Using a divide and conquer approach, DLASD0 computes the singular


 value decomposition (SVD) of a real upper bidiagonal N-by-M


 matrix B with diagonal D and offdiagonal E, where M = N + SQRE.


 The algorithm computes orthogonal matrices U and VT such that


 B = U * S * VT. The singular values S are overwritten on D.


 A related subroutine, DLASDA, computes only the singular values,


 and optionally, the singular vectors in compact form.

N

          N is INTEGER


         On entry, the row dimension of the upper bidiagonal matrix.


         This is also the dimension of the main diagonal array D.

SQRE

          SQRE is INTEGER


         Specifies the column dimension of the bidiagonal matrix.


         = 0: The bidiagonal matrix has column dimension M = N;


         = 1: The bidiagonal matrix has column dimension M = N+1;

D

          D is DOUBLE PRECISION array, dimension (N)


         On entry D contains the main diagonal of the bidiagonal


         matrix.


         On exit D, if INFO = 0, contains its singular values.

E

          E is DOUBLE PRECISION array, dimension (M-1)


         Contains the subdiagonal entries of the bidiagonal matrix.


         On exit, E has been destroyed.

U

          U is DOUBLE PRECISION array, dimension (LDU, N)


         On exit, U contains the left singular vectors, 


          if U passed in as (N, N) Identity.

LDU

          LDU is INTEGER


         On entry, leading dimension of U.

VT

          VT is DOUBLE PRECISION array, dimension (LDVT, M)


         On exit, VT**T contains the right singular vectors,


          if VT passed in as (M, M) Identity.

LDVT

          LDVT is INTEGER


         On entry, leading dimension of VT.

SMLSIZ

          SMLSIZ is INTEGER


         On entry, maximum size of the subproblems at the


         bottom of the computation tree.

IWORK

          IWORK is INTEGER array, dimension (8*N)

WORK

          WORK is DOUBLE PRECISION array, dimension (3*M**2+2*M)

INFO

          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.


          > 0:  if INFO = 1, a singular value did not converge

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

 Using a divide and conquer approach, SLASD0 computes the singular


 value decomposition (SVD) of a real upper bidiagonal N-by-M


 matrix B with diagonal D and offdiagonal E, where M = N + SQRE.


 The algorithm computes orthogonal matrices U and VT such that


 B = U * S * VT. The singular values S are overwritten on D.


 A related subroutine, SLASDA, computes only the singular values,


 and optionally, the singular vectors in compact form.

N

          N is INTEGER


         On entry, the row dimension of the upper bidiagonal matrix.


         This is also the dimension of the main diagonal array D.

SQRE

          SQRE is INTEGER


         Specifies the column dimension of the bidiagonal matrix.


         = 0: The bidiagonal matrix has column dimension M = N;


         = 1: The bidiagonal matrix has column dimension M = N+1;

D

          D is REAL array, dimension (N)


         On entry D contains the main diagonal of the bidiagonal


         matrix.


         On exit D, if INFO = 0, contains its singular values.

E

          E is REAL array, dimension (M-1)


         Contains the subdiagonal entries of the bidiagonal matrix.


         On exit, E has been destroyed.

U

          U is REAL array, dimension (LDU, N)


         On exit, U contains the left singular vectors,


          if U passed in as (N, N) Identity.

LDU

          LDU is INTEGER


         On entry, leading dimension of U.

VT

          VT is REAL array, dimension (LDVT, M)


         On exit, VT**T contains the right singular vectors,


          if VT passed in as (M, M) Identity.

LDVT

          LDVT is INTEGER


         On entry, leading dimension of VT.

SMLSIZ

          SMLSIZ is INTEGER


         On entry, maximum size of the subproblems at the


         bottom of the computation tree.

IWORK

          IWORK is INTEGER array, dimension (8*N)

WORK

          WORK is REAL array, dimension (3*M**2+2*M)

INFO

          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.


          > 0:  if INFO = 1, a singular value did not converge

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA