dtrttf.c

Go to the documentation of this file.

/* dtrttf.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Subroutine */ int dtrttf_(char *transr, char *uplo, integer *n, doublereal 
        *a, integer *lda, doublereal *arf, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;

    /* Local variables */
    integer i__, j, k, l, n1, n2, ij, nt, nx2, np1x2;
    logical normaltransr;
    extern logical lsame_(char *, char *);
    logical lower;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    logical nisodd;


/*  -- LAPACK routine (version 3.2)                                    -- */

/*  -- Contributed by Fred Gustavson of the IBM Watson Research Center -- */
/*  -- November 2008                                                   -- */

/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DTRTTF copies a triangular matrix A from standard full format (TR) */
/*  to rectangular full packed format (TF) . */

/*  Arguments */
/*  ========= */

/*  TRANSR   (input) CHARACTER */
/*          = 'N':  ARF in Normal form is wanted; */
/*          = 'T':  ARF in Transpose form is wanted. */

/*  UPLO    (input) CHARACTER */
/*          = 'U':  Upper triangle of A is stored; */
/*          = 'L':  Lower triangle of A is stored. */

/*  N       (input) INTEGER */
/*          The order of the matrix A. N >= 0. */

/*  A       (input) DOUBLE PRECISION array, dimension (LDA,N). */
/*          On entry, the triangular matrix A.  If UPLO = 'U', the */
/*          leading N-by-N upper triangular part of the array A contains */
/*          the upper triangular matrix, and the strictly lower */
/*          triangular part of A is not referenced.  If UPLO = 'L', the */
/*          leading N-by-N lower triangular part of the array A contains */
/*          the lower triangular matrix, and the strictly upper */
/*          triangular part of A is not referenced. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the matrix A. LDA >= max(1,N). */

/*  ARF     (output) DOUBLE PRECISION array, dimension (NT). */
/*          NT=N*(N+1)/2. On exit, the triangular matrix A in RFP format. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */

/*  Notes */
/*  ===== */

/*  We first consider Rectangular Full Packed (RFP) Format when N is */
/*  even. We give an example where N = 6. */

/*      AP is Upper             AP is Lower */

/*   00 01 02 03 04 05       00 */
/*      11 12 13 14 15       10 11 */
/*         22 23 24 25       20 21 22 */
/*            33 34 35       30 31 32 33 */
/*               44 45       40 41 42 43 44 */
/*                  55       50 51 52 53 54 55 */


/*  Let TRANSR = 'N'. RFP holds AP as follows: */
/*  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last */
/*  three columns of AP upper. The lower triangle A(4:6,0:2) consists of */
/*  the transpose of the first three columns of AP upper. */
/*  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first */
/*  three columns of AP lower. The upper triangle A(0:2,0:2) consists of */
/*  the transpose of the last three columns of AP lower. */
/*  This covers the case N even and TRANSR = 'N'. */

/*         RFP A                   RFP A */

/*        03 04 05                33 43 53 */
/*        13 14 15                00 44 54 */
/*        23 24 25                10 11 55 */
/*        33 34 35                20 21 22 */
/*        00 44 45                30 31 32 */
/*        01 11 55                40 41 42 */
/*        02 12 22                50 51 52 */

/*  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
/*  transpose of RFP A above. One therefore gets: */


/*           RFP A                   RFP A */

/*     03 13 23 33 00 01 02    33 00 10 20 30 40 50 */
/*     04 14 24 34 44 11 12    43 44 11 21 31 41 51 */
/*     05 15 25 35 45 55 22    53 54 55 22 32 42 52 */


/*  We first consider Rectangular Full Packed (RFP) Format when N is */
/*  odd. We give an example where N = 5. */

/*     AP is Upper                 AP is Lower */

/*   00 01 02 03 04              00 */
/*      11 12 13 14              10 11 */
/*         22 23 24              20 21 22 */
/*            33 34              30 31 32 33 */
/*               44              40 41 42 43 44 */


/*  Let TRANSR = 'N'. RFP holds AP as follows: */
/*  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last */
/*  three columns of AP upper. The lower triangle A(3:4,0:1) consists of */
/*  the transpose of the first two columns of AP upper. */
/*  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first */
/*  three columns of AP lower. The upper triangle A(0:1,1:2) consists of */
/*  the transpose of the last two columns of AP lower. */
/*  This covers the case N odd and TRANSR = 'N'. */

