tptrs(3)

NAME
tptrs - tptrs: triangular solve

SYNOPSIS

  Functions
subroutine ctptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
CTPTRS
subroutine dtptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
DTPTRS
subroutine stptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
STPTRS
subroutine ztptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
ZTPTRS

Detailed Description

Function Documentation

  subroutine ctptrs (character uplo, character trans, character diag, integer n, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldb, * ) b, integer ldb, integer info)

CTPTRS

Purpose:

     CTPTRS 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 stored in packed format,
     and B is an N-by-NRHS matrix.  A check is made to verify that A is
     nonsingular.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  A is upper triangular;
              = 'L':  A is lower triangular.

    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)

    DIAG

              DIAG is CHARACTER*1
              = 'N':  A is non-unit triangular;
              = 'U':  A is unit triangular.

    N

              N is INTEGER
              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.

    AP

              AP is COMPLEX array, dimension (N*(N+1)/2)
              The upper or lower triangular matrix A, packed columnwise in
              a linear array.  The j-th column of A is stored in the array
              AP as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

    B

              B is COMPLEX array, dimension (LDB,NRHS)
              On entry, the right hand side matrix B.
              On exit, if INFO = 0, 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
              > 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.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 129 of file ctptrs.f.

  subroutine dtptrs (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( * ) ap, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DTPTRS

Purpose:

     DTPTRS solves a triangular system of the form
        A * X = B  or  A**T * X = B,
     where A is a triangular matrix of order N stored in packed format,
     and B is an N-by-NRHS matrix.  A check is made to verify that A is
     nonsingular.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  A is upper triangular;
              = 'L':  A is lower triangular.

    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 = Transpose)

    DIAG

              DIAG is CHARACTER*1
              = 'N':  A is non-unit triangular;
              = 'U':  A is unit triangular.

    N

              N is INTEGER
              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.

    AP

              AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
              The upper or lower triangular matrix A, packed columnwise in
              a linear array.  The j-th column of A is stored in the array
              AP as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

    B

              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.

    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, the i-th diagonal element of A is zero,
                    indicating that the matrix is singular and the
                    solutions X have not been computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 129 of file dtptrs.f.

  subroutine stptrs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b, integer ldb, integer info)

STPTRS

Purpose:

     STPTRS solves a triangular system of the form
        A * X = B  or  A**T * X = B,
     where A is a triangular matrix of order N stored in packed format,
     and B is an N-by-NRHS matrix.  A check is made to verify that A is
     nonsingular.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  A is upper triangular;
              = 'L':  A is lower triangular.

    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 = Transpose)

    DIAG

              DIAG is CHARACTER*1
              = 'N':  A is non-unit triangular;
              = 'U':  A is unit triangular.

    N

              N is INTEGER
              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.

    AP

              AP is REAL array, dimension (N*(N+1)/2)
              The upper or lower triangular matrix A, packed columnwise in
              a linear array.  The j-th column of A is stored in the array
              AP as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

    B

              B is REAL array, dimension (LDB,NRHS)
              On entry, the right hand side matrix B.
              On exit, if INFO = 0, 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
              > 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.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 129 of file stptrs.f.

  subroutine ztptrs (character uplo, character trans, character diag, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZTPTRS

Purpose:

     ZTPTRS 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 stored in packed format,
     and B is an N-by-NRHS matrix.  A check is made to verify that A is
     nonsingular.

Parameters
    UPLO

              UPLO is CHARACTER*1
              = 'U':  A is upper triangular;
              = 'L':  A is lower triangular.

    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)

    DIAG

              DIAG is CHARACTER*1
              = 'N':  A is non-unit triangular;
              = 'U':  A is unit triangular.

    N

              N is INTEGER
              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.

    AP

              AP is COMPLEX*16 array, dimension (N*(N+1)/2)
              The upper or lower triangular matrix A, packed columnwise in
              a linear array.  The j-th column of A is stored in the array
              AP as follows:
              if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
              if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

    B

              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.

    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, the i-th diagonal element of A is zero,
                    indicating that the matrix is singular and the
                    solutions X have not been computed.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 129 of file ztptrs.f.

Author

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