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NAME
     csvdc - compute the singular value decomposition of  a  gen-
     eral matrix A.

SYNOPSIS
     SUBROUTINE DSVDC (DA, LDA, N, P, DSVALS,  DE,  DLSVEC,  LDL,
               DRSVEC, LDR, DWORK, JOB, INFO)

     SUBROUTINE SSVDC (SA, LDA, N, P, SSVALS,  SE,  SLSVEC,  LDL,
               SRSVEC, LDR, SWORK, JOB, INFO)

     SUBROUTINE ZSVDC (ZA, LDA, N, P, ZSVALS,  ZE,  ZLSVEC,  LDL,
               ZRSVEC, LDR, ZWORK, JOB, INFO)

     SUBROUTINE CSVDC (CA, LDA, N, P, CSVALS,  CE,  CLSVEC,  LDL,
               CRSVEC, LDR, CWORK, JOB, INFO)



     #include <sunperf.h>

     void dsvdc(double *dx, int ldx, int n,  int  p,  double  *s,
               double  *e,  double  *du,  int ldu, double *v, int
               ldv, int job, int *info) ;

     void ssvdc(float *sx, int ldx, int n, int p, float *s, float
               *e,  float  *su,  int  ldu, float *v, int ldv, int
               job, int *info) ;

     void zsvdc(doublecomplex *zx, int ldx, int n, int  p,  doub-
               lecomplex  *s, doublecomplex *e, doublecomplex *u,
               int ldu, doublecomplex *v, int ldv, int  job,  int
               *info) ;

     void csvdc(complex *cx, int ldx, int n, int p,  complex  *s,
               complex  *e, complex *cu, int ldu, complex *v, int
               ldv, int job, int *info) ;

ARGUMENTS
     xA        Matrix A.

     LDA       Leading dimension of the array A as specified in a
               dimension or type statement.  LDA >= max(1,N).

     N         Number of rows of the matrix A.  N >= 0.

     P         Number of columns of the matrix A.  P >= 0.

     xSVALS    On exit, the singular values of A arranged in des-
               cending order of magnitude.

     xE        On exit, normally  contains  zero,  but  see  INFO
               below.

     xLSVEC    On exit, the matrix of left singular vectors;  not
               referenced if the a digit of JOB = 0.

     LDL       Leading dimension  of  LSVEC  as  specified  in  a
               dimension or type statement.  LDL >= max(1,N).

     xRSVEC    On exit, the matrix of right singular vectors; not
               referenced if the b digit of JOB = 0.

     LDR       Leading dimension  of  RSVEC  as  specified  in  a
               dimension or type statement.  LDR >= max(1,P).

     xWORK     Scratch array with a dimension of N.

     JOB       Integer in the form ab; determines operation  sub-
               routine will perform:
                    a = 0     do not compute  the  left  singular
               vectors
                    a = 1     return the n left singular  vectors
               in LSVEC
                    a * 2     return the first min(N,P)  singular
               vectors in LSVEC
                    b = 0     do not compute the  right  singular
               vectors
                    b = 1     return the right  singular  vectors
               in RSVEC

     INFO      On exit, the singular values and their correspond-
               ing      singular      vectors      SVALS(INFO+1),
               SVALS(INFO+2),...,SVALS(min(N,P)) are correct.  If
               INFO  =  0  then  all singular values and singular
               vectors are correct.   The  matrix  B  defined  as
               LSVECT * A * RSVEC is the bidiagonal matrix with S
               on  its  diagonal  and  E  on  its  superdiagonal.
               Therefore  the  singular values of A and B are the
               same.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           JOB, LDL, LDR, LDX, N, P
           PARAMETER        (JOB = 21)
           PARAMETER        (N = 3)
           PARAMETER        (P = 3)
           PARAMETER        (LDL = N)
           PARAMETER        (LDR = P)
           PARAMETER        (LDX = N)
     C
           DOUBLE PRECISION  EPSLON, EXCEPT(P), LSVALS(LDL,N)
           DOUBLE PRECISION  RSVALS(LDR,P), SVALS(N), WORK(N), X(LDX,P)
           INTEGER           I, ICOL, INFO, IRANK, IROW
     C
           EXTERNAL          DSVDC
           INTRINSIC         ABS, SQRT
     C
     C     Initialize the array X to store the matrix X shown below.
     C
     C         1  1  3
     C     X = 0  1  1
     C         1  0  1
     C
           DATA X / 1.0D0, 0.0D0, 1.0D0, 1.0D0, 1.0D0, 0.0D0,
          $         3.0D0, 1.0D0, 1.0D0 /
     C
           PRINT 1000
           PRINT 1010, ((X(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
           CALL DSVDC (X, LDX, N, P, SVALS, EXCEPT, LSVALS, LDL,
          $            RSVALS, LDR, WORK, JOB, INFO)
           PRINT 1020
           PRINT 1030, SVALS
     C
     C     Compute the unit roundoff
     C
           EPSLON = 1.0D0
        10 IF (DBLE (1.0D0 + EPSLON) .NE. 1.0D0) THEN
             EPSLON = EPSLON / 2.0D0
             GO TO 10
           END IF
     C
     C     Make a conservative estimate of the rank of A.
     C
           IRANK = 0
           EPSLON = SQRT (EPSLON + EPSLON)
           DO 20, I = 1, N
             IF (ABS(SVALS(I)) .GT. EPSLON) THEN
               IRANK = IRANK + 1
             END IF
        20 CONTINUE
           PRINT 1040, IRANK
     C
      1000 FORMAT (1X, 'X:')
      1010 FORMAT (3(3X, F4.1))
      1020 FORMAT (/1X, 'Singular values of X:')
      1030 FORMAT (3X, F4.1)
      1040 FORMAT (/1X, 'The rank of X is ', I1)
     C
           END

SAMPLE OUTPUT
      X:
         1.0    1.0    3.0
         0.0    1.0    1.0
         1.0    0.0    1.0

      Singular values of X:
         3.7
         1.0
         0.3

      The rank of X is 3

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