------------------------------------------------------------------ Argument | Type | Mode | Dimension ------------------------------------------------------------------ CALL CSA1S (NI, | Integer | Input | XI, | Real | Input | NI YI, | Real | Input | NI KNOTS, | Integer | Input | NO, | Integer | Input | XO, | Real | Input | NO YO, | Real | Output | NO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = KNOTS * (KNOTS+3) IER) | Integer | Output | CALL CSA1D (NI, | Integer | Input | XI, | Double | Input | NI YI, | Double | Input | NI KNOTS, | Integer | Input | NO, | Integer | Input | XO, | Double | Input | NO YO, | Double | Output | NO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = KNOTS * (KNOTS+3) IER) | Integer | Output | ------------------------------------------------------------------

- NI
- The number of input data points. It must be that NI > 3 and, depending on the size of KNOTS below, NI may have to be larger.
- XI
- An array containing the X coordinates of the input data points.
- YI
- An array containing function values at the input XI values, that is, YI(L) is the value of the input function at XI(L) for L=1,NI.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS must be at least 4. The larger the value for KNOTS, the closer the approximated curve will come to passing through the input function values.
- NO
- The number of values to be calculated for the output curve.
- XO
- An array containing the X coordinates of the output curve.
- YO
- An array containing the calculated function values for the output curve.
- NWRK
- The size of the WORK array. NWRK must be at least KNOTS*(KNOTS+3).
- WORK
- A work array dimensioned for NWRK.
- IER
- An error return value. If IER is returned as 0, then no errors were detected. If IER is non-zero, then refer to the error list in the error table for details.

------------------------------------------------------------------- Argument | Type | Mode | Dimension ------------------------------------------------------------------- CALL CSA1XS (NI, | Integer | Input | XI, | Real | Input | NI YI, | Real | Input | NI WTS, | Real | Input | NI KNOTS, | Integer | Input | SMTH, | Real | Input | NDERIV, | Integer | Input | NO, | Integer | Input | XO, | Real | Input | NO YO, | Real | Output | NO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = KNOTS * (KNOTS+3) IER) | Integer | Output | CALL CSA1XD (NI, | Integer | Input | XI, | Double | Input | NI YI, | Double | Input | NI WTS, | Double | Input | NI KNOTS, | Integer | Input | SMTH, | Double | Input | NDERIV, | Integer | Input | NO, | Integer | Input | XO, | Double | Input | NO YO, | Double | Output | NO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = KNOTS * (KNOTS+3) IER) | Integer | Output | -------------------------------------------------------------------

- NI
- The number of input data points. It must be that NI > 3 and, depending on the size of KNOTS below, NI may have to be larger.
- XI
- An array containing the X coordinates of the input data points.
- YI
- An array containing function values at the input XI values, that is, YI(L) is the value of the input function at XI(L) for L=1,NI.
- WTS
- An array containing weights for the YI values at the input XI values, that is, WTS(L) is a weight for the value of YI(L) for L=1,NI. If you do not desire to weight the input YI values, then set WTS(1) to -1. The weights in the WTS array are relative and may be set to any non-negative value. When CSA1XS (CSA1XD) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS must be at least 4. The larger the value for KNOTS, the closer the approximated curve will come to passing through the input function values.
- SMTH
- A parameter that controls extrapolation into data sparse regions. If SMTH is zero, then nothing special is done in data sparse regions. A good first choice for SMTH is 1.
- NDERIV
- Specifies whether you want functional values (NDERIV=0), first derivative values (NDERIV=1), or second derivative values (NDERIV=2).
- NO
- The number of values to be calculated in the output curve.
- XO
- An array containing the X coordinates for the output curve.
- YO
- An array containing the calculated function values of the output curve.
- NWRK
- The size of the WORK array. NWRK must be at least KNOTS*(KNOTS+3).
- WORK
- A work array dimensioned for NWRK.
- IER
- An error return value. If IER is returned as 0, then no errors were detected. If IER is non-zero, then refer to the error list in the error table for details.

------------------------------------------------------------------ Argument | Type | Mode | Dimension ------------------------------------------------------------------ CALL CSA2S (NI, | Integer | Input | XI, | Real | Input | 2 x NI UI, | Real | Input | NI KNOTS, | Integer | Input | 2 NXO, | Integer | Input | NYO, | Integer | Input | XO, | Real | Input | NXO YO, | Real | Input | NYO UO, | Real | Output | NXO x NYO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) IER) | Integer | Output | CALL CSA2D (NI, | Integer | Input | XI, | Double | Input | 2 x NI UI, | Double | Input | NI KNOTS, | Integer | Input | 2 NXO, | Integer | Input | NYO, | Integer | Input | XO, | Double | Input | NXO YO, | Double | Input | NYO UO, | Double | Output | NXO x NYO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) IER) | Integer | Output | ------------------------------------------------------------------

- NI
- The number of input data points. It must be that NI > 3 and, depending on the size of KNOTS below, NI may have to be larger.
- XI
- An array containing the X - Y coordinates of the input data points. XI(1,L) is the X coordinate and XI(2,L) is the Y coordinate for the input domain for L=1,NI.
- UI
- An array containing the function values at the input XI values, that is UI(L) is the value of the input function at the coordinate (XI(1,L),XI(2,L)) for L=1,NI.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS(1) specifies the number of knots in the X direction and KNOTS(2) specifies the number of knots in the Y direction. Both KNOTS(1) and KNOTS(2) must be at least 4. The larger the values for KNOTS, the closer the approximated curve will come to passing through the input function values.
- NXO
- The number of X coordinate values in the output grid.
- NYO
- The number of Y coordinate values in the output grid.
- XO
- An array containing the X coordinates of the output surface.
- YO
- An array containing the Y coordinates of the output surface.
- UO
- An array containing the calculated function values for the output surface. UO(I,J) is the calculated functional value at (XO(I),YO(J)) for I=1,NXO and J=1,NYO.
- NWRK
- The size of the WORK array. NWRK must be at least KNOTS(1)*KNOTS(2)*(KNOTS(1)*KNOTS(2)+3).
- WORK
- A work array dimensioned for NWRK.
- IER
- An error return value. If IER is returned as 0, then no errors were detected. If IER is non-zero, then refer to the error list in the error table for details.

