ssbtrd.f.html

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      SUBROUTINE <a name="SSBTRD.1"></a><a href="ssbtrd.f.html#SSBTRD.1">SSBTRD</a>( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ,
     $                   WORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          UPLO, VECT
      INTEGER            INFO, KD, LDAB, LDQ, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ),
     $                   WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="SSBTRD.20"></a><a href="ssbtrd.f.html#SSBTRD.1">SSBTRD</a> reduces a real symmetric band matrix A to symmetric
</span><span class="comment">*</span><span class="comment">  tridiagonal form T by an orthogonal similarity transformation:
</span><span class="comment">*</span><span class="comment">  Q**T * A * Q = T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VECT    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  do not form Q;
</span><span class="comment">*</span><span class="comment">          = 'V':  form Q;
</span><span class="comment">*</span><span class="comment">          = 'U':  update a matrix X, by forming X*Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KD      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of superdiagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment">          or the number of subdiagonals if UPLO = 'L'.  KD &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AB      (input/output) REAL array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the symmetric band
</span><span class="comment">*</span><span class="comment">          matrix A, stored in the first KD+1 rows of the array.  The
</span><span class="comment">*</span><span class="comment">          j-th column of A is stored in the j-th column of the array AB
</span><span class="comment">*</span><span class="comment">          as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j&lt;=i&lt;=min(n,j+kd).
</span><span class="comment">*</span><span class="comment">          On exit, the diagonal elements of AB are overwritten by the
</span><span class="comment">*</span><span class="comment">          diagonal elements of the tridiagonal matrix T; if KD &gt; 0, the
</span><span class="comment">*</span><span class="comment">          elements on the first superdiagonal (if UPLO = 'U') or the
</span><span class="comment">*</span><span class="comment">          first subdiagonal (if UPLO = 'L') are overwritten by the
</span><span class="comment">*</span><span class="comment">          off-diagonal elements of T; the rest of AB is overwritten by
</span><span class="comment">*</span><span class="comment">          values generated during the reduction.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDAB    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array AB.  LDAB &gt;= KD+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The diagonal elements of the tridiagonal matrix T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (output) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The off-diagonal elements of the tridiagonal matrix T:
</span><span class="comment">*</span><span class="comment">          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Q       (input/output) REAL array, dimension (LDQ,N)
</span><span class="comment">*</span><span class="comment">          On entry, if VECT = 'U', then Q must contain an N-by-N
</span><span class="comment">*</span><span class="comment">          matrix X; if VECT = 'N' or 'V', then Q need not be set.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit:
</span><span class="comment">*</span><span class="comment">          if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;
</span><span class="comment">*</span><span class="comment">          if VECT = 'U', Q contains the product X*Q;
</span><span class="comment">*</span><span class="comment">          if VECT = 'N', the array Q is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDQ     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array Q.
</span><span class="comment">*</span><span class="comment">          LDQ &gt;= 1, and LDQ &gt;= N if VECT = 'V' or 'U'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Modified by Linda Kaufman, Bell Labs.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            INITQ, UPPER, WANTQ
      INTEGER            I, I2, IBL, INCA, INCX, IQAEND, IQB, IQEND, J,
     $                   J1, J1END, J1INC, J2, JEND, JIN, JINC, K, KD1,
     $                   KDM1, KDN, L, LAST, LEND, NQ, NR, NRT
      REAL               TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SLAR2V.105"></a><a href="slar2v.f.html#SLAR2V.1">SLAR2V</a>, <a name="SLARGV.105"></a><a href="slargv.f.html#SLARGV.1">SLARGV</a>, <a name="SLARTG.105"></a><a href="slartg.f.html#SLARTG.1">SLARTG</a>, <a name="SLARTV.105"></a><a href="slartv.f.html#SLARTV.1">SLARTV</a>, <a name="SLASET.105"></a><a href="slaset.f.html#SLASET.1">SLASET</a>, SROT,
     $                   <a name="XERBLA.106"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.112"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.113"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters
</span><span class="comment">*</span><span class="comment">
</span>      INITQ = <a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'V'</span> )
      WANTQ = INITQ .OR. <a name="LSAME.120"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'U'</span> )
      UPPER = <a name="LSAME.121"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      KD1 = KD + 1
      KDM1 = KD - 1
      INCX = LDAB - 1
      IQEND = 1
<span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( .NOT.WANTQ .AND. .NOT.<a name="LSAME.128"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'N'</span> ) ) THEN
         INFO = -1
      ELSE IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.130"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( KD.LT.0 ) THEN
         INFO = -4
      ELSE IF( LDAB.LT.KD1 ) THEN
         INFO = -6
      ELSE IF( LDQ.LT.MAX( 1, N ) .AND. WANTQ ) THEN
         INFO = -10
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.142"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SSBTRD.142"></a><a href="ssbtrd.f.html#SSBTRD.1">SSBTRD</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Initialize Q to the unit matrix, if needed
</span><span class="comment">*</span><span class="comment">
</span>      IF( INITQ )
     $   CALL <a name="SLASET.154"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'Full'</span>, N, N, ZERO, ONE, Q, LDQ )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Wherever possible, plane rotations are generated and applied in
</span><span class="comment">*</span><span class="comment">     vector operations of length NR over the index set J1:J2:KD1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     The cosines and sines of the plane rotations are stored in the
</span><span class="comment">*</span><span class="comment">     arrays D and WORK.
</span><span class="comment">*</span><span class="comment">
</span>      INCA = KD1*LDAB
      KDN = MIN( N-1, KD )
      IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span>         IF( KD.GT.1 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Reduce to tridiagonal form, working with upper triangle
</span><span class="comment">*</span><span class="comment">
</span>            NR = 0
            J1 = KDN + 2
            J2 = 1
<span class="comment">*</span><span class="comment">
</span>            DO 90 I = 1, N - 2
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