 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ schkst()

 subroutine schkst ( integer NSIZES, integer, dimension( * ) NN, integer NTYPES, logical, dimension( * ) DOTYPE, integer, dimension( 4 ) ISEED, real THRESH, integer NOUNIT, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) AP, real, dimension( * ) SD, real, dimension( * ) SE, real, dimension( * ) D1, real, dimension( * ) D2, real, dimension( * ) D3, real, dimension( * ) D4, real, dimension( * ) D5, real, dimension( * ) WA1, real, dimension( * ) WA2, real, dimension( * ) WA3, real, dimension( * ) WR, real, dimension( ldu, * ) U, integer LDU, real, dimension( ldu, * ) V, real, dimension( * ) VP, real, dimension( * ) TAU, real, dimension( ldu, * ) Z, real, dimension( * ) WORK, integer LWORK, integer, dimension( * ) IWORK, integer LIWORK, real, dimension( * ) RESULT, integer INFO )

SCHKST

Purpose:
``` SCHKST  checks the symmetric eigenvalue problem routines.

SSYTRD factors A as  U S U' , where ' means transpose,
S is symmetric tridiagonal, and U is orthogonal.
SSYTRD can use either just the lower or just the upper triangle
of A; SCHKST checks both cases.
U is represented as a product of Householder
transformations, whose vectors are stored in the first
n-1 columns of V, and whose scale factors are in TAU.

SSPTRD does the same as SSYTRD, except that A and V are stored
in "packed" format.

SORGTR constructs the matrix U from the contents of V and TAU.

SOPGTR constructs the matrix U from the contents of VP and TAU.

SSTEQR factors S as  Z D1 Z' , where Z is the orthogonal
matrix of eigenvectors and D1 is a diagonal matrix with
the eigenvalues on the diagonal.  D2 is the matrix of
eigenvalues computed when Z is not computed.

SSTERF computes D3, the matrix of eigenvalues, by the
PWK method, which does not yield eigenvectors.

SPTEQR factors S as  Z4 D4 Z4' , for a
symmetric positive definite tridiagonal matrix.
D5 is the matrix of eigenvalues computed when Z is not
computed.

SSTEBZ computes selected eigenvalues.  WA1, WA2, and
WA3 will denote eigenvalues computed to high
absolute accuracy, with different range options.
WR will denote eigenvalues computed to high relative
accuracy.

SSTEIN computes Y, the eigenvectors of S, given the
eigenvalues.

SSTEDC factors S as Z D1 Z' , where Z is the orthogonal
matrix of eigenvectors and D1 is a diagonal matrix with
the eigenvalues on the diagonal ('I' option). It may also
update an input orthogonal matrix, usually the output
from SSYTRD/SORGTR or SSPTRD/SOPGTR ('V' option). It may
also just compute eigenvalues ('N' option).

SSTEMR factors S as Z D1 Z' , where Z is the orthogonal
matrix of eigenvectors and D1 is a diagonal matrix with
the eigenvalues on the diagonal ('I' option).  SSTEMR
uses the Relatively Robust Representation whenever possible.

When SCHKST is called, a number of matrix "sizes" ("n's") and a
number of matrix "types" are specified.  For each size ("n")
and each type of matrix, one matrix will be generated and used
to test the symmetric eigenroutines.  For each matrix, a number
of tests will be performed:

(1)     | A - V S V' | / ( |A| n ulp ) SSYTRD( UPLO='U', ... )

(2)     | I - UV' | / ( n ulp )        SORGTR( UPLO='U', ... )

(3)     | A - V S V' | / ( |A| n ulp ) SSYTRD( UPLO='L', ... )

(4)     | I - UV' | / ( n ulp )        SORGTR( UPLO='L', ... )

(5-8)   Same as 1-4, but for SSPTRD and SOPGTR.

(9)     | S - Z D Z' | / ( |S| n ulp ) SSTEQR('V',...)

(10)    | I - ZZ' | / ( n ulp )        SSTEQR('V',...)

(11)    | D1 - D2 | / ( |D1| ulp )        SSTEQR('N',...)

(12)    | D1 - D3 | / ( |D1| ulp )        SSTERF

(13)    0 if the true eigenvalues (computed by sturm count)
of S are within THRESH of
those in D1.  2*THRESH if they are not.  (Tested using
SSTECH)

For S positive definite,

(14)    | S - Z4 D4 Z4' | / ( |S| n ulp ) SPTEQR('V',...)

(15)    | I - Z4 Z4' | / ( n ulp )        SPTEQR('V',...)

(16)    | D4 - D5 | / ( 100 |D4| ulp )       SPTEQR('N',...)

When S is also diagonally dominant by the factor gamma < 1,

(17)    max | D4(i) - WR(i) | / ( |D4(i)| omega ) ,
i
omega = 2 (2n-1) ULP (1 + 8 gamma**2) / (1 - gamma)**4
SSTEBZ( 'A', 'E', ...)

(18)    | WA1 - D3 | / ( |D3| ulp )          SSTEBZ( 'A', 'E', ...)

(19)    ( max { min | WA2(i)-WA3(j) | } +
i     j
max { min | WA3(i)-WA2(j) | } ) / ( |D3| ulp )
i     j
SSTEBZ( 'I', 'E', ...)

(20)    | S - Y WA1 Y' | / ( |S| n ulp )  SSTEBZ, SSTEIN

(21)    | I - Y Y' | / ( n ulp )          SSTEBZ, SSTEIN

(22)    | S - Z D Z' | / ( |S| n ulp )    SSTEDC('I')

(23)    | I - ZZ' | / ( n ulp )           SSTEDC('I')

(24)    | S - Z D Z' | / ( |S| n ulp )    SSTEDC('V')

(25)    | I - ZZ' | / ( n ulp )           SSTEDC('V')

(26)    | D1 - D2 | / ( |D1| ulp )           SSTEDC('V') and
SSTEDC('N')

Test 27 is disabled at the moment because SSTEMR does not
guarantee high relatvie accuracy.

(27)    max | D6(i) - WR(i) | / ( |D6(i)| omega ) ,
i
omega = 2 (2n-1) ULP (1 + 8 gamma**2) / (1 - gamma)**4
SSTEMR('V', 'A')

(28)    max | D6(i) - WR(i) | / ( |D6(i)| omega ) ,
i
omega = 2 (2n-1) ULP (1 + 8 gamma**2) / (1 - gamma)**4
SSTEMR('V', 'I')

Tests 29 through 34 are disable at present because SSTEMR
does not handle partial spectrum requests.

(29)    | S - Z D Z' | / ( |S| n ulp )    SSTEMR('V', 'I')

(30)    | I - ZZ' | / ( n ulp )           SSTEMR('V', 'I')

(31)    ( max { min | WA2(i)-WA3(j) | } +
i     j
max { min | WA3(i)-WA2(j) | } ) / ( |D3| ulp )
i     j
SSTEMR('N', 'I') vs. SSTEMR('V', 'I')

(32)    | S - Z D Z' | / ( |S| n ulp )    SSTEMR('V', 'V')

(33)    | I - ZZ' | / ( n ulp )           SSTEMR('V', 'V')

(34)    ( max { min | WA2(i)-WA3(j) | } +
i     j
max { min | WA3(i)-WA2(j) | } ) / ( |D3| ulp )
i     j
SSTEMR('N', 'V') vs. SSTEMR('V', 'V')

(35)    | S - Z D Z' | / ( |S| n ulp )    SSTEMR('V', 'A')

(36)    | I - ZZ' | / ( n ulp )           SSTEMR('V', 'A')

(37)    ( max { min | WA2(i)-WA3(j) | } +
i     j
max { min | WA3(i)-WA2(j) | } ) / ( |D3| ulp )
i     j
SSTEMR('N', 'A') vs. SSTEMR('V', 'A')

The "sizes" are specified by an array NN(1:NSIZES); the value of
each element 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 diagonal matrix with evenly spaced entries
1, ..., ULP  and random signs.
(ULP = (first number larger than 1) - 1 )
(4)  A diagonal matrix with geometrically spaced entries
1, ..., ULP  and random signs.
(5)  A diagonal matrix with "clustered" entries 1, ULP, ..., ULP
and random signs.

(6)  Same as (4), but multiplied by SQRT( overflow threshold )
(7)  Same as (4), but multiplied by SQRT( underflow threshold )

(8)  A matrix of the form  U' D U, where U is orthogonal and
D has evenly spaced entries 1, ..., ULP with random signs
on the diagonal.

(9)  A matrix of the form  U' D U, where U is orthogonal and
D has geometrically spaced entries 1, ..., ULP with random
signs on the diagonal.

(10) A matrix of the form  U' D U, where U is orthogonal and
D has "clustered" entries 1, ULP,..., ULP with random
signs on the diagonal.

(11) Same as (8), but multiplied by SQRT( overflow threshold )
(12) Same as (8), but multiplied by SQRT( underflow threshold )

(13) Symmetric matrix with random entries chosen from (-1,1).
(14) Same as (13), but multiplied by SQRT( overflow threshold )
(15) Same as (13), but multiplied by SQRT( underflow threshold )
(16) Same as (8), but diagonal elements are all positive.
(17) Same as (9), but diagonal elements are all positive.
(18) Same as (10), but diagonal elements are all positive.
