DORTHR(3)

SYNOPSIS
SUBROUTINE DORTHR (A, N, M, NRDA, IFLAG, IRANK, ISCALE, DIAG, + KPIVOT, SCALES, ROWS, RS)

NAME
dorthr - Subsidiary to DBVSUP and DSUDS

LIBRARY
SLATEC

TYPE
DOUBLE PRECISION (ORTHOR-S, DORTHR-D)

AUTHOR
Watts, H. A., (SNLA)

DESCRIPTION
Reduction of the matrix A to lower triangular form by a sequence of orthogonal HOUSEHOLDER transformations post-multiplying A. ********************************************************************* INPUT ********************************************************************* A -- Contains the matrix to be decomposed, must be dimensioned NRDA by N. N -- Number of rows in the matrix, N greater or equal to 1. M -- Number of columns in the matrix, M greater or equal to N. IFLAG -- Indicates the uncertainty in the matrix data. = 0 when the data is to be treated as exact. =-K when the data is assumed to be accurate to about K digits. ISCALE -- Scaling indicator. =-1 if the matrix is to be pre-scaled by columns when appropriate. Otherwise no scaling will be attempted. NRDA -- Row dimension of A, NRDA greater or equal to N. DIAG,KPIVOT,ROWS, -- Arrays of length at least N used internally RS,SCALES (except for SCALES which is M). ********************************************************************* OUTPUT ********************************************************************* IFLAG - Status indicator =1 for successful decomposition. =2 if improper input is detected. =3 if rank of the matrix is less than N. A -- Contains the reduced matrix in the strictly lower triangular part and transformation information. IRANK -- Contains the numerically determined matrix rank. DIAG -- Contains the diagonal elements of the reduced triangular matrix. KPIVOT -- Contains the pivotal information, the column interchanges performed on the original matrix are recorded here. SCALES -- Contains the column scaling parameters. *********************************************************************

SEE ALSO
DBVSUP, DSUDS

REFERENCES
G. Golub, Numerical methods for solving linear least squares problems, Numerische Mathematik 7, (1965), pp. 206-216. P. Businger and G. Golub, Linear least squares solutions by Householder transformations, Numerische Mathematik 7, (1965), pp. 269-276.

ROUTINES CALLED
D1MACH, DCSCAL, DDOT, XERMSG

REVISION HISTORY (YYMMDD)
750601 DATE WRITTEN
890531 Changed all specific intrinsics to generic. (WRB)
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
900328 Added TYPE section. (WRB)
910408 Updated the AUTHOR and REFERENCES sections. (WRB)
920501 Reformatted the REFERENCES section. (WRB)