Annotation of rpl/lapack/blas/zgbmv.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
! 2: * .. Scalar Arguments ..
! 3: DOUBLE COMPLEX ALPHA,BETA
! 4: INTEGER INCX,INCY,KL,KU,LDA,M,N
! 5: CHARACTER TRANS
! 6: * ..
! 7: * .. Array Arguments ..
! 8: DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
! 9: * ..
! 10: *
! 11: * Purpose
! 12: * =======
! 13: *
! 14: * ZGBMV performs one of the matrix-vector operations
! 15: *
! 16: * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or
! 17: *
! 18: * y := alpha*conjg( A' )*x + beta*y,
! 19: *
! 20: * where alpha and beta are scalars, x and y are vectors and A is an
! 21: * m by n band matrix, with kl sub-diagonals and ku super-diagonals.
! 22: *
! 23: * Arguments
! 24: * ==========
! 25: *
! 26: * TRANS - CHARACTER*1.
! 27: * On entry, TRANS specifies the operation to be performed as
! 28: * follows:
! 29: *
! 30: * TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
! 31: *
! 32: * TRANS = 'T' or 't' y := alpha*A'*x + beta*y.
! 33: *
! 34: * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y.
! 35: *
! 36: * Unchanged on exit.
! 37: *
! 38: * M - INTEGER.
! 39: * On entry, M specifies the number of rows of the matrix A.
! 40: * M must be at least zero.
! 41: * Unchanged on exit.
! 42: *
! 43: * N - INTEGER.
! 44: * On entry, N specifies the number of columns of the matrix A.
! 45: * N must be at least zero.
! 46: * Unchanged on exit.
! 47: *
! 48: * KL - INTEGER.
! 49: * On entry, KL specifies the number of sub-diagonals of the
! 50: * matrix A. KL must satisfy 0 .le. KL.
! 51: * Unchanged on exit.
! 52: *
! 53: * KU - INTEGER.
! 54: * On entry, KU specifies the number of super-diagonals of the
! 55: * matrix A. KU must satisfy 0 .le. KU.
! 56: * Unchanged on exit.
! 57: *
! 58: * ALPHA - COMPLEX*16 .
! 59: * On entry, ALPHA specifies the scalar alpha.
! 60: * Unchanged on exit.
! 61: *
! 62: * A - COMPLEX*16 array of DIMENSION ( LDA, n ).
! 63: * Before entry, the leading ( kl + ku + 1 ) by n part of the
! 64: * array A must contain the matrix of coefficients, supplied
! 65: * column by column, with the leading diagonal of the matrix in
! 66: * row ( ku + 1 ) of the array, the first super-diagonal
! 67: * starting at position 2 in row ku, the first sub-diagonal
! 68: * starting at position 1 in row ( ku + 2 ), and so on.
! 69: * Elements in the array A that do not correspond to elements
! 70: * in the band matrix (such as the top left ku by ku triangle)
! 71: * are not referenced.
! 72: * The following program segment will transfer a band matrix
! 73: * from conventional full matrix storage to band storage:
! 74: *
! 75: * DO 20, J = 1, N
! 76: * K = KU + 1 - J
! 77: * DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
! 78: * A( K + I, J ) = matrix( I, J )
! 79: * 10 CONTINUE
! 80: * 20 CONTINUE
! 81: *
! 82: * Unchanged on exit.
! 83: *
! 84: * LDA - INTEGER.
! 85: * On entry, LDA specifies the first dimension of A as declared
! 86: * in the calling (sub) program. LDA must be at least
! 87: * ( kl + ku + 1 ).
! 88: * Unchanged on exit.
! 89: *
! 90: * X - COMPLEX*16 array of DIMENSION at least
! 91: * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
! 92: * and at least
! 93: * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
! 94: * Before entry, the incremented array X must contain the
! 95: * vector x.
! 96: * Unchanged on exit.
! 97: *
! 98: * INCX - INTEGER.
! 99: * On entry, INCX specifies the increment for the elements of
! 100: * X. INCX must not be zero.
! 101: * Unchanged on exit.
! 102: *
! 103: * BETA - COMPLEX*16 .
