Annotation of rpl/lapack/blas/ztpmv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
! 2: * .. Scalar Arguments ..
! 3: INTEGER INCX,N
! 4: CHARACTER DIAG,TRANS,UPLO
! 5: * ..
! 6: * .. Array Arguments ..
! 7: DOUBLE COMPLEX AP(*),X(*)
! 8: * ..
! 9: *
! 10: * Purpose
! 11: * =======
! 12: *
! 13: * ZTPMV performs one of the matrix-vector operations
! 14: *
! 15: * x := A*x, or x := A'*x, or x := conjg( A' )*x,
! 16: *
! 17: * where x is an n element vector and A is an n by n unit, or non-unit,
! 18: * upper or lower triangular matrix, supplied in packed form.
! 19: *
! 20: * Arguments
! 21: * ==========
! 22: *
! 23: * UPLO - CHARACTER*1.
! 24: * On entry, UPLO specifies whether the matrix is an upper or
! 25: * lower triangular matrix as follows:
! 26: *
! 27: * UPLO = 'U' or 'u' A is an upper triangular matrix.
! 28: *
! 29: * UPLO = 'L' or 'l' A is a lower triangular matrix.
! 30: *
! 31: * Unchanged on exit.
! 32: *
! 33: * TRANS - CHARACTER*1.
! 34: * On entry, TRANS specifies the operation to be performed as
! 35: * follows:
! 36: *
! 37: * TRANS = 'N' or 'n' x := A*x.
! 38: *
! 39: * TRANS = 'T' or 't' x := A'*x.
! 40: *
! 41: * TRANS = 'C' or 'c' x := conjg( A' )*x.
! 42: *
! 43: * Unchanged on exit.
! 44: *
! 45: * DIAG - CHARACTER*1.
! 46: * On entry, DIAG specifies whether or not A is unit
! 47: * triangular as follows:
! 48: *
! 49: * DIAG = 'U' or 'u' A is assumed to be unit triangular.
! 50: *
! 51: * DIAG = 'N' or 'n' A is not assumed to be unit
! 52: * triangular.
! 53: *
! 54: * Unchanged on exit.
! 55: *
! 56: * N - INTEGER.
! 57: * On entry, N specifies the order of the matrix A.
! 58: * N must be at least zero.
! 59: * Unchanged on exit.
! 60: *
! 61: * AP - COMPLEX*16 array of DIMENSION at least
! 62: * ( ( n*( n + 1 ) )/2 ).
! 63: * Before entry with UPLO = 'U' or 'u', the array AP must
! 64: * contain the upper triangular matrix packed sequentially,
! 65: * column by column, so that AP( 1 ) contains a( 1, 1 ),
! 66: * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
! 67: * respectively, and so on.
! 68: * Before entry with UPLO = 'L' or 'l', the array AP must
! 69: * contain the lower triangular matrix packed sequentially,
! 70: * column by column, so that AP( 1 ) contains a( 1, 1 ),
! 71: * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
! 72: * respectively, and so on.
! 73: * Note that when DIAG = 'U' or 'u', the diagonal elements of
! 74: * A are not referenced, but are assumed to be unity.
! 75: * Unchanged on exit.
! 76: *
! 77: * X - COMPLEX*16 array of dimension at least
! 78: * ( 1 + ( n - 1 )*abs( INCX ) ).
! 79: * Before entry, the incremented array X must contain the n
! 80: * element vector x. On exit, X is overwritten with the
! 81: * tranformed vector x.
! 82: *
! 83: * INCX - INTEGER.
! 84: * On entry, INCX specifies the increment for the elements of
! 85: * X. INCX must not be zero.
! 86: * Unchanged on exit.
! 87: *
! 88: * Further Details
! 89: * ===============
! 90: *
! 91: * Level 2 Blas routine.
! 92: *
! 93: * -- Written on 22-October-1986.
! 94: * Jack Dongarra, Argonne National Lab.
! 95: * Jeremy Du Croz, Nag Central Office.
! 96: * Sven Hammarling, Nag Central Office.
! 97: * Richard Hanson, Sandia National Labs.
! 98: *
! 99: * =====================================================================
! 100: *
! 101: * .. Parameters ..
! 102: DOUBLE COMPLEX ZERO
! 103: PARAMETER (ZERO= (0.0D+0,0.0D+0))
! 104: * ..
