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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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| subroutine cdrvbd | ( | integer | NSIZES, |
| integer, dimension( * ) | MM, | ||
| integer, dimension( * ) | NN, | ||
| integer | NTYPES, | ||
| logical, dimension( * ) | DOTYPE, | ||
| integer, dimension( 4 ) | ISEED, | ||
| real | THRESH, | ||
| complex, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| complex, dimension( ldu, * ) | U, | ||
| integer | LDU, | ||
| complex, dimension( ldvt, * ) | VT, | ||
| integer | LDVT, | ||
| complex, dimension( lda, * ) | ASAV, | ||
| complex, dimension( ldu, * ) | USAV, | ||
| complex, dimension( ldvt, * ) | VTSAV, | ||
| real, dimension( * ) | S, | ||
| real, dimension( * ) | SSAV, | ||
| real, dimension( * ) | E, | ||
| complex, dimension( * ) | WORK, | ||
| integer | LWORK, | ||
| real, dimension( * ) | RWORK, | ||
| integer, dimension( * ) | IWORK, | ||
| integer | NOUNIT, | ||
| integer | INFO | ||
| ) |
CDRVBD
CDRVBD checks the singular value decomposition (SVD) driver CGESVD
and CGESDD.
CGESVD and CGESDD factors A = U diag(S) VT, where U and VT are
unitary and diag(S) is diagonal with the entries of the array S on
its diagonal. The entries of S are the singular values, nonnegative
and stored in decreasing order. U and VT can be optionally not
computed, overwritten on A, or computed partially.
A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN.
U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N.
When CDRVBD is called, a number of matrix "sizes" (M's and N's)
and a number of matrix "types" are specified. For each size (M,N)
and each type of matrix, and for the minimal workspace as well as
workspace adequate to permit blocking, an M x N matrix "A" will be
generated and used to test the SVD routines. For each matrix, A will
be factored as A = U diag(S) VT and the following 12 tests computed:
Test for CGESVD:
(1) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(2) | I - U'U | / ( M ulp )
(3) | I - VT VT' | / ( N ulp )
(4) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
(5) | U - Upartial | / ( M ulp ) where Upartial is a partially
computed U.
(6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
computed VT.
(7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
vector of singular values from the partial SVD
Test for CGESDD:
(1) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(2) | I - U'U | / ( M ulp )
(3) | I - VT VT' | / ( N ulp )
(4) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
(5) | U - Upartial | / ( M ulp ) where Upartial is a partially
computed U.
(6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
computed VT.
(7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
vector of singular values from the partial SVD
Test for CGESVJ:
(1) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(2) | I - U'U | / ( M ulp )
(3) | I - VT VT' | / ( N ulp )
(4) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
Test for CGEJSV:
(1) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(2) | I - U'U | / ( M ulp )
(3) | I - VT VT' | / ( N ulp )
(4) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
Test for CGESVDX( 'V', 'V', 'A' )/CGESVDX( 'N', 'N', 'A' )
(1) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(2) | I - U'U | / ( M ulp )
(3) | I - VT VT' | / ( N ulp )
(4) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
(5) | U - Upartial | / ( M ulp ) where Upartial is a partially
computed U.
(6) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
computed VT.
(7) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
vector of singular values from the partial SVD
Test for CGESVDX( 'V', 'V', 'I' )
(8) | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
(9) | I - U'U | / ( M ulp )
(10) | I - VT VT' | / ( N ulp )
Test for CGESVDX( 'V', 'V', 'V' )
(11) | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
(12) | I - U'U | / ( M ulp )
(13) | I - VT VT' | / ( N ulp )
The "sizes" are specified by the arrays MM(1:NSIZES) and
NN(1:NSIZES); the value of each element pair (MM(j),NN(j))
specifies one size. The "types" are specified by a logical array
DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type "j"
will be generated.
Currently, the list of possible types is:
(1) The zero matrix.
(2) The identity matrix.
(3) A matrix of the form U D V, where U and V are unitary and
D has evenly spaced entries 1, ..., ULP with random signs
on the diagonal.
(4) Same as (3), but multiplied by the underflow-threshold / ULP.
(5) Same as (3), but multiplied by the overflow-threshold * ULP. | [in] | NSIZES | NSIZES is INTEGER
The number of sizes of matrices to use. If it is zero,
CDRVBD does nothing. It must be at least zero. |
| [in] | MM | MM is INTEGER array, dimension (NSIZES)
An array containing the matrix "heights" to be used. For
each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j)
will be ignored. The MM(j) values must be at least zero. |
| [in] | NN | NN is INTEGER array, dimension (NSIZES)
An array containing the matrix "widths" to be used. For
each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j)
will be ignored. The NN(j) values must be at least zero. |
| [in] | NTYPES | NTYPES is INTEGER
The number of elements in DOTYPE. If it is zero, CDRVBD
does nothing. It must be at least zero. If it is MAXTYP+1
and NSIZES is 1, then an additional type, MAXTYP+1 is
defined, which is to use whatever matrices are in A and B.
