cdrvbd3

!>
!> CDRVBD checks the singular value decomposition (SVD) driver CGESVD,
!> CGESDD, CGESVJ, CGEJSV, CGESVDX, and CGESVDQ.
!>
!> 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  (M's and N's)
!> and a number of matrix  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  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:
!>
!> (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 CGESVDQ:
!>
!> (36)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
!>
!> (37)  | I - U'U | / ( M ulp )
!>
!> (38)  | I - VT VT' | / ( N ulp )
!>
!> (39)  S contains MNMIN nonnegative values in decreasing order.
!>       (Return 0 if true, 1/ULP if false.)
!>
!> Test for CGESVJ:
!>
!> (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 CGEJSV:
!>
!> (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.)
!>
!> Test for CGESVDX( 'V', 'V', 'A' )/CGESVDX( 'N', 'N', 'A' )
!>
!> (23)  | A - U diag(S) VT | / ( |A| max(M,N) ulp )
!>
!> (24)  | I - U'U | / ( M ulp )
!>
!> (25)  | I - VT VT' | / ( N ulp )
!>
!> (26)  S contains MNMIN nonnegative values in decreasing order.
!>       (Return 0 if true, 1/ULP if false.)
!>
!> (27)  | U - Upartial | / ( M ulp ) where Upartial is a partially
!>       computed U.
!>
!> (28)  | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
!>       computed VT.
!>
!> (29)  | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
!>       vector of singular values from the partial SVD
!>
!> Test for CGESVDX( 'V', 'V', 'I' )
!>
!> (30)  | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
!>
!> (31)  | I - U'U | / ( M ulp )
!>
!> (32)  | I - VT VT' | / ( N ulp )
!>
!> Test for CGESVDX( 'V', 'V', 'V' )
!>
!> (33)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )
!>
!> (34)   | I - U'U | / ( M ulp )
!>
!> (35)   | I - VT VT' | / ( N ulp )
!>
!> The  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  are specified by a logical array
!> DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type 
!> 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.
!> 

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.
!> 

MM

!>          MM is INTEGER array, dimension (NSIZES)
!>          An array containing the matrix  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.
!> 

NN

!>          NN is INTEGER array, dimension (NSIZES)
!>          An array containing the matrix  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.
!> 

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. .
!> 

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.
!> 

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.
!> 

THRESH

!>          THRESH is REAL
!>          A test will count as  if the , 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.
!> 

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.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of A.  It must be at
!>          least 1 and at least max( MM ).
!> 

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.
!> 

LDU

!>          LDU is INTEGER
!>          The leading dimension of U.  It must be at
!>          least 1 and at least max( MM ).
!> 

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.
!> 

LDVT

!>          LDVT is INTEGER
!>          The leading dimension of VT.  It must be at
!>          least 1 and at least max( NN ).
!> 

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.
!> 

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.
!> 

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.
!> 

S

!>          S is REAL array, dimension (max(min(MM,NN)))
!>          Contains the computed singular values.
!> 

SSAV

!>          SSAV is REAL array, dimension (max(min(MM,NN)))
!>          Contains another copy of the computed singular values.
!> 

E

!>          E is REAL array, dimension (max(min(MM,NN)))
!>          Workspace for CGESVD.
!> 

WORK

!>          WORK is COMPLEX array, dimension (LWORK)
!> 

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))
!> 

RWORK

!>          RWORK is REAL array,
!>                      dimension ( 5*max(max(MM,NN)) )
!> 

IWORK

!>          IWORK is INTEGER array, dimension at least 8*min(M,N)
!> 

NOUNIT

!>          NOUNIT is INTEGER
!>          The FORTRAN unit number for printing out error messages
!>          (e.g., if a routine returns IINFO not equal to 0.)
!> 

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.
!> 

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