dtrsm.c

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/* DTRSM.F -- translated by f2c (version 19941215).
   You must link the resulting object file with the libraries:
        -lf2c -lm   (in that order)
*/

#include "f2c.h"


/* *********************************************************************** */

/* Subroutine */ int dtrsm_(side, uplo, transa, diag, m, n, alpha, a, lda, b, 
        ldb, side_len, uplo_len, transa_len, diag_len)
char *side, *uplo, *transa, *diag;
integer *m, *n;
doublereal *alpha, *a;
integer *lda;
doublereal *b;
integer *ldb;
ftnlen side_len;
ftnlen uplo_len;
ftnlen transa_len;
ftnlen diag_len;
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;

    /* Local variables */
    static integer info;
    static doublereal temp;
    static integer i, j, k;
    static logical lside;
    extern logical lsame_();
    static integer nrowa;
    static logical upper;
    extern /* Subroutine */ int xerbla_();
    static logical nounit;

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

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

/*  DTRSM  solves one of the matrix equations */

/*     op( A )*X = alpha*B,   or   X*op( A ) = alpha*B, */

/*  where alpha is a scalar, X and B are m by n matrices, A is a unit, or 
*/
/*  non-unit,  upper or lower triangular matrix  and  op( A )  is one  of 
*/

/*     op( A ) = A   or   op( A ) = A'. */

/*  The matrix X is overwritten on B. */

/*  Parameters */
/*  ========== */

/*  SIDE   - CHARACTER*1. */
/*           On entry, SIDE specifies whether op( A ) appears on the left 
*/
/*           or right of X as follows: */

/*              SIDE = 'L' or 'l'   op( A )*X = alpha*B. */

/*              SIDE = 'R' or 'r'   X*op( A ) = alpha*B. */

/*           Unchanged on exit. */

/*  UPLO   - CHARACTER*1. */
/*           On entry, UPLO specifies whether the matrix A is an upper or 
*/
/*           lower triangular matrix as follows: */

/*              UPLO = 'U' or 'u'   A is an upper triangular matrix. */

/*              UPLO = 'L' or 'l'   A is a lower triangular matrix. */

/*           Unchanged on exit. */

/*  TRANSA - CHARACTER*1. */
/*           On entry, TRANSA specifies the form of op( A ) to be used in 
*/
/*           the matrix multiplication as follows: */

/*              TRANSA = 'N' or 'n'   op( A ) = A. */

/*              TRANSA = 'T' or 't'   op( A ) = A'. */

/*              TRANSA = 'C' or 'c'   op( A ) = A'. */

/*           Unchanged on exit. */

/*  DIAG   - CHARACTER*1. */
/*           On entry, DIAG specifies whether or not A is unit triangular 
*/
/*           as follows: */

/*              DIAG = 'U' or 'u'   A is assumed to be unit triangular. */

/*              DIAG = 'N' or 'n'   A is not assumed to be unit */
/*                                  triangular. */

/*           Unchanged on exit. */

/*  M      - INTEGER. */
/*           On entry, M specifies the number of rows of B. M must be at 
*/
/*           least zero. */
/*           Unchanged on exit. */

/*  N      - INTEGER. */
/*           On entry, N specifies the number of columns of B.  N must be 
*/
/*           at least zero. */
/*           Unchanged on exit. */

/*  ALPHA  - DOUBLE PRECISION. */
/*           On entry,  ALPHA specifies the scalar  alpha. When  alpha is 
*/
/*           zero then  A is not referenced and  B need not be set before 
*/
/*           entry. */
/*           Unchanged on exit. */

/*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m 
*/
/*           when  SIDE = 'L' or 'l'  and is  n  when  SIDE = 'R' or 'r'. 
*/
/*           Before entry  with  UPLO = 'U' or 'u',  the  leading  k by k 
*/
/*           upper triangular part of the array  A must contain the upper 
*/
/*           triangular matrix  and the strictly lower triangular part of 
*/
/*           A is not referenced. */
/*           Before entry  with  UPLO = 'L' or 'l',  the  leading  k by k 
*/
/*           lower triangular part of the array  A must contain the lower 
*/
/*           triangular matrix  and the strictly upper triangular part of 
*/
/*           A is not referenced. */
/*           Note that when  DIAG = 'U' or 'u',  the diagonal elements of 
*/
/*           A  are not referenced either,  but are assumed to be  unity. 
*/
/*           Unchanged on exit. */

/*  LDA    - INTEGER. */
/*           On entry, LDA specifies the first dimension of A as declared 
*/
/*           in the calling (sub) program.  When  SIDE = 'L' or 'l'  then 
*/
/*           LDA  must be at least  max( 1, m ),  when  SIDE = 'R' or 'r' 
*/
/*           then LDA must be at least max( 1, n ). */
/*           Unchanged on exit. */

