Modules in the IMSL Math LibrariesACBCB Add two complex band matrices, both in band storage mode.●

ACHAR Return the character whose ASCII value is the input integer argument.●

ACOSH (DACOSH) Arccosh(x).●

AI (DAI) Airy function Ai(x).●

AID (DAID) Derivative of the Airy function Ai(x).●

AIDE (DAIDE) Exponentially scaled derivative of the Airy function exp(x)dAi(x)/dx.●

AIE (DAIE) Exponentially scaled Airy function exp(x)Ai(x).●

AKEI0 (DKEI0) Kelvin function kei0(x).●

AKEI1 (DKEI1) Kelvin function kei1(x).●

AKEIP0 (DKEIP0) Derivative of the Kelvin function kei0(x).●

AKER0 (DKER0) Kelvin function ker0(x).●

AKER1 (DKER1) Kelvin function ker1(x).●

AKERP0 (DKERP0) Derivative of the Kelvin function ker0(x).●

ALBETA (DLBETA) Logarithm of the complete beta function for positive arguments.●

ALGAMS (DLGAMS) Ln(abs(gamma(x))) and sign(gamma(x)).●

ALI (DLI) Logarithmic integral, integral from 0 to x of 1/ln(t).●

ALNGAM (DLNGAM) Ln(abs(gamma(x))).●

ALNREL (DLNREL) Ln(1+x).●

AMACH (DMACH) Retrieve single-precision machine constants.●

ARBRB (DARBRB) Add two band matrices, both in band storage mode.●

ASINH (DASINH) Arcsinh(x).●

ATANH (DATANH) Arctanh(x).●

BCLSF (DBCLSF) Solve a nonlinear least-squares problem subject to bounds on the variablesusing ...

●

BCLSJ (DBCLSJ) Solve a nonlinear least-squares problem subject to bounds on the variables●

IMSL Fortran Numerical Libraries

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using ...

BCOAH (DBCOAH) Minimize a function of N variables subject to bounds on the variables usinga mo ...

●

BCODH (DBCODH) Minimize a function of N variables subject to bounds on the variables usinga mo ...

●

BCONF (DBCONF) Minimize a function of N variables subject to bounds on the variables using aqu ...

●

BCONG (DBCONG) Minimize a function of N variables subject to bounds on the variables usinga qu ...

●

BCPOL (DBCPOL) Minimize a function of N variables subject to bounds on the variables using adi ...

●

BEI0 (DBEI0) Kelvin function bei0(x).●

BEI1 (DBEI1) Kelvin function bei1(x).●

BEIP0 (DBEIP0) Derivative of the Kelvin function bei0(x).●

BER0 (DBER0) Kelvin function ber0(x).●

BER1 (DBER1) Kelvin function ber1(x).●

BERP0 (DBERP0) Derivative of the Kelvin function ber0(x).●

BETAI (DBETAI) Incomplete beta function.●

BI (DBI) Airy function Bi(x).●

BID (DBID) Derivative of the Airy function Bi(x).●

BIDE (DBIDE) Exponentially scaled derivative of the Airy function exp(-x)dBi(x)/dx.●

BIE (DBIE) Exponentially scaled Airy function exp(-x)Bi(x).●

BLINF (DBLINF) Compute the bilinear mode transpose(x)*A*y.●

BS1GD (DBS1GD) Evaluate the derivative of a spline on a grid, given its B-spline representation...

●

BS2DR (DBS2DR) Evaluate the derivative of a two-dimensional tensor-product spline, given its te...

●

BS2GD (DBS2GD) Evaluate the derivative of a two-dimensional tensor-product spline, given itste ...

●

BS2IG (DBS2IG) Evaluate the integral of a tensor-product spline on a rectangular domain, given...

●

BS2IN (DBS2IN) Compute a two-dimensional tensor-product spline interpolant, returning thetenso ...

●

BS2VL (DBS2VL) Evaluate a two-dimensional tensor-product spline, given its tensor-productB-spl ...

●

BS3DR (DBS3DR) Evaluate the derivative of a three-dimensional tensor-product spline, given its...

●

IMSL Fortran Numerical Libraries

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BS3GD (DBS3GD) Evaluate the derivative of a three-dimensional tensor-product spline, given its...

●

BS3IG (DBS3IG) Evaluate the integral of a tensor-product spline in three dimensions over a thre...

●

BS3IN (DBS3IN) Compute a three-dimensional tensor-product spline interpolant, returning the ten...

●

BS3VL (DBS3VL) Evaluate a three-dimensional tensor-product spline, given its tensor-productB-s ...

●

BSCPP (DBSCPP) Convert a spline in B-spline representation to piecewise polynomialrepresentati ...

●

BSDER (DBSDER) Evaluate the derivative of a spline, given its B-spline representation.●

BSI0 (DBSI0) Modified Bessel function I0(x).●

BSI0E (DBSI0E) Exponentially scaled modified Bessel function exp(-x)I0(x).●

BSI1 (DBSI1) Modified Bessel function I1(x).●

BSI1E (DBSI1E) Exponentially scaled modified Bessel function exp(-x)I1(x).●

BSIES (DBSIES) Sequence of exponentially scaled modified Bessel functions exp(-x)Ir(x), for r r...

●

BSINS (DBSINS) Sequence of modified Bessel functions In(x).●

BSINT (DBSINT) Compute the spline interpolant, returning the B-spline coefficients.●

BSIS (DBSIS) Sequence of modified Bessel functions Ir(x), for r nonnegative real and x positi ...●

BSITG (DBSITG) Evaluate the integral of a spline, given its B-spline representation.●

BSJ0 (DBSJ0) Bessel function J0(x).●

BSJ1 (DBSJ1) Bessel function J1(x).●

BSJNS (DBSJNS) Sequence of Bessel functions Jn(x).●

BSJS (DBSJS) Sequence of Bessel functions Jr(x), for r real and positive.●

BSK0 (DBSK0) Bessel function K0(x).●

BSK0E (DBSK0E) Exponentially scaled modified Bessel function exp(x)K0(x).●

BSK1 (DBSK1) Bessel function K1(x).●

BSK1E (DBSK1E) Exponentially scaled modified Bessel function exp(x)K1(x).●

BSKES (DBSKES) Sequence of exponentially scaled modified Bessel functions exp(x)Kr(x), forreal ...

●

BSKS (DBSKS) Sequence of modified Bessel functions Kr(x), for real r.●

BSLS2 (DBSLS2) Compute a two-dimensional tensor-product spline approximant usingleast-squares, ...

●

BSLS3 (DBSLS3) Compute a three-dimensional tensor-product spline approximant using leastsquare ...

●

IMSL Fortran Numerical Libraries

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BSLSQ (DBSLSQ) Compute a B-spline least-squares spline approximation to given data.●

BSNAK (DBSNAK) Compute the "not-a-knot" spline knot sequence.●

BSOPK (DBSOPK) Compute the optimal spline knot sequence.●

BSVAL (DBSVAL) Evaluate a spline, given its B-spline representation.●

BSVLS (DBSVLS) Compute the variable knot B-spline least-squares approximation to given data.●

BSY0 (DBSY0) Bessel function Y0(x).●

BSY1 (DBSY1) Bessel function Y1(x).●

BSYS (DBSYS) Sequence of Bessel functions Yr(x), for real nonnegative r and positive x.●

BVPFD (DBVPFD) Solve a system of differential equations with boundary conditions at twopoints, ...

●

BVPMS (DBVPMS) Solve a system of differential equations with boundary conditions at twopoints, ...

●

CACOS Arccos(z).●

CACOSH Arccosh(z).●

CADD Add a scalar to each component of a vector, x = x + a, all complex.●

CARG Argument of a complex number.●

CASIN Arcsin(z).●

CASINH Arcsinh(z).●

CATAN Arctan(z).●

CATAN2 Arctan(z1/z2).●

CATANH Arctanh(z).●

CAXPY Compute a scalar times a vector plus a vector, y = ax + y, all complex.●

CBETA Complex complete beta function.●

CBINS Sequence of modified Bessel functions In(z).●

CBIS (DCBIS) Evaluate a sequence of Modified Bessel functions of the first kind with real ord ...●

CBJNS Sequence of Bessel functions Jn(z).●

CBJS (DCBJS) Evaluate a sequence of Bessel functions of the first kind with real order and co ...●

CBKS (DCBKS) Evaluate a sequence of Modified Bessel functions of the second kind with real or...

●

CBRT (DCBRT) Cube root of a real argument.●

CBYS (DCBYS) Evaluate a sequence of Bessel functions of the second kind with real order and c...

●

CCBCB Copy a complex band matrix stored in complex band storage mode.●

CCBCG Convert a complex matrix in band storage mode to a complex matrix in full storag ...●

IMSL Fortran Numerical Libraries

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CCBRT Cube root of a complex argument.●

CCGCB Convert a complex matrix in full storage mode to a matrix in complex band storag ...●

CCGCG Copy a complex general matrix.●

CCONV (DCCONV) Compute the convolution of two complex vectors.●

CCOPY Copy a vector X to a vector Y, both complex.●

CCORL (DCCORL) Compute the correlation of two complex vectors.●

CCOSH Cosh(z).●

CCOT Cotan(z).●

CDGRD (DCDGRD) Approximate the gradient using central differences.●

CDOTC Compute the complex conjugate dot product, conjg(x)*y.●

CDOTU Compute the complex dot product x*y.●

CEJCN (DCEJCN) Evaluate the complex Jacobi elliptic function cn(z,m).●

CEJDN (DCEJDN) Evaluate the complex Jacobi elliptic function dn(z,m).●

CEJSN (DCEJSN) Evaluate the complex Jacobi elliptic function sn(z,m).●

CERFE Complex scaled complementary error function.●

CEXPRL (exp(z)-1)/z.●

CGAMMA Complex gamma function.●

CGAMR 1/gamma(z).●

CGBMV (ZGBMV) Perform one of the matrix-vector operations: y = alpha*A*x + beta*y, y =alpha*t ...

●

CGEMM (ZGEMM) Perform one of the following matrix-matrix multiplications: C=alpha*A*B +beta*C ...

●

CGEMV (ZGEMV) Perform one of the matrix-vector multiplications: y = alpha*A*x + beta*y y =alp ...

●

CGERC (ZGERC) Perform the rank-one matrix update: A = A + alpha*x*ctrans(y), wherectrans(y) i ...

●

CGERU (ZGERU) Perform the rank-one matrix update: A = A + alpha*x*trans(y), where trans(y)is ...

●

CHBCB Copy a complex Hermitian band matrix stored in band Hermitian storage mode to a ...●

CHBMV (ZHBMV) Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is aHermiti ...

●

CHEMM (ZHEMM) Perform one of the matrix-matrix operations: C = alpha*A*B + beta*C, or C= alp ...

●

CHEMV (ZHEMV) Perform the matrix-vector multiplication y = alpha*A*x + beta*y, where A isa He ...

●

IMSL Fortran Numerical Libraries

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CHER (ZHER) Perform the rank-one matrix update A = A + alpha*x*ctrans(x) to the Hermitianma ...

●

CHER2 (ZHER2) Perform a rank-two matrix update to the Hermitian matrix A, A = A +alpha*x*ctra ...

●

CHER2K (ZHER2K) Perform one of the Hermitian rank 2k operations C = alpha*A*ctrans( B ) +conjg ...

●

CHERK (ZHERK) Perform one of the Hermitian rank k operations C = alpha*A*ctrans( A ) +beta*C ...

●

CHFCG Extend a complex Hermitian matrix defined in its upper triangle to its lower tri ...●

CHGRD (DCHGRD) Check a user-supplied gradient of a function.●

CHHES (DCHHES) Check a user-supplied Hessian of an analytic function.●

CHI (DCHI) Hyperbolic cosine integral.●

CHJAC (DCHJAC) Check a user-supplied Jacobian of a system of equations with M functions inN un ...

●

CI (DCI) Cosine integral.●

CIN (DCIN) Evaluate a function closely related to the cosine integral.●

CINH (DCINH) Evaluate a function closely related to the hyperbolic cosine integral.●

CLBETA Complex logarithm of the complete beta function.●

CLNGAM Ln(gamma(z)).●

CLNREL Ln(1+z).●

CLOG10 Log(z).●

CONFT (DCONFT) Compute the least-squares constrained spline approximation, returning theB-spli ...

●

CONST (DCONST) Various mathematical and physical constants.●

COSDG (DCOSDG) Cos(x), x in degrees.●

COT (DCOT) Cotan(x).●

CPSEC Return CPU time used in seconds.●

CPSI Logarithmic derivative of the gamma function for a complex argument.●

CRBCB Convert a real matrix in band storage mode to a complex matrix in band storage m ...●

CRBRB (DCRBRB) Copy a real band matrix stored in band storage mode.●

CRBRG (DCRBRG) Convert a real matrix in band storage mode to a matrix in full storage mode.●

CRGCG Copy a real general matrix to a complex general matrix.●

CRGRB (DCRGRB) Convert a real matrix in full storage mode to a matrix in band storage mode.●

CRGRG (DCRGRG) Copy a real general matrix.●

CRRCR Copy a real rectangular matrix to a complex rectangular matrix.●

IMSL Fortran Numerical Libraries

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CS1GD (DCS1GD) Evaluate the derivative of a cubic spline on a grid.●

CSAKM (DCSAKM) Compute the Akima cubic spline interpolant.●

CSBRB (DCSBRB) Copy a real symmetric band matrix stored in band symmetric storage mode toa rea ...

●

CSCAL Multiply a vector by a scalar, y = ay, both complex.●

CSCON (DCSCON) Compute a cubic spline interpolant that is consistent with the concavity of the...

●

CSDEC (DCSDEC) Compute the cubic spline interpolant with specified derivative endpointconditio ...

●

CSDER (DCSDER) Evaluate the derivative of a cubic spline.●

CSET Set the components of a vector to a scalar, all complex.●

CSEVL Evaluate a series of Chebyshev polynomials.●

CSFRG (DCSFRG) Extend a real symmetric matrix defined in its upper triangle to its lower triang...

●

CSHER (DCSHER) Compute a Hermite cubic spline interpolant.●

CSIEZ (DCSIEZ) Compute the cubic spline interpolant with the "not-a-knot" condition and return...

●

CSINH Sinh(z).●

CSINT (DCSINT) Compute the cubic spline interpolant with the "not-a-knot" condition.●

CSITG (DCSITG) Evaluate the integral of a cubic spline.●

CSPER (DCSPER) Compute the cubic spline interpolant with periodic boundary conditions.●

CSROT Apply a complex Givens plane rotation.●

CSROTM Apply a complex modified Givens plane rotation.●

CSSCAL Multiply a complex vector by a single-precision scalar, y = ay.●

CSSCV (DCSSCV) Compute a smooth cubic spline approximation to noisy data usingcross-validation ...

●

CSSED (DCSSED) Smooth one-dimensional data by error detection.●

CSSMH (DCSSMH) Compute a smooth cubic spline approximation to noisy data.●

CSUB Subtract each component of a vector from a scalar, x = a - x, all complex.●

CSVAL (DCSVAL) Evaluate a cubic spline.●

CSVCAL Multiply a complex vector by a single-precision scalar and store the result in a ...●

CSWAP Interchange vectors X and Y, both complex.●

CSYMM (ZSYMM) Perform one of the matrix-matrix operations: C = alpha*A*B + beta*C, or C= alp ...

●

CSYR2K (ZSYR2K) Perform one of the symmetric rank 2k operations C = alpha*A*trans(B) +●

IMSL Fortran Numerical Libraries

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alpha*B* ...

CSYRK (ZSYRK) Perform one of the symmetric rank k operations C = alpha*A*trans(A) +beta*C, o ...

●

CTAN Tan(z).●

CTANH Tanh(z).●

CTBMV (ZTBMV) Perform one of the matrix-vector operations: x = A*x, x = trans(A)*x, x =ctrans ...

●

CTBSV (ZTBSV) Solve one of the triangular systems, x = inv(A)*x, x = inv(trans(A))*x, x = inv(...

●

CTRMM (ZTRMM) Perform one of the matrix-matrix operations: B = alpha*op( A )*B, or B =alpha* ...

●

CTRMV (ZTRMV) Perform one of the matrix-vector operations: x = A*x, x = trans(A)*x, or x =ctr ...

●

CTRSM (ZTRSM) Solve one of the matrix equations: op( A )*X = alpha*B, or X*op( A ) =alpha*B, ...

●

CTRSV (ZTRSV) Solve one of the triangular systems, x = inv(A)*x, x = inv(trans(A))*x, or x = i...

●

CUNIT (DCUNIT) Convert X in units XUNITS to Y in units YUNITS.●

CVCAL Multiply a vector by a scalar and store the result in another vector, y = ax, al ...●

CVTSI Convert a character string containing an integer number into the corresponding i ...●

CWPL Weierstrass P-function with primitive half-periods 1/2 [AMS55 (18.1)]. The corre ...●

CWPLD First derivative of CWPL.●

CWPQ Weierstrass P-function in the equianharmonic case for complex argument with unit ...●

CWPQD First derivative of CWPQ.●

CZCDOT Compute the sum of a complex scalar plus a complex conjugate dot product, a + co ...●

CZDOTA Compute the sum of a complex scalar, a complex dot product and the double-comple ...●

CZDOTC Compute the complex conjugate dot product, conjg(x)*y, using a double-precision ...●

CZDOTI Compute the sum of a complex scalar plus a complex dot product using a double-co ...●

CZDOTU Compute the complex dot product x*y using a double-precision accumulator.●

CZUDOT Compute the sum of a complex scalar plus a complex dot product, a + x*y, using a ...●

DACOSH (ACOSH) Arccosh(x), for double-precision x.●

DADD (SADD) Add a scalar to each component of a vector, x = x + a, all single-precision.●

DAI (AI) Airy function Ai(x).●

DAID (AID) Derivative of the Airy function Ai(x).●

DAIDE (AIDE) Exponentially scaled derivative of the Airy function exp(x)dAi(x)/dx.●

IMSL Fortran Numerical Libraries

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DAIE (AIE) Exponentially scaled Airy function exp(x)Ai(x).●

DARBRB (ARBRB) Add two band matrices, both in band storage mode.●

DASINH (ASINH) Arcsinh(x), for double-precision x.●

DASPG (DDASPG) Solve a first-order differential-algebraic system of equations, g(t,y,y')=0, usi...

●

DASUM (SASUM) Compute double-precision sum of absolute values of a single-precision vector.●

DATANH (ATANH) Arctanh(x), for double-precision x.●

DAWS (DDAWS) Dawson's integral.●

DAXPY (SAXPY) Compute the scalar times a vector plus a vector, y = ax + y, all double precisio...

●

DBCLSF (BCLSF) Solve a nonlinear least-squares problem subject to bounds on the variablesusing ...

●

DBCLSJ (BCLSJ) Solve a nonlinear least-squares problem subject to bounds on the variablesusing ...

●

DBCOAH (BCOAH) Minimize a function of N variables subject to bounds on the variables usinga mo ...

●

DBCODH (BCODH) Minimize a function of N variables subject to bounds on the variables usinga mo ...

●

DBCONF (BCONF) Minimize a function of N variables subject to bounds on the variables using aqu ...

●

DBCONG (BCONG) Minimize a function of N variables subject to bounds on the variables usinga qu ...

●

DBCPOL (BCPOL) Minimize a function of N variables subject to bounds on the variables using adi ...

●

DBEI0 (BEI0) Kelvin function bei, of order zero.●

DBEI1 (BEI1) Kelvin function bei, of order one.●

DBEIP0 (BEIP0) Derivative of the Kelvin function bei, of order zero.●

DBER0 (BER0) Kelvin function ber, of order zero.●

DBER1 (BER1) Kelvin function ber, of order one.●

DBERP0 (BERP0) Derivative of the Kelvin function ber, of order zero.●

DBETAI (BETAI) Incomplete beta function.●

DBI (BI) Airy function Bi(x).●

DBID (BID) Derivative of the Airy function Bi(x).●

DBIDE (BIDE) Exponentially scaled derivative of the Airy function exp(-x)dBi(x)/dx.●

DBIE (BIE) Exponentially scaled Airy function exp(-x)Bi(x).●

DBLINF (BLINF) Compute the bilinear mode transpose(x)*A*y.●

IMSL Fortran Numerical Libraries

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DBS1GD (BS1GD) Evaluate the derivative of a spline on a grid, given its B-spline representation...

●

DBS2DR (BS2DR) Evaluate the derivative of a two-dimensional tensor-product spline, given its te...

●

DBS2GD (BS2GD) Evaluate the derivative of a two-dimensional tensor-product spline, given itste ...

●

DBS2IG (BS2IG) Evaluate the integral of a tensor-product spline on a rectangular domain, given...

●

DBS2IN (BS2IN) Compute a two-dimensional tensor-product spline interpolant, returning thetenso ...

●

DBS2VL (BS2VL) Evaluate a two-dimensional tensor-product spline, given its tensor-productB-spl ...

●

DBS3DR (BS3DR) Evaluate the derivative of a three-dimensional tensor-product spline, given its...

●

DBS3GD (BS3GD) Evaluate the derivative of a three-dimensional tensor-product spline, given its...

●

DBS3IG (BS3IG) Evaluate the integral of a tensor-product spline in three dimensions over a thre...

●

DBS3IN (BS3IN) Compute a three-dimensional tensor-product spline interpolant, returning the ten...

●

DBS3VL (BS3VL) Evaluate a three-dimensional tensor-product spline, given its tensor-productB-s ...

●

DBSCPP (BSCPP) Convert a spline in B-spline representation to piecewise polynomialrepresentati ...

●

DBSDER (BSDER) Evaluate the derivative of a spline, given its B-spline representation.●

DBSI0 (BSI0) Modified Bessel function I0(x).●

DBSI0E (BSI0E) Exponentially scaled modified Bessel function exp(-x)I0(x).●

DBSI1 (BSI1) Modified Bessel function I1(x).●

DBSI1E (BSI1E) Exponentially scaled modified Bessel function exp(-x)I1(x).●

DBSIES (BSIES) Sequence of exponentially scaled modified Bessel functions exp(-x)Ir(x), for r r...

●

DBSINS (BSINS) Sequence of modified Bessel functions In(x).●

DBSINT (BSINT) Compute the spline interpolant, returning the B-spline coefficients.●

DBSIS (BSIS) Sequence of modified Bessel functions Ir(x), for r nonnegative real and x positi ...●

DBSITG (BSITG) Evaluate the integral of a spline, given its B-spline representation.●

DBSJ0 (BSJ0) Bessel function J0(x).●

DBSJ1 (BSJ1) Bessel function J1(x).●

IMSL Fortran Numerical Libraries

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DBSJNS (BSJNS) Sequence of Bessel functions Jn(x).●

DBSJS (BSJS) Sequence of Bessel functions Jr(x), for real and positive r.●

DBSK0 (BSK0) Bessel function K0(x).●

DBSK0E (BSK0E) Exponentially scaled modified Bessel function exp(x)K0(x).●

DBSK1 (BSK1) Bessel function K1(x).●

DBSK1E (BSK1E) Exponentially scaled modified Bessel function exp(x)K1(x).●

DBSKES (BSKES) Sequence of exponentially scaled modified Bessel functions exp(x)Kr(x), forreal ...

●

DBSKS (BSKS) Sequence of modified Bessel functions Kr(x), for real r.●

DBSLS2 (BSLS2) Compute a two-dimensional tensor-product spline approximant usingleast-squares, ...

●

DBSLS3 (BSLS3) Compute a three-dimensional tensor-product spline approximant using leastsquare ...