(19) Same as (16), but multiplied by SQRT( overflow threshold )
(20) Same as (16), but multiplied by SQRT( underflow threshold )
(21) A diagonally dominant tridiagonal matrix with geometrically
spaced diagonal entries 1, ..., ULP.```
Parameters
 [in] NSIZES ``` NSIZES is INTEGER The number of sizes of matrices to use. If it is zero, SCHKST does nothing. It must be at least zero.``` [in] NN ``` NN is INTEGER array, dimension (NSIZES) An array containing the sizes to be used for the matrices. Zero values will be skipped. The values must be at least zero.``` [in] NTYPES ``` NTYPES is INTEGER The number of elements in DOTYPE. If it is zero, SCHKST 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 matrix is in A. 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 in NN a matrix of that size and 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 SCHKST 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.``` [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.)``` [in,out] A ``` A is REAL array of dimension ( LDA , max(NN) ) Used to hold the matrix whose eigenvalues 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( NN ).``` [out] AP ``` AP is REAL array of dimension( max(NN)*max(NN+1)/2 ) The matrix A stored in packed format.``` [out] SD ``` SD is REAL array of dimension( max(NN) ) The diagonal of the tridiagonal matrix computed by SSYTRD. On exit, SD and SE contain the tridiagonal form of the matrix in A.``` [out] SE ``` SE is REAL array of dimension( max(NN) ) The off-diagonal of the tridiagonal matrix computed by SSYTRD. On exit, SD and SE contain the tridiagonal form of the matrix in A.``` [out] D1 ``` D1 is REAL array of dimension( max(NN) ) The eigenvalues of A, as computed by SSTEQR simlutaneously with Z. On exit, the eigenvalues in D1 correspond with the matrix in A.``` [out] D2 ``` D2 is REAL array of dimension( max(NN) ) The eigenvalues of A, as computed by SSTEQR if Z is not computed. On exit, the eigenvalues in D2 correspond with the matrix in A.``` [out] D3 ``` D3 is REAL array of dimension( max(NN) ) The eigenvalues of A, as computed by SSTERF. On exit, the eigenvalues in D3 correspond with the matrix in A.``` [out] D4 ``` D4 is REAL array of dimension( max(NN) ) The eigenvalues of A, as computed by SPTEQR(V). ZPTEQR factors S as Z4 D4 Z4* On exit, the eigenvalues in D4 correspond with the matrix in A.``` [out] D5 ``` D5 is REAL array of dimension( max(NN) ) The eigenvalues of A, as computed by SPTEQR(N) when Z is not computed. On exit, the eigenvalues in D4 correspond with the matrix in A.``` [out] WA1 ``` WA1 is REAL array of dimension( max(NN) ) All eigenvalues of A, computed to high absolute accuracy, with different range options. as computed by SSTEBZ.``` [out] WA2 ``` WA2 is REAL array of dimension( max(NN) ) Selected eigenvalues of A, computed to high absolute accuracy, with different range options. as computed by SSTEBZ. Choose random values for IL and IU, and ask for the IL-th through IU-th eigenvalues.``` [out] WA3 ``` WA3 is REAL array of dimension( max(NN) ) Selected eigenvalues of A, computed to high absolute accuracy, with different range options. as computed by SSTEBZ. Determine the values VL and VU of the IL-th and IU-th eigenvalues and ask for all eigenvalues in this range.``` [out] WR ``` WR is REAL array of dimension( max(NN) ) All eigenvalues of A, computed to high absolute accuracy, with different options. as computed by SSTEBZ.``` [out] U ``` U is REAL array of dimension( LDU, max(NN) ). The orthogonal matrix computed by SSYTRD + SORGTR.``` [in] LDU ``` LDU is INTEGER The leading dimension of U, Z, and V. It must be at least 1 and at least max( NN ).``` [out] V ``` V is REAL array of dimension( LDU, max(NN) ). The Housholder vectors computed by SSYTRD in reducing A to tridiagonal form. The vectors computed with UPLO='U' are in the upper triangle, and the vectors computed with UPLO='L' are in the lower triangle. (As described in SSYTRD, the sub- and superdiagonal are not set to 1, although the true Householder vector has a 1 in that position. The routines that use V, such as SORGTR, set those entries to 1 before using them, and then restore them later.)``` [out] VP ``` VP is REAL array of dimension( max(NN)*max(NN+1)/2 ) The matrix V stored in packed format.``` [out] TAU ``` TAU is REAL array of dimension( max(NN) ) The Householder factors computed by SSYTRD in reducing A to tridiagonal form.``` [out] Z ``` Z is REAL array of dimension( LDU, max(NN) ). The orthogonal matrix of eigenvectors computed by SSTEQR, SPTEQR, and SSTEIN.``` [out] WORK ``` WORK is REAL array of dimension( LWORK )``` [in] LWORK ``` LWORK is INTEGER The number of entries in WORK. This must be at least 1 + 4 * Nmax + 2 * Nmax * lg Nmax + 3 * Nmax**2 where Nmax = max( NN(j), 2 ) and lg = log base 2.``` [out] IWORK ``` IWORK is INTEGER array, Workspace.``` [out] LIWORK ``` LIWORK is INTEGER The number of entries in IWORK. This must be at least 6 + 6*Nmax + 5 * Nmax * lg Nmax where Nmax = max( NN(j), 2 ) and lg = log base 2.``` [out] RESULT ``` RESULT is REAL array, dimension (26) The values computed by the tests described above. The values are currently limited to 1/ulp, to avoid overflow.``` [out] INFO ``` INFO is INTEGER If 0, then everything ran OK. -1: NSIZES < 0 -2: Some NN(j) < 0 -3: NTYPES < 0 -5: THRESH < 0 -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ). -23: LDU < 1 or LDU < NMAX. -29: LWORK too small. If SLATMR, SLATMS, SSYTRD, SORGTR, SSTEQR, SSTERF, or SORMC2 returns an error code, the absolute value of it is returned. ----------------------------------------------------------------------- Some Local Variables and Parameters: ---- ----- --------- --- ---------- ZERO, ONE Real 0 and 1. MAXTYP The number of types defined. NTEST The number of tests performed, or which can be performed so far, for the current matrix. NTESTT The total number of tests performed so far. NBLOCK Blocksize as returned by ENVIR. NMAX Largest value in NN. NMATS The number of matrices generated so far. NERRS The number of tests which have exceeded THRESH so far. COND, IMODE Values to be passed to the matrix generators. ANORM Norm of A; passed to matrix generators. OVFL, UNFL Overflow and underflow thresholds. ULP, ULPINV Finest relative precision and its inverse. RTOVFL, RTUNFL Square roots of the previous 2 values. The following four arrays decode JTYPE: KTYPE(j) The general type (1-10) for type "j". KMODE(j) The MODE value to be passed to the matrix generator for type "j". KMAGN(j) The order of magnitude ( O(1), O(overflow^(1/2) ), O(underflow^(1/2) )```

Definition at line 587 of file schkst.f.

591 *
592 * -- LAPACK test routine --
593 * -- LAPACK is a software package provided by Univ. of Tennessee, --
594 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
595 *
596 * .. Scalar Arguments ..
597  INTEGER INFO, LDA, LDU, LIWORK, LWORK, NOUNIT, NSIZES,
598  \$ NTYPES
599  REAL THRESH
600 * ..
601 * .. Array Arguments ..
602  LOGICAL DOTYPE( * )
603  INTEGER ISEED( 4 ), IWORK( * ), NN( * )
604  REAL A( LDA, * ), AP( * ), D1( * ), D2( * ),
605  \$ D3( * ), D4( * ), D5( * ), RESULT( * ),
606  \$ SD( * ), SE( * ), TAU( * ), U( LDU, * ),
607  \$ V( LDU, * ), VP( * ), WA1( * ), WA2( * ),
608  \$ WA3( * ), WORK( * ), WR( * ), Z( LDU, * )
609 * ..
610 *
611 * =====================================================================
612 *
613 * .. Parameters ..
614  REAL ZERO, ONE, TWO, EIGHT, TEN, HUN
615  parameter( zero = 0.0e0, one = 1.0e0, two = 2.0e0,
616  \$ eight = 8.0e0, ten = 10.0e0, hun = 100.0e0 )
617  REAL HALF
618  parameter( half = one / two )
619  INTEGER MAXTYP
620  parameter( maxtyp = 21 )
621  LOGICAL SRANGE
622  parameter( srange = .false. )
623  LOGICAL SREL
624  parameter( srel = .false. )
625 * ..
626 * .. Local Scalars ..
628  INTEGER I, IINFO, IL, IMODE, ITEMP, ITYPE, IU, J, JC,
629  \$ JR, JSIZE, JTYPE, LGN, LIWEDC, LOG2UI, LWEDC,
630  \$ M, M2, M3, MTYPES, N, NAP, NBLOCK, NERRS,
631  \$ NMATS, NMAX, NSPLIT, NTEST, NTESTT
632  REAL ABSTOL, ANINV, ANORM, COND, OVFL, RTOVFL,
633  \$ RTUNFL, TEMP1, TEMP2, TEMP3, TEMP4, ULP,
634  \$ ULPINV, UNFL, VL, VU
635 * ..
636 * .. Local Arrays ..
637  INTEGER IDUMMA( 1 ), IOLDSD( 4 ), ISEED2( 4 ),
638  \$ KMAGN( MAXTYP ), KMODE( MAXTYP ),
639  \$ KTYPE( MAXTYP )
640  REAL DUMMA( 1 )
641 * ..