! 104: * On entry, BETA specifies the scalar beta. When BETA is
! 105: * supplied as zero then Y need not be set on input.
! 106: * Unchanged on exit.
! 107: *
! 108: * Y - COMPLEX*16 array of DIMENSION at least
! 109: * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
! 110: * and at least
! 111: * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
! 112: * Before entry, the incremented array Y must contain the
! 113: * vector y. On exit, Y is overwritten by the updated vector y.
! 114: *
! 115: *
! 116: * INCY - INTEGER.
! 117: * On entry, INCY specifies the increment for the elements of
! 118: * Y. INCY must not be zero.
! 119: * Unchanged on exit.
! 120: *
! 121: * Further Details
! 122: * ===============
! 123: *
! 124: * Level 2 Blas routine.
! 125: *
! 126: * -- Written on 22-October-1986.
! 127: * Jack Dongarra, Argonne National Lab.
! 128: * Jeremy Du Croz, Nag Central Office.
! 129: * Sven Hammarling, Nag Central Office.
! 130: * Richard Hanson, Sandia National Labs.
! 131: *
! 132: * =====================================================================
! 133: *
! 134: * .. Parameters ..
! 135: DOUBLE COMPLEX ONE
! 136: PARAMETER (ONE= (1.0D+0,0.0D+0))
! 137: DOUBLE COMPLEX ZERO
! 138: PARAMETER (ZERO= (0.0D+0,0.0D+0))
! 139: * ..
! 140: * .. Local Scalars ..
! 141: DOUBLE COMPLEX TEMP
! 142: INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
! 143: LOGICAL NOCONJ
! 144: * ..
! 145: * .. External Functions ..
! 146: LOGICAL LSAME
! 147: EXTERNAL LSAME
! 148: * ..
! 149: * .. External Subroutines ..
! 150: EXTERNAL XERBLA
! 151: * ..
! 152: * .. Intrinsic Functions ..
! 153: INTRINSIC DCONJG,MAX,MIN
! 154: * ..
! 155: *
! 156: * Test the input parameters.
! 157: *
! 158: INFO = 0
! 159: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
! 160: + .NOT.LSAME(TRANS,'C')) THEN
! 161: INFO = 1
! 162: ELSE IF (M.LT.0) THEN
! 163: INFO = 2
! 164: ELSE IF (N.LT.0) THEN
! 165: INFO = 3
! 166: ELSE IF (KL.LT.0) THEN
! 167: INFO = 4
! 168: ELSE IF (KU.LT.0) THEN
! 169: INFO = 5
! 170: ELSE IF (LDA.LT. (KL+KU+1)) THEN
! 171: INFO = 8
! 172: ELSE IF (INCX.EQ.0) THEN
! 173: INFO = 10
! 174: ELSE IF (INCY.EQ.0) THEN
! 175: INFO = 13
! 176: END IF
! 177: IF (INFO.NE.0) THEN
! 178: CALL XERBLA('ZGBMV ',INFO)
! 179: RETURN
! 180: END IF
! 181: *
! 182: * Quick return if possible.
! 183: *
! 184: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
! 185: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
! 186: *
! 187: NOCONJ = LSAME(TRANS,'T')
! 188: *
! 189: * Set LENX and LENY, the lengths of the vectors x and y, and set
! 190: * up the start points in X and Y.
! 191: *
! 192: IF (LSAME(TRANS,'N')) THEN
! 193: LENX = N
! 194: LENY = M
! 195: ELSE
! 196: LENX = M
! 197: LENY = N
! 198: END IF
! 199: IF (INCX.GT.0) THEN
! 200: KX = 1
! 201: ELSE
! 202: KX = 1 - (LENX-1)*INCX
! 203: END IF
! 204: IF (INCY.GT.0) THEN
! 205: KY = 1
! 206: ELSE
! 207: KY = 1 - (LENY-1)*INCY
! 208: END IF
! 209: *
! 210: * Start the operations. In this version the elements of A are
! 211: * accessed sequentially with one pass through the band part of A.
! 212: *
! 213: * First form y := beta*y.
