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| 2 | 1 | equemene | <HEAD>
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| 3 | 1 | equemene | <TITLE>HPL_dtrsm HPL 2.0 Library Functions September 10, 2008</TITLE> |
| 4 | 1 | equemene | </HEAD>
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| 5 | 1 | equemene | |
| 6 | 1 | equemene | <BODY BGCOLOR="WHITE" TEXT = "#000000" LINK = "#0000ff" VLINK = "#000099" |
| 7 | 1 | equemene | ALINK = "#ffff00"> |
| 8 | 1 | equemene | |
| 9 | 1 | equemene | <H1>Name</H1> |
| 10 | 1 | equemene | <B>HPL_dtrsm</B> B := A^{-1} * B or B := B * A^{-1}. |
| 11 | 1 | equemene | |
| 12 | 1 | equemene | <H1>Synopsis</H1> |
| 13 | 1 | equemene | <CODE>#include "hpl.h"</CODE><BR><BR> |
| 14 | 1 | equemene | <CODE>void</CODE> |
| 15 | 1 | equemene | <CODE>HPL_dtrsm(</CODE> |
| 16 | 1 | equemene | <CODE>const enum HPL_ORDER</CODE> |
| 17 | 1 | equemene | <CODE>ORDER</CODE>, |
| 18 | 1 | equemene | <CODE>const enum HPL_SIDE</CODE> |
| 19 | 1 | equemene | <CODE>SIDE</CODE>, |
| 20 | 1 | equemene | <CODE>const enum HPL_UPLO</CODE> |
| 21 | 1 | equemene | <CODE>UPLO</CODE>, |
| 22 | 1 | equemene | <CODE>const enum HPL_TRANS</CODE> |
| 23 | 1 | equemene | <CODE>TRANS</CODE>, |
| 24 | 1 | equemene | <CODE>const enum HPL_DIAG</CODE> |
| 25 | 1 | equemene | <CODE>DIAG</CODE>, |
| 26 | 1 | equemene | <CODE>const int</CODE> |
| 27 | 1 | equemene | <CODE>M</CODE>, |
| 28 | 1 | equemene | <CODE>const int</CODE> |
| 29 | 1 | equemene | <CODE>N</CODE>, |
| 30 | 1 | equemene | <CODE>const double</CODE> |
| 31 | 1 | equemene | <CODE>ALPHA</CODE>, |
| 32 | 1 | equemene | <CODE>const double *</CODE> |
| 33 | 1 | equemene | <CODE>A</CODE>, |
| 34 | 1 | equemene | <CODE>const int</CODE> |
| 35 | 1 | equemene | <CODE>LDA</CODE>, |
| 36 | 1 | equemene | <CODE>double *</CODE> |
| 37 | 1 | equemene | <CODE>B</CODE>, |
| 38 | 1 | equemene | <CODE>const int</CODE> |
| 39 | 1 | equemene | <CODE>LDB</CODE> |
| 40 | 1 | equemene | <CODE>);</CODE> |
| 41 | 1 | equemene | |
| 42 | 1 | equemene | <H1>Description</H1> |
| 43 | 1 | equemene | <B>HPL_dtrsm</B> |
| 44 | 1 | equemene | solves one of the matrix equations |
| 45 | 1 | equemene | |
| 46 | 1 | equemene | op( A ) * X = alpha * B, or X * op( A ) = alpha * B, |
| 47 | 1 | equemene | |
| 48 | 1 | equemene | where alpha is a scalar, X and B are m by n matrices, A is a unit, or |
| 49 | 1 | equemene | non-unit, upper or lower triangular matrix and op(A) is one of |
| 50 | 1 | equemene | |
| 51 | 1 | equemene | op( A ) = A or op( A ) = A^T. |
| 52 | 1 | equemene | |
| 53 | 1 | equemene | The matrix X is overwritten on B. |
| 54 | 1 | equemene | |
| 55 | 1 | equemene | No test for singularity or near-singularity is included in this |
| 56 | 1 | equemene | routine. Such tests must be performed before calling this routine. |
| 57 | 1 | equemene | |
| 58 | 1 | equemene | <H1>Arguments</H1> |
| 59 | 1 | equemene | <PRE>
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| 60 | 1 | equemene | ORDER (local input) const enum HPL_ORDER |
| 61 | 1 | equemene | On entry, ORDER specifies the storage format of the operands |
| 62 | 1 | equemene | as follows: |
| 63 | 1 | equemene | ORDER = HplRowMajor, |
| 64 | 1 | equemene | ORDER = HplColumnMajor. |
| 65 | 1 | equemene | </PRE>
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| 66 | 1 | equemene | <PRE>
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| 67 | 1 | equemene | SIDE (local input) const enum HPL_SIDE |
