version 1.5, 2010/08/07 13:22:44
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version 1.8, 2011/07/22 07:38:20
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SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO ) |
SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK routine (version 3.3.1) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* -- April 2011 -- |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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* 5-96 - Based on modifications by J. Lewis, Boeing Computer Services |
* 5-96 - Based on modifications by J. Lewis, Boeing Computer Services |
* Company |
* Company |
* |
* |
* If UPLO = 'U', then A = U*D*U', where |
* If UPLO = 'U', then A = U*D*U**T, where |
* U = P(n)*U(n)* ... *P(k)U(k)* ..., |
* U = P(n)*U(n)* ... *P(k)U(k)* ..., |
* i.e., U is a product of terms P(k)*U(k), where k decreases from n to |
* i.e., U is a product of terms P(k)*U(k), where k decreases from n to |
* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
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* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), |
* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), |
* and A(k,k), and v overwrites A(1:k-2,k-1:k). |
* and A(k,k), and v overwrites A(1:k-2,k-1:k). |
* |
* |
* If UPLO = 'L', then A = L*D*L', where |
* If UPLO = 'L', then A = L*D*L**T, where |
* L = P(1)*L(1)* ... *P(k)*L(k)* ..., |
* L = P(1)*L(1)* ... *P(k)*L(k)* ..., |
* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to |
* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to |
* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 |
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* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Factorize A as U*D*U' using the upper triangle of A |
* Factorize A as U*D*U**T using the upper triangle of A |
* |
* |
* K is the main loop index, decreasing from N to 1 in steps of |
* K is the main loop index, decreasing from N to 1 in steps of |
* 1 or 2 |
* 1 or 2 |
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KP = K |
KP = K |
ELSE |
ELSE |
* |
* |
* JMAX is the column-index of the largest off-diagonal |
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* element in row IMAX, and ROWMAX is its absolute value |
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* |
|
ROWMAX = ZERO |
ROWMAX = ZERO |
JMAX = IMAX |
JMAX = IMAX |
KX = IMAX*( IMAX+1 ) / 2 + IMAX |
KX = IMAX*( IMAX+1 ) / 2 + IMAX |
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* |
* |
* Perform a rank-1 update of A(1:k-1,1:k-1) as |
* Perform a rank-1 update of A(1:k-1,1:k-1) as |
* |
* |
* A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)' |
* A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T |
* |
* |
R1 = CONE / AP( KC+K-1 ) |
R1 = CONE / AP( KC+K-1 ) |
CALL ZSPR( UPLO, K-1, -R1, AP( KC ), 1, AP ) |
CALL ZSPR( UPLO, K-1, -R1, AP( KC ), 1, AP ) |
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* |
* |
* Perform a rank-2 update of A(1:k-2,1:k-2) as |
* Perform a rank-2 update of A(1:k-2,1:k-2) as |
* |
* |
* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )' |
* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T |
* = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )' |
* = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T |
* |
* |
IF( K.GT.2 ) THEN |
IF( K.GT.2 ) THEN |
* |
* |
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* |
* |
ELSE |
ELSE |
* |
* |
* Factorize A as L*D*L' using the lower triangle of A |
* Factorize A as L*D*L**T using the lower triangle of A |
* |
* |
* K is the main loop index, increasing from 1 to N in steps of |
* K is the main loop index, increasing from 1 to N in steps of |
* 1 or 2 |
* 1 or 2 |
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* |
* |
* Perform a rank-1 update of A(k+1:n,k+1:n) as |
* Perform a rank-1 update of A(k+1:n,k+1:n) as |
* |
* |
* A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)' |
* A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T |
* |
* |
R1 = CONE / AP( KC ) |
R1 = CONE / AP( KC ) |
CALL ZSPR( UPLO, N-K, -R1, AP( KC+1 ), 1, |
CALL ZSPR( UPLO, N-K, -R1, AP( KC+1 ), 1, |
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* |
* |
* Perform a rank-2 update of A(k+2:n,k+2:n) as |
* Perform a rank-2 update of A(k+2:n,k+2:n) as |
* |
* |
* A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )' |
* A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T |
* = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )' |
* = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T |
* |
* |
* where L(k) and L(k+1) are the k-th and (k+1)-th |
* where L(k) and L(k+1) are the k-th and (k+1)-th |
* columns of L |
* columns of L |