------------------------------------------------------------------ Argument | Type | Mode | Dimension ------------------------------------------------------------------ CALL CSA2XS (NI, | Integer | Input | XI, | Real | Input | 2 x NI UI, | Real | Input | NI WTS, | Real | Input | NI KNOTS, | Integer | Input | 2 SMTH, | Real | Input | NDERIV, | Integer | Input | 2 NXO, | Integer | Input | NYO, | Integer | Input | XO, | Real | Input | NXO YO, | Real | Input | NYO UO, | Real | Output | NXO x NYO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) IER) | Integer | Output | CALL CSA2XD (NI, | Integer | Input | XI, | Double | Input | 2 x NI UI, | Double | Input | NI WTS, | Double | Input | NI KNOTS, | Integer | Input | 2 SMTH, | Double | Input | NDERIV, | Integer | Input | 2 NXO, | Integer | Input | NYO, | Integer | Input | XO, | Double | Input | NXO YO, | Double | Input | NYO UO, | Double | Output | NXO x NYO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) IER) | Integer | Output | ------------------------------------------------------------------

- NI
- XI
- An array containing the X - Y coordinates of the input data points. XI(1,L) is the X coordinate and XI(2,L) is the Y coordinate for the input domain for L=1,NI.
- UI
- An array containing the function values at the input XI values, that is UI(L) is the value of the input function at the coordinate (XI(1,L),XI(2,L)) for L=1,NI.
- WTS
- An array containing weights for the UI values at the input XI values, that is, WTS(L) is a weight for the value of UI(L) for L=1,NI. If you do not desire to weight the input UI values, then set WTS(1) to -1. The weights in the WTS array are relative and may be set to any non-negative value. When CSA2XS (CSA2XD) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS(1) specifies the number of knots in the X direction and KNOTS(2) specifies the number of knots in the Y direction. Both KNOTS(1) and KNOTS(2) must be at least 4. The larger the value for KNOTS, the closer the approximated curve will come to passing through the input function values.
- SMTH
- A parameter that controls extrapolation into data sparse regions. If SMTH is zero, then nothing special is done in data sparse regions. A good first choice for SMTH is 1.
- NDERIV
- Specifies which partial derivatives are desired. NDERIV(1) indicates if the 0 th, 1 st, or 2 nd partial in the X direction is desired; NDERIV(2) indicates if the 0 th, 1 st, or 2 nd partial in the Y direction is desired.
- NXO
- The number of X coordinate values in the output grid.
- NYO
- The number of Y coordinate values in the output grid.
- XO
- An array containing the X coordinates of the output surface.
- YO
- An array containing the Y coordinates of the output surface.
- UO
- An array containing the calculated function values for the output surface. UO(I,J) is the calculated functional value at (XO(I),YO(J)) for I=1,NXO and J=1,NYO.
- NWRK
- The size of the WORK array. NWRK must be at least KNOTS(1)*KNOTS(2)*(KNOTS(1)*KNOTS(2)+3).
- WORK
- A work array dimensioned for NWRK.
- IER

------------------------------------------------------------------- Argument | Type | Mode | Dimension ------------------------------------------------------------------- CALL CSA2LS (NI, | Integer | Input | XI, | Real | Input | 2 x NI UI, | Real | Input | NI KNOTS, | Integer | Input | 2 NO, | Integer | Input | XO, | Real | Input | NO YO, | Real | Input | NO UO, | Real | Output | NO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) IER) | Integer | Output | CALL CSA2LD (NI, | Integer | Input | XI, | Double | Input | 2 x NI UI, | Double | Input | NI KNOTS, | Integer | Input | 2 NO, | Integer | Input | XO, | Double | Input | NO YO, | Double | Input | NO UO, | Double | Output | NO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) IER) | Integer | Output | -------------------------------------------------------------------

- NI
- XI
- An array containing the X - Y coordinates of the input data points. XI(1,L) is the X coordinate and XI(2,L) is the Y coordinate for the input domain for L=1,NI.
- UI
- An array containing the function values at the input XI values, that is UI(L) is the value of the input function at the coordinate (XI(1,L),XI(2,L)) for L=1,NI.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS(1) specifies the number of knots in the X direction and KNOTS(2) specifies the number of knots in the Y direction. Both KNOTS(1) and KNOTS(2) must be at least 4. The larger the value for KNOTS, the closer the approximated curve will come to passing through the input function values.
- NO
- The number of coordinate values in the output list. NO can be any positive number.
- XO
- An array containing the X coordinates of the output list.
- YO
- An array containing the Y coordinates of the output list.
- UO
- An array containing the calculated function values. UO(L) is the calculated functional value at (XO(L), YO(L)) for L=1,NO.
- NWRK
- The size of the WORK array. NWRK must be at least KNOTS(1)*KNOTS(2)*(KNOTS(1)*KNOTS(2)+3).
- WORK
- A work array dimensioned for NWRK.
- IER

-------------------------------------------------------------------- Argument | Type | Mode | Dimension -------------------------------------------------------------------- CALL CSA2LXS (NI, | Integer | Input | XI, | Real | Input | 2 x NI UI, | Real | Input | NI WTS, | Real | Input | NI KNOTS, | Integer | Input | 2 SMTH, | Real | Input | NDERIV, | Integer | Input | 2 NO, | Integer | Input | XO, | Real | Input | NO YO, | Real | Input | NO UO, | Real | Output | NO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) IER) | Integer | Output | CALL CSA2LXD (NI, | Integer | Input | XI, | Double | Input | 2 x NI UI, | Double | Input | NI WTS, | Double | Input | NI KNOTS, | Integer | Input | 2 SMTH, | Double | Input | NDERIV, | Integer | Input | 2 NO, | Integer | Input | XO, | Double | Input | NO YO, | Double | Input | NO UO, | Double | Output | NO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) IER) | Integer | Output | --------------------------------------------------------------------

