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SUBROUTINE SQRDC(X,LDX,N,P,QRAUX,JPVT,WORK,JOB)
INTEGER LDX,N,P,JOB
INTEGER JPVT(1)
REAL X(LDX,1),QRAUX(1),WORK(1)
C
C SQRDC USES HOUSEHOLDER TRANSFORMATIONS TO COMPUTE THE QR
C FACTORIZATION OF AN N BY P MATRIX X. COLUMN PIVOTING
C BASED ON THE 2-NORMS OF THE REDUCED COLUMNS MAY BE
C PERFORMED AT THE USERS OPTION.
C
C ON ENTRY
C
C X REAL(LDX,P), WHERE LDX .GE. N.
C X CONTAINS THE MATRIX WHOSE DECOMPOSITION IS TO BE
C COMPUTED.
C
C LDX INTEGER.
C LDX IS THE LEADING DIMENSION OF THE ARRAY X.
C
C N INTEGER.
C N IS THE NUMBER OF ROWS OF THE MATRIX X.
C
C P INTEGER.
C P IS THE NUMBER OF COLUMNS OF THE MATRIX X.
C
C JPVT INTEGER(P).
C JPVT CONTAINS INTEGERS THAT CONTROL THE SELECTION
C OF THE PIVOT COLUMNS. THE K-TH COLUMN X(K) OF X
C IS PLACED IN ONE OF THREE CLASSES ACCORDING TO THE
C VALUE OF JPVT(K).
C
C IF JPVT(K) .GT. 0, THEN X(K) IS AN INITIAL
C COLUMN.
C
C IF JPVT(K) .EQ. 0, THEN X(K) IS A FREE COLUMN.
C
C IF JPVT(K) .LT. 0, THEN X(K) IS A FINAL COLUMN.
C
C BEFORE THE DECOMPOSITION IS COMPUTED, INITIAL COLUMN
C ARE MOVED TO THE BEGINNING OF THE ARRAY X AND FINAL
C COLUMNS TO THE END. BOTH INITIAL AND FINAL COLUMNS
C ARE FROZEN IN PLACE DURING THE COMPUTATION AND ONLY
C FREE COLUMNS ARE MOVED. AT THE K-TH STAGE OF THE
C REDUCTION, IF X(K) IS OCCUPIED BY A FREE COLUMN
C IT IS INTERCHANGED WITH THE FREE COLUMN OF LARGEST
C REDUCED NORM. JPVT IS NOT REFERENCED IF
C JOB .EQ. 0.
C
C WORK REAL(P).
C WORK IS A WORK ARRAY. WORK IS NOT REFERENCED IF
C JOB .EQ. 0.
C
C JOB INTEGER.
C JOB IS AN INTEGER THAT INITIATES COLUMN PIVOTING.
C IF JOB .EQ. 0, NO PIVOTING IS DONE.
C IF JOB .NE. 0, PIVOTING IS DONE.
C
C ON RETURN
C
C X X CONTAINS IN ITS UPPER TRIANGLE THE UPPER
C TRIANGULAR MATRIX R OF THE QR FACTORIZATION.
C BELOW ITS DIAGONAL X CONTAINS INFORMATION FROM
C WHICH THE ORTHOGONAL PART OF THE DECOMPOSITION
C CAN BE RECOVERED. NOTE THAT IF PIVOTING HAS
C BEEN REQUESTED, THE DECOMPOSITION IS NOT THAT
C OF THE ORIGINAL MATRIX X BUT THAT OF X
C WITH ITS COLUMNS PERMUTED AS DESCRIBED BY JPVT.
C
C QRAUX REAL(P).
C QRAUX CONTAINS FURTHER INFORMATION REQUIRED TO RECOV
C THE ORTHOGONAL PART OF THE DECOMPOSITION.
C
C JPVT JPVT(K) CONTAINS THE INDEX OF THE COLUMN OF THE
C ORIGINAL MATRIX THAT HAS BEEN INTERCHANGED INTO
C THE K-TH COLUMN, IF PIVOTING WAS REQUESTED.
C
C LINPACK. THIS VERSION DATED 08/14/78 .
C G.W. STEWART, UNIVERSITY OF MARYLAND, ARGONNE NATIONAL LAB.
C
C SQRDC USES THE FOLLOWING FUNCTIONS AND SUBPROGRAMS.
C
C BLAS SAXPY,SDOT,SSCAL,SSWAP,SNRM2
C FORTRAN ABS,AMAX1,MIN0,SQRT
C