DDRVBD
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
DDRVBD checks the singular value decomposition (SVD) drivers
DGESVD, DGESDD, DGESVJ, and DGEJSV.
Both DGESVD and DGESDD factor A = U diag(S) VT, where U and VT are
orthogonal 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 DDRVBD 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 DGESVD:
(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 DGESDD:
(8) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(9) | I - U'U | / ( M ulp )
(10) | I - VT VT' | / ( N ulp )
(11) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
(12) | U - Upartial | / ( M ulp ) where Upartial is a partially
computed U.
(13) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
computed VT.
(14) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
vector of singular values from the partial SVD
Test for SGESVJ:
(15) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(16) | I - U'U | / ( M ulp )
(17) | I - VT VT' | / ( N ulp )
(18) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
Test for SGEJSV:
(19) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(20) | I - U'U | / ( M ulp )
(21) | I - VT VT' | / ( N ulp )
(22) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
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 orthogonal 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.
DGESVD, DGESDD, DGESVJ, and DGEJSV.
Both DGESVD and DGESDD factor A = U diag(S) VT, where U and VT are
orthogonal 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 DDRVBD 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 DGESVD:
(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 DGESDD:
(8) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(9) | I - U'U | / ( M ulp )
(10) | I - VT VT' | / ( N ulp )
(11) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
(12) | U - Upartial | / ( M ulp ) where Upartial is a partially
computed U.
(13) | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
computed VT.
(14) | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
vector of singular values from the partial SVD
Test for SGESVJ:
(15) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(16) | I - U'U | / ( M ulp )
(17) | I - VT VT' | / ( N ulp )
(18) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
Test for SGEJSV:
(19) | A - U diag(S) VT | / ( |A| max(M,N) ulp )
(20) | I - U'U | / ( M ulp )
(21) | I - VT VT' | / ( N ulp )
(22) S contains MNMIN nonnegative values in decreasing order.
(Return 0 if true, 1/ULP if false.)
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 orthogonal 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.
Arguments
| NSIZES |
(input) INTEGER
The number of matrix sizes (M,N) contained in the vectors
MM and NN. |
| MM |
(input) INTEGER array, dimension (NSIZES)
The values of the matrix row dimension M.
|
| NN |
(input) INTEGER array, dimension (NSIZES)
The values of the matrix column dimension N.
|
| NTYPES |
(input) INTEGER
The number of elements in DOTYPE. If it is zero, DDRVBD
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. . |
| DOTYPE |
(input) 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. |
| ISEED |
(input/output) INTEGER array, dimension (4)
On entry, 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. On exit, ISEED is changed and can be used in the next call to DDRVBD to continue the same random number sequence. |
| THRESH |
(input) DOUBLE PRECISION
The threshold value for the test ratios. A result is
included in the output file if RESULT >= THRESH. The test ratios are scaled to be O(1), so THRESH should be a small multiple of 1, e.g., 10 or 100. To have every test ratio printed, use THRESH = 0. |
| A |
(workspace) DOUBLE PRECISION array, dimension (LDA,NMAX)
where NMAX is the maximum value of N in NN.
|
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,MMAX),
where MMAX is the maximum value of M in MM. |
| U |
(workspace) DOUBLE PRECISION array, dimension (LDU,MMAX)
|
| LDU |
(input) INTEGER
The leading dimension of the array U. LDU >= max(1,MMAX).
|
| VT |
(workspace) DOUBLE PRECISION array, dimension (LDVT,NMAX)
|
| LDVT |
(input) INTEGER
The leading dimension of the array VT. LDVT >= max(1,NMAX).
|
| ASAV |
(workspace) DOUBLE PRECISION array, dimension (LDA,NMAX)
|
| USAV |
(workspace) DOUBLE PRECISION array, dimension (LDU,MMAX)
|
| VTSAV |
(workspace) DOUBLE PRECISION array, dimension (LDVT,NMAX)
|
| S |
(workspace) DOUBLE PRECISION array, dimension
(max(min(MM,NN)))
|
| SSAV |
(workspace) DOUBLE PRECISION array, dimension
(max(min(MM,NN)))
|
| E |
(workspace) DOUBLE PRECISION array, dimension
(max(min(MM,NN)))
|
| WORK |
(workspace) DOUBLE PRECISION array, dimension (LWORK)
|
| LWORK |
(input) INTEGER
The number of entries in WORK. This must be at least
max(3*MN+MX,5*MN-4)+2*MN**2 for all pairs pairs (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) ) |
| IWORK |
(workspace) INTEGER array, dimension at least 8*min(M,N)
|
| NOUT |
(input) INTEGER
The FORTRAN unit number for printing out error messages
(e.g., if a routine returns IINFO not equal to 0.) |
| INFO |
(output) 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) ). -21: LWORK too small. If DLATMS, or DGESVD returns an error code, the absolute value of it is returned. |