642 * .. External Functions ..
643  INTEGER ILAENV
644  REAL SLAMCH, SLARND, SSXT1
645  EXTERNAL ilaenv, slamch, slarnd, ssxt1
646 * ..
647 * .. External Subroutines ..
648  EXTERNAL scopy, slabad, slacpy, slaset, slasum, slatmr,
652 * ..
653 * .. Intrinsic Functions ..
654  INTRINSIC abs, int, log, max, min, real, sqrt
655 * ..
656 * .. Data statements ..
657  DATA ktype / 1, 2, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 8,
658  \$ 8, 8, 9, 9, 9, 9, 9, 10 /
659  DATA kmagn / 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1,
660  \$ 2, 3, 1, 1, 1, 2, 3, 1 /
661  DATA kmode / 0, 0, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 0,
662  \$ 0, 0, 4, 3, 1, 4, 4, 3 /
663 * ..
664 * .. Executable Statements ..
665 *
666 * Keep ftnchek happy
667  idumma( 1 ) = 1
668 *
669 * Check for errors
670 *
671  ntestt = 0
672  info = 0
673 *
674 * Important constants
675 *
677  tryrac = .true.
678  nmax = 1
679  DO 10 j = 1, nsizes
680  nmax = max( nmax, nn( j ) )
681  IF( nn( j ).LT.0 )
683  10 CONTINUE
684 *
685  nblock = ilaenv( 1, 'SSYTRD', 'L', nmax, -1, -1, -1 )
686  nblock = min( nmax, max( 1, nblock ) )
687 *
688 * Check for errors
689 *
690  IF( nsizes.LT.0 ) THEN
691  info = -1
692  ELSE IF( badnn ) THEN
693  info = -2
694  ELSE IF( ntypes.LT.0 ) THEN
695  info = -3
696  ELSE IF( lda.LT.nmax ) THEN
697  info = -9
698  ELSE IF( ldu.LT.nmax ) THEN
699  info = -23
700  ELSE IF( 2*max( 2, nmax )**2.GT.lwork ) THEN
701  info = -29
702  END IF
703 *
704  IF( info.NE.0 ) THEN
705  CALL xerbla( 'SCHKST', -info )
706  RETURN
707  END IF
708 *
709 * Quick return if possible
710 *
711  IF( nsizes.EQ.0 .OR. ntypes.EQ.0 )
712  \$ RETURN
713 *
714 * More Important constants
715 *
716  unfl = slamch( 'Safe minimum' )
717  ovfl = one / unfl
718  CALL slabad( unfl, ovfl )
719  ulp = slamch( 'Epsilon' )*slamch( 'Base' )
720  ulpinv = one / ulp
721  log2ui = int( log( ulpinv ) / log( two ) )
722  rtunfl = sqrt( unfl )
723  rtovfl = sqrt( ovfl )
724 *
725 * Loop over sizes, types
726 *
727  DO 20 i = 1, 4
728  iseed2( i ) = iseed( i )
729  20 CONTINUE
730  nerrs = 0
731  nmats = 0
732 *
733  DO 310 jsize = 1, nsizes
734  n = nn( jsize )
735  IF( n.GT.0 ) THEN
736  lgn = int( log( real( n ) ) / log( two ) )
737  IF( 2**lgn.LT.n )
738  \$ lgn = lgn + 1
739  IF( 2**lgn.LT.n )
740  \$ lgn = lgn + 1
741  lwedc = 1 + 4*n + 2*n*lgn + 4*n**2
742  liwedc = 6 + 6*n + 5*n*lgn
743  ELSE
744  lwedc = 8
745  liwedc = 12
746  END IF
747  nap = ( n*( n+1 ) ) / 2
748  aninv = one / real( max( 1, n ) )
749 *
750  IF( nsizes.NE.1 ) THEN
751  mtypes = min( maxtyp, ntypes )
752  ELSE
753  mtypes = min( maxtyp+1, ntypes )
754  END IF
755 *
756  DO 300 jtype = 1, mtypes
757  IF( .NOT.dotype( jtype ) )
758  \$ GO TO 300
759  nmats = nmats + 1
760  ntest = 0
761 *
762  DO 30 j = 1, 4
763  ioldsd( j ) = iseed( j )
764  30 CONTINUE
765 *
766 * Compute "A"
767 *
768 * Control parameters:
769 *
770 * KMAGN KMODE KTYPE
771 * =1 O(1) clustered 1 zero
772 * =2 large clustered 2 identity
773 * =3 small exponential (none)
774 * =4 arithmetic diagonal, (w/ eigenvalues)
775 * =5 random log symmetric, w/ eigenvalues
776 * =6 random (none)
777 * =7 random diagonal
778 * =8 random symmetric
779 * =9 positive definite
780 * =10 diagonally dominant tridiagonal
781 *
782  IF( mtypes.GT.maxtyp )
783  \$ GO TO 100
784 *
785  itype = ktype( jtype )
786  imode = kmode( jtype )
787 *
788 * Compute norm
789 *
790  GO TO ( 40, 50, 60 )kmagn( jtype )
791 *
792  40 CONTINUE
793  anorm = one
794  GO TO 70
795 *
796  50 CONTINUE
797  anorm = ( rtovfl*ulp )*aninv
798  GO TO 70
799 *
800  60 CONTINUE
801  anorm = rtunfl*n*ulpinv
802  GO TO 70
803 *
804  70 CONTINUE
805 *
806  CALL slaset( 'Full', lda, n, zero, zero, a, lda )
807  iinfo = 0
808  IF( jtype.LE.15 ) THEN
809  cond = ulpinv
810  ELSE
811  cond = ulpinv*aninv / ten
812  END IF
813 *
814 * Special Matrices -- Identity & Jordan block
815 *
816 * Zero
817 *
818  IF( itype.EQ.1 ) THEN
819  iinfo = 0
820 *
821  ELSE IF( itype.EQ.2 ) THEN
822 *
823 * Identity
824 *
825  DO 80 jc = 1, n
826  a( jc, jc ) = anorm
827  80 CONTINUE
828 *
829  ELSE IF( itype.EQ.4 ) THEN
830 *
831 * Diagonal Matrix, [Eigen]values Specified
832 *
833  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
834  \$ anorm, 0, 0, 'N', a, lda, work( n+1 ),
835  \$ iinfo )
836 *
837 *
838  ELSE IF( itype.EQ.5 ) THEN
839 *
840 * Symmetric, eigenvalues specified
841 *
842  CALL slatms( n, n, 'S', iseed, 'S', work, imode, cond,
843  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
844  \$ iinfo )
845 *
846  ELSE IF( itype.EQ.7 ) THEN
847 *
848 * Diagonal, random eigenvalues
849 *
850  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
851  \$ 'T', 'N', work( n+1 ), 1, one,
852  \$ work( 2*n+1 ), 1, one, 'N', idumma, 0, 0,
853  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
854 *
855  ELSE IF( itype.EQ.8 ) THEN
856 *
857 * Symmetric, random eigenvalues
858 *
859  CALL slatmr( n, n, 'S', iseed, 'S', work, 6, one, one,
860  \$ 'T', 'N', work( n+1 ), 1, one,
861  \$ work( 2*n+1 ), 1, one, 'N', idumma, n, n,
862  \$ zero, anorm, 'NO', a, lda, iwork, iinfo )
863 *
864  ELSE IF( itype.EQ.9 ) THEN
865 *
866 * Positive definite, eigenvalues specified.
867 *
868  CALL slatms( n, n, 'S', iseed, 'P', work, imode, cond,
869  \$ anorm, n, n, 'N', a, lda, work( n+1 ),
870  \$ iinfo )
871 *
872  ELSE IF( itype.EQ.10 ) THEN
873 *
874 * Positive definite tridiagonal, eigenvalues specified.
875 *
876  CALL slatms( n, n, 'S', iseed, 'P', work, imode, cond,
877  \$ anorm, 1, 1, 'N', a, lda, work( n+1 ),
878  \$ iinfo )
879  DO 90 i = 2, n
880  temp1 = abs( a( i-1, i ) ) /
881  \$ sqrt( abs( a( i-1, i-1 )*a( i, i ) ) )
882  IF( temp1.GT.half ) THEN
883  a( i-1, i ) = half*sqrt( abs( a( i-1, i-1 )*a( i,
884  \$ i ) ) )
885  a( i, i-1 ) = a( i-1, i )
886  END IF
887  90 CONTINUE
888 *
889  ELSE
890 *
891  iinfo = 1
892  END IF
893 *
894  IF( iinfo.NE.0 ) THEN
895  WRITE( nounit, fmt = 9999 )'Generator', iinfo, n, jtype,
896  \$ ioldsd
897  info = abs( iinfo )
898  RETURN
899  END IF
900 *
901  100 CONTINUE
902 *
903 * Call SSYTRD and SORGTR to compute S and U from
904 * upper triangle.