/*  B      - DOUBLE PRECISION array of DIMENSION ( LDB, n ). */
/*           Before entry,  the leading  m by n part of the array  B must 
*/
/*           contain  the  right-hand  side  matrix  B,  and  on exit  is 
*/
/*           overwritten by the solution matrix  X. */

/*  LDB    - INTEGER. */
/*           On entry, LDB specifies the first dimension of B as declared 
*/
/*           in  the  calling  (sub)  program.   LDB  must  be  at  least 
*/
/*           max( 1, m ). */
/*           Unchanged on exit. */


/*  Level 3 Blas routine. */


/*  -- Written on 8-February-1989. */
/*     Jack Dongarra, Argonne National Laboratory. */
/*     Iain Duff, AERE Harwell. */
/*     Jeremy Du Croz, Numerical Algorithms Group Ltd. */
/*     Sven Hammarling, Numerical Algorithms Group Ltd. */


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

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = a_dim1 + 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = b_dim1 + 1;
    b -= b_offset;

    /* Function Body */
    lside = lsame_(side, "L", 1L, 1L);
    if (lside) {
        nrowa = *m;
    } else {
        nrowa = *n;
    }
    nounit = lsame_(diag, "N", 1L, 1L);
    upper = lsame_(uplo, "U", 1L, 1L);

    info = 0;
    if (! lside && ! lsame_(side, "R", 1L, 1L)) {
        info = 1;
    } else if (! upper && ! lsame_(uplo, "L", 1L, 1L)) {
        info = 2;
    } else if (! lsame_(transa, "N", 1L, 1L) && ! lsame_(transa, "T", 1L, 1L) 
            && ! lsame_(transa, "C", 1L, 1L)) {
        info = 3;
    } else if (! lsame_(diag, "U", 1L, 1L) && ! lsame_(diag, "N", 1L, 1L)) {
        info = 4;
    } else if (*m < 0) {
        info = 5;
    } else if (*n < 0) {
        info = 6;
    } else if (*lda < max(1,nrowa)) {
        info = 9;
    } else if (*ldb < max(1,*m)) {
        info = 11;
    }
    if (info != 0) {
        xerbla_("DTRSM ", &info, 6L);
        return 0;
    }

/*     Quick return if possible. */

    if (*n == 0) {
        return 0;
    }

/*     And when  alpha.eq.zero. */

    if (*alpha == 0.) {
        i__1 = *n;
        for (j = 1; j <= i__1; ++j) {
            i__2 = *m;
            for (i = 1; i <= i__2; ++i) {
                b[i + j * b_dim1] = 0.;
/* L10: */
            }
/* L20: */
        }
        return 0;
    }

/*     Start the operations. */

    if (lside) {
        if (lsame_(transa, "N", 1L, 1L)) {

/*           Form  B := alpha*inv( A )*B. */

            if (upper) {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    if (*alpha != 1.) {
                        i__2 = *m;
                        for (i = 1; i <= i__2; ++i) {
                            b[i + j * b_dim1] = *alpha * b[i + j * b_dim1];
/* L30: */
                        }
                    }
                    for (k = *m; k >= 1; --k) {
                        if (b[k + j * b_dim1] != 0.) {
                            if (nounit) {
                                b[k + j * b_dim1] /= a[k + k * a_dim1];
                            }
                            i__2 = k - 1;
                            for (i = 1; i <= i__2; ++i) {
                                b[i + j * b_dim1] -= b[k + j * b_dim1] * a[i 
                                        + k * a_dim1];
/* L40: */
                            }
                        }
/* L50: */
                    }
/* L60: */
                }
            } else {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    if (*alpha != 1.) {
                        i__2 = *m;
                        for (i = 1; i <= i__2; ++i) {
                            b[i + j * b_dim1] = *alpha * b[i + j * b_dim1];
/* L70: */
                        }
                    }
                    i__2 = *m;
                    for (k = 1; k <= i__2; ++k) {
                        if (b[k + j * b_dim1] != 0.) {
                            if (nounit) {
                                b[k + j * b_dim1] /= a[k + k * a_dim1];
                            }
                            i__3 = *m;
                            for (i = k + 1; i <= i__3; ++i) {
                                b[i + j * b_dim1] -= b[k + j * b_dim1] * a[i 
                                        + k * a_dim1];
/* L80: */
                            }
                        }
/* L90: */
                    }
/* L100: */
                }
            }
        } else {

/*           Form  B := alpha*inv( A' )*B. */

            if (upper) {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = *m;
                    for (i = 1; i <= i__2; ++i) {
                        temp = *alpha * b[i + j * b_dim1];
                        i__3 = i - 1;
                        for (k = 1; k <= i__3; ++k) {
                            temp -= a[k + i * a_dim1] * b[k + j * b_dim1];
/* L110: */
                        }
                        if (nounit) {
                            temp /= a[i + i * a_dim1];
                        }
                        b[i + j * b_dim1] = temp;
/* L120: */
                    }
/* L130: */
                }
            } else {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    for (i = *m; i >= 1; --i) {
                        temp = *alpha * b[i + j * b_dim1];
                        i__2 = *m;
                        for (k = i + 1; k <= i__2; ++k) {
                            temp -= a[k + i * a_dim1] * b[k + j * b_dim1];
/* L140: */
                        }
                        if (nounit) {
                            temp /= a[i + i * a_dim1];
                        }
                        b[i + j * b_dim1] = temp;
/* L150: */
                    }
/* L160: */
                }
            }
        }
    } else {
        if (lsame_(transa, "N", 1L, 1L)) {