- NI
- XI
- UI
- WTS
- An array containing weights for the UI values at the input XI values, that is, WTS(L) is a weight for the value of UI(L) for L=1,NI. If you do not desire to weight the input UI values, then set WTS(1) to -1. The weights in the WTS array are relative and may be set to any non-negative value. When CSA2LXS (CSA2LXD) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS(1) specifies the number of knots in the X direction and KNOTS(2) specifies the number of knots in the Y direction. Both KNOTS(1) and KNOTS(2) must be at least 4. The larger the value for KNOTS, the closer the approximated curve will come to passing through the input function values.
- SMTH
- A parameter that controls extrapolation into data sparse regions. If SMTH is zero, then nothing special is done in data sparse regions. A good first choice for SMTH is 1.
- NDERIV
- Specifies which partial derivatives are desired. NDERIV(1) indicates if the 0 th, 1 st, or 2 nd partial in the X direction is desired; NDERIV(2) indicates if the 0 th, 1 st, or 2 nd partial in the Y direction is desired.
- NO
- The number of coordinate values in the output list. NO can be any positive number.
- XO
- An array containing the X coordinates of the output list.
- YO
- An array containing the Y coordinates of the output list.
- UO
- An array containing the calculated function values for the output surface. UO(L) is the calculated functional value at (XO(L), YO(L)) for L=1,NO.
- NWRK
- The size of the WORK array. NWRK must be at least KNOTS(1)*KNOTS(2)*(KNOTS(1)*KNOTS(2)+3).
- WORK
- A work array dimensioned for NWRK.
- IER

------------------------------------------------------------------------------ Argument | Type | Mode | Dimension ------------------------------------------------------------------------------ CALL CSA3S (NI, | Integer | Input | XI, | Real | Input | 3 x NI UI, | Real | Input | NI KNOTS, | Integer | Input | 3 NXO, | Integer | Input | NYO, | Integer | Input | NZO, | Integer | Input | XO, | Real | Input | NXO YO, | Real | Input | NYO ZO, | Real | Input | NZO UO, | Real | Output | NXO x NYO x NZO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) * KNOTS(3) IER) | Integer | Output | CALL CSA3D (NI, | Integer | Input | XI, | Double | Input | 3 x NI UI, | Double | Input | NI KNOTS, | Integer | Input | 3 NXO, | Integer | Input | NYO, | Integer | Input | NZO, | Integer | Input | XO, | Double | Input | NXO YO, | Double | Input | NYO ZO, | Double | Input | NZO UO, | Double | Output | NXO x NYO x NZO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) * KNOTS(3) IER) | Integer | Output | ------------------------------------------------------------------------------

- NI
- XI
- An array containing the X - Y - Z coordinates of the input data points. XI(1,L) is the X coordinate, XI(2,L) is the Y coordinate, and XI(2,L) is the Z coordinate for the input domain for L=1,NI.
- UI
- An array containing the function values at the input XI values, that is, UI(L) is the value of the input function at the coordinate (XI(1,L), XI(2,L), XI(3,L)) for L=1,NI.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS(1) specifies the number of knots in the X direction, KNOTS(2) specifies the number of knots in the Y direction and KNOTS(3) specifies the number of knots in the Z direction. KNOTS(I) must be at least 4 for I=1,3. The larger the value for KNOTS, the closer the approximated curve will come to passing through the input function values.
- NXO
- The number of X coordinate values in the output grid.
- NYO
- The number of Y coordinate values in the output grid.
- NZO
- The number of Z coordinate values in the output grid.
- XO
- An array containing the X coordinates of the output grid.
- YO
- An array containing the Y coordinates of the output grid.
- ZO
- An array containing the Z coordinates of the output grid.
- UO
- An array containing the calculated function values for the output function. UO(I,J,K) is the calculated functional value at (XO(I), YO(J), ZO(K)) for I=1,NXO and J=1,NYO and K=1,NZO.
- NWRK
- The size of the WORK array. NWRK must be at least NK*(NK+3) where NK=KNOTS(1)*KNOTS(2)*KNOTS(3).
- WORK
- A work array dimensioned for NWRK.
- IER

------------------------------------------------------------------------------- Argument | Type | Mode | Dimension ------------------------------------------------------------------------------- CALL CSA3XS (NI, | Integer | Input | XI, | Real | Input | 3 x NI UI, | Real | Input | NI WTS, | Real | Input | NI KNOTS, | Integer | Input | 3 SMTH, | Real | Input | NDERIV, | Integer | Input | 3 NXO, | Integer | Input | NYO, | Integer | Input | NZO, | Integer | Input | XO, | Real | Input | NXO YO, | Real | Input | NYO ZO, | Real | Input | NZO UO, | Real | Output | NXO x NYO x NZO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) * KNOTS(3) IER) | Integer | Output | CALL CSA3XD (NI, | Integer | Input | XI, | Double | Input | 3 x NI UI, | Double | Input | NI WTS, | Double | Input | NI KNOTS, | Integer | Input | 3 SMTH, | Double | Input | NDERIV, | Integer | Input | 3 NXO, | Integer | Input | NYO, | Integer | Input | NZO, | Integer | Input | XO, | Double | Input | NXO YO, | Double | Input | NYO ZO, | Double | Input | NZO UO, | Double | Output | NXO x NYO x NZO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) * KNOTS(3) IER) | Integer | Output | -------------------------------------------------------------------------------

- NI
- XI
- An array containing the X - Y - Z coordinates of the input data points. XI(1,L) is the X coordinate, XI(2,L) is the Y coordinate, and XI(3,L) is the Z coordinate for the input domain for L=1,NI.
- UI
- An array containing the function values at the input XI values, that is UI(L) is the value of the input function at the coordinate (XI(1,L), XI(2,L), XI(3,L)) for L=1,NI.
- WTS
- An array containing weights for the UI values at the input XI values, that is, WTS(L) is a weight for the value of UI(L) for L=1,NI. If you do not desire to weight the input UI values, then set WTS(1) to -1. The weights in the WTS array are relative and may be set to any non-negative value. When CSA3XS (CSA3XD) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS(1) specifies the number of knots in the X direction, KNOTS(2) specifies the number of knots in the Y direction and KNOTS(3) specifies the number of knots in the Z direction. KNOTS(I) must be at least 4 for I=1,3. The larger the values for KNOTS, the closer the approximated curve will come to passing through the input function values.
- SMTH
- NDERIV
- Specifies which partial derivatives are desired. NDERIV(1) indicates whether the 0 th, 1 st, or 2 nd partial in the X direction is desired; NDERIV(2) indicates whether the 0 th, 1 st, or 2 nd partial in the Y direction is desired; NDERIV(3) indicates whether the 0 th, 1 st, or 2 nd partial in the Z direction is desired.
- NXO
- The number of X coordinate values in the output grid.
- NYO
- The number of Y coordinate values in the output grid.
- NZO
- The number of Z coordinate values in the output grid.
- XO
- An array containing the X coordinates of the output grid.
- YO
- An array containing the Y coordinates of the output grid.
- ZO
- An array containing the Z coordinates of the output grid.
- UO
- An array containing the calculated function values for the output grid. UO(I,J,K) is the calculated functional value at (XO(I), YO(J), ZO(K)) for I=1,NXO and J=1,NYO and K=1,NZO.
- NWRK
- The size of the WORK array. NWRK must be at least NK*(NK+3) where NK=KNOTS(1)*KNOTS(2)*KNOTS(3)
- WORK
- A work array dimensioned for NWRK.
- IER

