!>
!> SDRVBD checks the singular value decomposition (SVD) drivers
!> SGESVD, SGESDD, SGESVDQ, SGESVJ, SGEJSV, and DGESVDX.
!>
!> Both SGESVD and SGESDD 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 SDRVBD 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 SGESVD:
!>
!> (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 SGESDD:
!>
!> (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 SGESVDQ:
!>
!> (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 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.)
!>
!> Test for SGESVDX( 'V', 'V', 'A' )/SGESVDX( '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 SGESVDX( '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 SGESVDX( '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 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.
!> 

NSIZES

!>          NSIZES is INTEGER
!>          The number of matrix sizes (M,N) contained in the vectors
!>          MM and NN.
!> 

MM

!>          MM is INTEGER array, dimension (NSIZES)
!>          The values of the matrix row dimension M.
!> 

NN

!>          NN is INTEGER array, dimension (NSIZES)
!>          The values of the matrix column dimension N.
!> 

NTYPES

!>          NTYPES is INTEGER
!>          The number of elements in DOTYPE.   If it is zero, SDRVBD
!>          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, 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
!>          SDRVBD to continue the same random number sequence.
!> 

THRESH

!>          THRESH is REAL
!>          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

!>          A is REAL array, dimension (LDA,NMAX)
!>          where NMAX is the maximum value of N in NN.
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,MMAX),
!>          where MMAX is the maximum value of M in MM.
!> 

U

!>          U is REAL array, dimension (LDU,MMAX)
!> 

LDU

!>          LDU is INTEGER
!>          The leading dimension of the array U.  LDU >= max(1,MMAX).
!> 

VT

!>          VT is REAL array, dimension (LDVT,NMAX)
!> 

LDVT

!>          LDVT is INTEGER
!>          The leading dimension of the array VT.  LDVT >= max(1,NMAX).
!> 

ASAV

!>          ASAV is REAL array, dimension (LDA,NMAX)
!> 

USAV

!>          USAV is REAL array, dimension (LDU,MMAX)
!> 

VTSAV

!>          VTSAV is REAL array, dimension (LDVT,NMAX)
!> 

S

!>          S is REAL array, dimension
!>                      (max(min(MM,NN)))
!> 

SSAV

!>          SSAV is REAL array, dimension
!>                      (max(min(MM,NN)))
!> 

E

!>          E is REAL array, dimension
!>                      (max(min(MM,NN)))
!> 

WORK

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

LWORK

!>          LWORK is 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

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

NOUT

!>          NOUT 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) ).
!>          -21: LWORK too small.
!>          If  SLATMS, or SGESVD returns an error code, the
!>              absolute value of it is returned.
!> 

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