SLATEC Routines --- ORTHOL ---

*DECK ORTHOL
      SUBROUTINE ORTHOL (A, M, N, NRDA, IFLAG, IRANK, ISCALE, DIAG,
     +   KPIVOT, SCALES, COLS, CS)
C***BEGIN PROLOGUE  ORTHOL
C***SUBSIDIARY
C***PURPOSE  Subsidiary to BVSUP
C***LIBRARY   SLATEC
C***TYPE      SINGLE PRECISION (ORTHOL-S)
C***AUTHOR  Watts, H. A., (SNLA)
C***DESCRIPTION
C
C   Reduction of the matrix A to upper triangular form by a sequence of
C   orthogonal HOUSEHOLDER transformations pre-multiplying A
C
C   Modeled after the ALGOL codes in the articles in the REFERENCES
C   section.
C
C **********************************************************************
C   INPUT
C **********************************************************************
C
C     A -- Contains the matrix to be decomposed, must be dimensioned
C           NRDA by N
C     M -- Number of rows in the matrix, M greater or equal to N
C     N -- Number of columns in the matrix, N greater or equal to 1
C     IFLAG -- Indicates the uncertainty in the matrix data
C             = 0 when the data is to be treated as exact
C             =-K when the data is assumed to be accurate to about
C                 K digits
C     ISCALE -- Scaling indicator
C               =-1 if the matrix A is to be pre-scaled by
C               columns when appropriate.
C               Otherwise no scaling will be attempted
C     NRDA -- Row dimension of A, NRDA greater or equal to M
C     DIAG,KPIVOT,COLS -- Arrays of length at least n used internally
C         ,CS,SCALES
C
C **********************************************************************
C   OUTPUT
C **********************************************************************
C
C     IFLAG - Status indicator
C            =1 for successful decomposition
C            =2 if improper input is detected
C            =3 if rank of the matrix is less than N
C     A -- Contains the reduced matrix in the strictly upper triangular
C          part and transformation information in the lower part
C     IRANK -- Contains the numerically determined matrix rank
C     DIAG -- Contains the diagonal elements of the reduced
C             triangular matrix
C     KPIVOT -- Contains the pivotal information, the column
C               interchanges performed on the original matrix are
C               recorded here.
C     SCALES -- Contains the column scaling parameters
C
C **********************************************************************
C
C***SEE ALSO  BVSUP
C***REFERENCES  G. Golub, Numerical methods for solving linear least
C                 squares problems, Numerische Mathematik 7, (1965),
C                 pp. 206-216.
C               P. Businger and G. Golub, Linear least squares
C                 solutions by Householder transformations, Numerische
C                 Mathematik  7, (1965), pp. 269-276.
C***ROUTINES CALLED  CSCALE, R1MACH, SDOT, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   750601  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C   900402  Added TYPE section.  (WRB)
C   910408  Updated the AUTHOR and REFERENCES sections.  (WRB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  ORTHOL