905 *
906  CALL slacpy( 'U', n, n, a, lda, v, ldu )
907 *
908  ntest = 1
909  CALL ssytrd( 'U', n, v, ldu, sd, se, tau, work, lwork,
910  \$ iinfo )
911 *
912  IF( iinfo.NE.0 ) THEN
913  WRITE( nounit, fmt = 9999 )'SSYTRD(U)', iinfo, n, jtype,
914  \$ ioldsd
915  info = abs( iinfo )
916  IF( iinfo.LT.0 ) THEN
917  RETURN
918  ELSE
919  result( 1 ) = ulpinv
920  GO TO 280
921  END IF
922  END IF
923 *
924  CALL slacpy( 'U', n, n, v, ldu, u, ldu )
925 *
926  ntest = 2
927  CALL sorgtr( 'U', n, u, ldu, tau, work, lwork, iinfo )
928  IF( iinfo.NE.0 ) THEN
929  WRITE( nounit, fmt = 9999 )'SORGTR(U)', iinfo, n, jtype,
930  \$ ioldsd
931  info = abs( iinfo )
932  IF( iinfo.LT.0 ) THEN
933  RETURN
934  ELSE
935  result( 2 ) = ulpinv
936  GO TO 280
937  END IF
938  END IF
939 *
940 * Do tests 1 and 2
941 *
942  CALL ssyt21( 2, 'Upper', n, 1, a, lda, sd, se, u, ldu, v,
943  \$ ldu, tau, work, result( 1 ) )
944  CALL ssyt21( 3, 'Upper', n, 1, a, lda, sd, se, u, ldu, v,
945  \$ ldu, tau, work, result( 2 ) )
946 *
947 * Call SSYTRD and SORGTR to compute S and U from
948 * lower triangle, do tests.
949 *
950  CALL slacpy( 'L', n, n, a, lda, v, ldu )
951 *
952  ntest = 3
953  CALL ssytrd( 'L', n, v, ldu, sd, se, tau, work, lwork,
954  \$ iinfo )
955 *
956  IF( iinfo.NE.0 ) THEN
957  WRITE( nounit, fmt = 9999 )'SSYTRD(L)', iinfo, n, jtype,
958  \$ ioldsd
959  info = abs( iinfo )
960  IF( iinfo.LT.0 ) THEN
961  RETURN
962  ELSE
963  result( 3 ) = ulpinv
964  GO TO 280
965  END IF
966  END IF
967 *
968  CALL slacpy( 'L', n, n, v, ldu, u, ldu )
969 *
970  ntest = 4
971  CALL sorgtr( 'L', n, u, ldu, tau, work, lwork, iinfo )
972  IF( iinfo.NE.0 ) THEN
973  WRITE( nounit, fmt = 9999 )'SORGTR(L)', iinfo, n, jtype,
974  \$ ioldsd
975  info = abs( iinfo )
976  IF( iinfo.LT.0 ) THEN
977  RETURN
978  ELSE
979  result( 4 ) = ulpinv
980  GO TO 280
981  END IF
982  END IF
983 *
984  CALL ssyt21( 2, 'Lower', n, 1, a, lda, sd, se, u, ldu, v,
985  \$ ldu, tau, work, result( 3 ) )
986  CALL ssyt21( 3, 'Lower', n, 1, a, lda, sd, se, u, ldu, v,
987  \$ ldu, tau, work, result( 4 ) )
988 *
989 * Store the upper triangle of A in AP
990 *
991  i = 0
992  DO 120 jc = 1, n
993  DO 110 jr = 1, jc
994  i = i + 1
995  ap( i ) = a( jr, jc )
996  110 CONTINUE
997  120 CONTINUE
998 *
999 * Call SSPTRD and SOPGTR to compute S and U from AP
1000 *
1001  CALL scopy( nap, ap, 1, vp, 1 )
1002 *
1003  ntest = 5
1004  CALL ssptrd( 'U', n, vp, sd, se, tau, iinfo )
1005 *
1006  IF( iinfo.NE.0 ) THEN
1007  WRITE( nounit, fmt = 9999 )'SSPTRD(U)', iinfo, n, jtype,
1008  \$ ioldsd
1009  info = abs( iinfo )
1010  IF( iinfo.LT.0 ) THEN
1011  RETURN
1012  ELSE
1013  result( 5 ) = ulpinv
1014  GO TO 280
1015  END IF
1016  END IF
1017 *
1018  ntest = 6
1019  CALL sopgtr( 'U', n, vp, tau, u, ldu, work, iinfo )
1020  IF( iinfo.NE.0 ) THEN
1021  WRITE( nounit, fmt = 9999 )'SOPGTR(U)', iinfo, n, jtype,
1022  \$ ioldsd
1023  info = abs( iinfo )
1024  IF( iinfo.LT.0 ) THEN
1025  RETURN
1026  ELSE
1027  result( 6 ) = ulpinv
1028  GO TO 280
1029  END IF
1030  END IF
1031 *
1032 * Do tests 5 and 6
1033 *
1034  CALL sspt21( 2, 'Upper', n, 1, ap, sd, se, u, ldu, vp, tau,
1035  \$ work, result( 5 ) )
1036  CALL sspt21( 3, 'Upper', n, 1, ap, sd, se, u, ldu, vp, tau,
1037  \$ work, result( 6 ) )
1038 *
1039 * Store the lower triangle of A in AP
1040 *
1041  i = 0
1042  DO 140 jc = 1, n
1043  DO 130 jr = jc, n
1044  i = i + 1
1045  ap( i ) = a( jr, jc )
1046  130 CONTINUE
1047  140 CONTINUE
1048 *
1049 * Call SSPTRD and SOPGTR to compute S and U from AP
1050 *
1051  CALL scopy( nap, ap, 1, vp, 1 )
1052 *
1053  ntest = 7
1054  CALL ssptrd( 'L', n, vp, sd, se, tau, iinfo )
1055 *
1056  IF( iinfo.NE.0 ) THEN
1057  WRITE( nounit, fmt = 9999 )'SSPTRD(L)', iinfo, n, jtype,
1058  \$ ioldsd
1059  info = abs( iinfo )
1060  IF( iinfo.LT.0 ) THEN
1061  RETURN
1062  ELSE
1063  result( 7 ) = ulpinv
1064  GO TO 280
1065  END IF
1066  END IF
1067 *
1068  ntest = 8
1069  CALL sopgtr( 'L', n, vp, tau, u, ldu, work, iinfo )
1070  IF( iinfo.NE.0 ) THEN
1071  WRITE( nounit, fmt = 9999 )'SOPGTR(L)', iinfo, n, jtype,
1072  \$ ioldsd
1073  info = abs( iinfo )
1074  IF( iinfo.LT.0 ) THEN
1075  RETURN
1076  ELSE
1077  result( 8 ) = ulpinv
1078  GO TO 280
1079  END IF
1080  END IF
1081 *
1082  CALL sspt21( 2, 'Lower', n, 1, ap, sd, se, u, ldu, vp, tau,
1083  \$ work, result( 7 ) )
1084  CALL sspt21( 3, 'Lower', n, 1, ap, sd, se, u, ldu, vp, tau,
1085  \$ work, result( 8 ) )
1086 *
1087 * Call SSTEQR to compute D1, D2, and Z, do tests.
1088 *
1089 * Compute D1 and Z
1090 *
1091  CALL scopy( n, sd, 1, d1, 1 )
1092  IF( n.GT.0 )
1093  \$ CALL scopy( n-1, se, 1, work, 1 )
1094  CALL slaset( 'Full', n, n, zero, one, z, ldu )
1095 *
1096  ntest = 9
1097  CALL ssteqr( 'V', n, d1, work, z, ldu, work( n+1 ), iinfo )
1098  IF( iinfo.NE.0 ) THEN
1099  WRITE( nounit, fmt = 9999 )'SSTEQR(V)', iinfo, n, jtype,
1100  \$ ioldsd
1101  info = abs( iinfo )
1102  IF( iinfo.LT.0 ) THEN
1103  RETURN
1104  ELSE
1105  result( 9 ) = ulpinv
1106  GO TO 280
1107  END IF
1108  END IF
1109 *
1110 * Compute D2
1111 *
1112  CALL scopy( n, sd, 1, d2, 1 )
1113  IF( n.GT.0 )
1114  \$ CALL scopy( n-1, se, 1, work, 1 )
1115 *
1116  ntest = 11
1117  CALL ssteqr( 'N', n, d2, work, work( n+1 ), ldu,
1118  \$ work( n+1 ), iinfo )
1119  IF( iinfo.NE.0 ) THEN
1120  WRITE( nounit, fmt = 9999 )'SSTEQR(N)', iinfo, n, jtype,
1121  \$ ioldsd
1122  info = abs( iinfo )
1123  IF( iinfo.LT.0 ) THEN
1124  RETURN
1125  ELSE
1126  result( 11 ) = ulpinv
1127  GO TO 280
1128  END IF
1129  END IF
1130 *
1131 * Compute D3 (using PWK method)
1132 *
1133  CALL scopy( n, sd, 1, d3, 1 )
1134  IF( n.GT.0 )
1135  \$ CALL scopy( n-1, se, 1, work, 1 )
1136 *
1137  ntest = 12
1138  CALL ssterf( n, d3, work, iinfo )
1139  IF( iinfo.NE.0 ) THEN
1140  WRITE( nounit, fmt = 9999 )'SSTERF', iinfo, n, jtype,
1141  \$ ioldsd
1142  info = abs( iinfo )
1143  IF( iinfo.LT.0 ) THEN
1144  RETURN
1145  ELSE
1146  result( 12 ) = ulpinv
1147  GO TO 280
1148  END IF
1149  END IF
1150 *
1151 * Do Tests 9 and 10
1152 *
1153  CALL sstt21( n, 0, sd, se, d1, dumma, z, ldu, work,
1154  \$ result( 9 ) )
1155 *
1156 * Do Tests 11 and 12
1157 *
1158  temp1 = zero
1159  temp2 = zero
1160  temp3 = zero
1161  temp4 = zero
1162 *
1163  DO 150 j = 1, n
1164  temp1 = max( temp1, abs( d1( j ) ), abs( d2( j ) ) )
1165  temp2 = max( temp2, abs( d1( j )-d2( j ) ) )
1166  temp3 = max( temp3, abs( d1( j ) ), abs( d3( j ) ) )
1167  temp4 = max( temp4, abs( d1( j )-d3( j ) ) )
1168  150 CONTINUE
1169 *
1170  result( 11 ) = temp2 / max( unfl, ulp*max( temp1, temp2 ) )
1171  result( 12 ) = temp4 / max( unfl, ulp*max( temp3, temp4 ) )
1172 *
1173 * Do Test 13 -- Sturm Sequence Test of Eigenvalues
1174 * Go up by factors of two until it succeeds
1175 *
1176  ntest = 13
1177  temp1 = thresh*( half-ulp )
1178 *
1179  DO 160 j = 0, log2ui
1180  CALL sstech( n, sd, se, d1, temp1, work, iinfo )
1181  IF( iinfo.EQ.0 )
1182  \$ GO TO 170
1183  temp1 = temp1*two
1184  160 CONTINUE
1185 *
1186  170 CONTINUE
1187  result( 13 ) = temp1
1188 *
1189 * For positive definite matrices ( JTYPE.GT.15 ) call SPTEQR
1190 * and do tests 14, 15, and 16 .