------------------------------------------------------------------------------- Argument | Type | Mode | Dimension ------------------------------------------------------------------------------- CALL CSA3LS (NI, | Integer | Input | XI, | Real | Input | 3 x NI UI, | Real | Input | NI KNOTS, | Integer | Input | 3 NO, | Integer | Input | XO, | Real | Input | NXO YO, | Real | Input | NYO ZO, | Real | Input | NZO UO, | Real | Output | NXO x NYO x NZO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) * KNOTS(3) IER) | Integer | Output | CALL CSA3LD (NI, | Integer | Input | XI, | Double | Input | 3 x NI UI, | Double | Input | NI KNOTS, | Integer | Input | 3 NO, | Integer | Input | XO, | Double | Input | NXO YO, | Double | Input | NYO ZO, | Double | Input | NZO UO, | Double | Output | NXO x NYO x NZO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) * KNOTS(3) IER) | Integer | Output | -------------------------------------------------------------------------------

- NI
- XI
- An array containing the X - Y - Z coordinates of the input data points. XI(1,L) is the X coordinate, XI(2,L) is the Y coordinate and XI(3,L) s the Z coordinate for the input domain for L=1,NI.
- UI
- An array containing the function values at the input XI values, that is UI(L) is the value of the input function at the coordinate (XI(1,L), XI(2,L), XI(3,L)) for L=1,NI.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS(1) specifies the number of knots in the X direction, KNOTS(2) specifies the number of knots in the Y direction and KNOTS(3) specifies the number of knots in the Z direction. KNOTS must be at least 4. The larger the value for KNOTS, the closer the approximated curve will come to passing through the input function values.
- NO
- The number of coordinate values in the output list. NO can be any positive number.
- XO
- An array containing the X coordinates of the output list.
- YO
- An array containing the Y coordinates of the output list.
- ZO
- An array containing the Y coordinates of the output list.
- UO
- An array containing the calculated function values for the output function. UO(L) is the calculated functional value at (XO(L), YO(L), ZO(L)) for L=1,NO.
- NWRK
- The size of the WORK array. NWRK must be at least NK*(NK+3) where NK=KNOTS(1)*KNOTS(2)*KNOTS(3).
- WORK
- A work array dimensioned for NWRK.
- IER

------------------------------------------------------------------------------- Argument | Type | Mode | Dimension ------------------------------------------------------------------------------- CALL CSA3LXS (NI, | Integer | Input | XI, | Real | Input | 3 x NI UI, | Real | Input | NI WTS, | Real | Input | NI KNOTS, | Integer | Input | 3 SMTH, | Real | Input | NDERIV, | Integer | Input | 3 NO, | Integer | Input | XO, | Real | Input | NO YO, | Real | Input | NO ZO, | Real | Input | NO UO, | Real | Output | NO NWRK, | Integer | Input | WORK, | Real | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) * KNOTS(3) IER) | Integer | Output | CALL CSA3LXD (NI, | Integer | Input | XI, | Double | Input | 3 x NI UI, | Double | Input | NI WTS, | Double | Input | NI KNOTS, | Integer | Input | 3 SMTH, | Double | Input | NDERIV, | Integer | Input | 3 NO, | Integer | Input | XO, | Double | Input | NO YO, | Double | Input | NO ZO, | Double | Input | NO UO, | Double | Output | NO NWRK, | Integer | Input | WORK, | Double | Input | NWRK = NK * (NK+3) where | | | NK = KNOTS(1) * KNOTS(2) * KNOTS(3) IER) | Integer | Output | -------------------------------------------------------------------------------

- NI
- XI
- An array containing the X - Y - Z coordinates of the input data points. XI(1,L) is the X coordinate, XI(2,L) is the Y coordinate, and XI(3,L) is the Z coordinate for the input domain for L=1,NI.
- UI
- An array containing the function values at the input XI values, that is UI(L) is the value of the input function at the coordinate (XI(1,L), XI(2,L), XI(3,L)) for L=1,NI.
- WTS
- An array containing weights for the UI values at the input XI values, that is, WTS(L) is a weight for the value of UI(L) for L=1,NI. If you do not desire to weight the input UI values, then set WTS(1) to -1. The weights in the WTS array are relative and may be set to any non-negative value. When CSA3LXS (CSA3LXD) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- KNOTS
- The number of knots to be used in constructing the approximation spline. KNOTS(1) specifies the number of knots in the X direction, KNOTS(2) specifies the number of knots in the Y direction and KNOTS(3) specifies the number of knots in the Z direction. KNOTS(I) must be at least 4 for I=1,3. The larger the value for KNOTS, the closer the approximated curve will come to passing through the input function values.
- SMTH
- NDERIV
- Specifies which partial derivatives are desired. NDERIV(1) indicates whether the 0 th, 1 st, or 2 nd partial in the X direction is desired; NDERIV(2) indicates whether the 0 th, 1 st, or 2 nd partial in the Y direction is desired; NDERIV(3) indicates whether the 0 th, 1 st, or 2 nd partial in the Z direction is desired.
- NO
- The number of coordinate values in the output list. NO can be any positive number.
- XO
- An array containing the X coordinates of the output list.
- YO
- An array containing the Y coordinates of the output list.
- ZO
- An array containing the Z coordinates of the output list.
- UO
- An array containing the calculated function values for the output surface. UO(L) is the calculated functional value at (XO(L), YO(L), ZO(L)) for L=1,NO.
- NWRK
- The size of the WORK array. NWRK must be at least NK*(NK+3) where NK=KNOTS(1)*KNOTS(2)*KNOTS(3).
- WORK
- A work array dimensioned for NWRK.
- IER

c_csa1s (c_csa1d) is called to find an approximating cubic spline for one-dimensional input data. If you want to weight the input data values, calculate derivatives, or handle data sparse areas specially, then you will need to use c_csa1xs (c_csa1xd).