| 68 | 1 | equemene | On entry, SIDE specifies whether op(A) appears on the left |
| 69 | 1 | equemene | or right of X as follows: |
| 70 | 1 | equemene | SIDE==HplLeft op( A ) * X = alpha * B, |
| 71 | 1 | equemene | SIDE==HplRight X * op( A ) = alpha * B. |
| 72 | 1 | equemene | </PRE>
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| 73 | 1 | equemene | <PRE>
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| 74 | 1 | equemene | UPLO (local input) const enum HPL_UPLO |
| 75 | 1 | equemene | On entry, UPLO specifies whether the upper or lower |
| 76 | 1 | equemene | triangular part of the array A is to be referenced. When |
| 77 | 1 | equemene | UPLO==HplUpper, only the upper triangular part of A is to be |
| 78 | 1 | equemene | referenced, otherwise only the lower triangular part of A is |
| 79 | 1 | equemene | to be referenced. |
| 80 | 1 | equemene | </PRE>
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| 81 | 1 | equemene | <PRE>
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| 82 | 1 | equemene | TRANS (local input) const enum HPL_TRANS |
| 83 | 1 | equemene | On entry, TRANSA specifies the form of op(A) to be used in |
| 84 | 1 | equemene | the matrix-matrix operation follows: |
| 85 | 1 | equemene | TRANSA==HplNoTrans : op( A ) = A, |
| 86 | 1 | equemene | TRANSA==HplTrans : op( A ) = A^T, |
| 87 | 1 | equemene | TRANSA==HplConjTrans : op( A ) = A^T. |
| 88 | 1 | equemene | </PRE>
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| 89 | 1 | equemene | <PRE>
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| 90 | 1 | equemene | DIAG (local input) const enum HPL_DIAG |
| 91 | 1 | equemene | On entry, DIAG specifies whether A is unit triangular or |
| 92 | 1 | equemene | not. When DIAG==HplUnit, A is assumed to be unit triangular, |
| 93 | 1 | equemene | and otherwise, A is not assumed to be unit triangular. |
| 94 | 1 | equemene | </PRE>
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| 95 | 1 | equemene | <PRE>
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| 96 | 1 | equemene | M (local input) const int |
| 97 | 1 | equemene | On entry, M specifies the number of rows of the matrix B. |
| 98 | 1 | equemene | M must be at least zero. |
| 99 | 1 | equemene | </PRE>
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| 100 | 1 | equemene | <PRE>
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| 101 | 1 | equemene | N (local input) const int |
| 102 | 1 | equemene | On entry, N specifies the number of columns of the matrix B. |
| 103 | 1 | equemene | N must be at least zero. |
| 104 | 1 | equemene | </PRE>
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| 105 | 1 | equemene | <PRE>
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| 106 | 1 | equemene | ALPHA (local input) const double |
| 107 | 1 | equemene | On entry, ALPHA specifies the scalar alpha. When ALPHA is |
| 108 | 1 | equemene | supplied as zero then the elements of the matrix B need not |
| 109 | 1 | equemene | be set on input. |
| 110 | 1 | equemene | </PRE>
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| 111 | 1 | equemene | <PRE>
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| 112 | 1 | equemene | A (local input) const double * |
| 113 | 1 | equemene | On entry, A points to an array of size equal to or greater |
| 114 | 1 | equemene | than LDA * k, where k is m when SIDE==HplLeft and is n |
| 115 | 1 | equemene | otherwise. Before entry with UPLO==HplUpper, the leading |
| 116 | 1 | equemene | k by k upper triangular part of the array A must contain the |