1191 *
1192  IF( jtype.GT.15 ) THEN
1193 *
1194 * Compute D4 and Z4
1195 *
1196  CALL scopy( n, sd, 1, d4, 1 )
1197  IF( n.GT.0 )
1198  \$ CALL scopy( n-1, se, 1, work, 1 )
1199  CALL slaset( 'Full', n, n, zero, one, z, ldu )
1200 *
1201  ntest = 14
1202  CALL spteqr( 'V', n, d4, work, z, ldu, work( n+1 ),
1203  \$ iinfo )
1204  IF( iinfo.NE.0 ) THEN
1205  WRITE( nounit, fmt = 9999 )'SPTEQR(V)', iinfo, n,
1206  \$ jtype, ioldsd
1207  info = abs( iinfo )
1208  IF( iinfo.LT.0 ) THEN
1209  RETURN
1210  ELSE
1211  result( 14 ) = ulpinv
1212  GO TO 280
1213  END IF
1214  END IF
1215 *
1216 * Do Tests 14 and 15
1217 *
1218  CALL sstt21( n, 0, sd, se, d4, dumma, z, ldu, work,
1219  \$ result( 14 ) )
1220 *
1221 * Compute D5
1222 *
1223  CALL scopy( n, sd, 1, d5, 1 )
1224  IF( n.GT.0 )
1225  \$ CALL scopy( n-1, se, 1, work, 1 )
1226 *
1227  ntest = 16
1228  CALL spteqr( 'N', n, d5, work, z, ldu, work( n+1 ),
1229  \$ iinfo )
1230  IF( iinfo.NE.0 ) THEN
1231  WRITE( nounit, fmt = 9999 )'SPTEQR(N)', iinfo, n,
1232  \$ jtype, ioldsd
1233  info = abs( iinfo )
1234  IF( iinfo.LT.0 ) THEN
1235  RETURN
1236  ELSE
1237  result( 16 ) = ulpinv
1238  GO TO 280
1239  END IF
1240  END IF
1241 *
1242 * Do Test 16
1243 *
1244  temp1 = zero
1245  temp2 = zero
1246  DO 180 j = 1, n
1247  temp1 = max( temp1, abs( d4( j ) ), abs( d5( j ) ) )
1248  temp2 = max( temp2, abs( d4( j )-d5( j ) ) )
1249  180 CONTINUE
1250 *
1251  result( 16 ) = temp2 / max( unfl,
1252  \$ hun*ulp*max( temp1, temp2 ) )
1253  ELSE
1254  result( 14 ) = zero
1255  result( 15 ) = zero
1256  result( 16 ) = zero
1257  END IF
1258 *
1259 * Call SSTEBZ with different options and do tests 17-18.
1260 *
1261 * If S is positive definite and diagonally dominant,
1262 * ask for all eigenvalues with high relative accuracy.
1263 *
1264  vl = zero
1265  vu = zero
1266  il = 0
1267  iu = 0
1268  IF( jtype.EQ.21 ) THEN
1269  ntest = 17
1270  abstol = unfl + unfl
1271  CALL sstebz( 'A', 'E', n, vl, vu, il, iu, abstol, sd, se,
1272  \$ m, nsplit, wr, iwork( 1 ), iwork( n+1 ),
1273  \$ work, iwork( 2*n+1 ), iinfo )
1274  IF( iinfo.NE.0 ) THEN
1275  WRITE( nounit, fmt = 9999 )'SSTEBZ(A,rel)', iinfo, n,
1276  \$ jtype, ioldsd
1277  info = abs( iinfo )
1278  IF( iinfo.LT.0 ) THEN
1279  RETURN
1280  ELSE
1281  result( 17 ) = ulpinv
1282  GO TO 280
1283  END IF
1284  END IF
1285 *
1286 * Do test 17
1287 *
1288  temp2 = two*( two*n-one )*ulp*( one+eight*half**2 ) /
1289  \$ ( one-half )**4
1290 *
1291  temp1 = zero
1292  DO 190 j = 1, n
1293  temp1 = max( temp1, abs( d4( j )-wr( n-j+1 ) ) /
1294  \$ ( abstol+abs( d4( j ) ) ) )
1295  190 CONTINUE
1296 *
1297  result( 17 ) = temp1 / temp2
1298  ELSE
1299  result( 17 ) = zero
1300  END IF
1301 *
1302 * Now ask for all eigenvalues with high absolute accuracy.
1303 *
1304  ntest = 18
1305  abstol = unfl + unfl
1306  CALL sstebz( 'A', 'E', n, vl, vu, il, iu, abstol, sd, se, m,
1307  \$ nsplit, wa1, iwork( 1 ), iwork( n+1 ), work,
1308  \$ iwork( 2*n+1 ), iinfo )
1309  IF( iinfo.NE.0 ) THEN
1310  WRITE( nounit, fmt = 9999 )'SSTEBZ(A)', iinfo, n, jtype,
1311  \$ ioldsd
1312  info = abs( iinfo )
1313  IF( iinfo.LT.0 ) THEN
1314  RETURN
1315  ELSE
1316  result( 18 ) = ulpinv
1317  GO TO 280
1318  END IF
1319  END IF
1320 *
1321 * Do test 18
1322 *
1323  temp1 = zero
1324  temp2 = zero
1325  DO 200 j = 1, n
1326  temp1 = max( temp1, abs( d3( j ) ), abs( wa1( j ) ) )
1327  temp2 = max( temp2, abs( d3( j )-wa1( j ) ) )
1328  200 CONTINUE
1329 *
1330  result( 18 ) = temp2 / max( unfl, ulp*max( temp1, temp2 ) )
1331 *
1332 * Choose random values for IL and IU, and ask for the
1333 * IL-th through IU-th eigenvalues.
1334 *
1335  ntest = 19
1336  IF( n.LE.1 ) THEN
1337  il = 1
1338  iu = n
1339  ELSE
1340  il = 1 + ( n-1 )*int( slarnd( 1, iseed2 ) )
1341  iu = 1 + ( n-1 )*int( slarnd( 1, iseed2 ) )
1342  IF( iu.LT.il ) THEN
1343  itemp = iu
1344  iu = il
1345  il = itemp
1346  END IF
1347  END IF
1348 *
1349  CALL sstebz( 'I', 'E', n, vl, vu, il, iu, abstol, sd, se,
1350  \$ m2, nsplit, wa2, iwork( 1 ), iwork( n+1 ),
1351  \$ work, iwork( 2*n+1 ), iinfo )
1352  IF( iinfo.NE.0 ) THEN
1353  WRITE( nounit, fmt = 9999 )'SSTEBZ(I)', iinfo, n, jtype,
1354  \$ ioldsd
1355  info = abs( iinfo )
1356  IF( iinfo.LT.0 ) THEN
1357  RETURN
1358  ELSE
1359  result( 19 ) = ulpinv
1360  GO TO 280
1361  END IF
1362  END IF
1363 *
1364 * Determine the values VL and VU of the IL-th and IU-th
1365 * eigenvalues and ask for all eigenvalues in this range.