/*           Form  B := alpha*B*inv( A ). */

            if (upper) {
                i__1 = *n;
                for (j = 1; j <= i__1; ++j) {
                    if (*alpha != 1.) {
                        i__2 = *m;
                        for (i = 1; i <= i__2; ++i) {
                            b[i + j * b_dim1] = *alpha * b[i + j * b_dim1];
/* L170: */
                        }
                    }
                    i__2 = j - 1;
                    for (k = 1; k <= i__2; ++k) {
                        if (a[k + j * a_dim1] != 0.) {
                            i__3 = *m;
                            for (i = 1; i <= i__3; ++i) {
                                b[i + j * b_dim1] -= a[k + j * a_dim1] * b[i 
                                        + k * b_dim1];
/* L180: */
                            }
                        }
/* L190: */
                    }
                    if (nounit) {
                        temp = 1. / a[j + j * a_dim1];
                        i__2 = *m;
                        for (i = 1; i <= i__2; ++i) {
                            b[i + j * b_dim1] = temp * b[i + j * b_dim1];
/* L200: */
                        }
                    }
/* L210: */
                }
            } else {
                for (j = *n; j >= 1; --j) {
                    if (*alpha != 1.) {
                        i__1 = *m;
                        for (i = 1; i <= i__1; ++i) {
                            b[i + j * b_dim1] = *alpha * b[i + j * b_dim1];
/* L220: */
                        }
                    }
                    i__1 = *n;
                    for (k = j + 1; k <= i__1; ++k) {
                        if (a[k + j * a_dim1] != 0.) {
                            i__2 = *m;
                            for (i = 1; i <= i__2; ++i) {
                                b[i + j * b_dim1] -= a[k + j * a_dim1] * b[i 
                                        + k * b_dim1];
/* L230: */
                            }
                        }
/* L240: */
                    }
                    if (nounit) {
                        temp = 1. / a[j + j * a_dim1];
                        i__1 = *m;
                        for (i = 1; i <= i__1; ++i) {
                            b[i + j * b_dim1] = temp * b[i + j * b_dim1];
/* L250: */
                        }
                    }
/* L260: */
                }
            }
        } else {

/*           Form  B := alpha*B*inv( A' ). */

            if (upper) {
                for (k = *n; k >= 1; --k) {
                    if (nounit) {
                        temp = 1. / a[k + k * a_dim1];
                        i__1 = *m;
                        for (i = 1; i <= i__1; ++i) {
                            b[i + k * b_dim1] = temp * b[i + k * b_dim1];
/* L270: */
                        }
                    }
                    i__1 = k - 1;
                    for (j = 1; j <= i__1; ++j) {
                        if (a[j + k * a_dim1] != 0.) {
                            temp = a[j + k * a_dim1];
                            i__2 = *m;
                            for (i = 1; i <= i__2; ++i) {
                                b[i + j * b_dim1] -= temp * b[i + k * b_dim1];
/* L280: */
                            }
                        }
/* L290: */
                    }
                    if (*alpha != 1.) {
                        i__1 = *m;
                        for (i = 1; i <= i__1; ++i) {
                            b[i + k * b_dim1] = *alpha * b[i + k * b_dim1];
/* L300: */
                        }
                    }
/* L310: */
                }
            } else {
                i__1 = *n;
                for (k = 1; k <= i__1; ++k) {
                    if (nounit) {
                        temp = 1. / a[k + k * a_dim1];
                        i__2 = *m;
                        for (i = 1; i <= i__2; ++i) {
                            b[i + k * b_dim1] = temp * b[i + k * b_dim1];
/* L320: */
                        }
                    }
                    i__2 = *n;
                    for (j = k + 1; j <= i__2; ++j) {
                        if (a[j + k * a_dim1] != 0.) {
                            temp = a[j + k * a_dim1];
                            i__3 = *m;
                            for (i = 1; i <= i__3; ++i) {
                                b[i + j * b_dim1] -= temp * b[i + k * b_dim1];
/* L330: */
                            }
                        }
/* L340: */
                    }
                    if (*alpha != 1.) {
                        i__2 = *m;
                        for (i = 1; i <= i__2; ++i) {
                            b[i + k * b_dim1] = *alpha * b[i + k * b_dim1];
/* L350: */
                        }
                    }
/* L360: */
                }
            }
        }
    }

    return 0;

/*     End of DTRSM . */

} /* dtrsm_ */

---