Function prototype:

float *c_csa1s(int, float [], float [], int, int, float [], int *); double *c_csa1d(int, double [], double [], int, int, double [], int *);Return value:

c_csa1s (c_cas1d) returns a pointer to a linear array of data that is
the approximated curve. That is, if *out* is declared as

float *out;and we set:

out = c_csa1s(n, x, y, z, knots, no, xo, &ier);then

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa1s (n, | int | xi, | float [] | n yi, | float [] | n knots, | int | m, | int | xo, | float [] | m ier | int * | ); double *c_csa1d (n, | int | xi, | double [] | n yi, | double [] | n knots, | int | m, | int | xo, | double [] | m ier | int * | ); -------------------------------------------------

- n
- The number of input data points. It must be that n > 3 and, depending on the size of knots below, n may have to be larger.
- xi
- An array containing the abscissae for the input function.
- yi
- An array containing the functional values of the input function -- yi[k] is the functional value at xi[k] for k=0,n-1.
- knots
- The number of knots to be used in constructing the approximation spline. knots must be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- m
- The number of values to be calculated for the output curve.
- xo
- An array containing the abscissae for the approximation output values.
- ier
- An error return value. If *ier is returned as 0, then no errors were detected. If *ier is non-zero, then refer to the error list in the error table for details.

Function prototype:

float *c_csa1xs(int, float [], float [], float [], int, float, int, int, float [], int *); double *c_csa1xd(int, double [], double [], double [], int, double, int, int, double [], int *);Return value:

c_csa1xs (c_csa1xd) returns a pointer to a linear array of data that
is the approximated curve. That is, if *out* is declared as

float *out;and we set:

out = c_csa1s(n, x, y, z, knots, smth, nderiv, no, xo, &ier);then

-------------------------------------------- Argument | Type | Size -------------------------------------------- float *c_csa1xs (n, | int | xi, | float [] | n yi, | float [] | n wts, | float [] | n knots, | int | smth, | float | nderiv, | int | m, | int | xo, | float [] | m ier) | int * | double *c_csa1xd (n, | int | xi, | double [] | n yi, | double [] | n wts, | double [] | n knots, | int | smth, | double | nderiv, | int | m, | int | xo, | double [] | m ier) | int * | --------------------------------------------

- n
- The number of input data points. It must be that n > 3 and,
depending on the size of
*knots*below, n may have to be larger. - xi
- An array containing the X coordinates of the input data points.
- yi
- An array containing function values at the input xi values, that is, yi[l] is the value of the input function at xi[l] for l=0,n-1.
- wts
- An array containing weights for the yi values at the input xi values, that is, wts[l] is a weight for the value of yi[l] for l=0,n-1. If you do not desire to weight the input yi values, then set wts[0] to -1. The weights in the wts array are relative and may be set to any non-negative value. When c_csa1xs (c_csa1xd) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- knots
- The number of knots to be used in constructing the approximation spline. knots must be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- smth
- A parameter that controls extrapolation into data sparse regions. If smth is zero, then nothing special is done in data sparse regions. A good first choice for smth is 1.
- nderiv
- Specifies whether you want functional values (nderiv=0), first derivative values (nderiv=1), or second derivative values (nderiv=2).
- m
- The number of values to be calculated in the output curve.
- xo
- An array containing the X coordinates for the output curve.
- ier
- An error return value. If *ier is returned as 0, then no errors were detected. If *ier is non-zero, then refer to the error list in the error table for details.

c_csa2s (c_csa2d) is called to find an approximating cubic spline surface for two-dimensional input data. If you want to weight the input data values, calculate derivatives, or handle data sparse areas specially, then you will need to use c_csa2xs (c_csa2xd).

Function prototype:

float *c_csa2s(int, float [], float [], float [], int [], int, int, float [], float [], int *); double *c_csa2d(int, double [], double [], double [], int [], int, int, double [], double [], int *);Return value:

c_csa2s (c_csa2d) returns a pointer to a linear array of data that is
the approximated grid stored in row-major order. That is, if
*out* is declared as

float *out;and we set:

out = c_csa2s(n, x, y, z, knots, no, mo, xo, yo, &ier);then

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa2s (n, | int | xi, | float [] | n yi, | float [] | n zi, | float [] | n knots, | int [] | 2 no, | int | mo, | int | xo, | float [] | no yo, | float [] | mo ier | int * | ); double *c_csa2d (n, | int | xi, | double [] | n yi, | double [] | n zi, | double [] | n knots, | int [] | 2 no, | int | mo, | int | xo, | double [] | no yo, | double [] | mo ier | int * | ); -------------------------------------------------

- n
- The number of input data points. It must be that n > 3 and,
depending on the size of
*knots*below, n may have to be larger. - xi
- An array containing the X coordinate values for the input function.
- yi
- An array containing the Y coordinate values for the input function.
- zi
- An array containing the functional values of the input function -- zi[k] is the functional value at (xi[k], yi[k]) for k=0,n-1.
- knots
- The number of knots to be used in constructing the approximation spline. knots[0] specifies the number of knots in the X direction and knots[1] specifies the number of knots in the Y direction. knots[0] and knots[1] must each be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- no
- The number of X coordinate values to be calculated for the output surface.
- mo
- The number of Y coordinate values to be calculated for the output surface.
- xo
- An array containing the X coordinate values for the output grid.
- yo
- An array containing the Y coordinate values for the output grid.
- ier
- An error return value. If *ier is returned as 0, then no errors were detected. If *ier is non-zero, then refer to the error list in the error table for details.

c_csa2xs (c_csa2xd) is called if you want to weight the input data values, calculate derivatives, or handle data sparse areas specially. If you do not want to do any of these three things, then use c_csa2s.