●

DBSLSQ (BSLSQ) Compute a B-spline least-squares spline approximation to given data.●

DBSNAK (BSNAK) Compute the "not-a-knot" spline knot sequence.●

DBSOPK (BSOPK) Compute the optimal spline knot sequence.●

DBSVAL (BSVAL) Evaluate a spline, given its B-spline representation.●

DBSVLS (BSVLS) Compute the variable knot B-spline least-squares to given data.●

DBSY0 (BSY0) Bessel function Y0(x).●

DBSY1 (BSY1) Bessel function Y1(x).●

DBSYS (BSYS) Sequence of Bessel functions Yr(x), for real nonnegative r and positive x.●

DBVPFD (BVPFD) Solve a system of differential equations with boundary conditions at twopoints, ...

●

DBVPMS (BVPMS) Solve a system of differential equations with boundary conditions at twopoints, ...

●

DCBIS (CBIS) Evaluate a sequence of Modified Bessel functions of the first kind with real ord ...●

DCBJS (CBJS) Evaluate a sequence of Bessel functions of the first kind with real order and co ...●

DCBKS (CBKS) Evaluate a sequence of Modified Bessel functions of the second kind with real or...

●

DCBRT (CBRT) Cube root of a double-precision real argument.●

DCBYS (CBYS) Evaluate a sequence of Bessel functions of the second kind with real order and c...

●

DCCONV (CCONV) Compute the convolution of two complex vectors.●

DCCORL (CCORL) Compute the correlation of two complex vectors.●

DCDGRD (CDGRD) Approximate the gradient using central differences.●

IMSL Fortran Numerical Libraries

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DCEJCN (CEJCN) Evaluate the complex Jacobi elliptic function cn(z,m).●

DCEJDN (CEJDN) Evaluate the complex Jacobi elliptic function dn(z,m).●

DCEJSN (CEJSN) Evaluate the complex Jacobi elliptic function sn(z,m).●

DCHGRD (CHGRD) Check a user-supplied gradient of a function.●

DCHHES (CHHES) Check a user-supplied Hessian of an analytic function.●

DCHI (CHI) Hyperbolic cosine integral.●

DCHJAC (CHJAC) Check a user-supplied Jacobian of a system of equations with M functions inN un ...

●

DCI (CI) Cosine integral.●

DCIN (CIN) Evaluate a function closely related to the cosine integral.●

DCINH (CINH) Evaluate a function closely related to the hyperbolic cosine integral.●

DCONFT (CONFT) Compute the least-squares constrained spline approximation, returning theB-spli ...

●

DCONST (CONST) Various mathematical and physical constants.●

DCOPY (SCOPY) Copy a vector X to a vector Y, both double-precision.●

DCOSDG (COSDG) Cos(x), for double-precision x in degrees.●

DCOT (COT) Cotan(x), for double-precision x.●

DCRBRB (CRBRB) Copy a real band matrix stored in band storage mode.●

DCRBRG (CRBRG) Convert a real matrix in band storage mode to a matrix in full storage mode.●

DCRGRB (CRGRB) Convert a real matrix in full storage mode to a matrix in band storage mode.●

DCRGRG (CRGRG) Copy a real general matrix.●

DCS1GD (CS1GD) Evaluate the derivative of a cubic spline on a grid.●

DCSAKM (CSAKM) Compute the Akima cubic spline interpolant.●

DCSBRB (CSBRB) Copy a real symmetric band matrix stored in band symmetric storage mode toa rea ...

●

DCSCON (CSCON) Compute a cubic spline interpolant that is consistent with the concavity of the...

●

DCSDEC (CSDEC) Compute the cubic spline interpolant with specified derivative endpointconditio ...

●

DCSDER (CSDER) Evaluate the derivative of a cubic spline.●

DCSFRG (CSFRG) Extend a real symmetric matrix defined in its upper triangle to its lower triang...

●

DCSHER (CSHER) Compute a Hermite cubic spline interpolant.●

DCSIEZ (CSIEZ) Compute the cubic spline interpolant with the `not-a-knot' condition and return...

●

IMSL Fortran Numerical Libraries

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DCSINT (CSINT) Compute the cubic spline interpolant with the 'not-a-knot' condition.●

DCSITG (CSITG) Evaluate the integral of a cubic spline.●

DCSPER (CSPER) Compute the cubic spline interpolant with periodic boundary conditions.●

DCSSCV (CSSCV) Compute a smooth cubic spline approximation to noisy data usingcross-validation ...

●

DCSSED (CSSED) Smooth one-dimensional data by error detection.●

DCSSMH (CSSMH) Compute a smooth cubic spline approximation to noisy data.●

DCSVAL (CSVAL) Evaluate a cubic spline.●

DCUNIT (CUNIT) Convert X in units XUNITS to Y in units YUNITS.●

DDASPG (DASPG) Solve a first order differential-algebraic system of equations, g(t,y,y')=0, usi...

●

DDAWS (DAWS) Double-precision Dawson integral.●

DDERIV (DERIV) Compute the first, second or third derivative of a user-supplied function.●

DDISL1 (DISL1) Compute the 1-norm distance between two points.●

DDISL2 (DISL2) Compute the Euclidean (2-norm) distance between two points.●

DDISLI (DISLI) Compute the infinity norm distance between two points.●

DDLPRS (DLPRS) Solve a linear programming problem via the revised simplex algorithm.●

DDOT (SDOT) Compute double-precision dot product x*y.●

DE1 (E1) Exponential integral for arguments greater than zero and the Cauchy principle va ...●

DEI (EI) Exponential integral for arguments greater than zero and the Cauchy principle va ...●

DEJCN (EJCN) Evaluate the Jacobi elliptic function cn(x,m).●

DEJDN (EJDN) Evaluate the Jacobi elliptic function dn(x,m).●

DEJSN (EJSN) Evaluate the Jacobi elliptic function sn(x,m).●

DELE (ELE) Complete elliptic integral E(m), see [AMS55 (17.3.3)].●

DELK (ELK) Complete elliptic integral K(m), see [AMS55 (17.3.1)].●

DELRC (ELRC) Carlson's incomplete elliptic integral RC(x,y).●

DELRD (ELRD) Carlson's incomplete elliptic integral RD(x,y,z).●

DELRF (ELRF) Carlson's incomplete elliptic integral RF(x,y,z).●

DELRJ (ELRJ) Carlson's incomplete elliptic integral RJ(x,y,z,p).●

DENE (ENE) Exponential integral of integer order for arguments greater than zero scaled by ...●

DEPISB (EPISB) Compute the performance index for a real symmetric eigensystem in bandsymmetric ...

●

DEPISF (EPISF) Compute the performance index for a real symmetric eigensystem.●

DERF (ERF) Double-precision error function, = (2 / square root of pi) * the integral from 0 ...●

IMSL Fortran Numerical Libraries

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DERFC (ERFC) Double-precision complementary error function, = (2 / square root of pi) * the i ...●

DERFCE (ERFCE) Exponentially scaled complementary error function.●

DERFCI (ERFCI) Inverse complementary error function.●

DERFI (ERFI) Inverse error function.●

DERIV (DDERIV) Compute the first, second or third derivative of a user-supplied function.●

DEVASB (EVASB) Compute the largest or smallest eigenvalues of a real symmetric matrix inband s ...

●

DEVASF (EVASF) Compute the largest or smallest eigenvalues of a real symmetric matrix.●

DEVBSB (EVBSB) Compute the eigenvalues in a given range of a real symmetric matrix stored inba ...

●

DEVBSF (EVBSF) Compute the eigenvalues in a given range of a real symmetric matrix.●

DEVCSB (EVCSB) Compute all of the eigenvalues and eigenvectors of a real symmetric matrix inba ...

●

DEVCSF (EVCSF) Compute all of the eigenvalues and eigenvectors of a real symmetric matrix.●

DEVESB (EVESB) Compute the largest or smallest eigenvalues and the correspondingeigenvectors o ...

●

DEVESF (EVESF) Compute the largest or smallest eigenvalues and the correspondingeigenvectors o ...

●

DEVFSB (EVFSB) Compute the eigenvalues in a given range and the corresponding eigenvectorsof a ...

●

DEVFSF (EVFSF) Compute the eigenvalues in a given range and the corresponding eigenvectorsof a ...

●

DEVLSB (EVLSB) Compute all of the eigenvalues of a real symmetric matrix in band symmetricstor ...

●

DEVLSF (EVLSF) Compute all of the eigenvalues of a real symmetric matrix.●

DEXPRL (EXPRL) (exp(x)-1)/x, for double-precision x.●

DFAC (FAC) Factorial. Input is integer; output is double-precision.●

DFCOST (FCOST) Discrete Fourier cosine transformation of an even sequence.●

DFDGRD (FDGRD) Approximate the gradient using forward differences.●

DFDHES (FDHES) Approximate the Hessian using forward differences and function values.●

DFDJAC (FDJAC) Approximate the Jacobian of M functions in N unknowns using forwarddifferences.

●

DFFT3B (FFT3B) Compute the inverse Fourier transform of a complex periodicthree-dimensional ar ...

●

DFFT3F (FFT3F) Compute Fourier coefficients of a complex periodic three-dimensional array.●

DFFTRB (FFTRB) Compute the real periodic sequence from its Fourier coefficients.●

IMSL Fortran Numerical Libraries

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DFFTRF (FFTRF) Compute the Fourier coefficients of a real periodic sequence.●

DFNLSQ (FNLSQ) Least-squares approximation with user-supplied basis functions.●

DFPS2H (FPS2H) Solve Poisson's or Helmholtz's equation on a two-dimensional rectangle using af ...

●

DFPS3H (FPS3H) Solve Poisson's or Helmholtz's equation on a three-dimensional box using a fast...

●

DFQRUL (FQRUL) Compute a Fejer quadrature rule with various classical weight functions.●

DFRESC (FRESC) Evaluate the cosine Fresnel integral.●

DFRESS (FRESS) Evaluate the sine Fresnel integral.●

DFSINT (FSINT) Discrete Fourier cosine transformation of an odd sequence.●

DGAMI (GAMI) Incomplete gamma function.●

DGAMIC (GAMIC) Complementary incomplete gamma function.●

DGAMIT (GAMIT) Tricomi's incomplete gamma function, for double-precision argument.●

DGAMMA (GAMMA) gamma(x), for double-precision x.●

DGAMR (GAMR) 1/gamma(x), for double-precision x.●

DGBMV (SGBMV) Perform one of the matrix-vector operations: y = alpha*A*x + beta*y or y =alpha ...

●

DGDHES (GDHES) Approximate the Hessian using forward differences and a user-suppliedgradient.

●

DGEMM (SGEMM) Perform one of the following matrix-matrix multiplications: C = alpha*A*B+ beta ...

●

DGEMV (SGEMV) Perform one of the matrix-vector operations: y = alpha*A*x + beta*y or y =alpha ...

●

DGGUES (GGUES) Generate points in an N-dimensional space.●

DGPISP (GPISP) Compute the performance index for a generalized real symmetric eigensystemprobl ...

●

DGQRCF (GQRCF) Compute a Gauss, Gauss-Radau or Gauss-Lobatto quadrature rule given therecurren ...

●

DGQRUL (GQRUL) Compute a Gauss, Gauss-Radau or Gauss-Lobatto quadrature rule withvarious class ...

●

DGVCSP (GVCSP) Compute all of the eigenvalues and eigenvectors of the generalized realsymmetri ...

●

DGVLSP (GVLSP) Compute all of the eigenvalues of the generalized real symmetric eigenvalueprob ...

●

DHPROD (SHPROD) Compute the Hadamard product of two single-precision vectors.●

DHRRRR (HRRRR) Compute the Hadamard product of two real matrices.●

IMSL Fortran Numerical Libraries

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DHYPOT (HYPOT) SQRT(A**2+B**2) without underflow or overflow.●

DISL1 (DDISL1) Compute the 1-norm distance between two points.●

DISL2 (DDISL2) Compute the Euclidean (2-norm) distance between two points.●

DISLI (DDISLI) Compute the infinity norm distance between two points.●

DIVPAG (IVPAG) Solve an initial-value problem for ordinary differential equations using anAdam ...

●

DIVPRK (IVPRK) Solve an initial-value problem for ordinary differential equations using the Run...

●

DJCGRC (JCGRC) Solve a real symmetric definite linear system using the Jacobi-preconditionedco ...

●

DKEI0 (AKEI0) Kelvin function kei0(x).●

DKEI1 (AKEI1) Kelvin function kei1(x).●

DKEIP0 (AKEIP0) Derivative of the Kelvin function kei0(x).●

DKER0 (AKER0) Kelvin function ker1(x).●

DKER1 (AKER1) Kelvin function ker1(x).●

DKERP0 (AKERP0) Derivative of the Kelvin function ker0(x).●

DLBETA (ALBETA) Logarithm of the complete beta function for positive arguments.●

DLCHRG (LCHRG) Compute the Cholesky decomposition of a symmetric positive semidefinitematrix w ...

●

DLCLSQ (LCLSQ) Solve a linear least-squares problem with linear constraints.●

DLCONF (LCONF) Minimize a general objective function subject to linear equality/inequalitycons ...

●

DLCONG (LCONG) Minimize a general objective function subject to linear equality/inequalitycons ...

●

DLDNCH (LDNCH) Downdate the transpose(R)*R Cholesky factorization of a real symmetricpositive ...

●

DLFCDS (LFCDS) Compute the transpose(R)*R Cholesky factorization of a real symmetricpositive d ...

●

DLFCQS (LFCQS) Compute the Cholesky factorization of a real symmetric positive definitematrix ...

●

DLFCRB (LFCRB) Compute the LU factorization of a real matrix in band storage mode andestimate ...

●

DLFCRG (LFCRG) Compute the LU factorization of a real general matrix and estimate its L1condit ...

●

DLFCRT (LFCRT) Estimate the condition number of a real triangular matrix.●

DLFCSF (LFCSF) Compute the U*D*transpose(U) factorization of a real symmetric matrix and●

IMSL Fortran Numerical Libraries

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estima ...

DLFDDS (LFDDS) Compute the determinant of a real symmetric positive definite matrix giventhe t ...

●

DLFDQS (LFDQS) Compute the determinant of a real symmetric positive definite matrix in bandsym ...

●

DLFDRB (LFDRB) Compute the determinant of a real matrix in band storage mode given the LUfacto ...

●

DLFDRG (LFDRG) Compute the determinant of a real general matrix given the LU factorizationof t ...

●

DLFDRT (LFDRT) Compute the determinant of a real triangular matrix.●

DLFDSF (LFDSF) Compute the determinant of a real symmetric matrix given theU*D*transpose(U) fa ...

●

DLFIDS (LFIDS) Use iterative refinement to improve the solution of a real symmetric positive de...

●

DLFIQS (LFIQS) Use iterative refinement to improve the solution of a real symmetric positive de...

●

DLFIRB (LFIRB) Use iterative refinement to improve the solution of a real system of linear equa...

●

DLFIRG (LFIRG) Use iterative refinement to improve the solution of a real general system of lin...

●

DLFISF (LFISF) Use iterative refinement to improve the solution of a real symmetric system of l...

●

DLFSDS (LFSDS) Solve a real symmetric positive definite system of linear equations given the tr...

●

DLFSQS (LFSQS) Solve a real symmetric positive definite system of linear equations given the fa...

●

DLFSRB (LFSRB) Solve a real system of linear equations given the LU factorization of the coeffi...

●

DLFSRG (LFSRG) Solve a real general system of linear equations given the LU factorization of th...

●

DLFSSF (LFSSF) Solve a real symmetric system of linear equations given the U*D*transpose(U)fac ...

●

DLFSXD (LFSXD) Solve a real sparse symmetric positive definite system of linear equations,give ...

●

DLFSXG (LFSXG) Solve a sparse system of linear equations given the LU factorization of thecoef ...

●

DLFSZD (LFSZD) Solve a complex sparse Hermitian positive definite system of linear equations,g ...

●

IMSL Fortran Numerical Libraries

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DLFTDS (LFTDS) Compute the transpose(R)*R Cholesky factorization of a real symmetricpositive d ...

●

DLFTQS (LFTQS) Compute the transpose(R)*R Cholesky factorization of a real symmetricpositive d ...

●

DLFTRB (LFTRB) Compute the LU factorization of a real matrix in band storage mode.●

DLFTRG (LFTRG) Compute the LU factorization of a real general matrix.●

DLFTSF (LFTSF) Compute the U*D*transpose(U) factorization of a real symmetric matrix.●

DLFTXG (LFTXG) Compute the LU factorization of a real general sparse matrix.●

DLFTZG (LFTZG) Compute the LU factorization of a complex general sparse matrix.●

DLGAMS (ALGAMS) Return the logarithm of the absolute value of the gamma function and thesign of ...

●

DLI (ALI) Logarithmic integral. Integral from 0 to x of 1/ln(t), for double-precision x an ...●

DLINDS (LINDS) Compute the inverse of a real symmetric positive definite matrix.●

DLINRG (LINRG) Compute the inverse of a real general matrix.●

DLINRT (LINRT) Compute the inverse of a real triangular matrix.●

DLNFXD (LNFXD) Compute the numerical Cholesky factorization of a sparse symmetricalmatrix A.

●

DLNFZD (LNFZD) Compute the numerical Cholesky factorization of a sparse Hermitian matrixA.

●

DLNGAM (ALNGAM) Ln(abs(gamma(x))).●

DLNREL (ALNREL) Ln(1+x), for double-precision x.●

DLPRS (DDLPRS) Solve a linear programming problem via the revised simplex algorithm.●

DLQERR (LQERR) Accumulate the orthogonal matrix Q from its factored form given the QRfactoriza ...

●

DLQRRR (LQRRR) Compute the QR decomposition using Householder transformations.●

DLQRRV (LQRRV) Compute the least-squares solution using Householder transformationsapplied in ...

●

DLQRSL (LQRSL) Compute the coordinate transformation, projection and solution for the leastsq ...

●

DLSADS (LSADS) Solve a real symmetric positive definite system of linear equations with iterati...

●

DLSAQS (LSAQS) Solve a real symmetric positive definite system of linear equations in bandsymm ...

●

DLSARB (LSARB) Solve a real system of linear equations in band storage mode with iterativerefi ...

●

DLSARG (LSARG) Solve a real general system of linear equations with iterative refinement.●

IMSL Fortran Numerical Libraries

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DLSASF (LSASF) Solve a real symmetric system of linear equations with iterative refinement.●

DLSBRR (LSBRR) Solve a linear least-squares problem with iterative refinement.●

DLSGRR (LSGRR) Compute the generalized inverse of a real matrix.●

DLSLCQ (LSLCQ) Compute the LDU factorization of a complex tridiagonal matrix A using acyclic r ...

●

DLSLCR (LSLCR) Compute the LDU factorization of a real tridiagonal matrix A using a cyclicredu ...

●

DLSLDS (LSLDS) Solve a real symmetric positive definite system of linear equations without iter...

●

DLSLPB (LSLPB) Compute the trans(R)*D*R Cholesky factorization of a real symmetric positivedef ...

●

DLSLQB (LSLQB) Compute the ctrans(R)*D*R Cholesky factorization of a complex Hermitianpositive ...

●

DLSLQS (LSLQS) Solve a real symmetric positive definite system of linear equations in bandsymm ...

●

DLSLRB (LSLRB) Solve a real system of linear equations in band storage mode without iterativer ...

●

DLSLRG (LSLRG) Solve a real general system of linear equations without iterative refinement.●

DLSLRT (LSLRT) Solve a real triangular system of linear equations.●

DLSLSF (LSLSF) Solve a real symmetric system of linear equations without iterative refinement.●

DLSLTO (LSLTO) Solve a real Toeplitz linear system.●

DLSLTQ (LSLTQ) Solve a complex tridiagonal system of linear equations.●

DLSLTR (LSLTR) Solve a real tridiagonal system of linear equations.●

DLSLXD (LSLXD) Solve a sparse system of symmetric positive definite linear algebraicequations ...

●

DLSLXG (LSLXG) Solve a sparse system of linear algebraic equations by Gaussian elimination.●

DLSLZD (LSLZD) Solve a complex sparse Hermitian-positive definite system of linear equationsby ...

●

DLSLZG (LSLZG) Solve a complex sparse system of linear equations by Gaussian elimination.●

DLSQRR (LSQRR) Solve a linear least-squares problem without iterative refinement.●

DLSVRR (LSVRR) Compute the singular value decomposition of a real matrix.●

DLUPCH (LUPCH) Update the transpose(R)*R Cholesky factorization of a real symmetricpositive de ...

●

DLUPQR (LUPQR) Compute an updated QR factorization after the rank-one matrixalpha*x*transpose( ...

●

DMACH (AMACH) Retrieve single-precision machine constants.●

IMSL Fortran Numerical Libraries

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DMATCE (MATCE) Evaluate a sequence of even, periodic, integer order, real Mathieu functions.●

DMATEE (MATEE) Evaluate the eigenvalues for the periodic Mathieu functions.●

DMATSE (MATSE) Evaluate a sequence of odd, periodic, integer order, real Mathieu functions.●

DMOLCH (MOLCH) Solve a system of partial differential equations of the form UT = FCN(X, T,U, U ...

●

DMRRRR (MRRRR) Multiply two real rectangular matrices, A*B.●

DMURBV (MURBV) Multiply a real band matrix in band storage mode by a real vector.●

DMURRV (MURRV) Multiply a real rectangular matrix by a vector.●

DMXTXF (MXTXF) Compute the transpose product of a matrix, transpose(A)*A.●

DMXTYF (MXTYF) Multiply the transpose of matrix A by matrix B, transpose(A)*B.●

DMXYTF (MXYTF) Multiply a matrix A by the transpose of a matrix B, A*transpose(B).●

DNCONF (NCONF) Solve a general nonlinear programming problem using the successivequadratic pro ...

●

DNCONG (NCONG) Solve a general nonlinear programming problem using the successivequadratic pro ...

●

DNEQBF (NEQBF) Solve a system of nonlinear equations using factored secant update with afinite ...

●

DNEQBJ (NEQBJ) Solve a system of nonlinear equations using factored secant update with auser-s ...

●

DNEQNF (NEQNF) Solve a system of nonlinear equations using the Levenberg-Marquardtalgorithm an ...

●

DNEQNJ (NEQNJ) Solve a system of nonlinear equations using the Levenberg-Marquardtalgorithm wi ...

●

DNR1RB (NR1RB) Compute the 1-norm of a real band matrix in band storage mode.●

DNR1RR (NR1RR) Compute the 1-norm of a real matrix.●

DNR2RR (NR2RR) Compute the Frobenius norm of a real rectangular matrix.●

DNRIRR (NRIRR) Compute the infinity norm of a real matrix.●

DNRM2 (SNRM2) Compute the Euclidean length or L2 norm of a single-precision vector.●

DPCGRC (PCGRC) Solve a real symmetric definite linear system using a preconditionedconjugate g ...

●

DPERMA (PERMA) Permute the rows or columns of a matrix.●

DPERMU (PERMU) Rearrange the elements of an array as specified by a permutation.●

DPLOTP (PLOTP) Print a plot of up to ten sets of points.●

DPOCH (POCH) Pochhammer's symbol. Input and output are double-precision.●

DPOCH1 (POCH1) Pochhammer's symbol from first order. Input and output are double-precision.●

IMSL Fortran Numerical Libraries

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DPOLRG (POLRG) Evaluate a real general matrix polynomial.●

DPP1GD (PP1GD) Evaluate the derivative of a piecewise polynomial on a grid.●

DPPDER (PPDER) Evaluate the derivative of a piecewise polynomial.●

DPPITG (PPITG) Evaluate the integral of a piecewise polynomial.●

DPPVAL (PPVAL) Evaluate a piecewise polynomial.●

DPRDCT (SPRDCT) Multiply the components of a single-precision vector.●

DPSI (PSI) Logarithmic derivative of the gamma function.●

DQADD Add a double-precision scalar to the accumulator in extended precision.●

DQAND (QAND) Integrate a function on a hyper-rectangle.●

DQCOSB (QCOSB) Compute a sequence from its cosine Fourier coefficients with only odd wavenumbe ...

●

DQCOSF (QCOSF) Compute the coefficients of the cosine Fourier transform with only odd wavenumb ...

●

DQD2DR (QD2DR) Evaluate the derivative of a function defined on a rectangular grid usingquadra ...

●

DQD2VL (QD2VL) Evaluate a function defined on a rectangular grid using quadraticinterpolation.

●

DQD3DR (QD3DR) Evaluate the derivative of a function defined on a rectangularthree-dimensional ...

●

DQD3VL (QD3VL) Evaluate a function defined on a rectangular three-dimensional grid usingquadra ...

●

DQDAG (QDAG) Integrate a function using a globally adaptive scheme based on Gauss-Kronrodrul ...

●

DQDAGI (QDAGI) Integrate a function over an infinite or semi-infinite interval.●

DQDAGP (QDAGP) Integrate a function with singularity points given.●

DQDAGS (QDAGS) Integrate a function (which may have endpoint singularities).●

DQDAWC (QDAWC) Integrate a function F(X)/(X-C) in the Cauchy principle value sense.●

DQDAWF (QDAWF) Compute a Fourier integral.●

DQDAWO (QDAWO) Integrate a function containing a sine or a cosine.●

DQDAWS (QDAWS) Integrate a function with algebraic-logarithmic singularities.●

DQDDER (QDDER) Evaluate the derivative of a function defined on a set of points usingquadratic ...

●

DQDDOT (SDSDOT) Compute the sum of a double-precision scalar and a double-precision dotproduct, ...

●

DQDNG (QDNG) Integrate a smooth function using a nonadaptive rule.●

DQDOTA (SDDOTA) Compute the sum of a double-precision scalar, a double-precision dot●

IMSL Fortran Numerical Libraries

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product and ...

DQDOTI (SDDOTI) Compute the sum of a double-precision scalar plus a double-precision dotproduct ...

●

DQDVAL (QDVAL) Evaluate a function defined on a set of points using quadratic interpolation.●

DQINI Initialize an extended-precision accumulator with a double-precision scalar.●

DQMUL Multiply double-precision scalars in extended precision.●

DQPROG (QPROG) Solve a quadratic programming problem subject to linear equality/inequalitycons ...

●

DQSINB (QSINB) Compute a sequence from its sine Fourier coefficients with only odd wavenumbers ...

●

DQSINF (QSINF) Compute the coefficients of the sine Fourier transform with only odd wavenumber ...

●

DQSTO Store a double-precision approximation to an extended-precision scalar.●

DRATCH (RATCH) Compute a rational weighted Chebyshev approximation to a continuousfunction on ...

●

DRCONV (RCONV) Compute the convolution of two real vectors.●

DRCORL (RCORL) Compute the correlation of two real vectors.●

DRECCF (RECCF) Compute recurrence coefficients for various monic polynomials.●

DRECQR (RECQR) Compute recurrence coefficients for monic polynomials given a quadraturerule.

●

DRLINE (RLINE) Fit a line to a set of data points using least-squares.●

DRNUN (RNUN) Generate pseudorandom numbers from a uniform (0,1) distribution.●

DRNUNF (RNUNF) Generate a pseudorandom number from a uniform (0,1) distribution.●

DROT (SROT) Apply Givens plane rotation to double-precision vector.●

DROTG (SROTG) Construct Givens plane rotation of a double-precision matrix.●

DROTM (SROTM) Apply modified Givens plane rotation to double-precision vector.●

DROTMG (SROTMG) Construct modified Givens plane rotation of double-precision matrix.●

DSBMV (SSBMV) Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is asymmetr ...

●

DSCAL (SSCAL) Compute a constant times a vector, y = ay, both double-precision.●

DSDOT Compute single-precision dot product x*y using double-precision accumulation.●

DSET (SSET) Set the components of a vector to a scalar, all double-precision.●

DSHI (SHI) Hyperbolic sine integral.●

DSI (SI) Sine integral.●

DSINDG (SINDG) Sin(x), for double-precision x in degrees.●

IMSL Fortran Numerical Libraries

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DSINLP (SINLP) Compute the inverse Laplace transform of a complex function.●

DSPENC (SPENC) Evaluate Spence's integral, see [AMS55 (27.7.1)].●

DSPLEZ (SPLEZ) Compute the values of a spline that either interpolates or fits user-supplied da...

●

DSRCH (SRCH) Search a sorted vector for a given scalar and return its index.●

DSUB (SSUB) Subtract each component of a vector from a scalar, x = a - x, all double precisi ...●

DSUM (SSUM) Sum the values of a double-precision vector.●

DSURF (SURF) Compute a smooth bivariate interpolant to scattered data that is locally a quin ...●

DSVRBN (SVRBN) Sort an array by absolute values.●

DSVRBP (SVRBP) Sort an array by absolute values and return a pointer array.●

DSVRGN (SVRGN) Sort an array by algebraic values.●

DSVRGP (SVRGP) Sort an array by algebraic values and return a pointer array.●

DSWAP (SSWAP) Interchange vectors X and Y, both double-precision.●

DSYMM (SSYMM) Perform one of the matrix-matrix operations: C = alpha*A*B + beta*C, or C= alp ...

●

DSYMV (SSYMV) Perform the matrix-vector multiplication: y = alpha*A*x + beta*y, where A isa s ...

●

DSYR (SSYR) Perform the rank-one symmetric matrix update A = A + alpha*x*trans(x), where Ai ...

●

DSYR2 (SSYR2) Perform the rank-two symmetric matrix update A = A + alpha*x*trans(y) +alpha*y* ...

●

DSYR2K (SSYR2K) Performs one of the symmetric rank 2k operations C = alpha*A*trans(B) +alpha*B* ...

●

DSYRK (SSYRK) Performs one of the symmetric rank k operations C = alpha*A*trans(A) +beta*C, o ...

●

DTBMV (STBMV) Perform one of the matrix-vector operations: x = A*x, or x = trans(A)*x,where A ...

●

DTBSV (STBSV) Solve one of the triangular systems, x = inv(A)*x, or x = inv(trans(A))*x,where ...

●

DTRMM (STRMM) Performs one of the matrix-matrix operations: B = alpha*op A )*B, or B =alpha*B ...

●

DTRMV (STRMV) Perform one of the matrix-vector operations: x = A*x, or x = trans(A)*x,where A ...

●

DTRNRR (TRNRR) Transpose a rectangular matrix.●

DTRSV (STRSV) Solve one of the triangular systems, x = inv(A)*x, or x = inv(trans(A))*x,where ...

●

IMSL Fortran Numerical Libraries

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DTWODQ (TWODQ) Compute a two-dimensional iterated integral using internal calls to a onedimens ...

●

DUMAG This routine handles MATH/LIBRARY and STAT/LIBRARY type DOUBLEPRECISION options ...

●

DUMCGF (UMCGF) Minimize a function of N variables using a conjugate gradient algorithm anda fi ...

●

DUMCGG (UMCGG) Minimize a function of N variables using a conjugate gradient algorithmand a us ...

●

DUMIAH (UMIAH) Minimize a function of N variables using a modified Newton method and auser-sup ...

●

DUMIDH (UMIDH) Minimize a function of N variables using a modified Newton method and afinite-d ...

●

DUMINF (UMINF) Minimize a function of N variables using a quasi-Newton method and afinite-diff ...

●

DUMING (UMING) Minimize a function of N variables using a quasi-Newton method and auser-suppli ...

●

DUMPOL (UMPOL) Minimize a function of N variables using a direct search polytope algorithm.●

DUNLSF (UNLSF) Solve a nonlinear least-squares problem using a modifiedLevenberg-Marquardt alg ...

●

DUNLSJ (UNLSJ) Solve a nonlinear least-squares problem using a modifiedLevenberg-Marquardt alg ...

●

DUVMGS (UVMGS) Find the minimum point of a nonsmooth function of a single variable.●

DUVMID (UVMID) Find the minimum point of a smooth function of a single variable using bothfunc ...

●

DUVMIF (UVMIF) Find the minimum point of a smooth function of a single variable using onlyfunc ...

●

DVCAL (SVCAL) Multiply a vector by a scalar and store the result in another vector, y = ax, al ...●

DWRRRL (WRRRL) Print a real rectangular matrix with a given format and labels.●

DWRRRN (WRRRN) Print a real rectangular matrix with integer row and column labels.●

DXYZ (SXYZ) Compute a double-precision XYZ product.●

DZBREN (ZBREN) Find a zero of a function that changes sign in a given interval.●

DZREAL (ZREAL) Find a real zero of a real function.●

E1 (DE1) Exponential integral for arguments greater than zero and the Cauchy principle va ...●

EI (DEI) Integral from -x to infinity of -exp(-t)/t. Exponential integral for arguments g ...●

EJCN (DEJCN) Evaluate the Jacobi elliptic function cn(x,m).●

EJDN (DEJDN) Evaluate the Jacobi elliptic function dn(x,m).●

IMSL Fortran Numerical Libraries

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EJSN (DEJSN) Evaluate the Jacobi elliptic function sn(x,m).●

ELE (DELE) Complete elliptic integral E(m), see [AMS55 (17.3.3)].●

ELK (DELK) Complete elliptic integral K(m), see [AMS55 (17.3.1)].●

ELRC (DELRC) Carlson's incomplete elliptic integral RC(x,y).●

ELRD (DELRD) Carlson's incomplete elliptic integral RD(x,y,z).●

ELRF (DELRF) Carlson's incomplete elliptic integral RF(x,y,z).●

ELRJ (DELRJ) Carlson's incomplete elliptic integral RJ(x,y,z,p).●

ENE (DENE) Exponential integral of integer order for arguments greater than zero scaled by ...●

EPICG Compute the performance index for a complex eigensystem.●

EPIHF Compute the performance index for a complex Hermitian eigensystem.●

EPIRG Compute the performance index for a real eigensystem.●

EPISB (DEPISB) Compute the performance index for a real symmetric eigensystem in bandsymmetric ...

●

EPISF (DEPISF) Compute the performance index for a real symmetric eigensystem.●

ERF (DERF) Error function, = (2 / square root of pi) * the integral from 0 to x of exp(-t** ...●

ERFC (DERFC) Complementary error function, = (2 / square root of pi) * the integral from x to ...●

ERFCE (DERFCE) Exponentially scaled complementary error function.●

ERFCI (DERFCI) Inverse complementary error function.●

ERFI (DERFI) Inverse error function.●

ERSET Set error handler default print and stop actions.●

EVAHF Compute the largest or smallest eigenvalues of a complex Hermitian matrix.●

EVASB (DEVASB) Compute the largest or smallest eigenvalues of a real symmetric matrix inband s ...

●

EVASF (DEVASF) Compute the largest or smallest eigenvalues of a real symmetric matrix.●

EVBHF Compute the eigenvalues in a given range of a complex Hermitian matrix.●

EVBSB (DEVBSB) Compute the eigenvalues in a given range of a real symmetric matrix stored inba ...

●

EVBSF (DEVBSF) Compute the eigenvalues in a given range of a real symmetric matrix.●

EVCCG Compute all of the eigenvalues and eigenvectors of a complex matrix.●

EVCCH Compute all of the eigenvalues and eigenvectors of a complex upper Hessenberg ma ...●

EVCHF Compute all of the eigenvalues and eigenvectors of a complex Hermitian matrix.●

EVCRG Compute all of the eigenvalues and eigenvectors of a real matrix.●

EVCRH Compute all of the eigenvalues and eigenvectors of a real upper Hessenberg matri ...●

EVCSB (DEVCSB) Compute all of the eigenvalues and eigenvectors of a real symmetric matrix in●

IMSL Fortran Numerical Libraries

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ba ...

EVCSF (DEVCSF) Compute all of the eigenvalues and eigenvectors of a real symmetric matrix.●

EVEHF Compute the largest or smallest eigenvalues and the corresponding eigenvectors o ...●

EVESB (DEVESB) Compute the largest or smallest eigenvalues and the correspondingeigenvectors o ...

●

EVESF (DEVESF) Compute the largest or smallest eigenvalues and the correspondingeigenvectors o ...

●

EVFHF Compute the eigenvalues in a given range and the corresponding eigenvectors of a ...●

EVFSB (DEVFSB) Compute the eigenvalues in a given range and the corresponding eigenvectorsof a ...

●

EVFSF (DEVFSF) Compute the eigenvalues in a given range and the corresponding eigenvectorsof a ...

●

EVLCG Compute all of the eigenvalues of a complex matrix.●

EVLCH Compute all of the eigenvalues of a complex upper Hessenberg matrix.●

EVLHF Compute all of the eigenvalues of a complex Hermitian matrix.●

EVLRG Compute all of the eigenvalues of a real matrix.●

EVLRH Compute all of the eigenvalues of a real upper Hessenberg matrix.●

EVLSB (DEVLSB) Compute all of the eigenvalues of a real symmetric matrix in band symmetricstor ...

●

EVLSF (DEVLSF) Compute all of the eigenvalues of a real symmetric matrix.●

EXPRL (DEXPRL) (exp(x)-1)/x.●

FAC (DFAC) Factorial. Input is integer; output is real.●

FCOST (DFCOST) Discrete Fourier cosine transformation of an even sequence.●

FDGRD (DFDGRD) Approximate the gradient using forward differences.●

FDHES (DFDHES) Approximate the Hessian using forward differences and function values.●

FDJAC (DFDJAC) Approximate the Jacobian of M functions in N unknowns using forwarddifferences.

●

FFT2B Inverse Fourier transform of a complex periodic two-dimensional array.●

FFT2D Compute Fourier coefficients of a complex periodic two-dimensional array.●

FFT3B (DFFT3B) Compute the inverse Fourier transform of a complex periodicthree-dimensional ar ...

●

FFT3F (DFFT3F) Compute Fourier coefficients of a complex periodic three-dimensional array.●

FFTCB Compute the complex periodic sequence from its Fourier coefficients.●

FFTCF Compute the Fourier coefficients of a complex periodic sequence.●

FFTRB (DFFTRB) Compute the real periodic sequence from its Fourier coefficients.●

IMSL Fortran Numerical Libraries

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FFTRF (DFFTRF) Compute the Fourier coefficients of a real periodic sequence.●

FNLSQ (DFNLSQ) Least squares approximation with user-supplied basis functions.●

FPS2H (DFPS2H) Solve Poisson's or Helmholtz's equation on a two-dimensional rectangle using af ...

●

FPS3H (DFPS3H) Solve Poisson's or Helmholtz's equation on a three-dimensional box using a fast...

●

FQRUL (DFQRUL) Compute a Fejer quadrature rule with various classical weight functions.●

FRESC (DFRESC) Evaluate the cosine Fresnel integral.●

FRESS (DFRESS) Evaluate the sine Fresnel integral.●

FSINT (DFSINT) Discrete Fourier cosine transformation of an odd sequence.●

GAMI (DGAMI) Incomplete gamma function.●

GAMIC (DGAMIC) Complementary incomplete gamma function.●

GAMIT (DGAMIT) Tricomi's incomplete gamma function.●

GAMMA (DGAMMA) gamma(x).●

GAMR (DGAMR) 1/gamma(x).●

GDHES (DGDHES) Approximate the Hessian using forward differences and a user-suppliedgradient.

●

GGUES (DGGUES) Generate points in an N-dimensional space.●

GPICG Compute the performance index for a generalized complex eigensystem Az=(lambda)B ...●

GPIRG Compute the performance index for a generalized real eigensystem Az=(lambda)Bz.●

GPISP (DGPISP) Compute the performance index for a generalized real symmetric eigensystemprobl ...

●

GQRCF (DGQRCF) Compute a Gauss, Gauss-Radau or Gauss-Lobatto quadrature rule given therecurren ...

●

GQRUL (DGQRUL) Compute a Gauss, Gauss-Radau or Gauss-Lobatto quadrature rule withvarious class ...

●

GVCCG Compute all of the eigenvalues and eigenvectors of a generalized complex eigensy ...●

GVCRG Compute all of the eigenvalues and eigenvectors of a generalized real eigensyste ...●

GVCSP (DGVCSP) Compute all of the eigenvalues and eigenvectors of the generalized realsymmetri ...

●

GVLCG Compute all of the eigenvalues of a generalized complex eigensystem Az=(lambda)B ...●

GVLRG Compute all of the eigenvalues of a generalized real eigensystem Az=(lambda)Bz.●

GVLSP (DGVLSP) Compute all of the eigenvalues of the generalized real symmetric eigenvalueprob ...

●

HRRRR (DHRRRR) Compute the Hadamard product of two real matrices.●

IMSL Fortran Numerical Libraries

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HYPOT (DHYPOT) SQRT(A**2+B**2) without underflow or overflow.●

IACHAR Return the integer ASCII value of a character argument.●

IADD Add a scalar to each component of a vector, x = x + a, all integer.●

ICAMAX Find the smallest index of the component of a complex vector having maximum magn...

●

ICAMIN Find the smallest index of the component of a complex vector having minimum magn ...●

ICASE Convert from character to the integer ASCII value without regard to case.●

ICOPY Copy a vector X to a vector Y, both integer.●

IDAMAX (ISAMAX) Find the smallest index of the component of a single-precision vectorhaving max ...

●

IDAMIN (ISAMIN) Find the smallest index of the component of a single-precision vector havingmin ...

●

IDMAX (ISMAX) Find the smallest index of the component of a single-precision vector havingmax ...

●

IDMIN (ISMIN) Find the smallest index of the component of a single-precision vector having min...

●

IDYWK Compute the day of the week for a given date.●

IERCD Retrieve the code for an informational error.●

IICSR Compare two character strings using the ASCII collating sequence but without reg ...●

IIDEX Determine the string position indicating the starting position at which a key ch ...●

IIMAX Find the smallest index of the maximum component of an integer vector.●

IIMIN Find the smallest index of the minimum of an integer vector.●

IMACH Retrieve integer machine constants.●

INITDS (INITS) Returns the number of terms of a given orthogonal series needed to ensure that t...

●

INITS (INITDS) Returns the number of terms of a given orthogonal series needed to ensure that t...

●

INLAP Inverse Laplace transform of a complex function.●

ISAMAX (IDAMAX) Find the smallest index of the component of a single-precision vectorhaving max ...

●

ISAMIN (IDAMIN) Find the smallest index of the component of a single-precision vector havingmin ...

●

ISET Set the components of a vector to a scalar, all integer.●

ISMAX (IDMAX) Find the smallest index of the component of a single-precision vector havingmax ...

●

ISMIN (IDMIN) Find the smallest index of the component of a single-precision vector having min●

IMSL Fortran Numerical Libraries

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...

ISRCH Search a sorted integer vector for a given integer and return its index.●

ISUB Subtract each component of a vector from a scalar, x = a - x, all integer.●

ISUM Sum the values of an integer vector.●

ISWAP Interchange vectors X and Y, both integer.●

IUMAG This routine handles MATH/LIBRARY and STAT/LIBRARY type INTEGER options.●

IVPAG (DIVPAG) Solve an initial-value problem for ordinary differential equations using anAdam ...

●

IVPRK (DIVPRK) Solve an initial-value problem for ordinary differential equations using the Run...

●

IWKCIN Initialize bookkeeping locations describing the character workspace stack.●

IWKIN Initialize bookkeeping locations describing the workspace stack.●

JCGRC (DJCGRC) Solve a real symmetric definite linear system using the Jacobi-preconditionedco ...

●

LCHRG (DLCHRG) Compute the Cholesky decomposition of a symmetric positive semidefinitematrix w ...

●

LCLSQ (DLCLSQ) Solve a linear least-squares problem with linear constraints.●

LCONF (DLCONF) Minimize a general objective function subject to linear equality/inequalitycons ...

●

LCONG (DLCONG) Minimize a general objective function subject to linear equality/inequalitycons ...

●

LDNCH (DLDNCH) Downdate the transpose(R)*R Cholesky factorization of a real symmetricpositive ...

●

LFCCB Compute the LU factorization of a complex matrix in band storage mode and estima ...●

LFCCG Compute the LU factorization of a complex general matrix and estimate its L1 con ...●

LFCCT Estimate the condition number of a complex triangular matrix.●

LFCDH Compute the Hermite(R)*R factorization of a complex Hermitian positive definite ...●

LFCDS (DLFCDS) Compute the transpose(R)*R Cholesky factorization of a real symmetricpositive d ...

●

LFCHF Compute the U*D*Hermite(U) factorization of a complex Hermitian matrix and estim ...●

LFCQH Compute the Hermite(R)*R factorization of a complex Hermitian positive definite ...●

LFCQS (DLFCQS) Compute the Cholesky factorization of a real symmetric positive definitematrix ...

●

LFCRB (DLFCRB) Compute the LU factorization of a real matrix in band storage mode andestimate ...

●

LFCRG (DLFCRG) Compute the LU factorization of a real general matrix and estimate its L1●

IMSL Fortran Numerical Libraries

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condit ...

LFCRT (DLFCRT) Estimate the condition number of a real triangular matrix.●

LFCSF (DLFCSF) Compute the U*D*transpose(U) factorization of a real symmetric matrix andestima ...

●

LFDCB Compute the determinant of a complex matrix given the LU factorization of the ma ...●

LFDCG Compute the determinant of a complex general matrix given the LU factorization o ...●

LFDCT Compute the determinant of a complex triangular matrix.●

LFDDH Compute the determinant of a complex Hermitian positive definite matrix given th ...●

LFDDS (DLFDDS) Compute the determinant of a real symmetric positive definite matrix giventhe t ...

●

LFDHF Compute the determinant of a complex Hermitian matrix given the U*D*Hermite(U) f ...●

LFDQH Compute the determinant of a complex Hermitian positive definite matrix given th ...●

LFDQS (DLFDQS) Compute the determinant of a real symmetric positive definite matrix in bandsym ...

●

LFDRB (DLFDRB) Compute the determinant of a real matrix in band storage mode given the LUfacto ...

●

LFDRG (DLFDRG) Compute the determinant of a real general matrix given the LU factorizationof t ...

●

LFDRT (DLFDRT) Compute the determinant of a real triangular matrix.●

LFDSF (DLFDSF) Compute the determinant of a real symmetric matrix given theU*D*transpose(U) fa ...

●

LFICB Use iterative refinement to improve the solution of a complex system of linear e ...●

LFICG Use iterative refinement to improve the solution of a complex general system of ...●

LFIDH Use iterative refinement to improve the solution of a complex Hermitian positive ...●

LFIDS (DLFIDS) Use iterative refinement to improve the solution of a real symmetric positive de...

●

LFIHF Use iterative refinement to improve the solution of a complex Hermitian system o ...●

LFIQH Use iterative refinement to improve the solution of a complex Hermitian positive ...●

LFIQS (DLFIQS) Use iterative refinement to improve the solution of a real symmetric positive de...

●

LFIRB (DLFIRB) Use iterative refinement to improve the solution of a real system of linear equa...

●

LFIRG (DLFIRG) Use iterative refinement to improve the solution of a real general system of lin...

●

LFISF (DLFISF) Use iterative refinement to improve the solution of a real symmetric system of l...

●

IMSL Fortran Numerical Libraries

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LFSCB Solve a complex system of linear equations given the LU factorization of the coe ...●

LFSCG Solve a complex general system of linear equations given the LU factorization of ...●

LFSDH Solve a complex Hermitian positive definite system of linear equations given the ...●

LFSDS (DLFSDS) Solve a real symmetric positive definite system of linear equations given the tr...

