/* -- translated by f2c (version 19940927). You must link the resulting object file with the libraries: -lf2c -lm (in that order) */ #include "f2c.h" /* Subroutine */ int ztrmm_(char *side, char *uplo, char *transa, char *diag, integer *m, integer *n, doublecomplex *alpha, doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb) { /* System generated locals */ integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublecomplex z__1, z__2, z__3; /* Builtin functions */ void d_cnjg(doublecomplex *, doublecomplex *); /* Local variables */ static integer info; static doublecomplex temp; static integer i, j, k; static logical lside; extern logical lsame_(char *, char *); static integer nrowa; static logical upper; extern /* Subroutine */ int xerbla_(char *, integer *); static logical noconj, nounit; /* Purpose ======= ZTRMM performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, 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' or op( A ) = conjg( A' ). Parameters ========== SIDE - CHARACTER*1. On entry, SIDE specifies whether op( A ) multiplies B from the left or right as follows: SIDE = 'L' or 'l' B := alpha*op( A )*B. SIDE = 'R' or 'r' B := alpha*B*op( A ). 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 ) = conjg( 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 - COMPLEX*16 . 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 - COMPLEX*16 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 - COMPLEX*16 array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the matrix B, and on exit is overwritten by the transformed matrix. 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. Test the input parameters. Parameter adjustments Function Body */ #define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)] #define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)] lside = lsame_(side, "L"); if (lside) { nrowa = *m; } else { nrowa = *n; } noconj = lsame_(transa, "T"); nounit = lsame_(diag, "N"); upper = lsame_(uplo, "U"); info = 0; if (! lside && ! lsame_(side, "R")) { info = 1; } else if (! upper && ! lsame_(uplo, "L")) { info = 2; } else if (! lsame_(transa, "N") && ! lsame_(transa, "T") && ! lsame_(transa, "C")) { info = 3; } else if (! lsame_(diag, "U") && ! lsame_(diag, "N")) { 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_("ZTRMM ", &info); return 0; } /* Quick return if possible. */ if (*n == 0) { return 0; } /* And when alpha.eq.zero. */ if (alpha->r == 0. && alpha->i == 0.) { i__1 = *n; for (j = 1; j <= *n; ++j) { i__2 = *m; for (i = 1; i <= *m; ++i) { i__3 = i + j * b_dim1; B(i,j).r = 0., B(i,j).i = 0.; /* L10: */ } /* L20: */ } return 0; } /* Start the operations. */ if (lside) { if (lsame_(transa, "N")) { /* Form B := alpha*A*B. */ if (upper) { i__1 = *n; for (j = 1; j <= *n; ++j) { i__2 = *m; for (k = 1; k <= *m; ++k) { i__3 = k + j * b_dim1; if (B(k,j).r != 0. || B(k,j).i != 0.) { i__3 = k + j * b_dim1; z__1.r = alpha->r * B(k,j).r - alpha->i * B(k,j) .i, z__1.i = alpha->r * B(k,j).i + alpha->i * B(k,j).r; temp.r = z__1.r, temp.i = z__1.i; i__3 = k - 1; for (i = 1; i <= k-1; ++i) { i__4 = i + j * b_dim1; i__5 = i + j * b_dim1; i__6 = i + k * a_dim1; z__2.r = temp.r * A(i,k).r - temp.i * A(i,k) .i, z__2.i = temp.r * A(i,k).i + temp.i * A(i,k).r; z__1.r = B(i,j).r + z__2.r, z__1.i = B(i,j) .i + z__2.i; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L30: */ } if (nounit) { i__3 = k + k * a_dim1; z__1.r = temp.r * A(k,k).r - temp.i * A(k,k) .i, z__1.i = temp.r * A(k,k).i + temp.i * A(k,k).r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = k + j * b_dim1; B(k,j).r = temp.r, B(k,j).i = temp.i; } /* L40: */ } /* L50: */ } } else { i__1 = *n; for (j = 1; j <= *n; ++j) { for (k = *m; k >= 1; --k) { i__2 = k + j * b_dim1; if (B(k,j).r != 0. || B(k,j).i != 0.) { i__2 = k + j * b_dim1; z__1.r = alpha->r * B(k,j).r - alpha->i * B(k,j) .i, z__1.i = alpha->r * B(k,j).i + alpha->i * B(k,j).r; temp.r = z__1.r, temp.i = z__1.i; i__2 = k + j * b_dim1; B(k,j).r = temp.r, B(k,j).i = temp.i; if (nounit) { i__2 = k + j * b_dim1; i__3 = k + j * b_dim1; i__4 = k + k * a_dim1; z__1.r = B(k,j).r * A(k,k).r - B(k,j).i * A(k,k).i, z__1.i = B(k,j).r * A(k,k).i + B(k,j).i * A(k,k).r; B(k,j).r = z__1.r, B(k,j).i = z__1.i; } i__2 = *m; for (i = k + 1; i <= *m; ++i) { i__3 = i + j * b_dim1; i__4 = i + j * b_dim1; i__5 = i + k * a_dim1; z__2.r = temp.r * A(i,k).r - temp.i * A(i,k) .i, z__2.i = temp.r * A(i,k).i + temp.i * A(i,k).r; z__1.r = B(i,j).r + z__2.r, z__1.i = B(i,j) .i + z__2.i; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L60: */ } } /* L70: */ } /* L80: */ } } } else { /* Form B := alpha*B*A' or B := alpha*B*conjg( A' ) . */ if (upper) { i__1 = *n; for (j = 1; j <= *n; ++j) { for (i = *m; i >= 1; --i) { i__2 = i + j * b_dim1; temp.r = B(i,j).r, temp.i = B(i,j).i; if (noconj) { if (nounit) { i__2 = i + i * a_dim1; z__1.r = temp.r * A(i,i).r - temp.i * A(i,i) .i, z__1.i = temp.r * A(i,i).i + temp.i * A(i,i).r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = i - 1; for (k = 1; k <= i-1; ++k) { i__3 = k + i * a_dim1; i__4 = k + j * b_dim1; z__2.r = A(k,i).r * B(k,j).r - A(k,i).i * B(k,j).i, z__2.i = A(k,i).r * B(k,j).i + A(k,i).i * B(k,j).r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L90: */ } } else { if (nounit) { d_cnjg(&z__2, &A(i,i)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = i - 1; for (k = 1; k <= i-1; ++k) { d_cnjg(&z__3, &A(k,i)); i__3 = k + j * b_dim1; z__2.r = z__3.r * B(k,j).r - z__3.i * B(k,j) .i, z__2.i = z__3.r * B(k,j).i + z__3.i * B(k,j).r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L100: */ } } i__2 = i + j * b_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L110: */ } /* L120: */ } } else { i__1 = *n; for (j = 1; j <= *n; ++j) { i__2 = *m; for (i = 1; i <= *m; ++i) { i__3 = i + j * b_dim1; temp.r = B(i,j).r, temp.i = B(i,j).i; if (noconj) { if (nounit) { i__3 = i + i * a_dim1; z__1.r = temp.r * A(i,i).r - temp.i * A(i,i) .i, z__1.i = temp.r * A(i,i).i + temp.i * A(i,i).r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (k = i + 1; k <= *m; ++k) { i__4 = k + i * a_dim1; i__5 = k + j * b_dim1; z__2.r = A(k,i).r * B(k,j).r - A(k,i).i * B(k,j).i, z__2.i = A(k,i).r * B(k,j).i + A(k,i).i * B(k,j).r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L130: */ } } else { if (nounit) { d_cnjg(&z__2, &A(i,i)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (k = i + 1; k <= *m; ++k) { d_cnjg(&z__3, &A(k,i)); i__4 = k + j * b_dim1; z__2.r = z__3.r * B(k,j).r - z__3.i * B(k,j) .i, z__2.i = z__3.r * B(k,j).i + z__3.i * B(k,j).r; z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i; temp.r = z__1.r, temp.i = z__1.i; /* L140: */ } } i__3 = i + j * b_dim1; z__1.r = alpha->r * temp.r - alpha->i * temp.i, z__1.i = alpha->r * temp.i + alpha->i * temp.r; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L150: */ } /* L160: */ } } } } else { if (lsame_(transa, "N")) { /* Form B := alpha*B*A. */ if (upper) { for (j = *n; j >= 1; --j) { temp.r = alpha->r, temp.i = alpha->i; if (nounit) { i__1 = j + j * a_dim1; z__1.r = temp.r * A(j,j).r - temp.i * A(j,j).i, z__1.i = temp.r * A(j,j).i + temp.i * A(j,j) .r; temp.r = z__1.r, temp.i = z__1.i; } i__1 = *m; for (i = 1; i <= *m; ++i) { i__2 = i + j * b_dim1; i__3 = i + j * b_dim1; z__1.r = temp.r * B(i,j).r - temp.i * B(i,j).i, z__1.i = temp.r * B(i,j).i + temp.i * B(i,j) .r; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L170: */ } i__1 = j - 1; for (k = 1; k <= j-1; ++k) { i__2 = k + j * a_dim1; if (A(k,j).r != 0. || A(k,j).i != 0.) { i__2 = k + j * a_dim1; z__1.r = alpha->r * A(k,j).r - alpha->i * A(k,j) .i, z__1.i = alpha->r * A(k,j).i + alpha->i * A(k,j).r; temp.r = z__1.r, temp.i = z__1.i; i__2 = *m; for (i = 1; i <= *m; ++i) { i__3 = i + j * b_dim1; i__4 = i + j * b_dim1; i__5 = i + k * b_dim1; z__2.r = temp.r * B(i,k).r - temp.i * B(i,k) .i, z__2.i = temp.r * B(i,k).i + temp.i * B(i,k).r; z__1.r = B(i,j).r + z__2.r, z__1.i = B(i,j) .i + z__2.i; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L180: */ } } /* L190: */ } /* L200: */ } } else { i__1 = *n; for (j = 1; j <= *n; ++j) { temp.r = alpha->r, temp.i = alpha->i; if (nounit) { i__2 = j + j * a_dim1; z__1.r = temp.r * A(j,j).r - temp.i * A(j,j).i, z__1.i = temp.r * A(j,j).i + temp.i * A(j,j) .r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *m; for (i = 1; i <= *m; ++i) { i__3 = i + j * b_dim1; i__4 = i + j * b_dim1; z__1.r = temp.r * B(i,j).r - temp.i * B(i,j).i, z__1.i = temp.r * B(i,j).i + temp.i * B(i,j) .r; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L210: */ } i__2 = *n; for (k = j + 1; k <= *n; ++k) { i__3 = k + j * a_dim1; if (A(k,j).r != 0. || A(k,j).i != 0.) { i__3 = k + j * a_dim1; z__1.r = alpha->r * A(k,j).r - alpha->i * A(k,j) .i, z__1.i = alpha->r * A(k,j).i + alpha->i * A(k,j).r; temp.r = z__1.r, temp.i = z__1.i; i__3 = *m; for (i = 1; i <= *m; ++i) { i__4 = i + j * b_dim1; i__5 = i + j * b_dim1; i__6 = i + k * b_dim1; z__2.r = temp.r * B(i,k).r - temp.i * B(i,k) .i, z__2.i = temp.r * B(i,k).i + temp.i * B(i,k).r; z__1.r = B(i,j).r + z__2.r, z__1.i = B(i,j) .i + z__2.i; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L220: */ } } /* L230: */ } /* L240: */ } } } else { /* Form B := alpha*B*A' or B := alpha*B*conjg( A' ) . */ if (upper) { i__1 = *n; for (k = 1; k <= *n; ++k) { i__2 = k - 1; for (j = 1; j <= k-1; ++j) { i__3 = j + k * a_dim1; if (A(j,k).r != 0. || A(j,k).i != 0.) { if (noconj) { i__3 = j + k * a_dim1; z__1.r = alpha->r * A(j,k).r - alpha->i * A(j,k).i, z__1.i = alpha->r * A(j,k) .i + alpha->i * A(j,k).r; temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &A(j,k)); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__3 = *m; for (i = 1; i <= *m; ++i) { i__4 = i + j * b_dim1; i__5 = i + j * b_dim1; i__6 = i + k * b_dim1; z__2.r = temp.r * B(i,k).r - temp.i * B(i,k) .i, z__2.i = temp.r * B(i,k).i + temp.i * B(i,k).r; z__1.r = B(i,j).r + z__2.r, z__1.i = B(i,j) .i + z__2.i; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L250: */ } } /* L260: */ } temp.r = alpha->r, temp.i = alpha->i; if (nounit) { if (noconj) { i__2 = k + k * a_dim1; z__1.r = temp.r * A(k,k).r - temp.i * A(k,k).i, z__1.i = temp.r * A(k,k).i + temp.i * A(k,k).r; temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &A(k,k)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } } if (temp.r != 1. || temp.i != 0.) { i__2 = *m; for (i = 1; i <= *m; ++i) { i__3 = i + k * b_dim1; i__4 = i + k * b_dim1; z__1.r = temp.r * B(i,k).r - temp.i * B(i,k).i, z__1.i = temp.r * B(i,k).i + temp.i * B(i,k).r; B(i,k).r = z__1.r, B(i,k).i = z__1.i; /* L270: */ } } /* L280: */ } } else { for (k = *n; k >= 1; --k) { i__1 = *n; for (j = k + 1; j <= *n; ++j) { i__2 = j + k * a_dim1; if (A(j,k).r != 0. || A(j,k).i != 0.) { if (noconj) { i__2 = j + k * a_dim1; z__1.r = alpha->r * A(j,k).r - alpha->i * A(j,k).i, z__1.i = alpha->r * A(j,k) .i + alpha->i * A(j,k).r; temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &A(j,k)); z__1.r = alpha->r * z__2.r - alpha->i * z__2.i, z__1.i = alpha->r * z__2.i + alpha->i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } i__2 = *m; for (i = 1; i <= *m; ++i) { i__3 = i + j * b_dim1; i__4 = i + j * b_dim1; i__5 = i + k * b_dim1; z__2.r = temp.r * B(i,k).r - temp.i * B(i,k) .i, z__2.i = temp.r * B(i,k).i + temp.i * B(i,k).r; z__1.r = B(i,j).r + z__2.r, z__1.i = B(i,j) .i + z__2.i; B(i,j).r = z__1.r, B(i,j).i = z__1.i; /* L290: */ } } /* L300: */ } temp.r = alpha->r, temp.i = alpha->i; if (nounit) { if (noconj) { i__1 = k + k * a_dim1; z__1.r = temp.r * A(k,k).r - temp.i * A(k,k).i, z__1.i = temp.r * A(k,k).i + temp.i * A(k,k).r; temp.r = z__1.r, temp.i = z__1.i; } else { d_cnjg(&z__2, &A(k,k)); z__1.r = temp.r * z__2.r - temp.i * z__2.i, z__1.i = temp.r * z__2.i + temp.i * z__2.r; temp.r = z__1.r, temp.i = z__1.i; } } if (temp.r != 1. || temp.i != 0.) { i__1 = *m; for (i = 1; i <= *m; ++i) { i__2 = i + k * b_dim1; i__3 = i + k * b_dim1; z__1.r = temp.r * B(i,k).r - temp.i * B(i,k).i, z__1.i = temp.r * B(i,k).i + temp.i * B(i,k).r; B(i,k).r = z__1.r, B(i,k).i = z__1.i; /* L310: */ } } /* L320: */ } } } } return 0; /* End of ZTRMM . */ } /* ztrmm_ */