dbdsdc
dbdsdc - compute the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B
SUBROUTINE DBDSDC( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
* WORK, IWORK, INFO)
CHARACTER * 1 UPLO, COMPQ
INTEGER N, LDU, LDVT, INFO
INTEGER IQ(*), IWORK(*)
DOUBLE PRECISION D(*), E(*), U(LDU,*), VT(LDVT,*), Q(*), WORK(*)
SUBROUTINE DBDSDC_64( UPLO, COMPQ, N, D, E, U, LDU, VT, LDVT, Q, IQ,
* WORK, IWORK, INFO)
CHARACTER * 1 UPLO, COMPQ
INTEGER*8 N, LDU, LDVT, INFO
INTEGER*8 IQ(*), IWORK(*)
DOUBLE PRECISION D(*), E(*), U(LDU,*), VT(LDVT,*), Q(*), WORK(*)
SUBROUTINE BDSDC( UPLO, COMPQ, [N], D, E, U, [LDU], VT, [LDVT], Q,
* IQ, [WORK], [IWORK], [INFO])
CHARACTER(LEN=1) :: UPLO, COMPQ
INTEGER :: N, LDU, LDVT, INFO
INTEGER, DIMENSION(:) :: IQ, IWORK
REAL(8), DIMENSION(:) :: D, E, Q, WORK
REAL(8), DIMENSION(:,:) :: U, VT
SUBROUTINE BDSDC_64( UPLO, COMPQ, [N], D, E, U, [LDU], VT, [LDVT],
* Q, IQ, [WORK], [IWORK], [INFO])
CHARACTER(LEN=1) :: UPLO, COMPQ
INTEGER(8) :: N, LDU, LDVT, INFO
INTEGER(8), DIMENSION(:) :: IQ, IWORK
REAL(8), DIMENSION(:) :: D, E, Q, WORK
REAL(8), DIMENSION(:,:) :: U, VT
#include <sunperf.h>
void dbdsdc(char uplo, char compq, int n, double *d, double *e, double *u, int ldu, double *vt, int ldvt, double *q, int *iq, int *info);
void dbdsdc_64(char uplo, char compq, long n, double *d, double *e, double *u, long ldu, double *vt, long ldvt, double *q, long *iq, long *info);
dbdsdc computes the singular value decomposition (SVD) of a real
N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT,
using a divide and conquer method, where S is a diagonal matrix
with non-negative 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 X-MP, Cray Y-MP, Cray C-90, or Cray-2.
It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none. See SLASD3 for details.
The code currently call SLASDQ if singular values only are desired.
However, it can be slightly modified to compute singular values
using the divide and conquer method.
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* UPLO (input)
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* COMPQ (input)
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Specifies whether singular vectors are to be computed
as follows:
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* N (input)
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The order of the matrix B. N >= 0.
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* D (input/output)
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On entry, the n diagonal elements of the bidiagonal matrix B.
On exit, if INFO=0, the singular values of B.
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* E (input/output)
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On entry, the elements of E contain the offdiagonal
elements of the bidiagonal matrix whose SVD is desired.
On exit, E has been destroyed.
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* U (output)
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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.
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* LDU (input)
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The leading dimension of the array U. LDU >= 1.
If singular vectors are desired, then LDU >= max( 1, N ).
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* VT (output)
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If COMPQ = 'I', then:
On exit, if INFO = 0, VT' contains the right singular
vectors of the bidiagonal matrix.
For other values of COMPQ, VT is not referenced.
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* LDVT (input)
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The leading dimension of the array VT. LDVT >= 1.
If singular vectors are desired, then LDVT >= max( 1, N ).
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* Q (input)
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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.
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* IQ (output)
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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.
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* WORK (workspace)
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If COMPQ = 'N' then LWORK >= (2 * N).
If COMPQ = 'P' then LWORK >= (6 * N).
If COMPQ = 'I' then LWORK >= (3 * N**2 + 4 * N).
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* IWORK (workspace)
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dimension(8*N)
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* INFO (output)
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