●

LFSHF Solve a complex Hermitian system of linear equations given the U*D*Hermite(U) fa ...●

LFSQH Solve a complex Hermitian positive definite system of linear equations given the ...●

LFSQS (DLFSQS) Solve a real symmetric positive definite system of linear equations given the fa...

●

LFSRB (DLFSRB) Solve a real system of linear equations given the LU factorization of the coeffi...

●

LFSRG (DLFSRG) Solve a real general system of linear equations given the LU factorization of th...

●

LFSSF (DLFSSF) Solve a real symmetric system of linear equations given the U*D*transpose(U)fac ...

●

LFSXD (DLFSXD) Solve a real sparse symmetric positive definite system of linear equations,give ...

●

LFSXG (DLFSXG) Solve a sparse system of linear equations given the LU factorization of thecoef ...

●

LFSZD (DLFSZD) Solve a complex sparse Hermitian positive definite system of linear equations,g ...

●

LFTCB Compute the LU factorization of a complex matrix in band storage mode.●

LFTCG Compute the LU factorization of a complex general matrix.●

LFTDH Compute the Hermite(R)*R factorization of a complex Hermitian positive definite ...●

LFTDS (DLFTDS) Compute the transpose(R)*R Cholesky factorization of a real symmetricpositive d ...

●

LFTHF Compute the U*D*Hermite(U) factorization of a complex Hermitian matrix.●

LFTQH Compute the Hermite(R)*R factorization of a complex Hermitian positive definite ...●

LFTQS (DLFTQS) Compute the transpose(R)*R Cholesky factorization of a real symmetricpositive d ...

●

LFTRB (DLFTRB) Compute the LU factorization of a real matrix in band storage mode.●

LFTRG (DLFTRG) Compute the LU factorization of a real general matrix.●

LFTSF (DLFTSF) Compute the U*D*transpose(U) factorization of a real symmetric matrix.●

LFTXG (DLFTXG) Compute the LU factorization of a real general sparse matrix.●

LFTZG (DLFTZG) Compute the LU factorization of a complex general sparse matrix.●

LINCG Compute the inverse of a complex general matrix.●

IMSL Fortran Numerical Libraries

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LINCT Compute the inverse of a complex triangular matrix.●

LINDS (DLINDS) Compute the inverse of a real symmetric positive definite matrix.●

LINRG (DLINRG) Compute the inverse of a real general matrix.●

LINRT (DLINRT) Compute the inverse of a real triangular matrix.●

LNFXD (DLNFXD) Compute the numerical Cholesky factorization of a sparse symmetricalmatrix A.

●

LNFZD (DLNFZD) Compute the numerical Cholesky factorization of a sparse Hermitian matrixA.

●

LQERR (DLQERR) Accumulate the orthogonal matrix Q from its factored form given the QRfactoriza ...

●

LQRRR (DLQRRR) Compute the QR decomposition using Householder transformations.●

LQRRV (DLQRRV) Compute the least-squares solution using Householder transformationsapplied in ...

●

LQRSL (DLQRSL) Compute the coordinate transformation, projection and solution for the leastsq ...

●

LSACB Solve a complex system of linear equations in band storage mode with iterative r ...●

LSACG Solve a complex general system of linear equations with iterative refinement.●

LSADH Solve a Hermitian positive definite system of linear equations with iterative re ...●

LSADS (DLSADS) Solve a real symmetric positive definite system of linear equations with iterati...

●

LSAHF Solve a complex Hermitian system of linear equations with iterative refinement.●

LSAQH Solve a complex Hermitian positive definite system of linear equations in band H ...●

LSAQS (DLSAQS) Solve a real symmetric positive definite system of linear equations in bandsymm ...

●

LSARB (DLSARB) Solve a real system of linear equations in band storage mode with iterativerefi ...

●

LSARG (DLSARG) Solve a real general system of linear equations with iterative refinement.●

LSASF (DLSASF) Solve a real symmetric system of linear equations with iterative refinement.●

LSBRR (DLSBRR) Solve a linear least-squares problem with iterative refinement.●

LSGRR (DLSGRR) Compute the generalized inverse of a real matrix.●

LSLCB Solve a complex system of linear equations in band storage mode without iterativ ...●

LSLCC Solve a complex circulant linear system.●

LSLCG Solve a complex general system of linear equations without iterative refinement.●

LSLCQ (DLSLCQ) Compute the LDU factorization of a complex tridiagonal matrix A using acyclic r ...

●

LSLCR (DLSLCR) Compute the LDU factorization of a real tridiagonal matrix A using a cyclic●

IMSL Fortran Numerical Libraries

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redu ...

LSLCT Solve a complex triangular system of linear equations.●

LSLDH Solve a complex Hermitian positive definite system of linear equations without i ...●

LSLDS (DLSLDS) Solve a real symmetric positive definite system of linear equations without iter...

●

LSLHF Solve a complex Hermitian system of linear equations without iterative refinemen ...●

LSLPB (DLSLPB) Compute the trans(R)*D*R Cholesky factorization of a real symmetric positivedef ...

●

LSLQB (DLSLQB) Compute the ctrans(R)*D*R Cholesky factorization of a complex hermitianpositive ...

●

LSLQH Solve a complex Hermitian positive definite system of linear equations in band H ...●

LSLQS (DLSLQS) Solve a real symmetric positive definite system of linear equations in bandsymm ...

●

LSLRB (DLSLRB) Solve a real system of linear equations in band storage mode without iterativer ...

●

LSLRG (DLSLRG) Solve a real general system of linear equations without iterative refinement.●

LSLRT (DLSLRT) Solve a real triangular system of linear equations.●

LSLSF (DLSLSF) Solve a real symmetric system of linear equations without iterative refinement.●

LSLTC Solve a complex Toeplitz linear system.●

LSLTO (DLSLTO) Solve a real Toeplitz linear system.●

LSLTQ (DLSLTQ) Solve a complex tridiagonal system of linear equations.●

LSLTR (DLSLTR) Solve a real tridiagonal system of linear equations.●

LSLXD (DLSLXD) Solve a sparse system of symmetric positive definite linear algebraicequations ...

●

LSLXG (DLSLXG) Solve a sparse system of linear algebraic equations by Gaussian elimination.●

LSLZD (DLSLZD) Solve a complex sparse Hermitian positive definite system of linear equationsby ...

●

LSLZG (DLSLZG) Solve a complex sparse system of linear equations by Gaussian elimination.●

LSQRR (DLSQRR) Solve a linear least-squares problem without iterative refinement.●

LSVCR Compute the singular value decomposition of a complex matrix.●

LSVRR (DLSVRR) Compute the singular value decomposition of a real matrix.●

LUPCH (DLUPCH) Update the transpose(R)*R Cholesky factorization of a real symmetricpositive de ...

●

LUPQR (DLUPQR) Compute an updated QR factorization after the rank-one matrix(alpha)x*transpose ...

●

MATCE (DMATCE) Evaluate a sequence of even, periodic, integer-order, real Mathieu functions.●

IMSL Fortran Numerical Libraries

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MATEE (DMATEE) Evaluate the eigenvalues for the periodic Mathieu functions.●

MATSE (DMATSE) Evaluate a sequence of odd, periodic, integer-order, real Mathieu functions.●

MCRCR Multiply two complex rectangular matrices, AB.●

MOLCH (DMOLCH) Solve a system of partial differential equations of the form UT = FCN(X, T,U, U ...

●

MRRRR (DMRRRR) Multiply two real rectangular matrices, AB.●

MUCBV Multiply a complex band matrix in band storage mode by a complex vector.●

MUCRV Multiply a complex rectangular matrix by a complex vector.●

MURBV (DMURBV) Multiply a real band matrix in band storage mode by a real vector.●

MURRV (DMURRV) Multiply a real rectangular matrix by a vector.●

MXTXF (DMXTXF) Compute the transpose product of a matrix, transpose(A)*A.●

MXTYF (DMXTYF) Multiply the transpose of matrix A by matrix B, transpose(A)*B.●

MXYTF (DMXYTF) Multiply a matrix A by the transpose of a matrix B, A*transpose(B).●

NCONF (DNCONF) Solve a general nonlinear programming problem using the successivequadratic pro ...

●

NCONG (DNCONG) Solve a general nonlinear programming problem using the successivequadratic pro ...

●

NDAYS Compute the number of days from January 1, 1900, to the given date.●

NDYIN Give the date corresponding to the number of days since January 1, 1900.●

NEQBF (DNEQBF) Solve a system of nonlinear equations using factored secant update with afinite ...

●

NEQBJ (DNEQBJ) Solve a system of nonlinear equations using factored secant update with auser-s ...

●

NEQNF (DNEQNF) Solve a system of nonlinear equations using the Levenberg-Marquardtalgorithm an ...

●

NEQNJ (DNEQNJ) Solve a system of nonlinear equations using the Levenberg-Marquardtalgorithm wi ...

●

NR1CB Compute the 1-norm of a complex band matrix in band storage mode.●

NR1RB (DNR1RB) Compute the 1-norm of a real band matrix in band storage mode.●

NR1RR (DNR1RR) Compute the 1-norm of a real matrix.●

NR2RR (DNR2RR) Compute the Frobenius norm of a real rectangular matrix.●

NRIRR (DNRIRR) Compute the infinity norm of a real matrix.●

PCGRC (DPCGRC) Solve a real symmetric definite linear system using a preconditionedconjugate g ...

●

PERMA (DPERMA) Permute the rows or columns of a matrix.●

IMSL Fortran Numerical Libraries

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PERMU (DPERMU) Rearrange the elements of an array as specified by a permutation.●

PGOPT Set or retrieve page width and length for printing.●

PLOTP (DPLOTP) Print a plot of up to ten sets of points.●

POCH (DPOCH) Generalization of Pochhammer's symbol.●

POCH1 (DPOCH1) Generalization of Pochhammer's symbol starting from first order.●

POLRG (DPOLRG) Evaluate a real general matrix polynomial.●

PP1GD (DPP1GD) Evaluate the derivative of a piecewise polynomial on a grid.●

PPDER (DPPDER) Evaluate the derivative of a piecewise polynomial.●

PPITG (DPPITG) Evaluate the integral of a piecewise polynomial.●

PPVAL (DPPVAL) Evaluate a piecewise polynomial.●

PRIME Decompose an integer into its prime factors.●

PSI (DPSI) Logarithmic derivative of the gamma function.●

QAND (DQAND) Integrate a function on a hyper-rectangle.●

QCOSB (DQCOSB) Compute a sequence from its cosine Fourier coefficients with only odd wavenumbe ...

●

QCOSF (DQCOSF) Compute the coefficients of the cosine Fourier transform with only odd wavenumb ...

●

QD2DR (DQD2DR) Evaluate the derivative of a function defined on a rectangular grid usingquadra ...

●

QD2VL (DQD2VL) Evaluate a function defined on a rectangular grid using quadraticinterpolation.

●

QD3DR (DQD3DR) Evaluate the derivative of a function defined on a rectangularthree-dimensional ...

●

QD3VL (DQD3VL) Evaluate a function defined on a rectangular three-dimensional grid usingquadra ...

●

QDAG (DQDAG) Integrate a function using a globally adaptive scheme based on Gauss-Kronrodrul ...

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QDAGI (DQDAGI) Integrate a function over an infinite or semi-infinite interval.●

QDAGP (DQDAGP) Integrate a function with singularity points given.●

QDAGS (DQDAGS) Integrate a function (which may have endpoint singularities).●

QDAWC (DQDAWC) Integrate a function F(X)/(X-C) in the Cauchy principle value sense.●

QDAWF (DQDAWF) Compute a Fourier integral.●

QDAWO (DQDAWO) Integrate a function containing a sine or a cosine.●

QDAWS (DQDAWS) Integrate a function with algebraic-logarithmic singularities.●

QDDER (DQDDER) Evaluate the derivative of a function defined on a set of points using●

IMSL Fortran Numerical Libraries

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quadratic ...

