Annotation of rpl/lapack/lapack/zsymv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
! 2: *
! 3: * -- LAPACK auxiliary routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: CHARACTER UPLO
! 10: INTEGER INCX, INCY, LDA, N
! 11: COMPLEX*16 ALPHA, BETA
! 12: * ..
! 13: * .. Array Arguments ..
! 14: COMPLEX*16 A( LDA, * ), X( * ), Y( * )
! 15: * ..
! 16: *
! 17: * Purpose
! 18: * =======
! 19: *
! 20: * ZSYMV performs the matrix-vector operation
! 21: *
! 22: * y := alpha*A*x + beta*y,
! 23: *
! 24: * where alpha and beta are scalars, x and y are n element vectors and
! 25: * A is an n by n symmetric matrix.
! 26: *
! 27: * Arguments
! 28: * ==========
! 29: *
! 30: * UPLO (input) CHARACTER*1
! 31: * On entry, UPLO specifies whether the upper or lower
! 32: * triangular part of the array A is to be referenced as
! 33: * follows:
! 34: *
! 35: * UPLO = 'U' or 'u' Only the upper triangular part of A
! 36: * is to be referenced.
! 37: *
! 38: * UPLO = 'L' or 'l' Only the lower triangular part of A
! 39: * is to be referenced.
! 40: *
! 41: * Unchanged on exit.
! 42: *
! 43: * N (input) INTEGER
! 44: * On entry, N specifies the order of the matrix A.
! 45: * N must be at least zero.
! 46: * Unchanged on exit.
! 47: *
! 48: * ALPHA (input) COMPLEX*16
! 49: * On entry, ALPHA specifies the scalar alpha.
! 50: * Unchanged on exit.
! 51: *
! 52: * A (input) COMPLEX*16 array, dimension ( LDA, N )
! 53: * Before entry, with UPLO = 'U' or 'u', the leading n by n
! 54: * upper triangular part of the array A must contain the upper
! 55: * triangular part of the symmetric matrix and the strictly
! 56: * lower triangular part of A is not referenced.
! 57: * Before entry, with UPLO = 'L' or 'l', the leading n by n
! 58: * lower triangular part of the array A must contain the lower
! 59: * triangular part of the symmetric matrix and the strictly
! 60: * upper triangular part of A is not referenced.
! 61: * Unchanged on exit.
! 62: *
! 63: * LDA (input) INTEGER
! 64: * On entry, LDA specifies the first dimension of A as declared
! 65: * in the calling (sub) program. LDA must be at least
! 66: * max( 1, N ).
! 67: * Unchanged on exit.
! 68: *
! 69: * X (input) COMPLEX*16 array, dimension at least
! 70: * ( 1 + ( N - 1 )*abs( INCX ) ).
! 71: * Before entry, the incremented array X must contain the N-
! 72: * element vector x.
! 73: * Unchanged on exit.
! 74: *
! 75: * INCX (input) INTEGER
! 76: * On entry, INCX specifies the increment for the elements of
! 77: * X. INCX must not be zero.
! 78: * Unchanged on exit.
! 79: *
! 80: * BETA (input) COMPLEX*16
! 81: * On entry, BETA specifies the scalar beta. When BETA is
! 82: * supplied as zero then Y need not be set on input.
! 83: * Unchanged on exit.
! 84: *
! 85: * Y (input/output) COMPLEX*16 array, dimension at least
! 86: * ( 1 + ( N - 1 )*abs( INCY ) ).
! 87: * Before entry, the incremented array Y must contain the n
! 88: * element vector y. On exit, Y is overwritten by the updated
! 89: * vector y.
! 90: *
! 91: * INCY (input) INTEGER
! 92: * On entry, INCY specifies the increment for the elements of
! 93: * Y. INCY must not be zero.
! 94: * Unchanged on exit.
! 95: *
! 96: * =====================================================================
! 97: *
! 98: * .. Parameters ..
! 99: COMPLEX*16 ONE
! 100: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
! 101: COMPLEX*16 ZERO
! 102: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
! 103: * ..
! 104: * .. Local Scalars ..
! 105: INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
! 106: COMPLEX*16 TEMP1, TEMP2
! 107: * ..
! 108: * .. External Functions ..
! 109: LOGICAL LSAME
! 110: EXTERNAL LSAME
! 111: * ..
! 112: * .. External Subroutines ..
! 113: EXTERNAL XERBLA
! 114: * ..
! 115: * .. Intrinsic Functions ..
! 116: INTRINSIC MAX
! 117: * ..
! 118: * .. Executable Statements ..
! 119: *
! 120: * Test the input parameters.
! 121: *
! 122: INFO = 0
! 123: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 124: INFO = 1
! 125: ELSE IF( N.LT.0 ) THEN
! 126: INFO = 2
! 127: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 128: INFO = 5
! 129: ELSE IF( INCX.EQ.0 ) THEN
! 130: INFO = 7
! 131: ELSE IF( INCY.EQ.0 ) THEN
! 132: INFO = 10
! 133: END IF
! 134: IF( INFO.NE.0 ) THEN
! 135: CALL XERBLA( 'ZSYMV ', INFO )
! 136: RETURN
! 137: END IF
! 138: *
! 139: * Quick return if possible.
