gbtrs(3)

NAME
gbtrs - gbtrs: triangular solve using factor

SYNOPSIS

  Functions

subroutine cgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
CGBTRS
subroutine dgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
DGBTRS
subroutine sgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
SGBTRS
subroutine zgbtrs (trans, n, kl, ku, nrhs, ab, ldab, ipiv, b, ldb, info)
ZGBTRS

Detailed Description

Function Documentation

  subroutine cgbtrs (character trans, integer n, integer kl, integer ku, integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

CGBTRS

Purpose:

    !>
    !> CGBTRS solves a system of linear equations
    !>    A * X = B,  A**T * X = B,  or  A**H * X = B
    !> with a general band matrix A using the LU factorization computed
    !> by CGBTRF.
    !>

Parameters
    TRANS

    !>          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)
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    NRHS

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

    AB

    !>          AB is COMPLEX array, dimension (LDAB,N)
    !>          Details of the LU factorization of the band matrix A, as
    !>          computed by CGBTRF.  U is stored as an upper triangular band
    !>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
    !>          the multipliers used during the factorization are stored in
    !>          rows KL+KU+2 to 2*KL+KU+1.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices; for 1 <= i <= N, row i of the matrix was
    !>          interchanged with row IPIV(i).
    !>

    B

    !>          B is COMPLEX array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dgbtrs (character trans, integer n, integer kl, integer ku, integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DGBTRS

Purpose:

    !>
    !> DGBTRS solves a system of linear equations
    !>    A * X = B  or  A**T * X = B
    !> with a general band matrix A using the LU factorization computed
    !> by DGBTRF.
    !>

Parameters
    TRANS

    !>          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)
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    NRHS

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

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
    !>          Details of the LU factorization of the band matrix A, as
    !>          computed by DGBTRF.  U is stored as an upper triangular band
    !>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
    !>          the multipliers used during the factorization are stored in
    !>          rows KL+KU+2 to 2*KL+KU+1.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices; for 1 <= i <= N, row i of the matrix was
    !>          interchanged with row IPIV(i).
    !>

    B

    !>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sgbtrs (character trans, integer n, integer kl, integer ku, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integer info)

SGBTRS

Purpose:

    !>
    !> SGBTRS solves a system of linear equations
    !>    A * X = B  or  A**T * X = B
    !> with a general band matrix A using the LU factorization computed
    !> by SGBTRF.
    !>

Parameters
    TRANS

    !>          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)
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    NRHS

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

    AB

    !>          AB is REAL array, dimension (LDAB,N)
    !>          Details of the LU factorization of the band matrix A, as
    !>          computed by SGBTRF.  U is stored as an upper triangular band
    !>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
    !>          the multipliers used during the factorization are stored in
    !>          rows KL+KU+2 to 2*KL+KU+1.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices; for 1 <= i <= N, row i of the matrix was
    !>          interchanged with row IPIV(i).
    !>

    B

    !>          B is REAL array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zgbtrs (character trans, integer n, integer kl, integer ku, integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZGBTRS

Purpose:

    !>
    !> ZGBTRS solves a system of linear equations
    !>    A * X = B,  A**T * X = B,  or  A**H * X = B
    !> with a general band matrix A using the LU factorization computed
    !> by ZGBTRF.
    !>

Parameters
    TRANS

    !>          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)
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    KL

    !>          KL is INTEGER
    !>          The number of subdiagonals within the band of A.  KL >= 0.
    !>

    KU

    !>          KU is INTEGER
    !>          The number of superdiagonals within the band of A.  KU >= 0.
    !>

    NRHS

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

    AB

    !>          AB is COMPLEX*16 array, dimension (LDAB,N)
    !>          Details of the LU factorization of the band matrix A, as
    !>          computed by ZGBTRF.  U is stored as an upper triangular band
    !>          matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
    !>          the multipliers used during the factorization are stored in
    !>          rows KL+KU+2 to 2*KL+KU+1.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices; for 1 <= i <= N, row i of the matrix was
    !>          interchanged with row IPIV(i).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          On entry, the right hand side matrix B.
    !>          On exit, the 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
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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