! 105: * .. Local Scalars ..
! 106: DOUBLE COMPLEX TEMP
! 107: INTEGER I,INFO,IX,J,JX,K,KK,KX
! 108: LOGICAL NOCONJ,NOUNIT
! 109: * ..
! 110: * .. External Functions ..
! 111: LOGICAL LSAME
! 112: EXTERNAL LSAME
! 113: * ..
! 114: * .. External Subroutines ..
! 115: EXTERNAL XERBLA
! 116: * ..
! 117: * .. Intrinsic Functions ..
! 118: INTRINSIC DCONJG
! 119: * ..
! 120: *
! 121: * Test the input parameters.
! 122: *
! 123: INFO = 0
! 124: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
! 125: INFO = 1
! 126: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
! 127: + .NOT.LSAME(TRANS,'C')) THEN
! 128: INFO = 2
! 129: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
! 130: INFO = 3
! 131: ELSE IF (N.LT.0) THEN
! 132: INFO = 4
! 133: ELSE IF (INCX.EQ.0) THEN
! 134: INFO = 7
! 135: END IF
! 136: IF (INFO.NE.0) THEN
! 137: CALL XERBLA('ZTPMV ',INFO)
! 138: RETURN
! 139: END IF
! 140: *
! 141: * Quick return if possible.
! 142: *
! 143: IF (N.EQ.0) RETURN
! 144: *
! 145: NOCONJ = LSAME(TRANS,'T')
! 146: NOUNIT = LSAME(DIAG,'N')
! 147: *
! 148: * Set up the start point in X if the increment is not unity. This
! 149: * will be ( N - 1 )*INCX too small for descending loops.
! 150: *
! 151: IF (INCX.LE.0) THEN
! 152: KX = 1 - (N-1)*INCX
! 153: ELSE IF (INCX.NE.1) THEN
! 154: KX = 1
! 155: END IF
! 156: *
! 157: * Start the operations. In this version the elements of AP are
! 158: * accessed sequentially with one pass through AP.
! 159: *
! 160: IF (LSAME(TRANS,'N')) THEN
! 161: *
! 162: * Form x:= A*x.
! 163: *
! 164: IF (LSAME(UPLO,'U')) THEN
! 165: KK = 1
! 166: IF (INCX.EQ.1) THEN
! 167: DO 20 J = 1,N
! 168: IF (X(J).NE.ZERO) THEN
! 169: TEMP = X(J)
! 170: K = KK
! 171: DO 10 I = 1,J - 1
! 172: X(I) = X(I) + TEMP*AP(K)
! 173: K = K + 1
! 174: 10 CONTINUE
! 175: IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
! 176: END IF
! 177: KK = KK + J
! 178: 20 CONTINUE
! 179: ELSE
! 180: JX = KX
! 181: DO 40 J = 1,N
! 182: IF (X(JX).NE.ZERO) THEN
! 183: TEMP = X(JX)
! 184: IX = KX
! 185: DO 30 K = KK,KK + J - 2
! 186: X(IX) = X(IX) + TEMP*AP(K)
! 187: IX = IX + INCX
! 188: 30 CONTINUE
! 189: IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
! 190: END IF
! 191: JX = JX + INCX
! 192: KK = KK + J
! 193: 40 CONTINUE
! 194: END IF
! 195: ELSE
! 196: KK = (N* (N+1))/2
! 197: IF (INCX.EQ.1) THEN
! 198: DO 60 J = N,1,-1
! 199: IF (X(J).NE.ZERO) THEN
! 200: TEMP = X(J)
! 201: K = KK
! 202: DO 50 I = N,J + 1,-1
! 203: X(I) = X(I) + TEMP*AP(K)
! 204: K = K - 1
! 205: 50 CONTINUE
! 206: IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
! 207: END IF
! 208: KK = KK - (N-J+1)
! 209: 60 CONTINUE
! 210: ELSE
! 211: KX = KX + (N-1)*INCX
! 212: JX = KX
! 213: DO 80 J = N,1,-1
! 214: IF (X(JX).NE.ZERO) THEN
! 215: TEMP = X(JX)
! 216: IX = KX
! 217: DO 70 K = KK,KK - (N- (J+1)),-1
! 218: X(IX) = X(IX) + TEMP*AP(K)
! 219: IX = IX - INCX
! 220: 70 CONTINUE
! 221: IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
! 222: END IF
! 223: JX = JX - INCX
! 224: KK = KK - (N-J+1)
! 225: 80 CONTINUE
! 226: END IF
! 227: END IF
! 228: ELSE
! 229: *
! 230: * Form x := A'*x or x := conjg( A' )*x.