/*         RFP A                   RFP A */

/*        02 03 04                00 33 43 */
/*        12 13 14                10 11 44 */
/*        22 23 24                20 21 22 */
/*        00 33 34                30 31 32 */
/*        01 11 44                40 41 42 */

/*  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the */
/*  transpose of RFP A above. One therefore gets: */

/*           RFP A                   RFP A */

/*     02 12 22 00 01             00 10 20 30 40 50 */
/*     03 13 23 33 11             33 11 21 31 41 51 */
/*     04 14 24 34 44             43 44 22 32 42 52 */

/*  Reference */
/*  ========= */

/*  ===================================================================== */

/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda - 1 - 0 + 1;
    a_offset = 0 + a_dim1 * 0;
    a -= a_offset;

    /* Function Body */
    *info = 0;
    normaltransr = lsame_(transr, "N");
    lower = lsame_(uplo, "L");
    if (! normaltransr && ! lsame_(transr, "T")) {
        *info = -1;
    } else if (! lower && ! lsame_(uplo, "U")) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DTRTTF", &i__1);
        return 0;
    }

/*     Quick return if possible */

    if (*n <= 1) {
        if (*n == 1) {
            arf[0] = a[0];
        }
        return 0;
    }

/*     Size of array ARF(0:nt-1) */

    nt = *n * (*n + 1) / 2;

/*     Set N1 and N2 depending on LOWER: for N even N1=N2=K */

    if (lower) {
        n2 = *n / 2;
        n1 = *n - n2;
    } else {
        n1 = *n / 2;
        n2 = *n - n1;
    }

/*     If N is odd, set NISODD = .TRUE., LDA=N+1 and A is (N+1)--by--K2. */
/*     If N is even, set K = N/2 and NISODD = .FALSE., LDA=N and A is */
/*     N--by--(N+1)/2. */

    if (*n % 2 == 0) {
        k = *n / 2;
        nisodd = FALSE_;
        if (! lower) {
            np1x2 = *n + *n + 2;
        }
    } else {
        nisodd = TRUE_;
        if (! lower) {
            nx2 = *n + *n;
        }
    }

    if (nisodd) {

/*        N is odd */

        if (normaltransr) {

/*           N is odd and TRANSR = 'N' */

            if (lower) {

/*              N is odd, TRANSR = 'N', and UPLO = 'L' */

                ij = 0;
                i__1 = n2;
                for (j = 0; j <= i__1; ++j) {
                    i__2 = n2 + j;
                    for (i__ = n1; i__ <= i__2; ++i__) {
                        arf[ij] = a[n2 + j + i__ * a_dim1];
                        ++ij;
                    }
                    i__2 = *n - 1;
                    for (i__ = j; i__ <= i__2; ++i__) {
                        arf[ij] = a[i__ + j * a_dim1];
                        ++ij;
                    }
                }

            } else {

/*              N is odd, TRANSR = 'N', and UPLO = 'U' */

                ij = nt - *n;
                i__1 = n1;
                for (j = *n - 1; j >= i__1; --j) {
                    i__2 = j;
                    for (i__ = 0; i__ <= i__2; ++i__) {
                        arf[ij] = a[i__ + j * a_dim1];
                        ++ij;
                    }
                    i__2 = n1 - 1;
                    for (l = j - n1; l <= i__2; ++l) {
                        arf[ij] = a[j - n1 + l * a_dim1];
                        ++ij;
                    }
                    ij -= nx2;
                }

            }

        } else {

/*           N is odd and TRANSR = 'T' */

            if (lower) {

/*              N is odd, TRANSR = 'T', and UPLO = 'L' */

                ij = 0;
                i__1 = n2 - 1;
                for (j = 0; j <= i__1; ++j) {
                    i__2 = j;
                    for (i__ = 0; i__ <= i__2; ++i__) {
                        arf[ij] = a[j + i__ * a_dim1];
                        ++ij;
                    }
                    i__2 = *n - 1;
                    for (i__ = n1 + j; i__ <= i__2; ++i__) {
                        arf[ij] = a[i__ + (n1 + j) * a_dim1];
                        ++ij;
                    }
                }
                i__1 = *n - 1;
                for (j = n2; j <= i__1; ++j) {
                    i__2 = n1 - 1;
                    for (i__ = 0; i__ <= i__2; ++i__) {
                        arf[ij] = a[j + i__ * a_dim1];
                        ++ij;
                    }
                }