This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
DOTYPE(MAXTYP+1) is .TRUE. . |
| [in] | DOTYPE | DOTYPE is LOGICAL array, dimension (NTYPES)
If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix
of type j will be generated. If NTYPES is smaller than the
maximum number of types defined (PARAMETER MAXTYP), then
types NTYPES+1 through MAXTYP will not be generated. If
NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through
DOTYPE(NTYPES) will be ignored. |
| [in,out] | ISEED | ISEED is INTEGER array, dimension (4)
On entry ISEED specifies the seed of the random number
generator. The array elements should be between 0 and 4095;
if not they will be reduced mod 4096. Also, ISEED(4) must
be odd. The random number generator uses a linear
congruential sequence limited to small integers, and so
should produce machine independent random numbers. The
values of ISEED are changed on exit, and can be used in the
next call to CDRVBD to continue the same random number
sequence. |
| [in] | THRESH | THRESH is REAL
A test will count as "failed" if the "error", computed as
described above, exceeds THRESH. Note that the error
is scaled to be O(1), so THRESH should be a reasonably
small multiple of 1, e.g., 10 or 100. In particular,
it should not depend on the precision (single vs. double)
or the size of the matrix. It must be at least zero. |
| [out] | A | A is COMPLEX array, dimension (LDA,max(NN))
Used to hold the matrix whose singular values are to be
computed. On exit, A contains the last matrix actually
used. |
| [in] | LDA | LDA is INTEGER
The leading dimension of A. It must be at
least 1 and at least max( MM ). |
| [out] | U | U is COMPLEX array, dimension (LDU,max(MM))
Used to hold the computed matrix of right singular vectors.
On exit, U contains the last such vectors actually computed. |
| [in] | LDU | LDU is INTEGER
The leading dimension of U. It must be at
least 1 and at least max( MM ). |
| [out] | VT | VT is COMPLEX array, dimension (LDVT,max(NN))
Used to hold the computed matrix of left singular vectors.
On exit, VT contains the last such vectors actually computed. |
| [in] | LDVT | LDVT is INTEGER
The leading dimension of VT. It must be at
least 1 and at least max( NN ). |
| [out] | ASAV | ASAV is COMPLEX array, dimension (LDA,max(NN))
Used to hold a different copy of the matrix whose singular
values are to be computed. On exit, A contains the last
matrix actually used. |
| [out] | USAV | USAV is COMPLEX array, dimension (LDU,max(MM))
Used to hold a different copy of the computed matrix of
right singular vectors. On exit, USAV contains the last such
vectors actually computed. |
| [out] | VTSAV | VTSAV is COMPLEX array, dimension (LDVT,max(NN))
Used to hold a different copy of the computed matrix of
left singular vectors. On exit, VTSAV contains the last such
vectors actually computed. |
| [out] | S | S is REAL array, dimension (max(min(MM,NN)))
Contains the computed singular values. |
| [out] | SSAV | SSAV is REAL array, dimension (max(min(MM,NN)))
Contains another copy of the computed singular values. |
| [out] | E | E is REAL array, dimension (max(min(MM,NN)))
Workspace for CGESVD. |
| [out] | WORK | WORK is COMPLEX array, dimension (LWORK) |
| [in] | LWORK | LWORK is INTEGER
The number of entries in WORK. This must be at least
MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all
pairs (M,N)=(MM(j),NN(j)) |
| [out] | RWORK | RWORK is REAL array,
dimension ( 5*max(max(MM,NN)) ) |
| [out] | IWORK | IWORK is INTEGER array, dimension at least 8*min(M,N) |
| [in] | NOUNIT | NOUNIT is INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IINFO not equal to 0.) |
| [out] | INFO | INFO is INTEGER
If 0, then everything ran OK.
-1: NSIZES < 0
-2: Some MM(j) < 0
-3: Some NN(j) < 0
-4: NTYPES < 0
-7: THRESH < 0
-10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
-12: LDU < 1 or LDU < MMAX.
-14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ).
-29: LWORK too small.
If CLATMS, or CGESVD returns an error code, the
absolute value of it is returned. |
Definition at line 391 of file cdrvbd.f.
1.8.10