! 231: *
! 232: IF (LSAME(UPLO,'U')) THEN
! 233: KK = (N* (N+1))/2
! 234: IF (INCX.EQ.1) THEN
! 235: DO 110 J = N,1,-1
! 236: TEMP = X(J)
! 237: K = KK - 1
! 238: IF (NOCONJ) THEN
! 239: IF (NOUNIT) TEMP = TEMP*AP(KK)
! 240: DO 90 I = J - 1,1,-1
! 241: TEMP = TEMP + AP(K)*X(I)
! 242: K = K - 1
! 243: 90 CONTINUE
! 244: ELSE
! 245: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
! 246: DO 100 I = J - 1,1,-1
! 247: TEMP = TEMP + DCONJG(AP(K))*X(I)
! 248: K = K - 1
! 249: 100 CONTINUE
! 250: END IF
! 251: X(J) = TEMP
! 252: KK = KK - J
! 253: 110 CONTINUE
! 254: ELSE
! 255: JX = KX + (N-1)*INCX
! 256: DO 140 J = N,1,-1
! 257: TEMP = X(JX)
! 258: IX = JX
! 259: IF (NOCONJ) THEN
! 260: IF (NOUNIT) TEMP = TEMP*AP(KK)
! 261: DO 120 K = KK - 1,KK - J + 1,-1
! 262: IX = IX - INCX
! 263: TEMP = TEMP + AP(K)*X(IX)
! 264: 120 CONTINUE
! 265: ELSE
! 266: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
! 267: DO 130 K = KK - 1,KK - J + 1,-1
! 268: IX = IX - INCX
! 269: TEMP = TEMP + DCONJG(AP(K))*X(IX)
! 270: 130 CONTINUE
! 271: END IF
! 272: X(JX) = TEMP
! 273: JX = JX - INCX
! 274: KK = KK - J
! 275: 140 CONTINUE
! 276: END IF
! 277: ELSE
! 278: KK = 1
! 279: IF (INCX.EQ.1) THEN
! 280: DO 170 J = 1,N
! 281: TEMP = X(J)
! 282: K = KK + 1
! 283: IF (NOCONJ) THEN
! 284: IF (NOUNIT) TEMP = TEMP*AP(KK)
! 285: DO 150 I = J + 1,N
! 286: TEMP = TEMP + AP(K)*X(I)
! 287: K = K + 1
! 288: 150 CONTINUE
! 289: ELSE
! 290: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
! 291: DO 160 I = J + 1,N
! 292: TEMP = TEMP + DCONJG(AP(K))*X(I)
! 293: K = K + 1
! 294: 160 CONTINUE
! 295: END IF
! 296: X(J) = TEMP
! 297: KK = KK + (N-J+1)
! 298: 170 CONTINUE
! 299: ELSE
! 300: JX = KX
! 301: DO 200 J = 1,N
! 302: TEMP = X(JX)
! 303: IX = JX
! 304: IF (NOCONJ) THEN
! 305: IF (NOUNIT) TEMP = TEMP*AP(KK)
! 306: DO 180 K = KK + 1,KK + N - J
! 307: IX = IX + INCX
! 308: TEMP = TEMP + AP(K)*X(IX)
! 309: 180 CONTINUE
! 310: ELSE
! 311: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
! 312: DO 190 K = KK + 1,KK + N - J
! 313: IX = IX + INCX
! 314: TEMP = TEMP + DCONJG(AP(K))*X(IX)
! 315: 190 CONTINUE
! 316: END IF
! 317: X(JX) = TEMP
! 318: JX = JX + INCX
! 319: KK = KK + (N-J+1)
! 320: 200 CONTINUE
! 321: END IF
! 322: END IF
! 323: END IF
! 324: *
! 325: RETURN
! 326: *
! 327: * End of ZTPMV .
! 328: *
! 329: END
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