gesv(3)

NAME
gesv - gesv: factor and solve

 - CGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver)

SYNOPSIS

  Functions/Subroutines

subroutine cgesv (n, nrhs, a, lda, ipiv, b, ldb, info)
subroutine dgesv (n, nrhs, a, lda, ipiv, b, ldb, info)
subroutine sgesv (n, nrhs, a, lda, ipiv, b, ldb, info)
subroutine zgesv (n, nrhs, a, lda, ipiv, b, ldb, info)

Detailed Description

CGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver)

ZGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver)

SGESV computes the solution to system of linear equations A * X = B for GE matrices (simple driver)

DGESV computes the solution to system of linear equations A * X = B for GE matrices

Function/Subroutine Documentation

  subroutine cgesv (integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

Purpose:

    !>
    !> 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.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          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).
    !>

    B

    !>          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.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,N).
    !>

    INFO

    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  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)

Purpose:

    !>
    !> 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.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          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).
    !>

    B

    !>          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.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,N).
    !>

    INFO

    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

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

Purpose:

    !>
    !> 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.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          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).
    !>

    B

    !>          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.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,N).
    !>

    INFO

    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  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)

Purpose:

    !>
    !> 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.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          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).
    !>

    B

    !>          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.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,N).
    !>

    INFO

    !>          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.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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