! 214: *
! 215: IF (BETA.NE.ONE) THEN
! 216: IF (INCY.EQ.1) THEN
! 217: IF (BETA.EQ.ZERO) THEN
! 218: DO 10 I = 1,LENY
! 219: Y(I) = ZERO
! 220: 10 CONTINUE
! 221: ELSE
! 222: DO 20 I = 1,LENY
! 223: Y(I) = BETA*Y(I)
! 224: 20 CONTINUE
! 225: END IF
! 226: ELSE
! 227: IY = KY
! 228: IF (BETA.EQ.ZERO) THEN
! 229: DO 30 I = 1,LENY
! 230: Y(IY) = ZERO
! 231: IY = IY + INCY
! 232: 30 CONTINUE
! 233: ELSE
! 234: DO 40 I = 1,LENY
! 235: Y(IY) = BETA*Y(IY)
! 236: IY = IY + INCY
! 237: 40 CONTINUE
! 238: END IF
! 239: END IF
! 240: END IF
! 241: IF (ALPHA.EQ.ZERO) RETURN
! 242: KUP1 = KU + 1
! 243: IF (LSAME(TRANS,'N')) THEN
! 244: *
! 245: * Form y := alpha*A*x + y.
! 246: *
! 247: JX = KX
! 248: IF (INCY.EQ.1) THEN
! 249: DO 60 J = 1,N
! 250: IF (X(JX).NE.ZERO) THEN
! 251: TEMP = ALPHA*X(JX)
! 252: K = KUP1 - J
! 253: DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
! 254: Y(I) = Y(I) + TEMP*A(K+I,J)
! 255: 50 CONTINUE
! 256: END IF
! 257: JX = JX + INCX
! 258: 60 CONTINUE
! 259: ELSE
! 260: DO 80 J = 1,N
! 261: IF (X(JX).NE.ZERO) THEN
! 262: TEMP = ALPHA*X(JX)
! 263: IY = KY
! 264: K = KUP1 - J
! 265: DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
! 266: Y(IY) = Y(IY) + TEMP*A(K+I,J)
! 267: IY = IY + INCY
! 268: 70 CONTINUE
! 269: END IF
! 270: JX = JX + INCX
! 271: IF (J.GT.KU) KY = KY + INCY
! 272: 80 CONTINUE
! 273: END IF
! 274: ELSE
! 275: *
! 276: * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y.
! 277: *
! 278: JY = KY
! 279: IF (INCX.EQ.1) THEN
! 280: DO 110 J = 1,N
! 281: TEMP = ZERO
! 282: K = KUP1 - J
! 283: IF (NOCONJ) THEN
! 284: DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
! 285: TEMP = TEMP + A(K+I,J)*X(I)
! 286: 90 CONTINUE
! 287: ELSE
! 288: DO 100 I = MAX(1,J-KU),MIN(M,J+KL)
! 289: TEMP = TEMP + DCONJG(A(K+I,J))*X(I)
! 290: 100 CONTINUE
! 291: END IF
! 292: Y(JY) = Y(JY) + ALPHA*TEMP
! 293: JY = JY + INCY
! 294: 110 CONTINUE
! 295: ELSE
! 296: DO 140 J = 1,N
! 297: TEMP = ZERO
! 298: IX = KX
! 299: K = KUP1 - J
! 300: IF (NOCONJ) THEN
! 301: DO 120 I = MAX(1,J-KU),MIN(M,J+KL)
! 302: TEMP = TEMP + A(K+I,J)*X(IX)
! 303: IX = IX + INCX
! 304: 120 CONTINUE
! 305: ELSE
! 306: DO 130 I = MAX(1,J-KU),MIN(M,J+KL)
! 307: TEMP = TEMP + DCONJG(A(K+I,J))*X(IX)
! 308: IX = IX + INCX
! 309: 130 CONTINUE
! 310: END IF
! 311: Y(JY) = Y(JY) + ALPHA*TEMP
! 312: JY = JY + INCY
! 313: IF (J.GT.KU) KX = KX + INCX
! 314: 140 CONTINUE
! 315: END IF
! 316: END IF
! 317: *
! 318: RETURN
! 319: *
! 320: * End of ZGBMV .
! 321: *
! 322: END
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