (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 SPTTRS solves a tridiagonal system of the form
    A * X = B
 using the L*D*L**T factorization of A computed by SPTTRF\&.  D is a
 diagonal matrix specified in the vector D, L is a unit bidiagonal
 matrix whose subdiagonal is specified in the vector E, and X and B
 are N by NRHS matrices\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the tridiagonal matrix A\&.  N >= 0\&.
.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
\fID\fP 
.PP
.nf
          D is REAL array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          L*D*L**T factorization of A\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is REAL array, dimension (N-1)
          The (n-1) subdiagonal elements of the unit bidiagonal factor
          L from the L*D*L**T factorization of A\&.  E can also be regarded
          as the superdiagonal of the unit bidiagonal factor U from the
          factorization A = U**T*D*U\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,NRHS)
          On entry, the right hand side vectors B for the system of
          linear equations\&.
          On exit, 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 zpttrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 ZPTTRS solves a tridiagonal system of the form
    A * X = B
 using the factorization A = U**H *D* U or A = L*D*L**H computed by ZPTTRF\&.
 D is a diagonal matrix specified in the vector D, U (or L) is a unit
 bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
 the vector E, and X and B are N by NRHS matrices\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies the form of the factorization and whether the
          vector E is the superdiagonal of the upper bidiagonal factor
          U or the subdiagonal of the lower bidiagonal factor L\&.
          = 'U':  A = U**H *D*U, E is the superdiagonal of U
          = 'L':  A = L*D*L**H, E is the subdiagonal of L
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the tridiagonal matrix A\&.  N >= 0\&.
.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
\fID\fP 
.PP
.nf
          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization A = U**H *D*U or A = L*D*L**H\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is COMPLEX*16 array, dimension (N-1)
          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
          bidiagonal factor U from the factorization A = U**H*D*U\&.
          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
          bidiagonal factor L from the factorization A = L*D*L**H\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the right hand side vectors B for the system of
          linear equations\&.
          On exit, 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 
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