laqtr - Man Page

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.

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.

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.