sgbbrd.f.html

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      SUBROUTINE <a name="SGBBRD.1"></a><a href="sgbbrd.f.html#SGBBRD.1">SGBBRD</a>( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q,
     $                   LDQ, PT, LDPT, C, LDC, 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          VECT
      INTEGER            INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               AB( LDAB, * ), C( LDC, * ), D( * ), E( * ),
     $                   PT( LDPT, * ), 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="SGBBRD.20"></a><a href="sgbbrd.f.html#SGBBRD.1">SGBBRD</a> reduces a real general m-by-n band matrix A to upper
</span><span class="comment">*</span><span class="comment">  bidiagonal form B by an orthogonal transformation: Q' * A * P = B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The routine computes B, and optionally forms Q or P', or computes
</span><span class="comment">*</span><span class="comment">  Q'*C for a given matrix C.
</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">          Specifies whether or not the matrices Q and P' are to be
</span><span class="comment">*</span><span class="comment">          formed.
</span><span class="comment">*</span><span class="comment">          = 'N': do not form Q or P';
</span><span class="comment">*</span><span class="comment">          = 'Q': form Q only;
</span><span class="comment">*</span><span class="comment">          = 'P': form P' only;
</span><span class="comment">*</span><span class="comment">          = 'B': form both.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the matrix A.  M &gt;= 0.
</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 number of columns of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NCC     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns of the matrix C.  NCC &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KL      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of subdiagonals of the matrix A. KL &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KU      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of superdiagonals of the matrix A. KU &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 m-by-n band matrix A, stored in rows 1 to
</span><span class="comment">*</span><span class="comment">          KL+KU+1. The j-th column of A is stored in the j-th column of
</span><span class="comment">*</span><span class="comment">          the array AB as follows:
</span><span class="comment">*</span><span class="comment">          AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)&lt;=i&lt;=min(m,j+kl).
</span><span class="comment">*</span><span class="comment">          On exit, A is overwritten by values generated during the
</span><span class="comment">*</span><span class="comment">          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 A. LDAB &gt;= KL+KU+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (output) REAL array, dimension (min(M,N))
</span><span class="comment">*</span><span class="comment">          The diagonal elements of the bidiagonal matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (output) REAL array, dimension (min(M,N)-1)
</span><span class="comment">*</span><span class="comment">          The superdiagonal elements of the bidiagonal matrix B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Q       (output) REAL array, dimension (LDQ,M)
</span><span class="comment">*</span><span class="comment">          If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.
</span><span class="comment">*</span><span class="comment">          If VECT = 'N' or 'P', 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;= max(1,M) if VECT = 'Q' or 'B'; LDQ &gt;= 1 otherwise.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  PT      (output) REAL array, dimension (LDPT,N)
</span><span class="comment">*</span><span class="comment">          If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.
</span><span class="comment">*</span><span class="comment">          If VECT = 'N' or 'Q', the array PT is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDPT    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array PT.
</span><span class="comment">*</span><span class="comment">          LDPT &gt;= max(1,N) if VECT = 'P' or 'B'; LDPT &gt;= 1 otherwise.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  C       (input/output) REAL array, dimension (LDC,NCC)
</span><span class="comment">*</span><span class="comment">          On entry, an m-by-ncc matrix C.
</span><span class="comment">*</span><span class="comment">          On exit, C is overwritten by Q'*C.
</span><span class="comment">*</span><span class="comment">          C is not referenced if NCC = 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDC     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array C.
</span><span class="comment">*</span><span class="comment">          LDC &gt;= max(1,M) if NCC &gt; 0; LDC &gt;= 1 if NCC = 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) REAL array, dimension (2*max(M,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">  =====================================================================
</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            WANTB, WANTC, WANTPT, WANTQ
      INTEGER            I, INCA, J, J1, J2, KB, KB1, KK, KLM, KLU1,
     $                   KUN, L, MINMN, ML, ML0, MN, MU, MU0, NR, NRT
      REAL               RA, RB, RC, RS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SLARGV.113"></a><a href="slargv.f.html#SLARGV.1">SLARGV</a>, <a name="SLARTG.113"></a><a href="slartg.f.html#SLARTG.1">SLARTG</a>, <a name="SLARTV.113"></a><a href="slartv.f.html#SLARTV.1">SLARTV</a>, <a name="SLASET.113"></a><a href="slaset.f.html#SLASET.1">SLASET</a>, SROT, <a name="XERBLA.113"></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.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.120"></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>      WANTB = <a name="LSAME.126"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'B'</span> )
      WANTQ = <a name="LSAME.127"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'Q'</span> ) .OR. WANTB
      WANTPT = <a name="LSAME.128"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'P'</span> ) .OR. WANTB
      WANTC = NCC.GT.0
      KLU1 = KL + KU + 1
      INFO = 0
      IF( .NOT.WANTQ .AND. .NOT.WANTPT .AND. .NOT.<a name="LSAME.132"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( VECT, <span class="string">'N'</span> ) )
     $     THEN
         INFO = -1
      ELSE IF( M.LT.0 ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
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