Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 1 | SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP) |
| 2 | * .. Scalar Arguments .. |
| 3 | REAL ALPHA |
| 4 | INTEGER INCX,N |
| 5 | CHARACTER UPLO |
| 6 | * .. |
| 7 | * .. Array Arguments .. |
| 8 | REAL AP(*),X(*) |
| 9 | * .. |
| 10 | * |
| 11 | * Purpose |
| 12 | * ======= |
| 13 | * |
| 14 | * SSPR performs the symmetric rank 1 operation |
| 15 | * |
| 16 | * A := alpha*x*x' + A, |
| 17 | * |
| 18 | * where alpha is a real scalar, x is an n element vector and A is an |
| 19 | * n by n symmetric matrix, supplied in packed form. |
| 20 | * |
| 21 | * Arguments |
| 22 | * ========== |
| 23 | * |
| 24 | * UPLO - CHARACTER*1. |
| 25 | * On entry, UPLO specifies whether the upper or lower |
| 26 | * triangular part of the matrix A is supplied in the packed |
| 27 | * array AP as follows: |
| 28 | * |
| 29 | * UPLO = 'U' or 'u' The upper triangular part of A is |
| 30 | * supplied in AP. |
| 31 | * |
| 32 | * UPLO = 'L' or 'l' The lower triangular part of A is |
| 33 | * supplied in AP. |
| 34 | * |
| 35 | * Unchanged on exit. |
| 36 | * |
| 37 | * N - INTEGER. |
| 38 | * On entry, N specifies the order of the matrix A. |
| 39 | * N must be at least zero. |
| 40 | * Unchanged on exit. |
| 41 | * |
| 42 | * ALPHA - REAL . |
| 43 | * On entry, ALPHA specifies the scalar alpha. |
| 44 | * Unchanged on exit. |
| 45 | * |
| 46 | * X - REAL array of dimension at least |
| 47 | * ( 1 + ( n - 1 )*abs( INCX ) ). |
| 48 | * Before entry, the incremented array X must contain the n |
| 49 | * element vector x. |
| 50 | * Unchanged on exit. |
| 51 | * |
| 52 | * INCX - INTEGER. |
| 53 | * On entry, INCX specifies the increment for the elements of |
| 54 | * X. INCX must not be zero. |
| 55 | * Unchanged on exit. |
| 56 | * |
| 57 | * AP - REAL array of DIMENSION at least |
| 58 | * ( ( n*( n + 1 ) )/2 ). |
| 59 | * Before entry with UPLO = 'U' or 'u', the array AP must |
| 60 | * contain the upper triangular part of the symmetric matrix |
| 61 | * packed sequentially, column by column, so that AP( 1 ) |
| 62 | * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) |
| 63 | * and a( 2, 2 ) respectively, and so on. On exit, the array |
| 64 | * AP is overwritten by the upper triangular part of the |
| 65 | * updated matrix. |
| 66 | * Before entry with UPLO = 'L' or 'l', the array AP must |
| 67 | * contain the lower triangular part of the symmetric matrix |
| 68 | * packed sequentially, column by column, so that AP( 1 ) |
| 69 | * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) |
| 70 | * and a( 3, 1 ) respectively, and so on. On exit, the array |
| 71 | * AP is overwritten by the lower triangular part of the |
| 72 | * updated matrix. |
| 73 | * |
| 74 | * Further Details |
| 75 | * =============== |
| 76 | * |
| 77 | * Level 2 Blas routine. |
| 78 | * |
| 79 | * -- Written on 22-October-1986. |
| 80 | * Jack Dongarra, Argonne National Lab. |
| 81 | * Jeremy Du Croz, Nag Central Office. |
| 82 | * Sven Hammarling, Nag Central Office. |
| 83 | * Richard Hanson, Sandia National Labs. |
| 84 | * |
| 85 | * ===================================================================== |
| 86 | * |
| 87 | * .. Parameters .. |
| 88 | REAL ZERO |
| 89 | PARAMETER (ZERO=0.0E+0) |
| 90 | * .. |
| 91 | * .. Local Scalars .. |
| 92 | REAL TEMP |
| 93 | INTEGER I,INFO,IX,J,JX,K,KK,KX |
| 94 | * .. |
| 95 | * .. External Functions .. |
| 96 | LOGICAL LSAME |
| 97 | EXTERNAL LSAME |
| 98 | * .. |
| 99 | * .. External Subroutines .. |
| 100 | EXTERNAL XERBLA |
| 101 | * .. |
| 102 | * |
| 103 | * Test the input parameters. |
| 104 | * |
| 105 | INFO = 0 |
| 106 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
| 107 | INFO = 1 |
| 108 | ELSE IF (N.LT.0) THEN |
| 109 | INFO = 2 |
| 110 | ELSE IF (INCX.EQ.0) THEN |
| 111 | INFO = 5 |
| 112 | END IF |
| 113 | IF (INFO.NE.0) THEN |
| 114 | CALL XERBLA('SSPR ',INFO) |
| 115 | RETURN |
| 116 | END IF |
| 117 | * |
| 118 | * Quick return if possible. |
| 119 | * |
| 120 | IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN |
| 121 | * |
| 122 | * Set the start point in X if the increment is not unity. |
| 123 | * |
| 124 | IF (INCX.LE.0) THEN |
| 125 | KX = 1 - (N-1)*INCX |
| 126 | ELSE IF (INCX.NE.1) THEN |
| 127 | KX = 1 |
| 128 | END IF |
| 129 | * |
| 130 | * Start the operations. In this version the elements of the array AP |
| 131 | * are accessed sequentially with one pass through AP. |
| 132 | * |
| 133 | KK = 1 |
| 134 | IF (LSAME(UPLO,'U')) THEN |
| 135 | * |
| 136 | * Form A when upper triangle is stored in AP. |
| 137 | * |
| 138 | IF (INCX.EQ.1) THEN |
| 139 | DO 20 J = 1,N |
| 140 | IF (X(J).NE.ZERO) THEN |
| 141 | TEMP = ALPHA*X(J) |
| 142 | K = KK |
| 143 | DO 10 I = 1,J |
| 144 | AP(K) = AP(K) + X(I)*TEMP |
| 145 | K = K + 1 |
| 146 | 10 CONTINUE |
| 147 | END IF |
| 148 | KK = KK + J |
| 149 | 20 CONTINUE |
| 150 | ELSE |
| 151 | JX = KX |
| 152 | DO 40 J = 1,N |
| 153 | IF (X(JX).NE.ZERO) THEN |
| 154 | TEMP = ALPHA*X(JX) |
| 155 | IX = KX |
| 156 | DO 30 K = KK,KK + J - 1 |
| 157 | AP(K) = AP(K) + X(IX)*TEMP |
| 158 | IX = IX + INCX |
| 159 | 30 CONTINUE |
| 160 | END IF |
| 161 | JX = JX + INCX |
| 162 | KK = KK + J |
| 163 | 40 CONTINUE |
| 164 | END IF |
| 165 | ELSE |
| 166 | * |
| 167 | * Form A when lower triangle is stored in AP. |
| 168 | * |
| 169 | IF (INCX.EQ.1) THEN |
| 170 | DO 60 J = 1,N |
| 171 | IF (X(J).NE.ZERO) THEN |
| 172 | TEMP = ALPHA*X(J) |
| 173 | K = KK |
| 174 | DO 50 I = J,N |
| 175 | AP(K) = AP(K) + X(I)*TEMP |
| 176 | K = K + 1 |
| 177 | 50 CONTINUE |
| 178 | END IF |
| 179 | KK = KK + N - J + 1 |
| 180 | 60 CONTINUE |
| 181 | ELSE |
| 182 | JX = KX |
| 183 | DO 80 J = 1,N |
| 184 | IF (X(JX).NE.ZERO) THEN |
| 185 | TEMP = ALPHA*X(JX) |
| 186 | IX = JX |
| 187 | DO 70 K = KK,KK + N - J |
| 188 | AP(K) = AP(K) + X(IX)*TEMP |
| 189 | IX = IX + INCX |
| 190 | 70 CONTINUE |
| 191 | END IF |
| 192 | JX = JX + INCX |
| 193 | KK = KK + N - J + 1 |
| 194 | 80 CONTINUE |
| 195 | END IF |
| 196 | END IF |
| 197 | * |
| 198 | RETURN |
| 199 | * |
| 200 | * End of SSPR . |
| 201 | * |
| 202 | END |