Function prototype:

float *c_csa2xs(int, float [], float [], float [], float [], int [], float, int [], int, int, float [], float [], int *); double *c_csa2xd(int, double [], double [], double [], double [], int [], double, int [], int, int, double [], double [], int *);Return value:

c_csa2xs (c_csa2xd) returns a pointer to a linear array of data that
is the approximated function on a grid stored in row-major order.
That is, if *out* is declared as

float *out;and we set:

out = c_csa2xs(ni, xi, yi, zi, wts, knots, smth, nderiv, no, mo, xo, yo, &ier);then

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa2xs (ni, | int | xi, | float [] | ni yi, | float [] | ni zi, | float [] | ni wts, | float [] | ni knots, | int [] | 2 smth, | float | nderiv | int [] | 2 no, | int | mo, | int | xo, | float [] | no yo, | float [] | mo ier | int * | ); double *c_csa2xd (ni, | int | xi, | double [] | ni yi, | double [] | ni zi, | double [] | ni wts, | double [] | ni knots, | int [] | 2 smth, | double | nderiv | int [] | 2 no, | int | mo, | int | xo, | double [] | no yo, | double [] | mo ier | int * | ); -------------------------------------------------

- ni
- The number of input data points. It must be that ni > 3 and,
depending on the size of
*knots*below, ni may have to be larger. - xi
- An array containing the X coordinate values for the input function.
- yi
- An array containing the Y coordinate values for the input function.
- zi
- An array containing the functional values of the input function -- zi[k] is the functional value at (xi[k],yi[k]) for k=0,n-1.
- wts
- An array containing weights for the zi values at the input xi and yi values, that is, wts[k] is a weight for the value of zi[k] for k=0,ni-1. If you do not desire to weight the input yi values, then set wts[0] to -1. The weights in the wts array are relative and may be set to any non-negative value. When c_csa2xs (c_csa2xd) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- knots
- The number of knots to be used in constructing the approximation spline. knots[0] specifies the number of knots in the X direction and knots[1] specifies the number of knots in the Y direction. knots[0] and knots[1] must each be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- smth
- A parameter that controls extrapolation into data sparse regions. If smth is 0., then nothing special is done in data sparse regions. A good first choice for smth is 1.
- nderiv
- For each of the two coordinate directions, specifies whether you want functional values (nderiv=0), first derivative values (nderiv=1), or second derivative values (nderiv=2). For example, if nderiv[0]=1 and nderiv[1]=1, then the second order mixed partial would be computed.
- no
- The number of X coordinate values to be calculated for the output surface.
- mo
- The number of Y coordinate values to be calculated for the output surface.
- xo
- An array containing the X coordinate values for the output grid.
- yo
- An array containing the Y coordinate values for the output grid.
- ier

c_csa2ls (c_csa2ld) is called to find values of an approximating cubic spline at specified two-dimensional coordinates. If you want to weight the input data values, calculate derivatives, or handle data sparse areas specially, then you will need to use c_csa2lxs (c_csa2lxd).

Function prototype:

float *c_csa2ls(int, float [], float [], float [], int [], int, float [], float [], int *); double *c_csa2ld(int, double [], double [], double [], int [], int, double [], double [], int *);Return value:

c_csa2ls (c_csa2ld) returns a pointer to a linear array of data that
contains the approximated values calculated at the input list of
coordinate values. That is, if *out* is declared as

float *out;and we set:

out = c_csa2ls(n, x, y, z, knots, no, xo, yo, &ier);then

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa2ls (n, | int | xi, | float [] | n yi, | float [] | n zi, | float [] | n knots, | int | 2 no, | int | xo, | float [] | no yo, | float [] | no ier | int * | ); double *c_csa2ld (n, | int | xi, | double [] | n yi, | double [] | n zi, | double [] | n knots, | int | 2 no, | int | xo, | double [] | no yo, | double [] | no ier | int * | ); -------------------------------------------------

- n
- The number of input data points. It must be that n > 3 and,
depending on the size of
*knots*below, n may have to be larger. - xi
- An array containing the X coordinate values for the input function.
- yi
- An array containing the Y coordinate values for the input function.
- zi
- An array containing the functional values of the input function -- zi[k] is the functional value at (xi[k], yi[k]) for k=0,n-1.
- knots
- The number of knots to be used in constructing the approximation spline. knots[0] specifies the number of knots in the X direction and knots[1] specifies the number of knots in the Y direction. knots[0] and knots[1] must each be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- no
- The number of X - Y coordinate values to be calculated for the output array.
- xo
- An array containing the X coordinate values for the output array.
- yo
- An array containing the Y coordinate values for the output array.
- ier

c_csa2lxs (c_csa2lxd) is called to find values of an approximating cubic spline at specified two-dimensional coordinates. c_csa2lxs (c_csa2lxd) is called if you want to weight the input data values, calculate derivatives, or handle data sparse areas specially. If you do not want to do any of these three things, then use c_csa2ls (c_csa2ld).

Function prototype:

float *c_csa2lxs(int, float [], float [], float [], float [], int [], float, int [], int, float [], float [], int *); double *c_csa2lxd(int, double [], double [], double [], double [], int [], double, int [], int, double [], double [], int *);Return value:

c_csa2lxs (c_csa2lxs) returns a pointer to a linear array of data that
contains the approximated values calculated at the input list of
coordinate values. That is, if *out* is declared as

float *out;and we set:

out = c_csa2lxs(n, x, y, z, wts, knots, smth, nderiv, no, xo, yo, &ier);then

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa2lxs (n, | int | xi, | float [] | n yi, | float [] | n zi, | float [] | n wts, | float [] | n knots, | int [] | 2 smth, | float | nderiv, | int [] | 2 no, | int | xo, | float [] | no yo, | float [] | no ier | int * | ); double *c_csa2lxd (n, | int | xi, | double [] | n yi, | double [] | n zi, | double [] | n wts, | double [] | n knots, | int [] | 2 smth, | double | nderiv, | int [] | 2 no, | int | xo, | double [] | no yo, | double [] | no ier | int * | );

- n
- The number of input data points. It must be that n > 3 and,
depending on the size of
*knots*below, n may have to be larger. - xi
- An array containing the X coordinate values for the input function.
- yi
- An array containing the Y coordinate values for the input function.
- zi
- An array containing the functional values of the input function -- zi[k] is the functional value at (xi[k],yi[k]) for k=0,n-1.
- wts
- An array containing weights for the zi values at the input xi and yi values, that is, wts[l] is a weight for the value of zi[l] for l=0,n-1. If you do not desire to weight the input zi values, then set wts[0] to -1. The weights in the wts array are relative and may be set to any non-negative value. When c_csa2lxs (c_csa2lxd) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- knots
- smth
- A parameter that controls extrapolation into data sparse regions. If smth is zero, then nothing special is done in data sparse regions. A good first choice for smth is 1.
- nderiv
- For each of the two coordinate direction, specifies whether you want functional values (nderiv=0), first derivative values (nderiv=1), or second derivative values (nderiv=2). For example, if nderiv[0]=1 and nderiv[1]=1, then the second order mixed partial would be computed.
- no
- The number of X - Y coordinate values to be calculated for the output array.
- xo
- An array containing the X coordinate values for the output array.
- yo
- An array containing the Y coordinate values for the output array.
- ier

c_csa3s (c_csa3d) is called to find an approximating cubic spline for three-dimensional input data. If you want to weight the input data values, calculate derivatives, or handle data sparse areas specially, then you will need to use c_csa3xs (c_csa3xd).