1366 *
1367  IF( n.GT.0 ) THEN
1368  IF( il.NE.1 ) THEN
1369  vl = wa1( il ) - max( half*( wa1( il )-wa1( il-1 ) ),
1370  \$ ulp*anorm, two*rtunfl )
1371  ELSE
1372  vl = wa1( 1 ) - max( half*( wa1( n )-wa1( 1 ) ),
1373  \$ ulp*anorm, two*rtunfl )
1374  END IF
1375  IF( iu.NE.n ) THEN
1376  vu = wa1( iu ) + max( half*( wa1( iu+1 )-wa1( iu ) ),
1377  \$ ulp*anorm, two*rtunfl )
1378  ELSE
1379  vu = wa1( n ) + max( half*( wa1( n )-wa1( 1 ) ),
1380  \$ ulp*anorm, two*rtunfl )
1381  END IF
1382  ELSE
1383  vl = zero
1384  vu = one
1385  END IF
1386 *
1387  CALL sstebz( 'V', 'E', n, vl, vu, il, iu, abstol, sd, se,
1388  \$ m3, nsplit, wa3, iwork( 1 ), iwork( n+1 ),
1389  \$ work, iwork( 2*n+1 ), iinfo )
1390  IF( iinfo.NE.0 ) THEN
1391  WRITE( nounit, fmt = 9999 )'SSTEBZ(V)', iinfo, n, jtype,
1392  \$ ioldsd
1393  info = abs( iinfo )
1394  IF( iinfo.LT.0 ) THEN
1395  RETURN
1396  ELSE
1397  result( 19 ) = ulpinv
1398  GO TO 280
1399  END IF
1400  END IF
1401 *
1402  IF( m3.EQ.0 .AND. n.NE.0 ) THEN
1403  result( 19 ) = ulpinv
1404  GO TO 280
1405  END IF
1406 *
1407 * Do test 19
1408 *
1409  temp1 = ssxt1( 1, wa2, m2, wa3, m3, abstol, ulp, unfl )
1410  temp2 = ssxt1( 1, wa3, m3, wa2, m2, abstol, ulp, unfl )
1411  IF( n.GT.0 ) THEN
1412  temp3 = max( abs( wa1( n ) ), abs( wa1( 1 ) ) )
1413  ELSE
1414  temp3 = zero
1415  END IF
1416 *
1417  result( 19 ) = ( temp1+temp2 ) / max( unfl, temp3*ulp )
1418 *
1419 * Call SSTEIN to compute eigenvectors corresponding to
1420 * eigenvalues in WA1. (First call SSTEBZ again, to make sure
1421 * it returns these eigenvalues in the correct order.)
1422 *
1423  ntest = 21
1424  CALL sstebz( 'A', 'B', n, vl, vu, il, iu, abstol, sd, se, m,
1425  \$ nsplit, wa1, iwork( 1 ), iwork( n+1 ), work,
1426  \$ iwork( 2*n+1 ), iinfo )
1427  IF( iinfo.NE.0 ) THEN
1428  WRITE( nounit, fmt = 9999 )'SSTEBZ(A,B)', iinfo, n,
1429  \$ jtype, ioldsd
1430  info = abs( iinfo )
1431  IF( iinfo.LT.0 ) THEN
1432  RETURN
1433  ELSE
1434  result( 20 ) = ulpinv
1435  result( 21 ) = ulpinv
1436  GO TO 280
1437  END IF
1438  END IF
1439 *
1440  CALL sstein( n, sd, se, m, wa1, iwork( 1 ), iwork( n+1 ), z,
1441  \$ ldu, work, iwork( 2*n+1 ), iwork( 3*n+1 ),
1442  \$ iinfo )
1443  IF( iinfo.NE.0 ) THEN
1444  WRITE( nounit, fmt = 9999 )'SSTEIN', iinfo, n, jtype,
1445  \$ ioldsd
1446  info = abs( iinfo )
1447  IF( iinfo.LT.0 ) THEN
1448  RETURN
1449  ELSE
1450  result( 20 ) = ulpinv
1451  result( 21 ) = ulpinv
1452  GO TO 280
1453  END IF
1454  END IF
1455 *
1456 * Do tests 20 and 21
1457 *
1458  CALL sstt21( n, 0, sd, se, wa1, dumma, z, ldu, work,
1459  \$ result( 20 ) )
1460 *
1461 * Call SSTEDC(I) to compute D1 and Z, do tests.
1462 *
1463 * Compute D1 and Z
1464 *
1465  CALL scopy( n, sd, 1, d1, 1 )
1466  IF( n.GT.0 )
1467  \$ CALL scopy( n-1, se, 1, work, 1 )
1468  CALL slaset( 'Full', n, n, zero, one, z, ldu )
1469 *
1470  ntest = 22
1471  CALL sstedc( 'I', n, d1, work, z, ldu, work( n+1 ), lwedc-n,
1472  \$ iwork, liwedc, iinfo )
1473  IF( iinfo.NE.0 ) THEN
1474  WRITE( nounit, fmt = 9999 )'SSTEDC(I)', iinfo, n, jtype,
1475  \$ ioldsd
1476  info = abs( iinfo )
1477  IF( iinfo.LT.0 ) THEN
1478  RETURN
1479  ELSE
1480  result( 22 ) = ulpinv
1481  GO TO 280
1482  END IF
1483  END IF
1484 *
1485 * Do Tests 22 and 23
1486 *
1487  CALL sstt21( n, 0, sd, se, d1, dumma, z, ldu, work,
1488  \$ result( 22 ) )
1489 *
1490 * Call SSTEDC(V) to compute D1 and Z, do tests.
1491 *
1492 * Compute D1 and Z
1493 *
1494  CALL scopy( n, sd, 1, d1, 1 )
1495  IF( n.GT.0 )
1496  \$ CALL scopy( n-1, se, 1, work, 1 )
1497  CALL slaset( 'Full', n, n, zero, one, z, ldu )
1498 *
1499  ntest = 24
1500  CALL sstedc( 'V', n, d1, work, z, ldu, work( n+1 ), lwedc-n,
1501  \$ iwork, liwedc, iinfo )
1502  IF( iinfo.NE.0 ) THEN
1503  WRITE( nounit, fmt = 9999 )'SSTEDC(V)', iinfo, n, jtype,
1504  \$ ioldsd
1505  info = abs( iinfo )
1506  IF( iinfo.LT.0 ) THEN
1507  RETURN
1508  ELSE
1509  result( 24 ) = ulpinv
1510  GO TO 280
1511  END IF
1512  END IF
1513 *
1514 * Do Tests 24 and 25
1515 *
1516  CALL sstt21( n, 0, sd, se, d1, dumma, z, ldu, work,
1517  \$ result( 24 ) )
1518 *
1519 * Call SSTEDC(N) to compute D2, do tests.
1520 *
1521 * Compute D2
1522 *
1523  CALL scopy( n, sd, 1, d2, 1 )
1524  IF( n.GT.0 )
1525  \$ CALL scopy( n-1, se, 1, work, 1 )
1526  CALL slaset( 'Full', n, n, zero, one, z, ldu )
1527 *
1528  ntest = 26
1529  CALL sstedc( 'N', n, d2, work, z, ldu, work( n+1 ), lwedc-n,
1530  \$ iwork, liwedc, iinfo )
1531  IF( iinfo.NE.0 ) THEN
1532  WRITE( nounit, fmt = 9999 )'SSTEDC(N)', iinfo, n, jtype,
1533  \$ ioldsd
1534  info = abs( iinfo )
1535  IF( iinfo.LT.0 ) THEN
1536  RETURN
1537  ELSE
1538  result( 26 ) = ulpinv
1539  GO TO 280
1540  END IF
1541  END IF
1542 *
1543 * Do Test 26
1544 *
1545  temp1 = zero
1546  temp2 = zero
1547 *
1548  DO 210 j = 1, n
1549  temp1 = max( temp1, abs( d1( j ) ), abs( d2( j ) ) )
1550  temp2 = max( temp2, abs( d1( j )-d2( j ) ) )
1551  210 CONTINUE
1552 *
1553  result( 26 ) = temp2 / max( unfl, ulp*max( temp1, temp2 ) )
1554 *
1555 * Only test SSTEMR if IEEE compliant
1556 *
1557  IF( ilaenv( 10, 'SSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 .AND.
1558  \$ ilaenv( 11, 'SSTEMR', 'VA', 1, 0, 0, 0 ).EQ.1 ) THEN
1559 *
1560 * Call SSTEMR, do test 27 (relative eigenvalue accuracy)
1561 *
1562 * If S is positive definite and diagonally dominant,
1563 * ask for all eigenvalues with high relative accuracy.
