laqtr(3) LAPACK laqtr(3)

laqtr - laqtr: quasi-triangular solve


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.

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.

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