            } else {

/*              N is odd, TRANSR = 'T', and UPLO = 'U' */

                ij = 0;
                i__1 = n1;
                for (j = 0; j <= i__1; ++j) {
                    i__2 = *n - 1;
                    for (i__ = n1; i__ <= i__2; ++i__) {
                        arf[ij] = a[j + i__ * a_dim1];
                        ++ij;
                    }
                }
                i__1 = n1 - 1;
                for (j = 0; j <= i__1; ++j) {
                    i__2 = j;
                    for (i__ = 0; i__ <= i__2; ++i__) {
                        arf[ij] = a[i__ + j * a_dim1];
                        ++ij;
                    }
                    i__2 = *n - 1;
                    for (l = n2 + j; l <= i__2; ++l) {
                        arf[ij] = a[n2 + j + l * a_dim1];
                        ++ij;
                    }
                }

            }

        }

    } else {

/*        N is even */

        if (normaltransr) {

/*           N is even and TRANSR = 'N' */

            if (lower) {

/*              N is even, TRANSR = 'N', and UPLO = 'L' */

                ij = 0;
                i__1 = k - 1;
                for (j = 0; j <= i__1; ++j) {
                    i__2 = k + j;
                    for (i__ = k; i__ <= i__2; ++i__) {
                        arf[ij] = a[k + j + i__ * a_dim1];
                        ++ij;
                    }
                    i__2 = *n - 1;
                    for (i__ = j; i__ <= i__2; ++i__) {
                        arf[ij] = a[i__ + j * a_dim1];
                        ++ij;
                    }
                }

            } else {

/*              N is even, TRANSR = 'N', and UPLO = 'U' */

                ij = nt - *n - 1;
                i__1 = k;
                for (j = *n - 1; j >= i__1; --j) {
                    i__2 = j;
                    for (i__ = 0; i__ <= i__2; ++i__) {
                        arf[ij] = a[i__ + j * a_dim1];
                        ++ij;
                    }
                    i__2 = k - 1;
                    for (l = j - k; l <= i__2; ++l) {
                        arf[ij] = a[j - k + l * a_dim1];
                        ++ij;
                    }
                    ij -= np1x2;
                }

            }

        } else {

/*           N is even and TRANSR = 'T' */

            if (lower) {

/*              N is even, TRANSR = 'T', and UPLO = 'L' */

                ij = 0;
                j = k;
                i__1 = *n - 1;
                for (i__ = k; i__ <= i__1; ++i__) {
                    arf[ij] = a[i__ + j * a_dim1];
                    ++ij;
                }
                i__1 = k - 2;
                for (j = 0; j <= i__1; ++j) {
                    i__2 = j;
                    for (i__ = 0; i__ <= i__2; ++i__) {
                        arf[ij] = a[j + i__ * a_dim1];
                        ++ij;
                    }
                    i__2 = *n - 1;
                    for (i__ = k + 1 + j; i__ <= i__2; ++i__) {
                        arf[ij] = a[i__ + (k + 1 + j) * a_dim1];
                        ++ij;
                    }
                }
                i__1 = *n - 1;
                for (j = k - 1; j <= i__1; ++j) {
                    i__2 = k - 1;
                    for (i__ = 0; i__ <= i__2; ++i__) {
                        arf[ij] = a[j + i__ * a_dim1];
                        ++ij;
                    }
                }

            } else {

/*              N is even, TRANSR = 'T', and UPLO = 'U' */

                ij = 0;
                i__1 = k;
                for (j = 0; j <= i__1; ++j) {
                    i__2 = *n - 1;
                    for (i__ = k; i__ <= i__2; ++i__) {
                        arf[ij] = a[j + i__ * a_dim1];
                        ++ij;
                    }
                }
                i__1 = k - 2;
                for (j = 0; j <= i__1; ++j) {
                    i__2 = j;
                    for (i__ = 0; i__ <= i__2; ++i__) {
                        arf[ij] = a[i__ + j * a_dim1];
                        ++ij;
                    }
                    i__2 = *n - 1;
                    for (l = k + 1 + j; l <= i__2; ++l) {
                        arf[ij] = a[k + 1 + j + l * a_dim1];
                        ++ij;
                    }
                }
/*              Note that here, on exit of the loop, J = K-1 */
                i__1 = j;
                for (i__ = 0; i__ <= i__1; ++i__) {
                    arf[ij] = a[i__ + j * a_dim1];
                    ++ij;
                }

            }

        }

    }

    return 0;

/*     End of DTRTTF */

} /* dtrttf_ */