.TH "gesv" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
gesv \- gesv: factor and solve
.PP
 \- \fB CGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver) \fP  

.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBcgesv\fP (n, nrhs, a, lda, ipiv, b, ldb, info)"
.br
.RI " "
.ti -1c
.RI "subroutine \fBdgesv\fP (n, nrhs, a, lda, ipiv, b, ldb, info)"
.br
.RI " "
.ti -1c
.RI "subroutine \fBsgesv\fP (n, nrhs, a, lda, ipiv, b, ldb, info)"
.br
.RI " "
.ti -1c
.RI "subroutine \fBzgesv\fP (n, nrhs, a, lda, ipiv, b, ldb, info)"
.br
.RI " "
.in -1c
.SH "Detailed Description"
.PP 
\fB CGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver) \fP 

\fB ZGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver) \fP
.PP
\fB SGESV computes the solution to system of linear equations A * X = B for GE matrices\fP (simple driver)
.PP
\fB DGESV computes the solution to system of linear equations A * X = B for GE matrices\fP
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine cgesv (integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 CGESV computes the solution to a complex system of linear equations
    A * X = B,
 where A is an N-by-N matrix and X and B are N-by-NRHS matrices\&.

 The LU decomposition with partial pivoting and row interchanges is
 used to factor A as
    A = P * L * U,
 where P is a permutation matrix, L is unit lower triangular, and U is
 upper triangular\&.  The factored form of A is then used to solve the
 system of equations A * X = B\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of linear equations, i\&.e\&., 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)
          On entry, the N-by-N coefficient matrix A\&.
          On exit, the factors L and U from the factorization
          A = P*L*U; the unit diagonal elements of L are not stored\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices that define the permutation matrix P;
          row i of the matrix was interchanged with row IPIV(i)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS matrix of right hand side matrix B\&.
          On exit, if INFO = 0, the N-by-NRHS 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, U(i,i) is exactly zero\&.  The factorization
                has been completed, but the factor U is exactly
                singular, so the solution could not be 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

.SS "subroutine dgesv (integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 DGESV computes the solution to a real system of linear equations
    A * X = B,
 where A is an N-by-N matrix and X and B are N-by-NRHS matrices\&.

 The LU decomposition with partial pivoting and row interchanges is
 used to factor A as
    A = P * L * U,
 where P is a permutation matrix, L is unit lower triangular, and U is
 upper triangular\&.  The factored form of A is then used to solve the
 system of equations A * X = B\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of linear equations, i\&.e\&., 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)
          On entry, the N-by-N coefficient matrix A\&.
          On exit, the factors L and U from the factorization
          A = P*L*U; the unit diagonal elements of L are not stored\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices that define the permutation matrix P;
          row i of the matrix was interchanged with row IPIV(i)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS matrix of right hand side matrix B\&.
          On exit, if INFO = 0, the N-by-NRHS 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, U(i,i) is exactly zero\&.  The factorization
                has been completed, but the factor U is exactly
                singular, so the solution could not be 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

.SS "subroutine sgesv (integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 SGESV computes the solution to a real system of linear equations
    A * X = B,
 where A is an N-by-N matrix and X and B are N-by-NRHS matrices\&.

 The LU decomposition with partial pivoting and row interchanges is
 used to factor A as
    A = P * L * U,
 where P is a permutation matrix, L is unit lower triangular, and U is
 upper triangular\&.  The factored form of A is then used to solve the
 system of equations A * X = B\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of linear equations, i\&.e\&., 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)
          On entry, the N-by-N coefficient matrix A\&.
          On exit, the factors L and U from the factorization
          A = P*L*U; the unit diagonal elements of L are not stored\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices that define the permutation matrix P;
          row i of the matrix was interchanged with row IPIV(i)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is REAL array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS matrix of right hand side matrix B\&.
          On exit, if INFO = 0, the N-by-NRHS 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, U(i,i) is exactly zero\&.  The factorization
                has been completed, but the factor U is exactly
                singular, so the solution could not be 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

.SS "subroutine zgesv (integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)"

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

.PP
.nf
 ZGESV computes the solution to a complex system of linear equations
    A * X = B,
 where A is an N-by-N matrix and X and B are N-by-NRHS matrices\&.

 The LU decomposition with partial pivoting and row interchanges is
 used to factor A as
    A = P * L * U,
 where P is a permutation matrix, L is unit lower triangular, and U is
 upper triangular\&.  The factored form of A is then used to solve the
 system of equations A * X = B\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The number of linear equations, i\&.e\&., 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)
          On entry, the N-by-N coefficient matrix A\&.
          On exit, the factors L and U from the factorization
          A = P*L*U; the unit diagonal elements of L are not stored\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices that define the permutation matrix P;
          row i of the matrix was interchanged with row IPIV(i)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the N-by-NRHS matrix of right hand side matrix B\&.
          On exit, if INFO = 0, the N-by-NRHS 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, U(i,i) is exactly zero\&.  The factorization
                has been completed, but the factor U is exactly
                singular, so the solution could not be 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

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.