QDNG (DQDNG) Integrate a smooth function using a nonadaptive rule.●

QDVAL (DQDVAL) Evaluate a function defined on a set of points using quadratic interpolation.●

QPROG (DQPROG) Solve a quadratic programming problem subject to linear equality/inequalitycons ...

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QSINB (DQSINB) Compute a sequence from its sine Fourier coefficients with only odd wavenumbers ...

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QSINF (DQSINF) Compute the coefficients of the sine Fourier transform with only odd wavenumber ...

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RATCH (DRATCH) Compute a rational weighted Chebyshev approximation to a continuousfunction on ...

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RCONV (DRCONV) Compute the convolution of two real vectors.●

RCORL (DRCORL) Compute the correlation of two real vectors.●

RECCF (DRECCF) Compute recurrence coefficients for various monic polynomials.●

RECQR (DRECQR) Compute recurrence coefficients for monic polynomials given a quadraturerule.

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RLINE (DRLINE) Fit a line to a set of data points using least-squares.●

RNGET Retrieve the current value of the seed used in the IMSL random number generators ...●

RNOPT Select the uniform (0,1) multiplicative congruential pseudorandom number generat ...●

RNSET Initialize a random seed for use in the IMSL random number generators.●

RNUN (DRNUN) Generate pseudorandom numbers from a uniform (0,1) distribution.●

RNUNF (DRNUNF) Generate a pseudorandom number from a uniform (0,1) distribution.●

SADD (DADD) Add a scalar to each component of a vector, x = x + a, all single-precision.●

SASUM (DASUM) Sum the absolute values of the components of a single-precision vector.●

SAXPY (DAXPY) Compute the scalar times a vector plus a vector, y = ax + y, all single precisio...

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SCASUM Sum the absolute values of the real part together with the absolute values of th ...●

SCNRM2 Compute the Euclidean norm of a complex vector.●

SCOPY (DCOPY) Copy a vector X to a vector Y, both single-precision.●

SDDOTA (DQDOTA) Compute the sum of a single-precision scalar, a single-precision dotproduct and ...

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SDDOTI (DQDOTI) Compute the sum of a single-precision scalar plus a single-precision dotproduct ...

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SDOT (DDOT) Compute the single-precision dot product x*y.●

SDSDOT (DQDDOT) Compute the sum of a single-precision scalar and a single-precision dotproduct, ...

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IMSL Fortran Numerical Libraries

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SGBMV (DGBMV) Perform one of the matrix-vector operations: y = alpha*A*x + beta*y or y =alpha ...

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SGEMM Perform one of the following matrix-matrix multiplications: C = alpha*A*B + beta ...●

SGEMV Perform one of the matrix-vector multiplications: y = alpha*A*x + beta*y y = alp ...●

SGER Perform the rank-one matrix update: A = alpha*x*trans(y) + A, where trans(y) is ...●

SHI (DSHI) Hyperbolic sine integral.●

SHPROD (DHPROD) Compute the Hadamard product of two single-precision vectors.●

SI (DSI) Sine integral.●

SINDG (DSINDG) Sin(x), x in degrees.●

SINLP (DSINLP) Compute the inverse Laplace transform of a complex function.●

SNRM2 (DNRM2) Compute the Euclidean length or L2 norm of a single-precision vector, withoutun ...

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SPENC (DSPENC) Evaluate Spence's integral, see [AMS55 (27.7.1)].●

SPLEZ (DSPLEZ) Compute the values of a spline that either interpolates or fits user-supplied da...

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SPRDCT (DPRDCT) Multiply the components of a single-precision vector.●

SRCH (DSRCH) Search a sorted vector for a given scalar and return its index.●

SROT (DROT) Apply Givens plane rotation to a single-precision vector.●

SROTG (DROTG) Construct Givens plane rotation of a single-precision matrix.●

SROTM (DROTM) Apply modified Givens plane rotation to single-precision vector.●

SROTMG (DROTMG) Construct modified Givens plane rotation of a single-precision matrix.●

SSBMV (DSBMV) Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is asymmetr ...

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SSCAL (DSCAL) Multiply a vector by a scalar, y =ay, both single-precision.●

SSET (DSET) Set the components of a vector to a scalar, all single-precision.●

SSRCH Search a character vector, sorted in ascending ASCII order, for a given string a ...●

SSUB (DSUB) Subtract each component of a vector from a scalar, x = a - x, all single precisi ...●

SSUM (DSUM) Sum the values of a single-precision vector.●

SSWAP (DSWAP) Interchange vectors X and Y, both single-precision.●

SSYMM (DSYMM) Perform one of the matrix-matrix operations: C = alpha*A*B + beta*C, or C= alp ...

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SSYMV (DSYMV) Perform the matrix-vector multiplication: y = alpha*A*x + beta*y, where A isa s ...

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SSYR (DSYR) Perform the rank-one symmetric matrix update A = A + alpha*x*trans(x), where Ai ...

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SSYR2 (DSYR2) Perform the rank-two symmetric matrix update A = A + alpha*x*trans(y) +alpha*y* ...

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SSYR2K (DSYR2K) Performs one of the symmetric rank 2k operations C = alpha*A*trans(B) +alpha*B* ...

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SSYRK (DSYRK) Performs one of the symmetric rank k operations C = alpha*A*trans(A) +beta*C, o ...

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STBMV (DTBMV) Perform one of the matrix-vector operations: x = A*x, or x = trans(A)*x,where A ...

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STBSV (DTBSV) Solve one of the triangular systems, x = inv(A)*x, or x = inv(trans(A))*x,where ...

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STRMM (DTRMM) Performs one of the matrix-matrix operations: B = alpha*op( A )*B, or B =alpha* ...

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STRMV (DTRMV) Perform one of the matrix-vector operations: x = A*x, or x = trans(A)*x,where A ...

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STRSV (DTRSV) Solve one of the triangular systems, x = inv(A)*x, or x = inv(trans(A))*x,where ...

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SUMAG This routine handles MATH/LIBRARY and STAT/LIBRARY type SINGLEPRECISION options ...

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SURF (DSURF) Compute a smooth bivariate interpolant to scattered data that is locally a quin ...●

SVCAL (DVCAL) Multiply a vector by a scalar and store the result in another vector, y = ax, al ...●

SVIBN Sort an integer array by absolute values.●

SVIBP Sort an integer array by absolute values and return a pointer array.●

SVIGN Sort an integer array by algebraic values.●

SVIGP Sort an integer array by algebraic values and return a pointer array.●

SVRBN (DSVRBN) Sort a real array by absolute values.●

SVRBP (DSVRBP) Sort a real array by absolute values and return a pointer array.●

SVRGN (DSVRGN) Sort a real array by algebraic values.●

SVRGP (DSVRGP) Sort a real array by algebraic values and return a pointer array.●

SXYZ (DXYZ) Compute a single-precision XYZ product.●

UMCGG (DUMCGG) Minimize a function of N variables using a conjugate gradient algorithmand a us ...

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UMIAH (DUMIAH) Minimize a function of N variables using a modified Newton method and auser-sup ...

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UMIDH (DUMIDH) Minimize a function of N variables using a modified Newton method and afinite-d ...

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UMINF (DUMINF) Minimize a function of N variables using a quasi-Newton method and afinite-diff ...

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IMSL Fortran Numerical Libraries

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UMING (DUMING) Minimize a function of N variables using a quasi-Newton method and auser-suppli ...

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UMPOL (DUMPOL) Minimize a function of N variables using a direct search polytope algorithm.●

UNLSF (DUNLSF) Solve a nonlinear least-squares problem using a modifiedLevenberg-Marquardt alg ...

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UNLSJ (DUNLSJ) Solve a nonlinear least-squares problem using a modifiedLevenberg-Marquardt alg ...

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UVMGS (DUVMGS) Find the minimum point of a nonsmooth function of a single variable.●

UVMID (DUVMID) Find the minimum point of a smooth function of a single variable using bothfunc ...

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UVMIF (DUVMIF) Find the minimum point of a smooth function of a single variable using onlyfunc ...

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VCONC Compute the convolution of two complex vectors.●

VCONR Compute the convolution of two real vectors.●

WRCRL Print a complex rectangular matrix with a given format and labels.●

WRCRN Print a complex rectangular matrix with integer row and column labels.●

WRIRL Print an integer rectangular matrix with a given format and labels.●

WRIRN Print an integer rectangular matrix with integer row and column labels.●

WROPT Set or retrieve an option for printing a matrix.●

WRRRL (DWRRRL) Print a real rectangular matrix with a given format and labels.●

WRRRN (DWRRRN) Print a real rectangular matrix with integer row and column labels.●

ZANLY Find a zero of a univariate analytic function.●

ZBREN (DZBREN) Find a zero of a function that changes sign in a given interval.●

ZGBMV (CGBMV) Perform one of the matrix-vector operations: y = alpha*A*x + beta*y, y =alpha*t ...

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ZGEMM (CGEMM) Perform one of the following matrix-matrix multiplications: C=alpha*A*B +beta*C ...

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ZGEMV (CGEMV) Perform one of the matrix-vector multiplications: y = alpha*A*x + beta*y y =alp ...

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ZGERC (CGERC) Perform the rank-one matrix update: A = A + alpha*x*ctrans(y), wherectrans(y) i ...

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ZGERU (CGERU) Perform the rank-one matrix update: A = A + alpha*x*trans(y), where trans(y)is ...

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ZHBMV (CHBMV) Perform the matrix-vector operation y = alpha*A*x + beta*y, where A is aHermiti ...

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ZHEMM (CHEMM) Perform one of the matrix-matrix operations: C = alpha*A*B + beta*C, or C●

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= alp ...

ZHEMV (CHEMV) Perform the matrix-vector multiplication y = alpha*A*x + beta*y, where A isa He ...

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ZHER (CHER) Perform the rank-one matrix update A = A + alpha*x*ctrans(x) to the Hermitianma ...

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ZHER2 (CHER2) Perform a rank-two matrix update to the Hermitian matrix A, A = A +alpha*x*ctra ...

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ZHER2K (CHER2K) Perform one of the Hermitian rank 2k operations C = alpha*A*ctrans( B ) +conjg ...

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ZHERK (CHERK) Perform one of the Hermitian rank k operations C = alpha*A*ctrans( A ) +beta*C ...

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ZPLRC Find the zeros of a polynomial with real coefficients using Laguerre's method.●

ZPOCC Find the zeros of a polynomial with complex coefficients.●

ZPORC Find the zeros of a polynomial with real coefficients using the Jenkins-Traub th ...●

ZREAL (DZREAL) Find a real zero of a real function.●

ZSYMM (CSYMM) Perform one of the matrix-matrix operations: C = alpha*A*B + beta*C, or C= alp ...

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ZSYR2K (CSYR2K) Perform one of the symmetric rank 2k operations C = alpha*A*trans(B) +alpha*B* ...

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ZSYRK (CSYRK) Perform one of the symmetric rank k operations C = alpha*A*trans(A) +beta*C, o ...

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ZTBMV (CTBMV) Perform one of the matrix-vector operations: x = A*x, x = trans(A)*x, x =ctrans ...

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ZTBSV (CTBSV) Solve one of the triangular systems, x = inv(A)*x, x = inv(trans(A))*x, x = inv(...

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ZTRMM (CTRMM) Perform one of the matrix-matrix operations: B = alpha*op( A )*B, or B =alpha* ...

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ZTRMV (CTRMV) Perform one of the matrix-vector operations: x = A*x, x = trans(A)*x, or x =ctr ...

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ZTRSM (CTRSM) Solve one of the matrix equations: op( A )*X = alpha*B, or X*op( A ) =alpha*B, ...

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ZTRSV (CTRSV) Solve one of the triangular systems, x = inv(A)*x, x = inv(trans(A))*x, or x = i...

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IMSL Fortran Numerical Libraries

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