.TH "trtrs" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
trtrs \- trtrs: triangular solve
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBctrtrs\fP (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)"
.br
.RI "\fBCTRTRS\fP "
.ti -1c
.RI "subroutine \fBdtrtrs\fP (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)"
.br
.RI "\fBDTRTRS\fP "
.ti -1c
.RI "subroutine \fBstrtrs\fP (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)"
.br
.RI "\fBSTRTRS\fP "
.ti -1c
.RI "subroutine \fBztrtrs\fP (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)"
.br
.RI "\fBZTRTRS\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine ctrtrs (character uplo, character trans, character diag, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 CTRTRS solves a triangular system of the form

    A * X = B,  A**T * X = B,  or  A**H * X = B,

 where A is a triangular matrix of order N, and B is an N-by-NRHS
 matrix\&.  A check is made to verify that A is nonsingular\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular\&.
.fi
.PP
.br
\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
\fIDIAG\fP 
.PP
.nf
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the 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
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          The triangular matrix A\&.  If UPLO = 'U', the leading N-by-N
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced\&.  If UPLO = 'L', the leading N-by-N lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced\&.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B\&.
          On exit, if INFO = 0, the solution matrix 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
          > 0: if INFO = i, the i-th diagonal element of A is zero,
               indicating that the matrix is singular and the solutions
               X have not been computed\&.
.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 \fB138\fP of file \fBctrtrs\&.f\fP\&.
.SS "subroutine dtrtrs (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 DTRTRS solves a triangular system of the form

    A * X = B  or  A**T * X = B,

 where A is a triangular matrix of order N, and B is an N-by-NRHS
 matrix\&.  A check is made to verify that A is nonsingular\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular\&.
.fi
.PP
.br
\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 = Transpose)
.fi
.PP
.br
\fIDIAG\fP 
.PP
.nf
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the 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
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The triangular matrix A\&.  If UPLO = 'U', the leading N-by-N
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced\&.  If UPLO = 'L', the leading N-by-N lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced\&.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B\&.
          On exit, if INFO = 0, the solution matrix 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
          > 0: if INFO = i, the i-th diagonal element of A is zero,
               indicating that the matrix is singular and the solutions
               X have not been computed\&.
.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 \fB138\fP of file \fBdtrtrs\&.f\fP\&.
.SS "subroutine strtrs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 STRTRS solves a triangular system of the form

    A * X = B  or  A**T * X = B,

 where A is a triangular matrix of order N, and B is an N-by-NRHS
 matrix\&.  A check is made to verify that A is nonsingular\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular\&.
.fi
.PP
.br
\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 = Transpose)
.fi
.PP
.br
\fIDIAG\fP 
.PP
.nf
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the 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
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
          The triangular matrix A\&.  If UPLO = 'U', the leading N-by-N
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced\&.  If UPLO = 'L', the leading N-by-N lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced\&.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B\&.
          On exit, if INFO = 0, the solution matrix 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
          > 0: if INFO = i, the i-th diagonal element of A is zero,
               indicating that the matrix is singular and the solutions
               X have not been computed\&.
.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 \fB138\fP of file \fBstrtrs\&.f\fP\&.
.SS "subroutine ztrtrs (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 ZTRTRS solves a triangular system of the form

    A * X = B,  A**T * X = B,  or  A**H * X = B,

 where A is a triangular matrix of order N, and B is an N-by-NRHS
 matrix\&.  A check is made to verify that A is nonsingular\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  A is upper triangular;
          = 'L':  A is lower triangular\&.
.fi
.PP
.br
\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
\fIDIAG\fP 
.PP
.nf
          DIAG is CHARACTER*1
          = 'N':  A is non-unit triangular;
          = 'U':  A is unit triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the 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
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          The triangular matrix A\&.  If UPLO = 'U', the leading N-by-N
          upper triangular part of the array A contains the upper
          triangular matrix, and the strictly lower triangular part of
          A is not referenced\&.  If UPLO = 'L', the leading N-by-N lower
          triangular part of the array A contains the lower triangular
          matrix, and the strictly upper triangular part of A is not
          referenced\&.  If DIAG = 'U', the diagonal elements of A are
          also not referenced and are assumed to be 1\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the right hand side matrix B\&.
          On exit, if INFO = 0, the solution matrix 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
          > 0: if INFO = i, the i-th diagonal element of A is zero,
               indicating that the matrix is singular and the solutions
               X have not been computed\&.
.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 \fB138\fP of file \fBztrtrs\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.