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