Function prototype:

float *c_csa3s(int, float [], float [], float [], float [], int [], int, int, int, float [], float [], float [], int *); double *c_csa3d(int, double [], double [], double [], double [], int [], int, int, int, double [], double [], double [], int *);Return value:

c_csa3s (c_csa3d) returns a pointer to a linear array of data that is the approximation spline stored in row-major order. That is, if out is declared as

float *out;and we set:

out = c_csa3s(n, x, y, z, u, knots, nx, ny, nz, xo, yo, zo, &ier);then out[nz*ny*i + nz*j + k] is the approximation function value at coordinate point (xo[i], yo[j], zo[k]) for 0 <= i < nx, 0 <= j < ny, and 0 <= k < nz. The space for out is allocated internal to c_csa3s (c_csa3d) and is nx*ny*nz floats (doubles) in size.

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa3s (ni, | int | xi, | float [] | ni yi, | float [] | ni zi, | float [] | ni ui, | float [] | ni knots, | int [] | 3 nxo, | int | nyo, | int | nzo, | int | xo, | float [] | nxo yo, | float [] | nyo zo, | float [] | nzo ier | int * | ); double *c_csa3d (ni, | int | xi, | double [] | ni yi, | double [] | ni zi, | double [] | ni ui, | double [] | ni knots, | int [] | 3 nxo, | int | nyo, | int | nzo, | int | xo, | double [] | nxo yo, | double [] | nyo zo, | double [] | nzo ier | int * | ); -------------------------------------------------

- ni
- The number of input data points. It must be that ni > 3 and,
depending on the size of
*knots*below, ni may have to be larger. - xi
- An array containing the X coordinate values for the input function.
- yi
- An array containing the Y coordinate values for the input function.
- zi
- An array containing the Z coordinate values for the input function.
- ui
- An array containing the functional values of the input function -- ui[k] is the functional value at (xi[k], yi[k], zi[k]) for k=0,ni-1.
- knots
- The number of knots to be used in constructing the approximation spline. knots[0] specifies the number of knots in the X direction, knots[1] specifies the number of knots in the Y direction and knots[2] specifies the number of knots in the Z direction. knots[0], knots[1] and knots[2] must each be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- nxo
- The number of X coordinate values to be calculated for the output grid.
- nyo
- The number of Y coordinate values to be calculated for the output grid.
- nzo
- The number of Z coordinate values to be calculated for the output grid.
- xo
- An array containing the X coordinate values for the output grid.
- yo
- An array containing the Y coordinate values for the output grid.
- zo
- An array containing the Z coordinate values for the output grid.
- ier

c_csa3xs (c_csa3xd) is called to find an approximating cubic spline surface for three-dimensional input data. c_csa3xs (c_csa3xd) is called if you want to weight the input data values, calculate derivatives, or handle data sparse areas specially. If you do not want to do any of these three things, then use c_csa3s (c_csa3d).

Function prototype:

float *c_csa3xs(int, float [], float [], float [], float [], float [], int [], float, int [], int, int, int, float [], float [], float [], int *); double *c_csa3xd(int, double [], double [], double [], double [], double [], int [], double, int [], int, int, int, double [], double [], double [], int *);Return value:

c_csa3xs (c_csa3xd) returns a pointer to a linear array of data that
is the approximated function on a grid stored in row-major order.
That is, if *out* is declared as

float *out;and we set:

out = c_csa3xs(ni, xi, yi, zi, ui, wts, knots, smth, nderiv, nxo, nyo, nzo, xo, yo, zo, &ier)then out[nz*ny*i + nz*j + k] is the approximation function value at coordinate point (xo[i], yo[j], zo[k]) for 0 <= i < nx, 0 <= j < ny, and 0 <= k < nz. The space for out is allocated internal to c_csa3xs (c_csa3xd) and is nx*ny*nz floats (doubles) in size.

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa3xs (ni, | int | xi, | float [] | ni yi, | float [] | ni zi, | float [] | ni ui, | float [] | ni wts, | float [] | ni knots, | int [] | 3 smth, | float | nderiv | int [] | 3 nxo, | int | nyo, | int | nzo, | int | xo, | float [] | nxo yo, | float [] | nyo yo, | float [] | nzo ier | int * | ); double *c_csa3xd (ni, | int | xi, | double [] | ni yi, | double [] | ni zi, | double [] | ni ui, | double [] | ni wts, | double [] | ni knots, | int [] | 3 smth, | double | nderiv | int [] | 3 nxo, | int | nyo, | int | nzo, | int | xo, | double [] | nxo yo, | double [] | nyo yo, | double [] | nzo ier | int * | ); -------------------------------------------------

- ni
- The number of input data points. It must be that ni > 3 and,
depending on the size of
*knots*below, ni may have to be larger. - xi
- An array containing the X coordinate values for the input function.
- yi
- An array containing the Y coordinate values for the input function.
- zi
- An array containing the Z coordinate values for the input function.
- ui
- An array containing the functional values of the input function -- ui[k] is the functional value at (xi[k],yi[k],zi[k]) for k=0,n-1.
- wts
- An array containing weights for the ui values at the input values, that is, wts[l] is a weight for the value of ui[l] for l=0,ni-1. If you do not desire to weight the input ui values, then set wts[0] to -1. The weights in the wts array are relative and may be set to any non-negative value. When c_csa3xs (c_csa3xd) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- knots
- The number of knots to be used in constructing the approximation spline. knots[0] specifies the number of knots in the X direction, knots[1] specifies the number of knots in the Y direction and knots[2] specifies the number of knots in the Z direction. knots[0], knots[1], and knots[2] must each be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- smth
- A parameter that controls extrapolation into data sparse regions. If smth is zero, then nothing special is done in data sparse regions. A good first choice for smth is 1.
- nderiv
- For each of the three coordinate direction, specifies whether you want functional values (nderiv=0), first derivative values (nderiv=1), or second derivative values (nderiv=2). For example, if nderiv[0]=1, nderiv[1]=1, and nderiv[2]=0, then the second order mixed partial with respect to X and Y would be computed.
- nxo
- The number of X coordinate values to be calculated for the output grid.
- nyo
- The number of Y coordinate values to be calculated for the output grid.
- nzo
- The number of Z coordinate values to be calculated for the output grid.
- xo
- An array containing the X coordinate values for the output grid.
- yo
- An array containing the Y coordinate values for the output grid.
- zo
- An array containing the Z coordinate values for the output grid.
- ier

