laqtr(3)

NAME
laqtr - laqtr: quasi-triangular solve

SYNOPSIS

  Functions
subroutine dlaqtr (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)
DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.
subroutine slaqtr (ltran, lreal, n, t, ldt, b, w, scale, x, work, info)
SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

Detailed Description

Function Documentation

  subroutine dlaqtr (logical ltran, logical lreal, integer n, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) b, double precision w, double precision scale, double precision, dimension( * ) x, double precision, dimension( * ) work, integer info)

DLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

Purpose:

     DLAQTR solves the real quasi-triangular system
                  op(T)*p = scale*c,               if LREAL = .TRUE.
     or the complex quasi-triangular systems
                op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE.
     in real arithmetic, where T is upper quasi-triangular.
     If LREAL = .FALSE., then the first diagonal block of T must be
     1 by 1, B is the specially structured matrix
                    B = [ b(1) b(2) ... b(n) ]
                        [       w            ]
                        [           w        ]
                        [              .     ]
                        [                 w  ]
     op(A) = A or A**T, A**T denotes the transpose of
     matrix A.
     On input, X = [ c ].  On output, X = [ p ].
                   [ d ]                  [ q ]
     This subroutine is designed for the condition number estimation
     in routine DTRSNA.

Parameters
    LTRAN

              LTRAN is LOGICAL
              On entry, LTRAN specifies the option of conjugate transpose:
                 = .FALSE.,    op(T+i*B) = T+i*B,
                 = .TRUE.,     op(T+i*B) = (T+i*B)**T.

    LREAL

              LREAL is LOGICAL
              On entry, LREAL specifies the input matrix structure:
                 = .FALSE.,    the input is complex
                 = .TRUE.,     the input is real

    N

              N is INTEGER
              On entry, N specifies the order of T+i*B. N >= 0.

    T

              T is DOUBLE PRECISION array, dimension (LDT,N)
              On entry, T contains a matrix in Schur canonical form.
              If LREAL = .FALSE., then the first diagonal block of T mu
              be 1 by 1.

    LDT

              LDT is INTEGER
              The leading dimension of the matrix T. LDT >= max(1,N).

    B

              B is DOUBLE PRECISION array, dimension (N)
              On entry, B contains the elements to form the matrix
              B as described above.
              If LREAL = .TRUE., B is not referenced.

    W

              W is DOUBLE PRECISION
              On entry, W is the diagonal element of the matrix B.
              If LREAL = .TRUE., W is not referenced.

    SCALE

              SCALE is DOUBLE PRECISION
              On exit, SCALE is the scale factor.

    X

              X is DOUBLE PRECISION array, dimension (2*N)
              On entry, X contains the right hand side of the system.
              On exit, X is overwritten by the solution.

    WORK

              WORK is DOUBLE PRECISION array, dimension (N)

    INFO

              INFO is INTEGER
              On exit, INFO is set to
                 0: successful exit.
                   1: the some diagonal 1 by 1 block has been perturbed by
                      a small number SMIN to keep nonsingularity.
                   2: the some diagonal 2 by 2 block has been perturbed by
                      a small number in DLALN2 to keep nonsingularity.
              NOTE: In the interests of speed, this routine does not
                    check the inputs for errors.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 163 of file dlaqtr.f.

  subroutine slaqtr (logical ltran, logical lreal, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) b, real w, real scale, real, dimension( * ) x, real, dimension( * ) work, integer info)

SLAQTR solves a real quasi-triangular system of equations, or a complex quasi-triangular system of special form, in real arithmetic.

Purpose:

     SLAQTR solves the real quasi-triangular system
                  op(T)*p = scale*c,               if LREAL = .TRUE.
     or the complex quasi-triangular systems
                op(T + iB)*(p+iq) = scale*(c+id),  if LREAL = .FALSE.
     in real arithmetic, where T is upper quasi-triangular.
     If LREAL = .FALSE., then the first diagonal block of T must be
     1 by 1, B is the specially structured matrix
                    B = [ b(1) b(2) ... b(n) ]
                        [       w            ]
                        [           w        ]
                        [              .     ]
                        [                 w  ]
     op(A) = A or A**T, A**T denotes the transpose of
     matrix A.
     On input, X = [ c ].  On output, X = [ p ].
                   [ d ]                  [ q ]
     This subroutine is designed for the condition number estimation
     in routine STRSNA.

Parameters
    LTRAN

              LTRAN is LOGICAL
              On entry, LTRAN specifies the option of conjugate transpose:
                 = .FALSE.,    op(T+i*B) = T+i*B,
                 = .TRUE.,     op(T+i*B) = (T+i*B)**T.

    LREAL

              LREAL is LOGICAL
              On entry, LREAL specifies the input matrix structure:
                 = .FALSE.,    the input is complex
                 = .TRUE.,     the input is real

    N

              N is INTEGER
              On entry, N specifies the order of T+i*B. N >= 0.

    T

              T is REAL array, dimension (LDT,N)
              On entry, T contains a matrix in Schur canonical form.
              If LREAL = .FALSE., then the first diagonal block of T must
              be 1 by 1.

    LDT

              LDT is INTEGER
              The leading dimension of the matrix T. LDT >= max(1,N).

    B

              B is REAL array, dimension (N)
              On entry, B contains the elements to form the matrix
              B as described above.
              If LREAL = .TRUE., B is not referenced.

    W

              W is REAL
              On entry, W is the diagonal element of the matrix B.
              If LREAL = .TRUE., W is not referenced.

    SCALE

              SCALE is REAL
              On exit, SCALE is the scale factor.

    X

              X is REAL array, dimension (2*N)
              On entry, X contains the right hand side of the system.
              On exit, X is overwritten by the solution.

    WORK

              WORK is REAL array, dimension (N)

    INFO

              INFO is INTEGER
              On exit, INFO is set to
                 0: successful exit.
                   1: the some diagonal 1 by 1 block has been perturbed by
                      a small number SMIN to keep nonsingularity.
                   2: the some diagonal 2 by 2 block has been perturbed by
                      a small number in SLALN2 to keep nonsingularity.
              NOTE: In the interests of speed, this routine does not
                    check the inputs for errors.

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 163 of file slaqtr.f.

Author

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