1564 *
1565  vl = zero
1566  vu = zero
1567  il = 0
1568  iu = 0
1569  IF( jtype.EQ.21 .AND. srel ) THEN
1570  ntest = 27
1571  abstol = unfl + unfl
1572  CALL sstemr( 'V', 'A', n, sd, se, vl, vu, il, iu,
1573  \$ m, wr, z, ldu, n, iwork( 1 ), tryrac,
1574  \$ work, lwork, iwork( 2*n+1 ), lwork-2*n,
1575  \$ iinfo )
1576  IF( iinfo.NE.0 ) THEN
1577  WRITE( nounit, fmt = 9999 )'SSTEMR(V,A,rel)',
1578  \$ iinfo, n, jtype, ioldsd
1579  info = abs( iinfo )
1580  IF( iinfo.LT.0 ) THEN
1581  RETURN
1582  ELSE
1583  result( 27 ) = ulpinv
1584  GO TO 270
1585  END IF
1586  END IF
1587 *
1588 * Do test 27
1589 *
1590  temp2 = two*( two*n-one )*ulp*( one+eight*half**2 ) /
1591  \$ ( one-half )**4
1592 *
1593  temp1 = zero
1594  DO 220 j = 1, n
1595  temp1 = max( temp1, abs( d4( j )-wr( n-j+1 ) ) /
1596  \$ ( abstol+abs( d4( j ) ) ) )
1597  220 CONTINUE
1598 *
1599  result( 27 ) = temp1 / temp2
1600 *
1601  il = 1 + ( n-1 )*int( slarnd( 1, iseed2 ) )
1602  iu = 1 + ( n-1 )*int( slarnd( 1, iseed2 ) )
1603  IF( iu.LT.il ) THEN
1604  itemp = iu
1605  iu = il
1606  il = itemp
1607  END IF
1608 *
1609  IF( srange ) THEN
1610  ntest = 28
1611  abstol = unfl + unfl
1612  CALL sstemr( 'V', 'I', n, sd, se, vl, vu, il, iu,
1613  \$ m, wr, z, ldu, n, iwork( 1 ), tryrac,
1614  \$ work, lwork, iwork( 2*n+1 ),
1615  \$ lwork-2*n, iinfo )
1616 *
1617  IF( iinfo.NE.0 ) THEN
1618  WRITE( nounit, fmt = 9999 )'SSTEMR(V,I,rel)',
1619  \$ iinfo, n, jtype, ioldsd
1620  info = abs( iinfo )
1621  IF( iinfo.LT.0 ) THEN
1622  RETURN
1623  ELSE
1624  result( 28 ) = ulpinv
1625  GO TO 270
1626  END IF
1627  END IF
1628 *
1629 *
1630 * Do test 28
1631 *
1632  temp2 = two*( two*n-one )*ulp*
1633  \$ ( one+eight*half**2 ) / ( one-half )**4
1634 *
1635  temp1 = zero
1636  DO 230 j = il, iu
1637  temp1 = max( temp1, abs( wr( j-il+1 )-d4( n-j+
1638  \$ 1 ) ) / ( abstol+abs( wr( j-il+1 ) ) ) )
1639  230 CONTINUE
1640 *
1641  result( 28 ) = temp1 / temp2
1642  ELSE
1643  result( 28 ) = zero
1644  END IF
1645  ELSE
1646  result( 27 ) = zero
1647  result( 28 ) = zero
1648  END IF
1649 *
1650 * Call SSTEMR(V,I) to compute D1 and Z, do tests.
1651 *
1652 * Compute D1 and Z
1653 *
1654  CALL scopy( n, sd, 1, d5, 1 )
1655  IF( n.GT.0 )
1656  \$ CALL scopy( n-1, se, 1, work, 1 )
1657  CALL slaset( 'Full', n, n, zero, one, z, ldu )
1658 *
1659  IF( srange ) THEN
1660  ntest = 29
1661  il = 1 + ( n-1 )*int( slarnd( 1, iseed2 ) )
1662  iu = 1 + ( n-1 )*int( slarnd( 1, iseed2 ) )
1663  IF( iu.LT.il ) THEN
1664  itemp = iu
1665  iu = il
1666  il = itemp
1667  END IF
1668  CALL sstemr( 'V', 'I', n, d5, work, vl, vu, il, iu,
1669  \$ m, d1, z, ldu, n, iwork( 1 ), tryrac,
1670  \$ work( n+1 ), lwork-n, iwork( 2*n+1 ),
1671  \$ liwork-2*n, iinfo )
1672  IF( iinfo.NE.0 ) THEN
1673  WRITE( nounit, fmt = 9999 )'SSTEMR(V,I)', iinfo,
1674  \$ n, jtype, ioldsd
1675  info = abs( iinfo )
1676  IF( iinfo.LT.0 ) THEN
1677  RETURN
1678  ELSE
1679  result( 29 ) = ulpinv
1680  GO TO 280
1681  END IF
1682  END IF
1683 *
1684 * Do Tests 29 and 30
1685 *
1686  CALL sstt22( n, m, 0, sd, se, d1, dumma, z, ldu, work,
1687  \$ m, result( 29 ) )
1688 *
1689 * Call SSTEMR to compute D2, do tests.
1690 *
1691 * Compute D2
1692 *
1693  CALL scopy( n, sd, 1, d5, 1 )
1694  IF( n.GT.0 )
1695  \$ CALL scopy( n-1, se, 1, work, 1 )
1696 *
1697  ntest = 31
1698  CALL sstemr( 'N', 'I', n, d5, work, vl, vu, il, iu,
1699  \$ m, d2, z, ldu, n, iwork( 1 ), tryrac,
1700  \$ work( n+1 ), lwork-n, iwork( 2*n+1 ),
1701  \$ liwork-2*n, iinfo )
1702  IF( iinfo.NE.0 ) THEN
1703  WRITE( nounit, fmt = 9999 )'SSTEMR(N,I)', iinfo,
1704  \$ n, jtype, ioldsd
1705  info = abs( iinfo )
1706  IF( iinfo.LT.0 ) THEN
1707  RETURN
1708  ELSE
1709  result( 31 ) = ulpinv
1710  GO TO 280
1711  END IF
1712  END IF
1713 *
1714 * Do Test 31
1715 *
1716  temp1 = zero
1717  temp2 = zero
1718 *
1719  DO 240 j = 1, iu - il + 1
1720  temp1 = max( temp1, abs( d1( j ) ),
1721  \$ abs( d2( j ) ) )
1722  temp2 = max( temp2, abs( d1( j )-d2( j ) ) )
1723  240 CONTINUE
1724 *
1725  result( 31 ) = temp2 / max( unfl,
1726  \$ ulp*max( temp1, temp2 ) )
1727 *
1728 *
1729 * Call SSTEMR(V,V) to compute D1 and Z, do tests.
1730 *
1731 * Compute D1 and Z
1732 *
1733  CALL scopy( n, sd, 1, d5, 1 )
1734  IF( n.GT.0 )
1735  \$ CALL scopy( n-1, se, 1, work, 1 )
1736  CALL slaset( 'Full', n, n, zero, one, z, ldu )
1737 *
1738  ntest = 32
1739 *
1740  IF( n.GT.0 ) THEN
1741  IF( il.NE.1 ) THEN
1742  vl = d2( il ) - max( half*
1743  \$ ( d2( il )-d2( il-1 ) ), ulp*anorm,
1744  \$ two*rtunfl )
1745  ELSE
1746  vl = d2( 1 ) - max( half*( d2( n )-d2( 1 ) ),
1747  \$ ulp*anorm, two*rtunfl )
1748  END IF
1749  IF( iu.NE.n ) THEN
1750  vu = d2( iu ) + max( half*
1751  \$ ( d2( iu+1 )-d2( iu ) ), ulp*anorm,
1752  \$ two*rtunfl )
1753  ELSE
1754  vu = d2( n ) + max( half*( d2( n )-d2( 1 ) ),
1755  \$ ulp*anorm, two*rtunfl )
1756  END IF
1757  ELSE
1758  vl = zero
1759  vu = one
1760  END IF
1761 *
1762  CALL sstemr( 'V', 'V', n, d5, work, vl, vu, il, iu,
1763  \$ m, d1, z, ldu, n, iwork( 1 ), tryrac,
1764  \$ work( n+1 ), lwork-n, iwork( 2*n+1 ),
1765  \$ liwork-2*n, iinfo )
1766  IF( iinfo.NE.0 ) THEN
1767  WRITE( nounit, fmt = 9999 )'SSTEMR(V,V)', iinfo,
1768  \$ n, jtype, ioldsd
1769  info = abs( iinfo )
1770  IF( iinfo.LT.0 ) THEN
1771  RETURN
1772  ELSE
1773  result( 32 ) = ulpinv
1774  GO TO 280
1775  END IF
1776  END IF
1777 *
1778 * Do Tests 32 and 33
1779 *
1780  CALL sstt22( n, m, 0, sd, se, d1, dumma, z, ldu, work,
1781  \$ m, result( 32 ) )
1782 *
1783 * Call SSTEMR to compute D2, do tests.
1784 *
1785 * Compute D2
1786 *
1787  CALL scopy( n, sd, 1, d5, 1 )
1788  IF( n.GT.0 )
1789  \$ CALL scopy( n-1, se, 1, work, 1 )
1790 *
1791  ntest = 34
1792  CALL sstemr( 'N', 'V', n, d5, work, vl, vu, il, iu,
1793  \$ m, d2, z, ldu, n, iwork( 1 ), tryrac,
1794  \$ work( n+1 ), lwork-n, iwork( 2*n+1 ),
1795  \$ liwork-2*n, iinfo )
1796  IF( iinfo.NE.0 ) THEN
1797  WRITE( nounit, fmt = 9999 )'SSTEMR(N,V)', iinfo,
1798  \$ n, jtype, ioldsd
1799  info = abs( iinfo )
1800  IF( iinfo.LT.0 ) THEN
1801  RETURN
1802  ELSE
1803  result( 34 ) = ulpinv
1804  GO TO 280
1805  END IF
1806  END IF
1807 *
1808 * Do Test 34
1809 *
1810  temp1 = zero
1811  temp2 = zero
1812 *
1813  DO 250 j = 1, iu - il + 1
1814  temp1 = max( temp1, abs( d1( j ) ),
1815  \$ abs( d2( j ) ) )
1816  temp2 = max( temp2, abs( d1( j )-d2( j ) ) )
1817  250 CONTINUE
1818 *
1819  result( 34 ) = temp2 / max( unfl,
1820  \$ ulp*max( temp1, temp2 ) )
1821  ELSE
1822  result( 29 ) = zero
1823  result( 30 ) = zero
1824  result( 31 ) = zero
1825  result( 32 ) = zero
1826  result( 33 ) = zero
1827  result( 34 ) = zero
1828  END IF
1829 *
1830 *
1831 * Call SSTEMR(V,A) to compute D1 and Z, do tests.
