1SGBBRD(1)                LAPACK routine (version 3.1)                SGBBRD(1)
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NAME

6       SGBBRD - a real general m-by-n band matrix A to upper bidiagonal form B
7       by an orthogonal transformation
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SYNOPSIS

10       SUBROUTINE SGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT,
11                          LDPT, C, LDC, WORK, INFO )
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13           CHARACTER      VECT
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15           INTEGER        INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC
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17           REAL           AB(  LDAB,  *  ),  C(  LDC, * ), D( * ), E( * ), PT(
18                          LDPT, * ), Q( LDQ, * ), WORK( * )
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PURPOSE

21       SGBBRD reduces a real general m-by-n band matrix A to upper  bidiagonal
22       form B by an orthogonal transformation: Q' * A * P = B.
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24       The  routine computes B, and optionally forms Q or P', or computes Q'*C
25       for a given matrix C.
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ARGUMENTS

29       VECT    (input) CHARACTER*1
30               Specifies whether or not the  matrices  Q  and  P'  are  to  be
31               formed.  = 'N': do not form Q or P';
32               = 'Q': form Q only;
33               = 'P': form P' only;
34               = 'B': form both.
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36       M       (input) INTEGER
37               The number of rows of the matrix A.  M >= 0.
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39       N       (input) INTEGER
40               The number of columns of the matrix A.  N >= 0.
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42       NCC     (input) INTEGER
43               The number of columns of the matrix C.  NCC >= 0.
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45       KL      (input) INTEGER
46               The number of subdiagonals of the matrix A. KL >= 0.
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48       KU      (input) INTEGER
49               The number of superdiagonals of the matrix A. KU >= 0.
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51       AB      (input/output) REAL array, dimension (LDAB,N)
52               On  entry,  the  m-by-n  band  matrix  A,  stored  in rows 1 to
53               KL+KU+1. The j-th column of A is stored in the j-th  column  of
54               the  array  AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-
55               ku)<=i<=min(m,j+kl).  On exit, A is overwritten by values  gen‐
56               erated during the reduction.
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58       LDAB    (input) INTEGER
59               The leading dimension of the array A. LDAB >= KL+KU+1.
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61       D       (output) REAL array, dimension (min(M,N))
62               The diagonal elements of the bidiagonal matrix B.
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64       E       (output) REAL array, dimension (min(M,N)-1)
65               The superdiagonal elements of the bidiagonal matrix B.
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67       Q       (output) REAL array, dimension (LDQ,M)
68               If  VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q.  If VECT
69               = 'N' or 'P', the array Q is not referenced.
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71       LDQ     (input) INTEGER
72               The leading dimension of the array Q.  LDQ >= max(1,M) if  VECT
73               = 'Q' or 'B'; LDQ >= 1 otherwise.
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75       PT      (output) REAL array, dimension (LDPT,N)
76               If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'.  If VECT
77               = 'N' or 'Q', the array PT is not referenced.
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79       LDPT    (input) INTEGER
80               The leading dimension of the array PT.   LDPT  >=  max(1,N)  if
81               VECT = 'P' or 'B'; LDPT >= 1 otherwise.
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83       C       (input/output) REAL array, dimension (LDC,NCC)
84               On  entry,  an m-by-ncc matrix C.  On exit, C is overwritten by
85               Q'*C.  C is not referenced if NCC = 0.
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87       LDC     (input) INTEGER
88               The leading dimension of the array C.  LDC >= max(1,M) if NCC >
89               0; LDC >= 1 if NCC = 0.
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91       WORK    (workspace) REAL array, dimension (2*max(M,N))
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93       INFO    (output) INTEGER
94               = 0:  successful exit.
95               < 0:  if INFO = -i, the i-th argument had an illegal value.
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99 LAPACK routine (version 3.1)    November 2006                       SGBBRD(1)
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