LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

Go to the source code of this file.
Functions/Subroutines  
subroutine  sbdsdc (UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ, WORK, IWORK, INFO) 
SBDSDC 
subroutine sbdsdc  (  character  UPLO, 
character  COMPQ,  
integer  N,  
real, dimension( * )  D,  
real, dimension( * )  E,  
real, dimension( ldu, * )  U,  
integer  LDU,  
real, dimension( ldvt, * )  VT,  
integer  LDVT,  
real, dimension( * )  Q,  
integer, dimension( * )  IQ,  
real, dimension( * )  WORK,  
integer, dimension( * )  IWORK,  
integer  INFO  
) 
SBDSDC
Download SBDSDC + dependencies [TGZ] [ZIP] [TXT]SBDSDC computes the singular value decomposition (SVD) of a real NbyN (upper or lower) bidiagonal matrix B: B = U * S * VT, using a divide and conquer method, where S is a diagonal matrix with nonnegative diagonal elements (the singular values of B), and U and VT are orthogonal matrices of left and right singular vectors, respectively. SBDSDC can be used to compute all singular values, and optionally, singular vectors or singular vectors in compact form. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See SLASD3 for details. The code currently calls SLASDQ if singular values only are desired. However, it can be slightly modified to compute singular values using the divide and conquer method.
[in]  UPLO  UPLO is CHARACTER*1 = 'U': B is upper bidiagonal. = 'L': B is lower bidiagonal. 
[in]  COMPQ  COMPQ is CHARACTER*1 Specifies whether singular vectors are to be computed as follows: = 'N': Compute singular values only; = 'P': Compute singular values and compute singular vectors in compact form; = 'I': Compute singular values and singular vectors. 
[in]  N  N is INTEGER The order of the matrix B. N >= 0. 
[in,out]  D  D is REAL array, dimension (N) On entry, the n diagonal elements of the bidiagonal matrix B. On exit, if INFO=0, the singular values of B. 
[in,out]  E  E is REAL array, dimension (N1) On entry, the elements of E contain the offdiagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E has been destroyed. 
[out]  U  U is REAL array, dimension (LDU,N) If COMPQ = 'I', then: On exit, if INFO = 0, U contains the left singular vectors of the bidiagonal matrix. For other values of COMPQ, U is not referenced. 
[in]  LDU  LDU is INTEGER The leading dimension of the array U. LDU >= 1. If singular vectors are desired, then LDU >= max( 1, N ). 
[out]  VT  VT is REAL array, dimension (LDVT,N) If COMPQ = 'I', then: On exit, if INFO = 0, VT**T contains the right singular vectors of the bidiagonal matrix. For other values of COMPQ, VT is not referenced. 
[in]  LDVT  LDVT is INTEGER The leading dimension of the array VT. LDVT >= 1. If singular vectors are desired, then LDVT >= max( 1, N ). 
[out]  Q  Q is REAL array, dimension (LDQ) If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain the left and right singular vectors in a compact form, requiring O(N log N) space instead of 2*N**2. In particular, Q contains all the REAL data in LDQ >= N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is returned by ILAENV and is equal to the maximum size of the subproblems at the bottom of the computation tree (usually about 25). For other values of COMPQ, Q is not referenced. 
[out]  IQ  IQ is INTEGER array, dimension (LDIQ) If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain the left and right singular vectors in a compact form, requiring O(N log N) space instead of 2*N**2. In particular, IQ contains all INTEGER data in LDIQ >= N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is returned by ILAENV and is equal to the maximum size of the subproblems at the bottom of the computation tree (usually about 25). For other values of COMPQ, IQ is not referenced. 
[out]  WORK  WORK is REAL array, dimension (MAX(1,LWORK)) If COMPQ = 'N' then LWORK >= (4 * N). If COMPQ = 'P' then LWORK >= (6 * N). If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N). 
[out]  IWORK  IWORK is INTEGER array, dimension (8*N) 
[out]  INFO  INFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: The algorithm failed to compute a singular value. The update process of divide and conquer failed. 
Definition at line 205 of file sbdsdc.f.