1832 *
1833 * Compute D1 and Z
1834 *
1835  CALL scopy( n, sd, 1, d5, 1 )
1836  IF( n.GT.0 )
1837  \$ CALL scopy( n-1, se, 1, work, 1 )
1838 *
1839  ntest = 35
1840 *
1841  CALL sstemr( 'V', 'A', n, d5, work, vl, vu, il, iu,
1842  \$ m, d1, z, ldu, n, iwork( 1 ), tryrac,
1843  \$ work( n+1 ), lwork-n, iwork( 2*n+1 ),
1844  \$ liwork-2*n, iinfo )
1845  IF( iinfo.NE.0 ) THEN
1846  WRITE( nounit, fmt = 9999 )'SSTEMR(V,A)', iinfo, n,
1847  \$ jtype, ioldsd
1848  info = abs( iinfo )
1849  IF( iinfo.LT.0 ) THEN
1850  RETURN
1851  ELSE
1852  result( 35 ) = ulpinv
1853  GO TO 280
1854  END IF
1855  END IF
1856 *
1857 * Do Tests 35 and 36
1858 *
1859  CALL sstt22( n, m, 0, sd, se, d1, dumma, z, ldu, work, m,
1860  \$ result( 35 ) )
1861 *
1862 * Call SSTEMR to compute D2, do tests.
1863 *
1864 * Compute D2
1865 *
1866  CALL scopy( n, sd, 1, d5, 1 )
1867  IF( n.GT.0 )
1868  \$ CALL scopy( n-1, se, 1, work, 1 )
1869 *
1870  ntest = 37
1871  CALL sstemr( 'N', 'A', n, d5, work, vl, vu, il, iu,
1872  \$ m, d2, z, ldu, n, iwork( 1 ), tryrac,
1873  \$ work( n+1 ), lwork-n, iwork( 2*n+1 ),
1874  \$ liwork-2*n, iinfo )
1875  IF( iinfo.NE.0 ) THEN
1876  WRITE( nounit, fmt = 9999 )'SSTEMR(N,A)', iinfo, n,
1877  \$ jtype, ioldsd
1878  info = abs( iinfo )
1879  IF( iinfo.LT.0 ) THEN
1880  RETURN
1881  ELSE
1882  result( 37 ) = ulpinv
1883  GO TO 280
1884  END IF
1885  END IF
1886 *
1887 * Do Test 34
1888 *
1889  temp1 = zero
1890  temp2 = zero
1891 *
1892  DO 260 j = 1, n
1893  temp1 = max( temp1, abs( d1( j ) ), abs( d2( j ) ) )
1894  temp2 = max( temp2, abs( d1( j )-d2( j ) ) )
1895  260 CONTINUE
1896 *
1897  result( 37 ) = temp2 / max( unfl,
1898  \$ ulp*max( temp1, temp2 ) )
1899  END IF
1900  270 CONTINUE
1901  280 CONTINUE
1902  ntestt = ntestt + ntest
1903 *
1904 * End of Loop -- Check for RESULT(j) > THRESH
1905 *
1906 *
1907 * Print out tests which fail.
1908 *
1909  DO 290 jr = 1, ntest
1910  IF( result( jr ).GE.thresh ) THEN
1911 *
1912 * If this is the first test to fail,
1913 * print a header to the data file.
1914 *
1915  IF( nerrs.EQ.0 ) THEN
1916  WRITE( nounit, fmt = 9998 )'SST'
1917  WRITE( nounit, fmt = 9997 )
1918  WRITE( nounit, fmt = 9996 )
1919  WRITE( nounit, fmt = 9995 )'Symmetric'
1920  WRITE( nounit, fmt = 9994 )
1921 *
1922 * Tests performed
1923 *
1924  WRITE( nounit, fmt = 9988 )
1925  END IF
1926  nerrs = nerrs + 1
1927  WRITE( nounit, fmt = 9990 )n, ioldsd, jtype, jr,
1928  \$ result( jr )
1929  END IF
1930  290 CONTINUE
1931  300 CONTINUE
1932  310 CONTINUE
1933 *
1934 * Summary
1935 *
1936  CALL slasum( 'SST', nounit, nerrs, ntestt )
1937  RETURN
1938 *
1939  9999 FORMAT( ' SCHKST: ', a, ' returned INFO=', i6, '.', / 9x, 'N=',
1940  \$ i6, ', JTYPE=', i6, ', ISEED=(', 3( i5, ',' ), i5, ')' )
1941 *
1942  9998 FORMAT( / 1x, a3, ' -- Real Symmetric eigenvalue problem' )
1943  9997 FORMAT( ' Matrix types (see SCHKST for details): ' )
1944 *
1945  9996 FORMAT( / ' Special Matrices:',
1946  \$ / ' 1=Zero matrix. ',
1947  \$ ' 5=Diagonal: clustered entries.',
1948  \$ / ' 2=Identity matrix. ',
1949  \$ ' 6=Diagonal: large, evenly spaced.',
1950  \$ / ' 3=Diagonal: evenly spaced entries. ',
1951  \$ ' 7=Diagonal: small, evenly spaced.',
1952  \$ / ' 4=Diagonal: geometr. spaced entries.' )
1953  9995 FORMAT( ' Dense ', a, ' Matrices:',
1954  \$ / ' 8=Evenly spaced eigenvals. ',
1955  \$ ' 12=Small, evenly spaced eigenvals.',
1956  \$ / ' 9=Geometrically spaced eigenvals. ',
1957  \$ ' 13=Matrix with random O(1) entries.',
1958  \$ / ' 10=Clustered eigenvalues. ',
1959  \$ ' 14=Matrix with large random entries.',
1960  \$ / ' 11=Large, evenly spaced eigenvals. ',
1961  \$ ' 15=Matrix with small random entries.' )
1962  9994 FORMAT( ' 16=Positive definite, evenly spaced eigenvalues',
1963  \$ / ' 17=Positive definite, geometrically spaced eigenvlaues',
1964  \$ / ' 18=Positive definite, clustered eigenvalues',
1965  \$ / ' 19=Positive definite, small evenly spaced eigenvalues',
1966  \$ / ' 20=Positive definite, large evenly spaced eigenvalues',
1967  \$ / ' 21=Diagonally dominant tridiagonal, geometrically',
1968  \$ ' spaced eigenvalues' )
1969 *
1970  9990 FORMAT( ' N=', i5, ', seed=', 4( i4, ',' ), ' type ', i2,
1971  \$ ', test(', i2, ')=', g10.3 )
1972 *
1973  9988 FORMAT( / 'Test performed: see SCHKST for details.', / )
1974 * End of SCHKST
1975 *
subroutine slaset(UPLO, M, N, ALPHA, BETA, A, LDA)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: slaset.f:110
subroutine slacpy(UPLO, M, N, A, LDA, B, LDB)
SLACPY copies all or part of one two-dimensional array to another.
Definition: slacpy.f:103
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
SSTEQR
Definition: ssteqr.f:131
subroutine sstedc(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
SSTEDC
Definition: sstedc.f:188
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine sstebz(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO)
SSTEBZ
Definition: sstebz.f:273
real function slarnd(IDIST, ISEED)
SLARND
Definition: slarnd.f:73
subroutine slatms(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, KL, KU, PACK, A, LDA, WORK, INFO)
SLATMS
Definition: slatms.f:321
subroutine slatmr(M, N, DIST, ISEED, SYM, D, MODE, COND, DMAX, RSIGN, GRADE, DL, MODEL, CONDL, DR, MODER, CONDR, PIVTNG, IPIVOT, KL, KU, SPARSE, ANORM, PACK, A, LDA, IWORK, INFO)
SLATMR
Definition: slatmr.f:471
subroutine ssptrd(UPLO, N, AP, D, E, TAU, INFO)
SSPTRD
Definition: ssptrd.f:150
subroutine sopgtr(UPLO, N, AP, TAU, Q, LDQ, WORK, INFO)
SOPGTR
Definition: sopgtr.f:114
subroutine sstemr(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, IWORK, LIWORK, INFO)
SSTEMR
Definition: sstemr.f:321
subroutine sstein(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO)
SSTEIN
Definition: sstein.f:174
subroutine sorgtr(UPLO, N, A, LDA, TAU, WORK, LWORK, INFO)
SORGTR
Definition: sorgtr.f:123
subroutine spteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
SPTEQR
Definition: spteqr.f:145
subroutine ssytrd(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO)
SSYTRD
Definition: ssytrd.f:192
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine sstech(N, A, B, EIG, TOL, WORK, INFO)
SSTECH
Definition: sstech.f:101
subroutine sstt21(N, KBAND, AD, AE, SD, SE, U, LDU, WORK, RESULT)
SSTT21
Definition: sstt21.f:127
real function ssxt1(IJOB, D1, N1, D2, N2, ABSTOL, ULP, UNFL)
SSXT1
Definition: ssxt1.f:106
subroutine sstt22(N, M, KBAND, AD, AE, SD, SE, U, LDU, WORK, LDWORK, RESULT)
SSTT22
Definition: sstt22.f:139
subroutine ssyt21(ITYPE, UPLO, N, KBAND, A, LDA, D, E, U, LDU, V, LDV, TAU, WORK, RESULT)
SSYT21
Definition: ssyt21.f:207
subroutine sspt21(ITYPE, UPLO, N, KBAND, AP, D, E, U, LDU, VP, TAU, WORK, RESULT)
SSPT21
Definition: sspt21.f:221
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
subroutine slasum(TYPE, IOUNIT, IE, NRUN)
SLASUM
Definition: slasum.f:41
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