! 140: *
! 141: IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
! 142: $ RETURN
! 143: *
! 144: * Set up the start points in X and Y.
! 145: *
! 146: IF( INCX.GT.0 ) THEN
! 147: KX = 1
! 148: ELSE
! 149: KX = 1 - ( N-1 )*INCX
! 150: END IF
! 151: IF( INCY.GT.0 ) THEN
! 152: KY = 1
! 153: ELSE
! 154: KY = 1 - ( N-1 )*INCY
! 155: END IF
! 156: *
! 157: * Start the operations. In this version the elements of A are
! 158: * accessed sequentially with one pass through the triangular part
! 159: * of A.
! 160: *
! 161: * First form y := beta*y.
! 162: *
! 163: IF( BETA.NE.ONE ) THEN
! 164: IF( INCY.EQ.1 ) THEN
! 165: IF( BETA.EQ.ZERO ) THEN
! 166: DO 10 I = 1, N
! 167: Y( I ) = ZERO
! 168: 10 CONTINUE
! 169: ELSE
! 170: DO 20 I = 1, N
! 171: Y( I ) = BETA*Y( I )
! 172: 20 CONTINUE
! 173: END IF
! 174: ELSE
! 175: IY = KY
! 176: IF( BETA.EQ.ZERO ) THEN
! 177: DO 30 I = 1, N
! 178: Y( IY ) = ZERO
! 179: IY = IY + INCY
! 180: 30 CONTINUE
! 181: ELSE
! 182: DO 40 I = 1, N
! 183: Y( IY ) = BETA*Y( IY )
! 184: IY = IY + INCY
! 185: 40 CONTINUE
! 186: END IF
! 187: END IF
! 188: END IF
! 189: IF( ALPHA.EQ.ZERO )
! 190: $ RETURN
! 191: IF( LSAME( UPLO, 'U' ) ) THEN
! 192: *
! 193: * Form y when A is stored in upper triangle.
! 194: *
! 195: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
! 196: DO 60 J = 1, N
! 197: TEMP1 = ALPHA*X( J )
! 198: TEMP2 = ZERO
! 199: DO 50 I = 1, J - 1
! 200: Y( I ) = Y( I ) + TEMP1*A( I, J )
! 201: TEMP2 = TEMP2 + A( I, J )*X( I )
! 202: 50 CONTINUE
! 203: Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
! 204: 60 CONTINUE
! 205: ELSE
! 206: JX = KX
! 207: JY = KY
! 208: DO 80 J = 1, N
! 209: TEMP1 = ALPHA*X( JX )
! 210: TEMP2 = ZERO
! 211: IX = KX
! 212: IY = KY
! 213: DO 70 I = 1, J - 1
! 214: Y( IY ) = Y( IY ) + TEMP1*A( I, J )
! 215: TEMP2 = TEMP2 + A( I, J )*X( IX )
! 216: IX = IX + INCX
! 217: IY = IY + INCY
! 218: 70 CONTINUE
! 219: Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
! 220: JX = JX + INCX
! 221: JY = JY + INCY
! 222: 80 CONTINUE
! 223: END IF
! 224: ELSE
! 225: *
! 226: * Form y when A is stored in lower triangle.
! 227: *
! 228: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
! 229: DO 100 J = 1, N
! 230: TEMP1 = ALPHA*X( J )
! 231: TEMP2 = ZERO
! 232: Y( J ) = Y( J ) + TEMP1*A( J, J )
! 233: DO 90 I = J + 1, N
! 234: Y( I ) = Y( I ) + TEMP1*A( I, J )
! 235: TEMP2 = TEMP2 + A( I, J )*X( I )
! 236: 90 CONTINUE
! 237: Y( J ) = Y( J ) + ALPHA*TEMP2
! 238: 100 CONTINUE
! 239: ELSE
! 240: JX = KX
! 241: JY = KY
! 242: DO 120 J = 1, N
! 243: TEMP1 = ALPHA*X( JX )
! 244: TEMP2 = ZERO
! 245: Y( JY ) = Y( JY ) + TEMP1*A( J, J )
! 246: IX = JX
! 247: IY = JY
! 248: DO 110 I = J + 1, N
! 249: IX = IX + INCX
! 250: IY = IY + INCY
! 251: Y( IY ) = Y( IY ) + TEMP1*A( I, J )
! 252: TEMP2 = TEMP2 + A( I, J )*X( IX )
! 253: 110 CONTINUE
! 254: Y( JY ) = Y( JY ) + ALPHA*TEMP2
! 255: JX = JX + INCX
! 256: JY = JY + INCY
! 257: 120 CONTINUE
! 258: END IF
! 259: END IF
! 260: *
! 261: RETURN
! 262: *
! 263: * End of ZSYMV
! 264: *
! 265: END
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