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Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Matrices/standard_complex_qr_decomposition.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Natural_Vectors;
        !             2: with Standard_Complex_Vectors;
        !             3: with Standard_Complex_Matrices;
        !             4:
        !             5: package Standard_Complex_QR_Decomposition is
        !             6:
        !             7: -- DESCRIPTION :
        !             8: --   This package provides an implementation of QR-decomposition for
        !             9: --   matrices of standard complex numbers.
        !            10:
        !            11:   procedure QRD ( x : in out Standard_Complex_Matrices.Matrix;
        !            12:                   qraux : in out Standard_Complex_Vectors.Vector;
        !            13:                   jpvt : in out Standard_Natural_Vectors.Vector;
        !            14:                   piv : in boolean );
        !            15:
        !            16:   -- DESCRIPTION :
        !            17:   --   Uses Householder transformations to compute the QR decomposition of x.
        !            18:   --   Column pivoting based on 2-norms of reduced columns is optional.
        !            19:
        !            20:   -- REQUIRED : jpvt'range = x'range(2) = qraux'range,
        !            21:   --            x'length(1) >= x'length(2)
        !            22:
        !            23:   -- ON ENTRY :
        !            24:   --   x          matrix whose decomposition is to be computed;
        !            25:   --   jpvt       controls the selection of the pivot columns.
        !            26:   --              The k-th column x(k) of x is placed in one of three classes
        !            27:   --              according to the value of jpvt(k):
        !            28:   --                if jpvt(k) > 0, then x(k) is an initial column.
        !            29:   --                if jpvt(k) = 0, then x(k) is a free column.
        !            30:   --                if jpvt(k) < 0, then x(k) is a final column.
        !            31:   --              before the decomposition is computed, initial columns are
        !            32:   --              moved to the beginning of the array x and final columns to
        !            33:   --              the end.  Both initial and final columns are frozen in place
        !            34:   --              during the computation and only free columns are moved.
        !            35:   --              At the k-th stage of the reduction, if x(k) is occupied by a
        !            36:   --              free column it is interchanged with the free column of
        !            37:   --              largest reduced norm.  jpvt is not referenced if not piv.
        !            38:   --   piv        column pivoting is performed if and only if piv is true.
        !            39:
        !            40:   -- ON RETURN :
        !            41:   --   x          x contains in its upper triangle the upper triangular matrix
        !            42:   --              R of the QR factorization.  Below its diagonal x contains
        !            43:   --              information from which the orthogonal part of the
        !            44:   --              decomposition can be recovered.  Note that if pivoting has
        !            45:   --              been requested, the decomposition is not that of the original
        !            46:   --              matrix x but that of x with its columns permuted as described
        !            47:   --              by jpvt.
        !            48:   --   qraux      qraux contains further information required to recover
        !            49:   --              the orthogonal part of the decomposition.
        !            50:   --   jpvt       jpvt(k) contains the index of the column of the original
        !            51:   --              matrix that has been interchanged into the k-th column,
        !            52:   --              if pivoting was requested.
        !            53:
        !            54:   -- ACKNOWLEDGMENT :
        !            55:   --   This Ada Version is a translation of the LINPACK version, dated 08/14/78,
        !            56:   --   written by G.W. Stewart, University of Maryland, Argonne National Lab.
        !            57:
        !            58:   procedure Basis ( qr : in out Standard_Complex_Matrices.Matrix;
        !            59:                     x : in Standard_Complex_Matrices.Matrix );
        !            60:
        !            61:   -- DESCRIPTION :
        !            62:   --   Retrieves the orthogonal part of the decomposition.
        !            63:   --   The columns of qr on output correspond to the column span of x.
        !            64:
        !            65:   -- IMPORTANT :
        !            66:   --   Note that this does not work when pivoting was requested.
        !            67:
        !            68:   -- REQUIRED : qr'range(1) = qr'range(2) = x'range(1).
        !            69:
        !            70:   -- ON ENTRY :
        !            71:   --   qr         contains output of the routine qrd;
        !            72:   --   x          original matrix as part of the input of qrd.
        !            73:
        !            74:   -- ON RETURN :
        !            75:   --   qr         orthogonal part of the QR-decomposition.
        !            76:
        !            77: end Standard_Complex_QR_Decomposition;