| 117 | 1 | equemene | upper triangular matrix and the strictly lower triangular |
| 118 | 1 | equemene | part of A is not referenced. When UPLO==HplLower on entry, |
| 119 | 1 | equemene | the leading k by k lower triangular part of the array A must |
| 120 | 1 | equemene | contain the lower triangular matrix and the strictly upper |
| 121 | 1 | equemene | triangular part of A is not referenced. |
| 122 | 1 | equemene | |
| 123 | 1 | equemene | Note that when DIAG==HplUnit, the diagonal elements of A |
| 124 | 1 | equemene | not referenced either, but are assumed to be unity. |
| 125 | 1 | equemene | </PRE>
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| 126 | 1 | equemene | <PRE>
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| 127 | 1 | equemene | LDA (local input) const int |
| 128 | 1 | equemene | On entry, LDA specifies the leading dimension of A as |
| 129 | 1 | equemene | declared in the calling (sub) program. LDA must be at |
| 130 | 1 | equemene | least MAX(1,m) when SIDE==HplLeft, and MAX(1,n) otherwise. |
| 131 | 1 | equemene | </PRE>
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| 132 | 1 | equemene | <PRE>
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| 133 | 1 | equemene | B (local input/output) double * |
| 134 | 1 | equemene | On entry, B points to an array of size equal to or greater |
| 135 | 1 | equemene | than LDB * n. Before entry, the leading m by n part of the |
| 136 | 1 | equemene | array B must contain the matrix B, except when beta is zero, |
| 137 | 1 | equemene | in which case B need not be set on entry. On exit, the array |
| 138 | 1 | equemene | B is overwritten by the m by n solution matrix. |
| 139 | 1 | equemene | </PRE>
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| 140 | 1 | equemene | <PRE>
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| 141 | 1 | equemene | LDB (local input) const int |
| 142 | 1 | equemene | On entry, LDB specifies the leading dimension of B as |
| 143 | 1 | equemene | declared in the calling (sub) program. LDB must be at |
| 144 | 1 | equemene | least MAX(1,m). |
| 145 | 1 | equemene | </PRE>
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| 146 | 1 | equemene | |
| 147 | 1 | equemene | <H1>Example</H1> |
| 148 | 1 | equemene | <CODE>#include "hpl.h"</CODE><BR><BR> |
| 149 | 1 | equemene | <PRE>
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| 150 | 1 | equemene | int main(int argc, char *argv[]) |
| 151 | 1 | equemene | {
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| 152 | 1 | equemene | double a[2*2], b[2*2]; |
| 153 | 1 | equemene | a[0] = 4.0; a[1] = 1.0; a[2] = 2.0; a[3] = 5.0; |
| 154 | 1 | equemene | b[0] = 2.0; b[1] = 1.0; b[2] = 1.0; b[3] = 2.0; |
| 155 | 1 | equemene | HPL_dtrsm( HplColumnMajor, HplLeft, HplUpper, |
| 156 | 1 | equemene | HplNoTrans, HplNonUnit, 2, 2, 2.0, |
| 157 | 1 | equemene | a, 2, b, 2 ); |
| 158 | 1 | equemene | printf(" [%f,%f]\n", b[0], b[2]);
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| 159 | 1 | equemene | printf("b=[%f,%f]\n", b[1], b[3]);
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| 160 | 1 | equemene | exit(0); return(0); |
| 161 | 1 | equemene | } |
| 162 | 1 | equemene | </PRE>
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| 163 | 1 | equemene | |
| 164 | 1 | equemene | <H1>See Also</H1> |
| 165 | 1 | equemene | <A HREF="HPL_dgemm.html">HPL_dgemm</A>. |
| 166 | 1 | equemene | |
| 167 | 1 | equemene | </BODY>
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