c_csa3ls (c_csa3ld) is called to find values of an approximating cubic spline at specified three-dimensional coordinates. If you want to weight the input data values, calculate derivatives, or handle data sparse areas specially, then you will need to use c_csa3lxs (c_csa3lxd).

Function prototype:

float *c_csa3ls(int, float [], float [], float [], float [], int [], int, float [], float [], float[], int *); double *c_csa3ld(int, double [], double [], double [], double [], int [], int, double [], double [], double[], int *);Return value:

c_csa3ls (c_csa3ld) returns a pointer to a linear array of data that
contains the approximated values calculated at the input list of
coordinate values. That is, if *out* is declared as

float *out;and we set:

out = c_csa3ls(n, x, y, z, u, knots, no, xo, yo, zo, &ier);then

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa3ls (n, | int | xi, | float [] | n yi, | float [] | n zi, | float [] | n ui, | float [] | n knots, | int [] | 3 no, | int | xo, | float [] | no yo, | float [] | no zo, | float [] | no ier | int * | ); double *c_csa3ld (n, | int | xi, | double [] | n yi, | double [] | n zi, | double [] | n ui, | double [] | n knots, | int [] | 3 no, | int | xo, | double [] | no yo, | double [] | no zo, | double [] | no ier | int * | ); -------------------------------------------------

- n
- The number of input data points. It must be that n > 3 and,
depending on the size of
*knots*below, n may have to be larger. - xi
- An array containing the X coordinate values for the input function.
- yi
- An array containing the Y coordinate values for the input function.
- zi
- An array containing the Z coordinate values for the input function.
- ui
- An array containing the functional values of the input function -- ui[k] is the functional value at (xi[k], yi[k], zi[k]) for k=0,n-1.
- knots
- The number of knots to be used in constructing the approximation spline. knots[0] specifies the number of knots in the X direction, knots[1] specifies the number of knots in the Y direction and knots[2] specifies the number of knots in the Z direction. knots[0] and knots[1] must each be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- no
- The number of X - Y - Z coordinate values to be calculated for the output array.
- xo
- An array containing the X coordinate values for the output array.
- yo
- An array containing the Y coordinate values for the output array.
- zo
- An array containing the Z coordinate values for the output array.
- ier

c_csa3lxs (c_csa3lxd) is called to find values of an approximating cubic spline at specified three-dimensional coordinates. c_csa3lxs (c_csa3lxd) is called if you want to weight the input data values, calculate derivatives, or handle data sparse areas specially. If you do not want to do any of these three things, then use c_csa3ls (c_csa3ld).

Function prototype:

float *c_csa3lxs(int, float [], float [], float [], float [], float [], int [], float, int [], int, float [], float [], float [], int *); double *c_csa3lxd(int, double [], double [], double [], double [], double [], int [], double, int [], int, double [], double [], double [], int *);Return value:

c_csa3lxs (c_csa3lxd) returns a pointer to a linear array of data that
contains the approximated values calculated at the input list of
coordinate values. That is, if *out* is declared as

float *out;and we set:

out = c_csa3lxs(n, x, y, z, u, wts, knots, smth, nderiv, no, xo, yo, zo, &ier);then

Argument description:

------------------------------------------------- Argument | Type | Size ------------------------------------------------- float *c_csa3lxs (ni, | int | xi, | float [] | ni yi, | float [] | ni zi, | float [] | ni ui, | float [] | ni wts, | float [] | ni knots, | int [] | 3 smth, | float | nderiv, | int [] | 3 no, | int | xo, | float [] | no yo, | float [] | no zo, | float [] | no ier | int * | ); double *c_csa3lxd (ni, | int | xi, | double [] | ni yi, | double [] | ni zi, | double [] | ni ui, | double [] | ni wts, | double [] | ni knots, | int [] | 3 smth, | double | nderiv, | int [] | 3 no, | int | xo, | double [] | no yo, | double [] | no zo, | double [] | no ier | int * | ); -------------------------------------------------

- ni
- The number of input data points. It must be that ni > 3 and,
depending on the size of
*knots*below, ni may have to be larger. - xi
- An array containing the X coordinate values for the input function.
- yi
- An array containing the Y coordinate values for the input function.
- zi
- An array containing the Y coordinate values for the input function.
- ui
- An array containing the functional values of the input function -- ui[k] is the functional value at (xi[k], yi[k], zi[k]) for k=0,n-1.
- wts
- An array containing weights for the ui values at the input values, that is, wts[l] is a weight for the value of ui[l] for l=0,n-1. If you do not desire to weight the input yi values, then set wts[0] to -1. The weights in the wts array are relative and may be set to any non-negative value. When c_csa3lxs (c_csa3lxd) is called, the weights are summed and the individual weights are normalized so that the weight sum is unity.
- knots
- The number of knots to be used in constructing the approximation spline. knots[0] specifies the number of knots in the X direction, knots[1] specifies the number of knots in the Y direction and knots[2] specifies the number of knots in the Z direction. knots[0], knots[1], and knots[2] must each be at least 4. The larger the value for knots, the closer the approximated curve will come to passing through the input function values.
- smth
- nderiv
- For each of the three coordinate direction, specifies whether you want functional values (nderiv=0), first derivative values (nderiv=1), or second derivative values (nderiv=2). For example, if nderiv[0]=1, nderiv[1]=1, and nderiv[2]=0, then the second order mixed partial with respect to X and Y would be computed.
- no
- The number of X - Y - Z coordinate values to be calculated for the output array.
- xo
- An array containing the X coordinate values for the output array.
- yo
- An array containing the Y coordinate values for the output array.
- zo
- An array containing the Z coordinate values for the output array.
- ier